CIGRÉ TB640-A 2015 Guide for Rating Calculations of Insulated Cables

640

A Guide for Rating Calculations of Insulated Cables

Working Group B1.35

December 2015

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES Working group B1.35

Members Frank DE WILD, convenor (NL), Jos VAN ROSSUM, secretary (NL), George ANDERS (CA), Rusty BASCOM (US), Bruno BRIJS (BE), Pietro CORSARO (CH), Antony FALCONER (ZA), Alberto GONZALEZ (ES), Georg HÜLSKEN (DE), Nikola KULJACA (IT), Bo MARTINSSON (SE), Aleksandra RAKOWSKA (PL), Christian RÉMY (FR), Francis WAITE & James PILGRIM (GB) Corresponding Members Marcio COELHO (BR), Seok-Hyun NAM (KR), Tsuguhiro TAKAHASHI (JP)

Copyright © 2015 “Ownership of a CIGRE publication, whether in paper form or on electronic support only infers right of use for personal purposes. Unless explicitly agreed by CIGRE in writing, total or partial reproduction of the publication and/or transfer to a third party is prohibited other than for personal use by CIGRE Individual Members or for use within CIGRE Collective Member organisations. Circulation on any intranet or other company network is forbidden for all persons. As an exception, CIGRE Collective Members are allowed to reproduce the publication only”.

Disclaimer notice “CIGRE gives no warranty or assurance about the contents of this publication, nor does it accept any responsibility, as to the accuracy or exhaustiveness of the information. All implied warranties and conditions are excluded to the maximum extent permitted by law”.

ISBN :978-2-85873-343-9

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES Technical Brochure of working group B1.35 on cable ratings

Table of Contents EXECUTIVE SUMMARY ................................................................................................................. 7 1

INTRODUCTION...................................................................................................................... 9 1.1

A Guide to this Technical Brochure .................................................................................. 10

1.2

Information regarding the Working Group’s Objectives .................................................... 11

1.3

Information regarding the Terms of Reference and Scope of Work ................................. 12

1.4

Introduction to the Questionnaire...................................................................................... 13

2

OVERALL ISSUES WITH RATING CALCULATIONS ......................................................... 15 2.1

How to calculate the Current Rating of a Power Cable .................................................... 16

2.2

Basis for the Calculation ................................................................................................... 19

2.3

Margin in Cable Rating Calculations................................................................................. 20

3

STARTING POINTS FOR RATING CALCULATIONS.......................................................... 22 3.1

Identification of an Underground Cable System ............................................................... 22

3.2

Cataloguing the Installation Conditions along the Cable Route ....................................... 25

3.3

Identify the Thermal Properties of Soils and Special Backfills.......................................... 30

3.4

Selection of Ambient Soil Temperature ............................................................................ 32

3.5 Collected Practices ........................................................................................................... 33 3.5.1 Common Installation Method.......................................................................................... 34 3.5.2 Soil / Seabed / Tunnel Ambient Temperature ................................................................ 34 3.5.3 Soil / Seabed Thermal Resistivities................................................................................ 38 3.5.4 Soil Dry Out .................................................................................................................... 40 3.5.5 Thermal resistance and Characterisation of Backfill ...................................................... 42 3.5.6 Limiting Factors in Current Rating Calculations ............................................................. 42 3.5.7 Operating Conditions...................................................................................................... 42 3.6 Discussion on Starting Points ........................................................................................... 43 3.6.1 Conclusion...................................................................................................................... 45

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4

CALCULATION METHODS AND PROCEDURES ............................................................... 46 4.1

Symbols used.................................................................................................................... 48

4.2

Definitions ......................................................................................................................... 53

5

DUTY ASPECTS IN CABLE RATING CALCULATIONS ..................................................... 56 5.1 Loading (Current) .............................................................................................................. 56 5.1.1 Continuous Loads........................................................................................................... 56 5.1.2 Time Varying Loading .................................................................................................... 57 5.1.2.1 Cyclic ....................................................................................................................... 57 5.1.2.2 Emergency .............................................................................................................. 60 5.1.2.3 Arbitrary Load Patterns ........................................................................................... 61 5.1.2.4 Long Time to Reach Steady State .......................................................................... 62 5.1.2.5 “Short” (less than 5 second) Loading Patterns ....................................................... 62 5.1.3 Dynamic.......................................................................................................................... 63 5.2

Voltage .............................................................................................................................. 63

5.3 Frequency and one, two and three phase systems .......................................................... 63 5.3.1 AC Frequency................................................................................................................. 64 5.3.2 One, two and three phase systems................................................................................ 65 5.3.3 DC Current Ratings ........................................................................................................ 66 5.3.4 Other AC Frequencies.................................................................................................... 67 5.3.5 Harmonics ...................................................................................................................... 67 6

CABLE ASPECTS IN CABLE RATING CALCULATIONS .................................................. 70 6.1 Conductor.......................................................................................................................... 70 6.1.1 Skin and Proximity Effect ............................................................................................... 71 6.2 Insulation........................................................................................................................... 71 6.2.1 Thermal Resistance........................................................................................................ 71 6.2.2 Dielectric Loss ................................................................................................................ 72 6.3 Arrangement of Cores in a Cable ..................................................................................... 74 6.3.1 Single Core Cables......................................................................................................... 74 6.3.2 Multi-core Cables (including three core)......................................................................... 74 6.3.3 Pipe type Cables ............................................................................................................ 75 6.3.4 Concentric Cables .......................................................................................................... 75 6.4 Metal Sheaths and Screens.............................................................................................. 76 6.4.1 Metal Sheath and Screen Losses .................................................................................. 76 6.4.2 Multiple Sheaths and/or Screens ................................................................................... 77 6.5

Armour Bedding ................................................................................................................ 77

6.6 Armour and Metal Pipes ................................................................................................... 78 6.6.1 Armour Loss in Multicore Cables ................................................................................... 78 6.7 7

Outer Covering.................................................................................................................. 81 INSTALLATION ASPECTS IN CABLE RATING CALCULATIONS .................................... 82

7.1 Features Common to Many Installation Types ................................................................. 82 7.1.1 Cable Spacing / Arrangement ........................................................................................ 82 7.1.2 Bonding of cable sheaths ............................................................................................... 82

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7.1.3 Multiple Parallel Circuits ................................................................................................. 83 7.1.3.1 Conductor ac Resistance ........................................................................................ 83 7.1.3.2 Impact on Sheath Loss for Specially Bonded Cable System.................................. 83 7.1.3.3 Impact on Sheath Loss for Solidly Bonded and Earthed Cable System................. 87 7.1.3.4 Impact on Armour Losses ....................................................................................... 87 7.1.3.5 Thermal Impact of Multiple Circuits ......................................................................... 87 7.1.4 Multiple Cables per Phase ............................................................................................. 87 7.1.5 Circuits Crossing ............................................................................................................ 88 7.1.6 Long Lengths (charging currents) .................................................................................. 88 7.1.6.1 Critical Length ......................................................................................................... 88 7.1.6.2 Power Transfer for Long Circuits ............................................................................ 89 7.1.7 Joints .............................................................................................................................. 91 7.1.7.1 Single Isolated Joints .............................................................................................. 91 7.1.7.2 Multiple Joints.......................................................................................................... 94 7.1.8 Terminations................................................................................................................... 95 7.1.9 Metalwork ....................................................................................................................... 95 7.1.10 Short Lengths different to rest of Installation (longitudinal heat flow) ............................ 95 7.1.11 Parallel Metallic Paths (e.g. earth continuity conductor ) ............................................... 96 7.2 Buried installations (not tunnels)....................................................................................... 97 7.2.1 Common Aspects and Direct Buried installations .......................................................... 97 7.2.1.1 Multiple Parallel Circuits: Thermal Impact............................................................... 97 7.2.1.2 Unequally Loaded Circuits ...................................................................................... 98 7.2.1.3 Circuit Crossings ................................................................................................... 100 7.2.1.4 Soil dry-out ............................................................................................................ 102 7.2.1.5 Multiple thermal resistivity values (e.g. backfill) .................................................... 103 7.2.1.6 Water cooled cable systems ................................................................................. 103 7.2.1.7 Non-cable Objects................................................................................................. 104 7.2.1.8 Method of Determining Ambient Temperature ...................................................... 105 7.2.1.9 Very Deep Installations ......................................................................................... 106 7.2.1.10 Variable Inter-axial Spacing ................................................................................ 107 7.2.2 Duct installations including directional drillings ............................................................ 107 7.2.2.1 Duct filling Material or Casing Grouting Material................................................... 108 7.2.2.2 Losses in Steel Casings ........................................................................................ 111 7.2.2.3 Multiple thermal resistances of Duct Bank Environments..................................... 112 7.2.3 Surface Trough and Shallow Installation...................................................................... 112 7.2.3.1 Filled surface troughs or shallow installations....................................................... 113 7.2.3.2 Unventilated and Naturally Ventilated Troughs..................................................... 113 7.2.3.3 Force Ventilated Troughs ...................................................................................... 115 7.2.3.4 Effect of Solar Radiation........................................................................................ 116 7.3 Installations in air ............................................................................................................ 116 7.3.1 Transients..................................................................................................................... 116 7.3.1.1 IEC approach ........................................................................................................ 116 7.3.2 Solar Radiation ............................................................................................................. 117 7.3.3 Cables cleated to walls................................................................................................. 117 7.3.4 Cable bridges ............................................................................................................... 118 7.3.5 Riser Poles ................................................................................................................... 118 7.3.5.1 Energy Conservation Equations............................................................................ 120

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7.3.5.2 7.3.5.3 7.3.5.4 7.3.5.5 7.3.5.6

Energy Conservation Equation for the Cable Outside Surface............................. 120 Energy Conservation Equation for the Wall Inside Surface .................................. 120 Energy Conservation Equation for the Wall Outside Surface ............................... 121 Energy Conservation Equations – Heat Transfer ................................................. 121 Convection Coefficients in Riser Applications....................................................... 122

7.4 Tunnel installations ......................................................................................................... 123 7.4.1 Naturally ventilated / unventilated tunnel installations.................................................. 123 7.4.2 Forced air ventilated tunnel installations ...................................................................... 124 7.4.3 Water cooled tunnel installations.................................................................................. 126 7.4.4 Method of Determining Ambient Temperature ............................................................. 129 7.4.4.1 Notes on Air Ambient Temperature....................................................................... 129 7.5 Submarine cable installations ......................................................................................... 130 7.5.1 Seabed burial installations ........................................................................................... 130 7.5.1.1 Buried submarine cable rating calculations........................................................... 130 7.5.1.2 Thermal Resistivity of the Seabed Soil ................................................................. 130 7.5.1.3 Ambient Temperature of the Sea Floor................................................................. 131 7.5.1.4 Seafloor Conditions Changing with Time .............................................................. 131 7.5.2 Cables Installed on the Seabed ................................................................................... 132 7.5.3 Cables Installed in Free Water ..................................................................................... 132 7.5.4 Submarine Cables installed in Risers (J-tubes) ........................................................... 133 7.5.5 Cable Protection Systems ............................................................................................ 133 8

USING CALCULATION TOOLS AND TECHNIQUES ........................................................ 135 8.1

Steady State and Transient Rating Tools ....................................................................... 135

8.2 Dynamic (or real time) Rating Tools ............................................................................... 137 8.2.1 Inputs ............................................................................................................................ 137 8.2.2 Outputs ......................................................................................................................... 138 8.2.3 Use of Cable Dynamic Rating System ......................................................................... 139 8.2.4 Verification and Testing of Cable Dynamic Rating System.......................................... 140 8.3 Calculation Techniques................................................................................................... 141 8.3.1 Analytical ...................................................................................................................... 141 8.3.2 Empirical....................................................................................................................... 141 8.3.3 Numerical ..................................................................................................................... 142 8.3.4 Dynamic Rating Techniques ........................................................................................ 142 8.4 Discussion of Survey Results ......................................................................................... 144 8.4.1 Emergency Rating methods ......................................................................................... 144 8.4.2 Method of Calculation of Steady State Current Ratings............................................... 146 8.4.3 Comparison of Calculated and Measured Cable Temperatures .................................. 146 8.4.4 Transient Rating Methods ............................................................................................ 147 8.4.5 Limitations or Difficulties with Cyclic or Emergency Ratings........................................ 148 8.4.6 Cyclic or Emergency Ratings fully Integrated into the Network or Stand-alone .......... 149 8.4.7 Real Time Temperature Monitoring Systems............................................................... 149 8.4.8 Position of the Optical Fibre Sensor for DTS Monitoring Systems .............................. 149 8.4.9 Use of Fixed or Mobile DTS Systems .......................................................................... 150 8.4.10 Overall Accuracy Check for the DTS System .............................................................. 150 8.4.11 Limitations or Difficulties Experienced with DTS Monitoring Systems ......................... 150

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8.4.12 Number of Companies using Real Time Current Rating Systems............................... 151 8.4.13 Use of Optical fibre (DTS) System as Input to Real Time Current Rating System ...... 152 8.4.14 Use of Safety Factors in Real Time Current Rating System ........................................ 153 8.4.15 Number of Integrated and Standalone Real Time Current Rating Systems ................ 153 8.4.16 Limitations or Difficulties Experienced with Real Time Current Rating Systems ......... 153 9 10

CONCLUSIONS AND RECOMMENDATIONS ................................................................... 155 REFERENCES .................................................................................................................. 157

APPENDIX A: QUESTIONNAIRE (EMPTY) ............................................................................... 169 APPENDIX B: QUESTIONNAIRE – INCLUDING REPLIES SUMMARY .................................. 185 APPENDIX C: TABLE OF POTENTIAL IMPROVEMENTS TO IEC STANDARDS .................. 263 APPENDIX D: MIND MAP OF CURRENT RATING CALCULATIONS ..................................... 266 APPENDIX E: BONDING SCHEMES OF CABLE SYSTEMS ................................................... 269

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André-Marie Ampère (20 January 1775 – 10 June 1836) – French physicist and mathematician

Acknowledgement The working group would like to thank all responders to the questionnaire for their time to create input to the working group. Many responders completed the questionnaire in a very thorough way, giving meaningful insights to the working group. Furthermore, the working group would like to express their sincere thanks to our team of reviewers of this report. The content of the report was reviewed by Mr. Brakelmann, Mr. Coates and Mr. Dorison, as well as by many SC B1 members. Their comments provided both multiple improvements as well as useful guidance in the finalization of this report. Thank you!

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EXECUTIVE SUMMARY The current rating of insulated power cables, including buried, submarine and in-air installations, is 1 considered in detail in this technical brochure, which addresses problems establishing the ampacity of new and existing power cables. There is a wide variety of power cable types and installation conditions, which all influence a power cable’s current rating, and although there are well-known standards that govern ampacity calculations, these standards are not fully complete. For new power cable installations, there is a need to establish the current rating on common grounds. The current rating is an important indicator of the performance of the power cable, and as such receives a lot of attention when a power cable and an installation condition are selected for a planned underground or submarine cable connection. Also for existing power cable installations, the current rating is an important topic to consider. Installation conditions may have changed since the times of engineering and installation (for example, due to nearby installation of other utilities), and also the current rating calculation methods have evolved over time. This means that the current rating of an existing power cable presently in operation might be quite different from the original engineering assessment. In order to establish the actual current rating of an existing power cable circuit, a reassessment of its ampacity is often of interest. To help cable engineers to perform current rating calculations, this technical brochure was developed by CIGRE. The report covers three major topics:



A consideration of the starting points for cable rating calculations.



A guide to methods for calculating current rating in situations which are not (fully) described in the existing IEC standards.



A discussion concerning the tools and techniques available for performing cable rating calculations.

The calculation of cable rating is actually very similar for medium, high and extra high voltage power cables (Figure 1 gives an impression). Therefore, the Working Group believes that this report is quite well usable for many power cable types, including submarine and HVDC cables. The intended usage of this report is as follows:



If a user wants to understand what topics are important to consider before calculating the current rating of a power cable in a certain situation, it is advised to read Chapter 3 describing the starting points of the calculations. From this Chapter, it can be learned how the calculations are approached around the world and what should be considered when defining starting points.



If a user wants to calculate the current rating of a power cable in a certain situation, it is advised to follow IEC standards as much as possible (as e.g. IEC 60287, IEC 60853). However, if the situation facing the designer is not exactly described in the IEC standard, this brochure can give guidance on how to proceed. The reader is encouraged to start with the mind map in appendix D to find the CIGRE recommendation on the calculation method to be used.



If a user wants to understand the background and capabilities of the calculation tools (mostly computer programs) or dynamic rating systems, the guidelines in Chapter 8 may give interesting

1

The term ampacity is widely used in North America to denote current rating capability. Both terms, ampacity and current rating, will be used interchangeably in this report.

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information helping to make an informed choice or to understand important details about the calculation tools.



If a user is in general interested in the current rating of cable circuits, the Working Group advises to read though the complete brochure to gain an understanding on how well current rating calculations for power cables can be done today as well as review the supporting references listed throughout the document. More development work still needs to be done, as was defined by the WG in various places in the document. The most important of those have been listed in the recommendations in Chapter 9 of this document.

It has been the WG’s goal to provide guidance to a user trying to calculate, or to understand the current rating of a power cable system. It is hoped that this brochure, the related Electra article or the tutorial presentation, which also is available, provide the needed guidance and will help the user forward in the quest to understand the current rating of the power cable in his or her situation.

FIGURE 1: (EXTRA) HIGH VOLTAGE CABLE TYPES – AN IMPRESSION

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1

Int rodu ct ion

This technical brochure is the final report of the CIGRE Working Group (WG) B1.35 and discusses the issues related to power cable ratings. The report has been drafted in the period 2010 to 2014 and gives guidance on performing cable rating calculations. The report is intended for power cable engineers having the need to calculate or to understand the loading possibilities of new or existing power cables. The topic of cable rating (or “cable current rating”, “ampere capacity” or “ampacity”) refers to the amount of current (in Ampères) a cable system can transmit without exceeding design limitations of the cable system at any position along the circuit. Together with the capability of the cable insulation material to withstand a certain voltage gradient, this capability leads to the power transmission capacity of the cable system. Being so fundamental, it is interesting to note that safeguarding the current rating is performed completely differently from safeguarding the voltage withstand capabilities. The latter is directly tested in the high voltage laboratories while the former is typically not tested or verified but only calculated, largely due to the fact that the current rating cannot be sufficiently assessed without also considering the installation conditions and actual circuit loading may be far below rated conditions much of the time. It is, therefore, very important that the calculation is performed correctly, in order to result into a representative cable rating & power transmission capability for the power cable system under consideration. This report supports the user in that important task by providing an index to world-wide industry experience located in standards, publications, methods and tables. The topic of cable rating is not new. Various numerical methods and analytical approaches have been developed over the years. Many members of the cable community are familiar with the International Electrotechnical Commission (IEC) standards in this area such as the IEC 60287 and IEC 60853 series and with related fundamental work such as described by J.H. Neher and M.H. McGrath (1957). As power cables have been used since about the 1880s, the cable rating is a topic which has been considered by engineers for more than a century. Being one of the most important requirements for a power cable system, the topic of cable ratings is on the agenda of utilities, manufacturers, consultants and universities, mainly during the following phases of a cable life: 1. The contractual phase, in which a power cable having a certain capability to transport current is bought by a utility / user. Although this contractual phase is before design and engineering takes place, the current rating of the power cable is often discussed when evaluating the bids of suppliers. 2. The design and engineering phase, where the cable rating is usually calculated by the manufacturer, and has to meet specific requirements (steady state or dynamic) set by the utility / user leading to reviews or recalculations by utility engineers or consultants. This theoretical exercise is often the only background behind a cable’s current rating as testing the current rating is a very seldom used option. 3. The operation phase of power cables, where cables often become increasingly loaded. For utilities initially planning a new underground cable, it is not easy to set the current rating requirements for the 30 – 50 years to come in the expected operating life of the system, as there are very many rapid changes in the world of electric energy generation, transmission, distribution and consumption. When the loading of an existing power cable grows close to the allowable rating according to the (old) engineering calculations, it is becoming very important to understand the exact limitations regarding the cable

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rating. The importance is related to both the prevention of severe overloading and timely investment in new transmission facilities.

Therefore, there is a need to establish a reliable and representative rating for each power cable system whatever its situation or age. However, this is easier said than done. The standards and long history referenced above does not imply that the calculations of the current rating are fully understood, or absolutely correct. Existing methods are not fully complete for different reasons, for example, the on-going developments of the cable systems and joints for land and submarine applications, the increasing complexity of cable trenches and cable installation conditions, the dependency of the cable rating on the thermal parameters of the cable environment, the resulting complicated calculations and the lengthy development time for verified calculation methods to address special situations. All these reasons lead to difficulties when calculating the current rating of cable systems.

1.1

A Guide to this Technical Brochure

This technical brochure intends to support the user trying to calculate the current rating of a new or existing cable system by giving guidance in the topics of establishing starting points for rating calculations, performing rating calculations in complex situations, and choosing rating calculation methods. The technical brochure should be used as a reference book in which guidance can be found regarding implication of choices made in the process of calculating the current rating, or in which guidance can be found in the case of a limitation that has to be overcome when performing a rating calculation. Do note that this technical brochure is not a standard. The brochure is to be used in addition to the standards and other references and contains guidance from the CIGRE Working Group (WG) experts on current ratings for power cable engineers with the intention to calculate or to understand the loading possibilities of new or existing power cables. The work has predominantly been based on:  

IEC 60287 IEC 60853.

It is noted that these standards are revised from time to time. As such any recommendations in this TB should be reviewed with reference to the latest standard as some recommendations in this TB may become outdated.

Inside this technical brochure, the following information can be found: In Chapter one, the subject of current ratings is introduced, and the goal, scope of work and terms of reference posed to the WG are given. Furthermore, general information on the questionnaire used by the WG to collect experiences worldwide is provided. It will be shown that the questionnaire has an important, worldwide coverage. Chapter two gives general information on the way rating calculations are performed around the world. More importantly perhaps, overall issues with rating calculations are considered which need to be addressed on a more strategic level before calculations are performed.

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Chapter three provides information on starting points for rating calculations. After all, without the correct starting points, rating calculations will end up producing misleading results. Within this Chapter, the questionnaire results are used to provide information on what kind of starting points are actually used in practice, while, on the other hand, it will be discussed what starting points are actually needed for performing rating calculations correctly. From a gap analysis performed between these two, recommendations are given to improve the setting of starting points. A subsequent section of the report is composed of Chapters 4, 5, 6 and 7. Together, these Chapters can be used as a guide for performing rating calculations in situations which are not (fully) described in the IEC standards. Chapter 4 will provide an introduction on how to use the calculation guide, including an overview in the form of a lookup table and a visual “mind map” (e.g., a flow chart illustrating the divergent factors contributing to a specific rating case), to give a quick access to the information contained in Chapter 5, 6 and 7. Chapter 5 describes the impact that (time varying) voltage and current have on the current rating of a cable system, Chapter 6 discusses construction details of cables and their impact on the current rating and Chapter 7 describes the effect of installation features. Chapter 8 is the third and last major part of the document and provides information on available calculation techniques and tools. The information is based on the survey questionnaire that was distributed to various utilities and other organizations, and it provides a good overview to those considering various calculation techniques – both steady state and dynamic – as well as the usage of Distributed Temperature Sensing (“DTS”). Chapter 9 contains a set of conclusions and recommendations. Future work is recommended both to cable engineers as well as to CIGRE and some reflections from the WG members are given on the applicability of the brochure. Chapter 10 provides all references used or referred to in this brochure. This list gives the reader access to further information. Appendix A contains the questionnaire sent out and analysed by the WG as background information to readers and other CIGRE working groups. In Appendix B, a summary of all questionnaire replies received is provided. Appendix C provides an overview of potential improvements to IEC standard IEC60287/ IEC60853 and references to the sections in this report. Appendix D contains an overview (Mind Map) of current rating calculations sub areas with references to the clauses in this brochure as an aid the reader. In Appendix E, bonding schemes of cable systems are depicted, for information only.

1.2

Information regarding the Working Group’s Objectives

The Working Group which prepared this brochure was started in order to reach three different, related objectives. These goals are listed below, with the background for each of these objectives. 1. Starting points for rating calculations Starting points for rating calculations deal with establishing the thermal properties of the cable environment. As the cable environments can become quite complex (tunnels, multi layered soils, submarine installations, and so on), establishing the thermal properties also becomes quite complex. Furthermore, the way thermal properties are established differs significantly over the world, leading to a varying amount of uncertainty, depending on the method used. Being complex and having an uncertainty, these starting points are extremely important for rating calculations. If the starting points are not defined correctly, or if errors are made here, these will have a significant influence on the outcome of the cable rating calculation.

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For this reason, it has been the WG’s goal to report experiences and information on starting points for cable rating calculations, and to provide practical recommendations regarding acquiring starting points (refer to Chapter 3). 2. Performing rating calculations Rating calculations themselves are nowadays mostly based on the IEC 60287, 60853 or IEEE standards. Although these standards are reasonably easy to use and regularly updated, they do not cover all installation or operating conditions where cables are used. Given the increasing complexity of environments in which cables are installed, and given the continuous development of the cable systems themselves, it is often unclear how to proceed with performing a rating calculation. This means that many cable engineers, manufacturers, utilities and consultants make their own interpretations, either in the calculation method or the data used in the calculations, and subsequent calculations, possibly leading to a discrepancy in the calculation results. For this reason, it has been the WG’s goal to give guidance in performing rating calculations in situations where there is no standard approach reported in the IEC or IEEE (refer to Chapters 4 to 7). 3. Calculation tools Calculation tools are also an important consideration. Understanding the difficulties in establishing starting points, and the existing uncertainties of how to actually calculate the current rating, it is important to correctly understand how rating calculations are performed in practice. Another development is the use of dynamic rating systems in which the current rating is calculated in real time to allow for more optimal utilisation of the cable systems. Calculations performed by the computer programs, as well as the basis (method or model) of these calculations, should be fully understood as increasingly, utilities will base their power market decisions on the output of these tools. For this reason, it has been the WG’s goal to report calculation methods used and to report recent developments in (dynamic) rating programs and systems (refer to Chapter 7). In summary, the challenge posed to the WG was to give guidance to the user such that reliable and representative cable rating calculations can be performed, using a correct set of starting points and appropriate calculation techniques and tools, applicable to power cables whatever their type, construction, age or installation conditions may be.

1.3

Information regarding the Terms of Reference and Scope of Work

The Working Group considered the following terms of reference: 1. To collect experiences and information from different countries regarding: a. Acquiring the starting points for cable engineering (e.g. soil properties, ambient temperature properties), b. Calculation methods used (e.g. type of software, differences in software, sources of information other than IEC, recent developments in dynamic rating software, temporary ratings. Note that no benchmark of software whatsoever took place). 2. To assess and interpret the result of 1a and to make conclusions and practical recommendations regarding acquiring the starting points to use within a cable rating study.

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3. To set up a general framework to guide the user to calculate the (steady state and dynamic) current ratings of a cable circuit in any situation. 4. To list special situations in cable circuits (e.g. crossing cables and heat sources, deep cable, cable in horizontal directional drilled locations, cable in open trough, cable on sea floor). 5. To recommend an existing calculation method, to highlight possible calculation methods or to give indications for the calculation of the cable rating in every situation listed under point 4. 6. To assess and interpret the result of 1b and to report potential difficulties and problems with the methods as well as to report recent developments in the methods (this includes recent developments in dynamic rating methods). 7. To prepare the deliverables including an indexed bibliography regarding cable rating standards, publications or other references.

The scope of work considered by the Working Group is: All AC and DC cables with emphasis on the high and extra high voltage areas, but where possible extended to the medium voltage area as much as possible, excluding accessories.

1.4

Introduction to the Questionnaire

Power cable rating calculations are performed worldwide on a regular basis. In order to learn from the experiences gained around the world, a questionnaire was prepared and distributed by the Working Group. This questionnaire was focused on the calculation techniques used, on the way starting points are selected and on the need for cable rating calculation improvements. The questionnaire turned out to be rather extensive (see Appendix A for the full questionnaire) but was nevertheless answered by more than 100 companies. Figure 2 gives an overview of the countries from which responses (sometimes multiple answers, from multiple companies) have been received. Given the multitude of answers, it is believed that the questionnaire outcome gives a realistic representation of the practice worldwide. Although the questionnaire is believed to give a realistic representation, this does not mean that each answer given may be correct. The working group decided not to change any answer received, and is thus representing the input of the questionnaire respondents ‘as was put forward’. All answers received are reported in appendix B showing reactions on open questions. Furthermore, throughout this report statistics and overviews are given showing typical values and typical numbers. These numbers thus have not been verified by the working group and should be regarded as being ‘typical’. The questionnaires have been completed by employees working for utilities (57%), cable manufacturers (22%), consultancy companies (13%) and others (8%, of which 50% Universities). Table 1 provides some more details about this distribution of responses among the various types of organizations.

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FIGURE 2: COUNTRIES RESPONDING TO THE QUESTIONNAIRE

TABLE 1: ORGANIZATIONS COMPLETING THE SURVEY VERSUS GEOGRAPHICAL LOCATION (QUESTION 1.1)

Number of responses Company type Cable manufacturer Consultancy company Utility Other (specify) Grand total

North America number 1

South America number 1

Europe number 13

Africa number 0

Asia number 7

Oceania number 0

2

1

8

0

1

0

11 0

2 0

24 4

2 0

12 4

8 0

4

49

2

24

8

14 101 replies in total

The questionnaire results are fully integrated in the report wherever needed to provide useful information to the user.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

2

O v er al l I ss ue s w it h R at i ng Ca l cul at ion s

Cable rating calculations are performed by different companies in different moments of the life cycle of power cables as was already mentioned in Chapter 1. Table 2 and Table 3 coming from the questionnaire, confirm this.

TABLE 2: WHEN PERFORMING RATING CALCULATIONS, WHO DOES THE CALCULATION?

Organization

Yes

No

Blank

Internal Supplier Consultants Other

89 45 24 8

4 34 39 0

8 22 38 0

TABLE 3: AT WHAT STAGES ARE RATING CALCULATIONS PERFORMED?

Stage

Feasibility Specifications Detailed design As-build Future modifications Reassessment Other

Yes

No

Blank

83 69 76 56 67 61 6

9 20 15 32 22 25 0

9 12 10 13 12 15 0

A few important phases exist where the current rating will receive a significant amount of attention: A. Feasibility phase In case of feasibility studies, often utilities are evaluating ideas about the development of their networks. This comes with coarse estimates regarding the power cable type, the trench dimensions, major route features, cable configuration and the current rating. B. Tendering phase When a bid is requested from the market place, suppliers will give a current rating of the proposed cable system usually in response to the owner’s requirements. In this phase, the current rating is often based on a set of estimations (either forwarded in specifications or not) and on an intended installation method. The calculations performed during this phase are very important for manufacturers because a contract could be won or lost because of it. Unexplained differences in the current rating stated between bids can easily lead to confusion. Note that if the utility / owner is taking responsibility for specifying the cable size, the calculation responsibility belongs to the utility / owner rather than to the manufacturer. C. Design phase When a detailed design is made and agreed upon, the current rating of the cable system to be constructed is usually established and agreed. In this phase, it is customary to replace estimations and assumptions by measurements and agreements, and to perform a relatively accurate current rating study. Again, it is typically the supplier who calculates the current rating, while the utility or his consultant will review the calculation. Sometimes the utility or a third party (consultant, etc.) evaluates the as-built ampacity of the system.

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D. Operation phase During modifications of existing situations and reassessments of the capabilities of the network, the utility is often responsible for performing current rating calculations or hiring a consultant to perform these calculations on their behalf. It is often the utility that is performing the current rating calculation. It is often the goal to redefine the current rating of an existing power cable because the circuit’s environment was changed (see Houwelingen and Rossum, 2007); the load pattern (daily load factor) has changed, or because there is a desire to increase the rating on the circuit (“uprating” or “increased power flow” studies). In this Chapter, it is discussed how these rating calculations are typically done, and what the strategy of the calculation might be in terms of the margin and the approach. Therefore, a reference will be made to the above.

Relation to the voltage level It is common to perform current rating calculations for all voltage classes (57%), see Figure 3. However, 37% of the respondents claim to only perform current rating calculations above a certain voltage class, while sometimes the importance of the connection is taken into account when deciding if the current rating needs to be calculated or not. The latter two categories may be related to the redundancy of the network at a certain voltage level, or to the impact of a cable failure, which makes sense according to the WG. Due to the increasing cost with respect to voltage, greater care in developing cable ratings is often used because there are better economies of optimization at the higher voltages. This was, however, not questioned and, therefore, remains unknown.

All

above a certain voltage

depending on the importance of the network

FIGURE 3: WHEN A CALCULATION IS PERFORMED (QUESTION 1.5)

2.1

How to calculate the Current Rating of a Power Cable

The current rating can be calculated or established in different ways, fulfilling also different needs. In case of feasibility studies for example, the current rating may need to be understood only roughly. A more coarse approach to find the current rating of a power cable may then be used.

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In the case of a bidding phase, the current rating needs to be known already more precisely. However, exact starting points and installation conditions may not be known, and of course, the detailed design phase is yet to come. In this phase, it is believed to be best to list the assumptions made regarding starting points and installation conditions, and subsequently perform current rating calculations for the cable types under consideration. These current rating calculations should follow IEC or IEEE guidelines as much as possible. If IEC and IEEE are not applicable, the guidelines in this brochure could be used to come to an answer. Ratings for estimating purposes are also published in rating tables (IEC 60055-2 and IEC 60502) that prescribe a given set of conditions but do not require specific calculations to be performed by the user. In the case of a detailed design, starting points and installation conditions ideally should be completely defined. Starting points can be deduced by taking measurements or by making estimations, as will be discussed in Chapter 3. However, it is important that in this phase, the error margin on the starting points is known and taken into account. The same is valid for installation conditions which must be known, and whose variations must be understood and taken into account. Only when these variations are taken into account, the current rating of the cable system can be established accurately. Despite these best efforts in the detailed design phase, there is often some degree of construction variability that may not be accounted for. As a result, as-built ampacity calculations are often performed at the conclusion of a construction project. In the case of a cable already in the operation phase, the starting points for a cable rating study will most likely need to be verified or set. Starting points may actually change over time, and in history, starting points were regularly estimated rather than measured or engineered. When the starting points and installation details are known, the current rating of the cable system can be calculated more accurately than when using estimated values. As-built plan and profile drawings are often a resource for this purpose. Some points regarding the above variations when calculating the current rating must be clearly understood: Starting points Starting points play a very important part in rating calculations. This is further detailed in Chapter 3. Circuit rating For almost every application, the current rating from busbar to busbar, i.e., the “circuit rating”, is the value which is needed for operation. That means that besides the current rating of a power cable in its normal installation condition, also the current rating of joints, terminations, as well as any switchgear, current transformers and other equipment in between the busbars needs to be taken into account. After all, it is no use of having a high 1000A current rating for a power cable, while the limitation is given by a switchgear which may not be loaded higher than 800A. It is therefore advised to always consider busbar to busbar ratings, in which the cable may, and may not be the limiting factor. The scope of this technical brochure is limited to the cable portion of the circuit. When considering a busbar to busbar rating, a power cable may be found in series with an overhead line or a power transformer. Those other primary components also have a maximum current rating, which is governed by different aspects compared to the power cable. When the components are in series, the limiting component will limit the loading of the other primary components as well. It must be noted that as the current rating limitation of a power cable depends on the type of rating calculation and the cable environment, the actual limitation may change in time. Having components in series thus may lead to changes in the limiting component (e.g.: in winter, the power cable is limiting, in summer the overhead line in series), see for an example Wild et al. (2007).

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Rating versus loading The rating of a cable circuit gives information on how much current a cable circuit could transport. It is very different from the loading of a cable circuit, which is the amount of current which is actually transported by the cable circuit. The loading of a power cable will depend on the load flows in the network, which in itself depends on the impedances of the various components in the network, and the location of generators and load centres. For transmission systems in utilities, typically redundancy is present leading to loadings much lower than the rating of cable systems. For distribution systems in utilities and especially factories, the loading may be closer to the rating of cable circuits. However, any network operator must be able to rely on the availability of the full rating of a cable system in order to accommodate emergency situations in the network and to prevent forced outages. This explains the importance of the rating of both new and older cable systems. Thermal degradation The loading versus the rating of a power cable system gives information about the possibility of thermal degradation of the power cable. The cable rating and cable degradation are thus related to each other. More information about this relation can be found in CIGRE (2008). Maximum temperatures Loading a power cable system will lead to heating of that power cable system. There is a limitation on this heating in the form of maximum temperatures. When such a limitation is reached, the cable system is fully loaded (up to its rating). Temperature limitations exist because of the materials in or around the power cable, as: 

A limitation on the conductor temperature to avoid overheating of the adjacent insulation material. This is a very important limitation to the loading of a power cable often used in rating calculations. Increasing the temperature beyond this limitation will have impact on degradation and remaining lifetime of the power cable which typically is irreversible.



A limitation on the temperature of the outside jacket (outside surface) of the power cable. When installed inside a soil, this limitation typically aims to prevent dry out of the soil. Dry out of the soil will lead to significant deterioration of the soil thermal properties, which leads to increased heating. In such an event, the cable itself can easily become significantly overheated (a thermal runaway). Dry out can be both reversible and irreversible depending on the soil type. When installed inside a tunnel, this limitation typically presents a limitation because of safety (think of burning a hand).



When installed inside a selected-sand backfill having a high dry out temperature, the limitation may be on the interface between the selected-sand backfill and the native soil rather than on the jacket temperature of the power cable.



A limitation on the temperature of the air around the power cable. Where a power cable is installed in a tunnel or cellar, there may be limitations on the temperature of the air inside that tunnel or cellar. Typically countries have maximum temperature limitations on working environments for personnel. In case a tunnel or cellar is such a working environment (it typically is), the air temperature may be one of the more severe limitations for the rating of a power cable.

Other temperature limitations may exist in other installation situations or in specific cable designs, and also limitations to temperature differences may exist. For HVDC cables these limitations are discussed in section 5.3.3. In general it is advised to understand the temperature limitations very well before a current rating calculation is performed.

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Temperatures during emergency situations During emergency situations, refer to Chapter 8, the temperature of the conductor is often allowed to rise above the maximum operating temperature of the power cable. From the questionnaire (for details refer to appendix B), it was learned that: 

The duration of such emergencies seems to range from less than 10 minutes up to 15 days, strongly depending on the company answering the questionnaire.



The maximum temperature specified at the end of such an emergency situation is reported to range between the normal maximum operating temperature (90 ºC for XLPE insulated cables, so no increase beyond the normal maximum operating temperature) and 130 ºC (excluding extreme entries), with the most popular maximum emergency temperature being 105 ºC, see also Tang et al. (2014).

The working group notes that care must be taken not to increase the emergency temperature, or the emergency duration at an increased temperature, too much. This may lead to irreversible damage to the insulation material of the power cable. Such damage may shorten the cables’ lifetime, or – when emergency temperatures are very high – may lead to immediate defects in the cable system over the complete length. Local differences along the cable route Different cable environments will lead to different cable temperatures. As such, the temperatures along the cable route will change with changes in the cable environment and with changes in the cable configuration. Given the temperature limitations, there will be several locations along the cable route which will come close to the temperature limitation when the cable circuit is fully loaded (to its rating). It is critical to understand where these locations are situated along the route, and to keep the properties of these situations under full control. In case of a situation with a limited length, typically 5 m, there will be axial heat flows reducing the impact of such a situation, although even small length situations will have a thermal impact. For reasons of practicality, in rating calculations typically situations are considered with a length greater than 5 meters. Smaller length situations are typically neglected. However, in cases of extremely worsening environmental changes (e.g. a situation in which a cable crosses a 1 meter thick foam insulation block having very bad thermal conductivity), it is advised to also consider those smaller sized situations.

2.2

Basis for the Calculation

The calculation of the current rating itself is often performed on the basis of the IEC or IEEE standards. The questionnaire indicated that IEC standards are always/often used by 79% of the respondent (see Table 4) worldwide. Only 6% of the respondents replied that IEC standards are never used as a reference. In these cases, national standards are used for calculating the current rating (Japan, Germany). In Japan, the JCS standard (Japanese Electric Wires & Cable makers) 0501’ Calculation of the current rating of power cables for rated voltages more than 66kV’ and JCS 168 E1995 is commonly used which is similar to IEC with some small differences. In North America, the IEEE standards 835 and 848 are often used.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES TABLE 4: ORGANIZATIONS VERSUS IEC USAGE FOR CABLE RATING CALCULATIONS (QUESTION 1.2)

Results Company type

Always

Often

Occasional

Rare

Never

Other

A cable manufacturer A consultancy company A utility Other (specify)

13 7 14 5

6 6 27 1

1 9 1

2

5

2 1

Grand total

39

40

11

2

6

3

1

Note: References to commercial cable rating software are given as non-standard IEC method by some respondents.

The fact that the vast majority of the companies worldwide use the IEC standards for rating calculations does not mean that an answer is always easily reached with the IEC standards. Many needs for improvements regarding the steady state rating calculations were indicated by the users in the questionnaire. Furthermore, most system designers experience the limitations of the present current rating calculation methods. In those cases the following options (workarounds) are followed: The ‘Finite Element Method’ (FEM) is the most used method; this was reported by 17% of the questionnaire responses. Remarkably approximation, which is the very opposite of FEM, was the second most popular method, reported by 12% of the responses. Other methods are ‘contact/hire a consultant’ (9%), ‘ask the cable manufacturer’ (7%.), ‘use site measurements’ (3%) and ‘discuss with the client’ (3%). Only a small number of respondents reported that they have not experienced such a case so far (7%). While FEM appears to see prominent use, the WG expects that this method is seldom applied by utilities directly and instead is requested by utilities from manufacturers or consultants. The above, once again, confirms that the topic of current rating is one of importance for many companies around the world, as was indicated in Chapter 1.

2.3

Margin in Cable Rating Calculations

Power cables seem to have a certain margin for higher loading. After all, cases in which power cable systems fail during operation because of overloading are rather rare (though these have happened in multiple countries in the world). However, this finding may be merely a symptom of the way power cables are utilized to date. They are very seldom loaded close to their thermal limit. Refer also to the bullet list in section 2.1. Given the changing usage of transmission and distribution networks in the future (CIGRE 2010) the loading of power cables may come closer to the limitations. Especially in those cases, it is very important to understand the capabilities and limitations of the power cable in enough detail to prevent unplanned overloading situations. This means that there is a need to understand the current rating of a power cable in operation quite well. This, in turn means that the current rating calculation itself, and the starting points, must be accurately determined. Also dynamic rating systems or other software tools must provide enough accuracy to determine the dynamic current rating of a power cable.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

The quality of the definition of the starting points, the calculation method and the calculation tools used thus must be in balance. It is obviously of no use to have a very accurate and time consuming FEM calculation for some complex cable environment if, in the same study, there is a possible error margin of tens of percents regarding the dry-out temperature or thermal resistivity of the native soil. In such a case, balance must be created first by dedicating attention to the establishment of realistic, reasonable starting points, possibly at the cost of some accuracy of the FEM calculation, to yield the best result. To detect these cases, the reader is referred to Chapter 3 on starting points. Accurate models for cable ratings are known, but the reader should be aware that detailed knowledge of the native soil thermal environment is often not known better than to within 10 - 20%. The accuracy of the current rating calculations is typically limited by inaccuracies in the starting points, limitations to accurately understand input parameters and fundamental limits in calculation methods and models. This implies that it is good engineering practice to have some margin between the current rating of a power cable and the expected maximum loading of the circuit. Obviously, dynamic rating calculations (real time) can come closer to the actual rating of a power cable because they provide more realistic calculation results compared to the offline loading calculations, which are often based on the assumed system conditions. In cases where the dynamic rating systems are applied, the margin in the calculations is also an important subject to consider before applying such a system (predicted loadings) to control the power flow in the network. The questionnaire was used to investigate the current practice regarding safety margins, details can be found in Appendix B. The questionnaire shows that currently safety margins are not commonly applied except that some designers apply a lower conductor temperature if the soil conditions are not known (as per AEIC CG1 and CG6 : -10 °C), and that other designers limit the cable outer sheath temperature such that soil drying out is prevented or limited (i.e. 45-50 °C outer sheath temperature). The same holds true for safety margins in transient rating calculations. A number of methods are in use by a small group of cable system designers to include a certain margin in the calculated current rating of a cable system, such as a reduction of the cable conductor temperature (5%), assuming a higher thermal resistance on site (3%), or other imposed limitations (7%) such as rounding down the calculated rating to 5 or 10 A accurate numbers, impose a maximum outer sheath temperature (e.g. 45 °C) or assume worst case conditions. The following guidelines on the topic of margin in cable rating calculations can be given: 

Balance the accuracy in starting points, calculation methods and calculation tools relatively evenly. Do note that although it is realistic to have a calculation method with accuracy down to a few percent for some situations, it is not realistic to expect the same accuracy for the starting points.



Discuss the margin in any rating calculations in the bidding phase and design phase of the project as well as in the operation phase when the existing cables are considered.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

3

St ar t in g Po int s f o r R at i ng Ca l cul at ion s

Insulated power cable ratings must be calculated with consideration of many parameters. The steps to approach these ratings must be carefully considered by the engineer performing the calculations. This section of the guide identifies the main considerations for addressing rating calculations when presented with a particular set of circumstances. Sections 3.1 to 3.5 discuss the aspects and starting points needed for a rating calculation, while Section 3.6 discusses how starting points are currently established based on the questionnaire results. Section 3.7 concludes this Chapter with important learning points.

3.1

Identification of an Underground Cable System

The user of this guide should understand the basic cable construction features and identify the cable system type. Within this context, the cable types that might be encountered include: 

Extruded cable including cross-linked polyethylene (XLPE, see Figure 4) and ethylene propylene rubber (EPR, see Figure 5). This type of cable is available in voltages from secondary distribution up to 550 kV. Most cables are constructed with one core, although three-core cable has been commercially supplied up to 220 kV. Conductors may be made of stranded or solid copper or aluminium. The outer metallic cable layers vary widely but can include a stranded copper or aluminium wire shield, a taped copper or aluminium shield, copper, aluminium or stainless steel corrugated sheath, or extruded lead sheath; combinations of these shield and sheath constructions have been used.

FIGURE 4: 220/380KV XLPE INSULATED CABLE WITH 2000 mm2 CU MILLIKEN CONDUCTOR AND SMOOTH ALUMINIUM SHEATH

FIGURE 5: 46KV 3x500 mm2 SUBMARINE CABLE, CORES EPR INSULATED

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

Self-contained fluid-filled cable, sometime referred to as low-pressure oil filled or mediumpressure oil filled cable, has been used commercially from typically medium voltage up to 525 kV. Single-core cable constructions usually consist of a hollow-core copper conductor, oilimpregnated paper insulation, lead or corrugated aluminium or copper sheath, and insulating jacket (see Figure 6). Three-core cables often have fluid ducts in the interstices between conductors.

FIGURE 6: 400KV LOW PRESSURE OIL FILLED CABLE WITH LEAD SHEATH AND PVC JACKET



Paper-insulated lead-covered cable (PILC) typically has a stranded copper conductor, sector or circular shaped, and mass impregnated paper insulation with a lead sheath (see Figure 7). Some constructions have an insulating jacket over the lead sheath. Both single-core and three-core cables are commercially available.

FIGURE 7: LEFT PICTURE: BELTED CABLE WITH COMMON LEAD SHEATH, RIGHT PICTURE: SINGLE LEAD SHEATH ON EACH INSULATED CORE

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

Pipe-type cables (common in North America but with very limited applications elsewhere) consist of a carbon steel pipe in which the three cable phases are installed (Figure 8). Each phase consists of a stranded copper or aluminium conductor, oil-impregnated paper or paperpolypropylene-paper (PPP) insulation, metallic taped shield and metallic skid wire (stainless steel, brass, bronze, zinc or aluminium). The interior of the pipe together with the cables is pressurized with dry nitrogen gas or dielectric oil (mineral oil, alkyl-benzene or polybutene).

FIGURE 8: HIGH-PRESSURE FLUID FILLED CABLE

The user should be familiar with these cable system types and have them identified for a particular cable circuit rating study. Within a certain cable route, transitions between cable types are sometimes used. Common transitions include:   

Change in conductor size within the same cable type. Transition from self-contained fluid-filled or PILC cable to extruded cable. Transition from pipe-type to extruded.

As an initial step in preparing to evaluate cable ratings, the user should identify all of the cable types along the route and gather the respective data about the cable construction. Often, this data may be located in utility records or in manufacturer cable sheets and will indicate dimensions (thickness, areas) and materials used for cable construction. Industry guidelines (such as IEC standards 60287 and 60853) will provide standard material characteristics for the cable components (electrical resistivity of metallic components, thermal resistivity and volumetric specific heat for non-metallic components), etc. Generally, only main characteristics are provided in the factory acceptance test results as well as the factory data sheets. If the customer intends to make “accurate” calculations, it is useful to make measurements on the cable provided. One of the challenges of developing cable data is the variation in information that may be available. Sources of cable construction are often obtained from manufacturer’s data sheets, but there is variability in what may be reported on these sheets. The dimensions may include the thickness of each cable layer, or the nominal diameter of each layer. The manufacturer is allowed to apply tolerances when making the cable, so the data sheets may vary from the actual manufactured cable. Factory acceptance test reports usually include dimensional checks of the cable as it is manufactured, but there are also variations during a production run such that these are not entirely

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

uniform for an entire batch of cable. The reader is encouraged to get the most accurate information available to describe the cable. In general, this means selecting data from the following list with a decreasing quality of information: 

Factory Acceptance Test Results – These provide actual dimensions of how the cable was made.



Cable Factory Data Sheets – These sheets provide a good description of the cable but do not necessarily reflect the manufacturing tolerances or the actual deviation from the design of the cable system to that which is actually put into production. They may include specific measured material characteristics as well.



Specifications and Industry standards – Generally, cables of a given voltage class and conductor size will have characteristics within the parameters of industry standards and specifications. If better sources of information are not available due to lost or unavailable records, industry practice with similar voltage and conductor cable may be the only alternative.

3.2

Cataloguing the Installation Conditions along the Cable Route

In addition to cable construction details, the installation conditions along the route have a strong influence on the cable rating. Therefore, establishing a cable rating for a circuit requires careful study of the information about the route. Much of this information is established from records including plan and profile drawings. The difficulty for some circuits is that these records are lost, incomplete or inaccurate. In these situations, estimates must be made or investigations need to be executed before a rating calculation is performed. A cable circuit rating is based on determining the worst combination of installation conditions along the route that results in the highest operating temperature and, therefore, the lowest rating. The factors that should be ascertained for cables buried in the ground, or installed in pipes or ducts in the ground are: 

Burial depth – The path for heat leaving the cable which ultimately passes to the earth’s surface becomes longer with increased burial depth. This longer heat path, other factors held constant, increases the thermal resistance to heat leaving the cable and lowers the cable rating.



Phase and circuit separation – Mutual heating among cables causes a de-rating effect due to the closer proximity among cables. Closer spacing lowers ampacity because of greater mutual heating effect (except sometimes in the case of multiple-point bonded systems where circulating current losses may increase at a faster rate than the reduction in mutual heating).



Mutual heating from adjacent circuits, either in parallel or crossing the circuit of interest – In addition to cables among the same circuit or system of cables, nearby cables whether transmission or distribution or other underground heat sources (e.g., steam lines) can cause mutual heating when running in parallel or crossing the circuit being rated.



Native soil thermal resistivity – Areas with increased soil thermal resistivity will provide a greater thermal resistance to heat escaping from the buried cable. Therefore, it is important to identify these areas to account for the soil characteristics in rating calculations. In case of changes to the environment (e.g. a paving is made or soil is exchanged) the soil thermal resistivity is likely to be changed.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

Extent and characteristics of special backfill – As with the native soil, the characteristics of the backfill, both the material thermal resistivity and quantity and dimensions installed around the cables, should be known.



Local ambient soil temperature – Higher ambient soil temperature limits the allowable temperature rise for current-carrying capacity of the cable and therefore lowers the cable rating. The native soil temperature must be known at cable depth to properly evaluate the cable rating. Areas under roadways and pavements may have a higher ambient temperature due to increased solar absorptivity, and summer ambient temperatures are greater than winter temperatures which can be important for cable circuits concerned with seasonal ratings.

Where the cable system is cooled, installed in tunnels or installed in air then different or additional information will be required to calculate the current rating. Establishing the above mentioned parameters is best done during new circuit design. Some projects are designed based on estimated parameters which, in some cases, are later examined through field work. Selecting the worst case situation amongst many situations encountered is quite difficult. For this reason, it may be necessary to perform multiple rating calculations for a given route. The type of cable installation also must be well defined in order to both develop a thorough understanding of the hot spots along the cable route and to select the model to be used for ampacity calculations. Some of the major types of cable system installations include: 

Direct buried (see Figure 9) – The cable surface is in direct contact with either the native soil or special thermal backfill. The smaller diameter (as compared to cables installed in conduits) can result in an increase in the heat flux leaving the cable surface although the thermal resistances from the cable surface to conduit and conduit itself are not present. Conduit installations often have direct buried segments near risers.

FIGURE 9: DIRECT BURIED CABLE CIRCUIT

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

Cable in Conduit (see Figure 10) – The cable is pulled into a previously-installed conduit. The conduits are often backfilled with special materials including fluidized thermal backfill (FTB) and concrete. The conduit type (PVC, HDPE, fiberglass reinforced epoxy) must be known as they have different heat transfer characteristics.

FIGURE 10: CABLES IN CONDUIT



Pipe-Type Cable – The cable pipe is buried much like a conduit for other cable types and then backfilled with a granular backfill or fluidized thermal backfill.



Submarine Cables (see Figure 11) – The cables are placed on the water bottom (sea bed, lake bed or river bed) or embedded below the water bottom.

FIGURE 11: LANDING OF A SUBMARINE CABLE

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

In-air Cable Installations (see Figure 12) – Cables may be installed either vertically or horizontally in air including at termination structures and along riser poles. The extent to which the cables have free air ventilation must also be assessed in determining the rating.

FIGURE 12: IN-AIR CABLE INSTALLATION



Trenchless Installation Methods – Cables may be installed without a trench excavated from the surface through methods such as pipe-jacking, micro-tunnelling or horizontal directional drilling. These “trenchless” methods can involve the installation of a casing pipe that consists of steel or high-density polyethylene. Each of the pipes may be filled or unfilled.



Steel Casing (see Figure 13) – This casing type is often selected by civil engineering firms because of its high longitudinal tensile strength, but extruded and self-contained cables installed within the casings will induce hysteresis and eddy current losses in the steel. The extent and type of grout or presence of air within the casing between the inner conduits and casing wall must also be carefully evaluated.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

FIGURE 13: CABLES INSTALLED IN A STEEL CASING



HDPE Casing – This casing type is often more flexible than a steel casing, but the thick casing wall consisting of high-density polyethylene has a high thermal resistances but with no additional electrical losses. The extent and type of grout or presence of air within the casing between the inner conduits and casing wall must also be carefully evaluated.



No Casing – This type of installation involves pulling a bundle of conduits directly into the bore hole. There is generally no opportunity to grout the space between the boring and the bundle of conduits, so the characteristics of the soil left around the conduits – usually consisting of a combination of drilling mud and native soil – and relative depth to the water table must be assessed for rating purposes.



Trenchless installations of cable often use much heavier wall conduit materials to provide greater tensile strength for pull back during installation of the conduits. This heavier wall introduces a greater thermal resistance to heat leaving the cable system.



Laying in troughs – a trough is either a prefabricated U-shaped element or it can be cast-in-place as sections or as a continuous concrete casting. The cables are pulled in, and the trough is eventually backfilled. Finally, a cover is placed on top of the trough.



Tunnels are used in cities when more circuits or more utilities have to use the same route and when the transmission capacity cannot be obtained by burying cables. When the surroundings allow it, the tunnel can be made by excavating from ground level, after which the tunnel is constructed. When traffic, buildings or other installations in the ground do not allow for using the excavation method, the tunnel can be dug by using a tunnel excavation machine working underground an placing tunnel segments and jointing them together. Tunnels can also be dug by means of pipe jacking: this method also entails placing segments next to each other and joining them together. The diameter of a circular tunnel can vary from less than 2 m up to 14 m. Installation in tunnels requires consideration of measures to avoid fire propagation and the

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

establishment of fire doors/sections et cetera. In connection with tunnels, shafts and ventilation systems must typically also be established. 

Bridges can be used for cable systems to cross roads, rivers and railways. Vibration, elongation, bending at junctions, expansion joints heat and wind must also be considered.

The reader is also reminded that increased burial depth of trenchless installations often means that mutual heating effects of parallel circuits or heat courses have a greater zone of influence that must be considered for rating purposes.

3.3

Identify the Thermal Properties of Soils and Special Backfills

While insulated cables may be installed in free air, tunnels or manholes, the predominant type of installation is underground. Because of this, soil thermal resistivity is a critical parameter for cable ratings as it represents 50-75% of the thermal resistance between heat leaving the conductor and ambient earth. For this reason, it is one of the most important parameters and also one of the least understood. Soil testing can be performed to characterize the soil thermal resistivity. The sensitivity of the thermal resistivity with respect to moisture content is important due to the soil drying that may occur in the presence of cable heating, see: CIGRE(1982), CIGRE (1992-4), Arrighi et al. (1970), Donnazzi et al. (1979), Koopmans and Kuiper (1990) and Groeneveld et al. (1984). Soil testing is often used, both in the field and on samples in the laboratory. Soil characteristics vary both along the route and with depth, especially with the soil type and the groundwater table. Heat leaving the cable is generally acknowledged to move away from the cables towards the earth’s surface, so variations in the strata of soil can impact the heat transfer as well. Most rating methods assume that the soil has uniform properties outside of the cable trench, but this is not always the case. Other analytical methods or finite element analysis may be required where the soil cannot be assumed to have uniform thermal characteristics. Soil testing for submarine environments is essentially done in the same manner as for conventional buried cables aside from the increased complexity of performing the in situ measurements and obtaining samples. When measurements are not performed, there are few alternatives for determining the native soil thermal resistivity as this is a parameter not commonly catalogued except within the cable rating community. A good starting point is IEC standard 60287-3-1 “Electric cables – Calculation of the current rating – Part 3-1: Sections on operating conditions – Reference operating conditions and selection of cable type”, but these values should be used with caution (see Section 3.5.3).

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Several parameters affect the thermal resistivity of the soil. These include (but also refer to section 03.5.5 and 3.6): 1. Soil composition a. Type of mineral b. Organic content c. Bonding between particles 2. Texture a. Fine - coarse b. Grain size distribution c. Natural or crushed 3. Water content a. Wet, moist, damp, dry 4. Dry density a. Solids content b. Loose, compact, dense c. Pore size and distribution 5. Other factors a. Loss of fines b. Dissolved salts/minerals.

Once installed, the dry density, type and most other factors of the soil does not change. Only the moisture content will change because of an environmental change (summer, winter, rain, etc.). The cable itself can also negatively influence the moisture content of the soil by means of the dry out process. The moisture content has a profound effect on the soil thermal resistivity as illustrated in Figure 14. Establishing the thermal properties for calculation means that, once soil properties are well known, a choice is to be made regarding the moisture content to take into account. It is often possible to detect the lowest groundwater table in a soil analysis. Given the soil properties, from the lowest groundwater table, the lowest moisture content of the soil around the power cables can be deduced. This lowest moisture content is subsequently used to calculate (or measure – in a laboratory environment) the thermal properties of the soil around the power cable for cable rating considerations. Note that in a normal situation, typically there is more moisture in the soil than expected on the basis of the lowest groundwater table (it may have rained, the groundwater table may have risen because of some other reason), and thus the thermal properties of the soil may be better than in the worst case. This is something to take into account when conducting field measurements: for engineering the current rating, the worst case thermal situation is needed, while in a field measurement the actual situation is measured instead of the worst case situation. Figure 14 indicates that the difference between the two may be very large. For example if the moisture content of uniform sand is measured at 15% moisture content, then the thermal resistivity will be less than 50 °C∙cm/W (point A). However the conditions may change with the sand drying out and the thermal resistivity will increase to over 250 °C∙cm/W (point B). If the current rating of the cable is calculated assuming the measured values then the current rating will not be valid when the conditions change.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

FIGURE 14: THERMAL RESISTIVITY OF VARIOUS SOILS AS A FUNCTION OF THE MOISTURE CONTENT, LETTERS A AND B DENOTE WET AND DRY DOMAINS

The degree of compaction of the soil will also influence its thermal resistivity. Thus during any laboratory measurements and reinstatement of the cable route it is important that the appropriate degree of compaction is achieved.

3.4

Selection of Ambient Soil Temperature

The soil temperature imposes a limitation on the allowable temperature rise in cable conductors and therefore restricts the current carrying capacity of cables. The IEC standards all use the hypothesis of Kennelly, which assumes that the earth surface must be an isotherm. In IEC 60287 (see reference list, Chapter 10), this isotherm is referred to as θa which can vary substantially depending on geographic location and time of the year. The ambient temperature is, according to IEC60287-1-1, section 1.4.1.1, the temperature of the surrounding medium under normal conditions, at a situation in which cables are installed, or are to be installed, including the effect of any local source of heat, but not the increase of temperature in the immediate neighbourhood of the cables due to heat arising therefrom. These temperatures are usually established during a route thermal survey or based on historical values. Factors that determine the temperature of the ground can be grouped in three general categories: meteorological, terrain and subsurface variables. Large-scale regional differences in ground temperature are determined primarily by meteorological variables such as solar radiation, air temperature, rainfall and precipitation. Micro- or local variations are caused by differences in terrain, surface characteristics and ground thermal properties (including moisture content and/or water table).

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Meteorological elements, primarily solar radiation and air temperature, influence surface and subsurface temperature by affecting the rate at which heat is transferred to or from the atmosphere and the ground. Solar radiation is probably the most important factor. Other meteorological factors such as wind or rain can cause significant local variations. Since many of these parameters change in a seasonal cycle, or irregularly with time, it is impossible to predict exactly the earth temperature at any given location or any given time in the future, particularly at locations near the earth's surface. Earth temperature predictions, therefore, are of a statistical nature and some deviation from the average is to be expected in any given day, season, or year. Ideally, the ambient temperature should be obtained from measurements. Published references such as IEC 60287 include tables of ambient temperature by region but usually these are not sufficiently specific for the purposes of preparing an accurate cable rating. Methods can be used for characterizing the ambient soil temperature using air temperature data. Surface conditions and burial depth, particularly for shallower depths, must be considered when selecting a temperature for ratings. For depths shallower than 0.5-0.75 m, the ambient temperature may be 5 °C greater than the prevailing temperature in the area due to higher solar absorptivity below asphalt. Cables laid on the bottom of a large body of water, but not buried, generally do not have thermal constraints due to the heat being absorbed and convected away from the cables. However, many submarine installations involve embedding the cables below the sea floor. In these situations, the subsurface temperature will be closely aligned with the water temperature at the same depth and moderated by seasonal fluctuations in the water temperature.

3.5

Collected Practices

Now that starting points needed for calculations are discussed, it is interesting to understand how starting points are used and deduced in practice. The collected practices regarding starting points are based on the questionnaire replies to questions 1.6 to 3.3 and question 4.2, see Appendix B, and are divided in the following, subsequent, subclauses:      

Installation method Soil/ seabed / tunnel ambient temperature Soil / seabed thermal resistivities Soil dry out temperature Backfill thermal resistance and characterisation Limiting factors in current rating calculations.

It is noted that the questionnaire responses should be regarded to reflect typical values. Their individual entries have not been verified by the working group. See also section 1.4.

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3.5.1

Common Installation Method

Based on the questionnaire replies on questions 1.6 to 1.8, the most common installation configuration can be defined:     

Single core HV cables Direct buried Installed in close trefoil or in flat formation Installed between 0.4 m and 2.0 m deep With pavement/ asphalt/road as typical covering on top of the trench.

It must be emphasized that specific installations are more dominant per continent such as concrete encased duct banks in North America and buried tunnels in Asia. Also, the installation of (large) submarine connections and inter-array connections (cables connecting a number of turbines in a string to a collecting off-shore platform) for off-shore wind farms indicates the need for more detailing of starting conditions for these types of circuits. As cables are often installed in urban areas, pavement / asphalt / tarmac are frequently covering the top of the trench. The type of ground surface may influence the ambient temperature by absorbing solar radiation, or may influence the soil moisture content. This is seldom considered by the designers.

3.5.2

Soil / Seabed / Tunnel Ambient Temperature

From question 2.1, it can be concluded that the soil or seabed temperature is often assumed (72%) and occasionally measured (21%). The reasons for undertaking site measurements are various and were mostly reported for submarine cable circuits, provided by customer/utility, and done for direct buried cables. Various methods for measuring the soil temperature have been reported: mostly by thermocouples at various installation depths (0.5 m, 1.0 m, 1.2 m, 1.5 m and even 5.0 m) along the cable route (every 500 m or at possible hot spots). The usage of DTS measurements is increasing: the soil ambient temperature is then measured before the circuit goes live. A few respondents indicated that measurements are done in that time of the year with the highest ambient temperatures. Soil and seabed temperatures are most of the time assumed by the designer, often due to a lack of detailed information about the site conditions. The usage of seasonal or regional values is confirmed by respectively 51% and 40% of the responses. Figure 15 shows the typical soil temperatures per country, for hot conditions, with Figure 16 showing the same for the cold conditions.

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Soil temperature (°C)

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

45 40 35 30 25 20 15 10 5 0

FIGURE 15: TYPICAL SOIL TEMPERATURE RANGE FOR HOT CONDITIONS PER COUNTRY

50 40

Soil temperature (°C)

30 20 10 0 -10 -20 -30 -40 -50 FIGURE 16: TYPICAL SOIL TEMPERATURE RANGE FOR COLD CONDITIONS PER COUNTRY

The variation between neighbour countries, or even within one small country, is considerable. Figure 17 shows the assumed seabed temperatures per country, for hot conditions, in Figure 18 this is depicted for cold conditions.

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45

Seabed temperature (°C)

40 35 30 25 20 15 10 5 0

FIGURE 17: TYPICAL SEABED TEMPERATURE RANGE FOR HOT CONDITIONS PER COUNTRY

Seabed temperature (°C)

30 25 20 15 10 5 0

FIGURE 18: TYPICAL SEABED TEMPERATURE RANGE FOR COLD CONDITIONS PER COUNTRY

Around the world, there seems to be consistent adoption of the seabed temperature in hot and cold condition: the variation is relatively small. Figure 19 shows the assumed air temperatures in tunnels/galleries per country, for hot conditions, and the same in Figure 20 for cold conditions.

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Tunnel / gallery temperature (°C)

60 50 40 30 20 10 0

Tunnel / Gallery temperature (°C)

FIGURE 19: TYPICAL TUNNEL / GALLERY TEMPERATURE RANGE FOR HOT SEASON CONDITIONS PER COUNTRY

60 50 40 30 20 10 0

FIGURE 20: TYPICAL TUNNEL / GALLERY TEMPERATURE RANGE FOR COLD SEASON CONDITIONS PER COUNTRY

The data references for the soil, seabed and tunnel temperatures were reported as follows:      

Assumed Measured (Local) standards Historical data Provided by client Based on meteorological data

26 responses 17 responses 15 responses 8 responses 8 responses 3 responses

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The ambient temperature is an important parameter in the current rating calculations; most values for this parameter are assumed and vary considerably per user or per region. The international standard IEC60287-3-1‘Operating Conditions’ is seldom referred to as reference.

3.5.3

Soil / Seabed Thermal Resistivities

From all respondents on question 2.2, 70% indicate that the soil or seabed thermal resistivities are assumed values. Reasons stated include: lack of data, small cable project, low voltage class, pretendering phase. However, there is a growing interest in measuring the soil/seabed thermal resistivities as reported by twenty five (25%) responses, especially for new cable projects, submarine links, on customers request and for critical site conditions like in congested areas. Reported methods of measuring the soil/seabed thermal resistivities:    

Frequency: soil samples are taken every 50 m to 500 m or at suspected hot spots or at random. Location: specific depths, specific layers in the trench and changes in soil types. Measured parameters: thermal resistivity, moisture content and density, critical temperature. Deduce worst case for engineering purpose: highest thermal resistivity, deepest point of the route or soil conditions with full or partially dry soil. The uses of seasonal and/or regional values are not applied by most responses (63% respectively 55%). Figure 21 until Figure 23 provide an overview of the applied soil and seabed thermal resistivities in various countries.

Soil thermal resistivity (K.m/W)

8 7 6 5 4 3 2 1 0

FIGURE 21: TYPICAL SOIL THERMAL RESISTIVITY RANGE FOR DRY SEASONS PER COUNTRY

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Soil thermal resistivity (K.m/W)

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

3,5 3 2,5 2 1,5 1 0,5 0

FIGURE 22: TYPICAL SOIL THERMAL RESISTIVITY RANGE FOR WET SEASONS PER COUNTRY

Note: the reported high thermal resistivities for Finland and the Netherlands refer to dry and wet peat. Seabed thermal resistivity (K.m/W)

3,5 3 2,5 2 1,5 1 0,5 0

FIGURE 23: TYPICAL SEABED THERMAL RESISTIVITY RANGE PER COUNTRY

Reported references for given values in:     

Historical data and/ or papers Assumed Local standards Provided by customers Laboratory tests on samples

23 responses 17 responses 16 responses 6 responses 2 responses

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3.5.4

Soil Dry Out

Another important parameter for direct buried cable is, besides the soil thermal resistivities, the dry out temperature of the soil surrounding the cable circuit (question 2.3). Soil drying-out is considered by most respondents (63%) but more than one third of the respondents (36%) do not consider this parameter at all. Given reasons for considering the soil drying out are: known soil characteristics, water table, customer specification, cable class.

Soil thermal resistivity for dried- out soil (K.m/W)

Figure 24 and Figure 25 provide an overview of the typical applied thermal resistance of backfill as in use in various countries, for the dried out and for wet soil. 8 7 6 5 4 3 2 1 0

FIGURE 24: TYPICAL THERMAL RESISTIVITY RANGE FOR DRIED-OUT SOIL PER COUNTRY

Soil thermal resistivity for surrounding wet soil (K.m/W)

Note: the reported high thermal resistivity for the Netherlands refers to dry peat.

3 2,5 2 1,5 1 0,5 0

FIGURE 25: TYPICAL THERMAL RESISTIVITY RANGE FOR WET SOIL, SURROUNDING DRIED-OUT SOIL PER COUNTRY

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Critical isotherm temperature (°C)

The variation in applied thermal resistances for dried out soil is considerable whereas for wet soil is remarkable uniformly. Figure 26 summarise the responses replies for the critical isotherm values.

80 70 60 50 40 30 20 10 0

FIGURE 26: TYPICAL CRITICAL ISOTHERM FOR SOIL DRYING OUT PER COUNTRY

Note: the large difference in dry out temperatures in the Netherlands results from the wide variety of soils encountered (cables are typically installed in native soil in the Netherlands) and from the wide variety in the groundwater tables. Exceptionally good soils are present, as well as exceptionally bad soils (for instance badly graded sands with poor moisture retention) in terms of dry out temperature.

Reported references for the values given in Figure 24 to Figure 26 :       

Measured (Local) standards Literature Assumed Historical data Customer spec Common practice

13 responses 9 responses 6 responses 4 responses 3 responses 3 responses 1 response

A resting time to allow re-hydration of the soil is normally not considered, this is only reported by 10% of the responders.

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3.5.5

Thermal resistance and Characterisation of Backfill

Backfill, directly surrounding the cable(s), is usually characterized by the users (question 2.4) with the following parameters:   

Thermal resistivity Grain size distribution Compaction

: : :

88% of the responses 47% of the responses 57% of the responses

Other reported parameters are thermal resistance at a specific moisture content /minimum moisture content (4 responses), reference to standard/specify material (4 responses) and usage of fluid thermal backfill. Control on the rest of the backfill material is done by 42% whereas 45% does not. If control is given to the rest of backfill materials, compaction level (38%) and thermal resistivity (29%) are measured or cross checked with customer provided specification (17%).

3.5.6

Limiting Factors in Current Rating Calculations

The influence of other heat sources in the cable ratings is handled in different ways by the respondents (question 2.5), varying from ‘calculating the exact influence’ (68%), via ‘adding a margin to ambient temperature’ (30%) and ‘usage of de-rating tables’ (26%) to ‘not taken into account at all’ (4%). For the calculation of the exact influence, IEC is the ruling reference (20%), followed by usage of commercial software (19%) and FEM (13%). The margin that is added to the ambient temperature varies from +5 °C (27%) to +10 °C (20%), while +15 °C and +20 °C are reported by one respondent 2 3 each. For de-rating tables, standards like IEC, VDE and JCS are used (31%) or generated by software (15%). Another approach which is adopted by some countries according to the results of the questionnaire is to take a minimum separation between cable circuit and heat source into account to ensure thermal independence of the cable systems. One response mentioned 1000 mm when laid in parallel and 500 mm when crossing. Do note that this approach is questionable while the numbers will only be valid in certain specific laying conditions. However, this approach is reported to be adopted by some countries.

3.5.7

Operating Conditions

A maximum conductor temperature is used as a limitation by 85% of all respondents. Those that do not use maximum conductor temperature (question 3.1) clearly show that the IEC calculation method is indeed implemented and that the limitation of the current rating through the maximum conductor temperature is substituted by different limiting parameters as, for example, cable surface temperature to avoid drying out of the soil around the cable. The answers to questions 3.2 in the Questionnaire demonstrate in more detail which alternative limiting parameters are in use. The differentiation of the answers to item 3.2 shows also a clear 2

VDE: ‘Verband der Elektrotechniek’, German association

3

JCS: Japanese Electric Wires & Cable makers

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

understanding of the physical model in use of the IEC standard. The most usual thermal design limitations are the conductor temperature and the native soil/surrounding conditions/operating conditions. An interesting reference is Zhang (2014): this paper refers to the use of a 2 K maximum increase in environment temperature criteria used in Germany, including wind load statistics. The survey did not ask the question regarding other temperature limitations. In some, rare cases, the backfill/duct bank maximum temperature are limited to avoid soil dry out. Question 3.3 dealt with using an assumed daily load cycle instead of calculations based on a continuous load. Assuming a load cycle often results in peak load currents which are significantly higher than those with a continuous load. The majority of users used assumed daily load cycles while 32% of the users preferred to calculate the current rating based on continuous loadings. While some of these users may not be fully loading their cables given that most cables are unlikely to be on a continuous load, some users may be using dynamic ratings. Variations of the load factor down to 0.7 are obviously common practice and in some cases values down to 0.6 and more could be found. A few others use measurements as base for the load factor. The questionnaire ended with a few open questions in relation to starting points (question 4.2) Other reported limitations/regulations influencing cable ratings are EMF limitations (21%), heat source/thermal influence other heat sources (11%) and maximum allowed temperature rise near the cables (7%). The following reasons for thermal break downs in cable systems, because of overheating, were reported:        

Overloading Selection of cables, in-correct special bonding system High thermal resistance soil Changes in operating conditions Field situation different from engineered situation Thermal impacts to laminated cables Remaining life time exceeded Large no. of 11kV cables, under asphalt buried in beach sand.

4 responses 2 responses 2 responses 2 response 2 response 1 response 1 response 1 response

The majority of cable failures due to overheating seems to be related to differences in starting points during engineering phase and the in-situ situation, i.e.: overloading, changes in operating conditions and field different from engineered situations. As an interesting recommendation given by the respondents, a data sheet is mentioned which should be used between the engineering company and the cable system user, detailing the starting points for the performed rating calculations. Also synchronization and clarification of calculation methods is recommended.

3.6

Discussion on Starting Points

The results of the questionnaire items as described in Section 3.1 to 3.5, dealing with the starting points for cable rating calculations are summarized below: 

IEC / Neher-McGrath method is the prevailing method for cable rating calculations; these calculations are performed during all stages of a cable system lifetime and are also widely used for determining the influence of secondary heat sources.

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

A worldwide most common installation configuration can be defined: Single core HV cables, Direct buried, Installed in close trefoil or in flat formation, Installed between 0.4 m and 2.0 m deep, With pavement/ asphalt/road as a typical soil/air interface. Soil/seabed ambient temperature is mostly assumed without a clear reference. Occasionally, it is measured for important connections, such as for submarine installations and various other reasons. Seasonal and / or regional values are taken into account by ~ 50% of the respondents. The variation of the assumed soil/seabed temperature between countries and even within countries is considerable.



Soil/seabed thermal resistivity is also normally assumed, based on historical data, although it was mentioned that this parameter is now measured for new circuits and for submarine connections indicating the growing awareness of this very important parameter. A large variation in the assumed values is observed: not only between countries and continents, but also within one country. Also, the use of seasonal and / or regional values for the thermal resistance is not common; this is only taken into account by ~40% of the respondents. When the soil / seabed thermal resistance is measured, the following parameters are measured: thermal resistivity, moisture content, density and critical temperature.



Soil drying out is considered by ~ 60% of the respondents, with a dry out isotherm varying between 20 °C and 70 °C indicating that there is not universal agreement on this parameter. It is uncommon to take into account a re-hydration of the soil after a drying out period.



When backfill is applied around the cables, the thermal resistance is usually determined, based on the compaction level and grain size distribution.



The influences of secondary heat sources are calculated by most respondents, IEC / NeherMcGrath are the preferred methods.



The conductor temperature is the limiting factor, but additional limitation towards outer sheath temperatures are also taken into account.



Load factors are normally not considered.



An EMF limit requirement is some times a developing current rating limitation.



System failure as a consequence of overheating is very rare.

The questionnaire part related to starting points indicates that most starting points are assumed in the current rating calculations although respondents indicated that the use of measured parameters is increasing for new (and important, such as submarine) connections. However, this uncertainty in starting points seldom led to system failures due to overheating; this is more related to applying incorrect information at the design stage. It is expected that given the many uncertainties in the assumed starting points, the need for more accurate starting points will be larger than the need for more detailed current rating calculation techniques.

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3.6.1

Conclusion

As shown in the questionnaire results, starting points, such as ambient soil/ seabed temperatures and in-situ soil thermal resistivities, are just assumed by the majority of the respondents. A wide tolerance in the assumed parameters indicates the need for measured, trustworthy, values as this will lead to more realistic current rating calculations.

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4

Ca lc ul at i on M et ho ds and Pr oc edu r e s

There are a number of different methods and procedures that can be used to calculate the current rating of a cable system. Not only the cable system design, but also the calculation methods and procedures used, will have an impact on the current rating. This section (together with sections 5, 6 and 7) is intended to have two main uses. One is to guide engineers considering specific cable systems to gain an insight into the impact of various cable system design choices and find the appropriate calculation methods. There are many standards, reports and technical papers that give methods for the calculation of current ratings but no one document gives methods for all situations. In some situations there is more than one calculation method published. In general this document does not provide the appropriate calculation method but refers to publications that contain these methods where they exist, giving guidance on the relative merits of each method where more than one exists. Given the large body of literature published regarding current ratings, while this document references an extensive number of other documents, it is not the aim to cover a complete list of all documents written regarding this subject. The second intended use for this document is to identify where the existing body of standards, books, reports and technical papers can be improved. Where no published method of calculation exists for specific cable system arrangements, these are identified in the hope that methods will be developed and published. Some methods published as reports or technical papers may deserve to be considered for more formal publication, by example being incorporated into standards. Finally, where a weakness has been found, particularly in the IEC standards, this has been identified. Any guidance that could be given by the WG to the user in a specific situation is given in this brochure. The guidance comes in several variations. Reference to an existing standard is the strongest, while hints, tips and descriptions unanimously accepted by the WG members is the weakest variation. The WG found it to be most important to give guidance as much as possible to the engineer dealing with a difficult rating calculation. In the majority of cases, the current rating of a cable system is set by the cable and not the other parts of the cable system (for example, the joints and terminations). These additional components should be designed and installed so as not to limit the cable current rating. Hence, this document concentrates on the current rating of the cable itself. There are cases where the rating of the cable system is not limited by the cable and some of these cases have been noted. In the end the users should focus on busbar to busbar rating of the circuit, as highlighted in Chapter 2. The calculation methods covered in this section of the report are generally analytical approaches where the solution can be found by entering parameters into a function or equation. With the widespread availability of fast computers there are also a number of numerical methods such as finite element analysis, which are not fully covered in this document. A more detailed discussion of these numerical methods can be found in Section 8.3.3. Preference has been given to analytical methods since these give independently reproducible results. Where numerical methods have been discussed it is hoped that future work may be able to find analytical approximations. Most underground cable ratings calculated using analytical methods are evaluated based on the fundamental concept of heat transfer through a solid medium by thermal conduction. The basis for this evaluation is an equivalent thermal circuit that is developed to model a specific cable construction; the thermal equivalent is based on a temperature rise resulting from heat flowing through a thermal resistance and capacitance. The thermal capacitance of the various cable layers and surrounding earth introduces a delay in the response of the temperature to changing load conditions based on the specific heat characteristics of the cable components and the environment in which the cable system is installed. An example equivalent thermal circuit for an extruded or selfcontained fluid filled cable installed in a conduit is shown in Figure 27.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

FIGURE 27: EQUIVALENT THERMAL CIRCUIT FOR AN EXTRUDED OR SELF-CONTAINED FLUID FILLED CABLE INSTALLED IN A CONDUIT

The cable system design parameters that affect current ratings can be summarised into three broad areas: duty, cable design and installation. This is summarized in Figure 28.

FIGURE 28: OVERVIEW OF ASPECTS THAT CAN AFFECT CURRENT RATINGS

In the following sections a more detailed evaluation of each aspect is made together with recommendations on methods of calculation that can accommodate the described situation. Appendix D gives detailed mind maps for each of the sections to aid the reader. In section 7.1 common aspects that may affect many cable installation types (such as the impact of any parallel metal conductors) are covered, rather than repeating the description under each installation. In other parts of section 6 and 7, some aspects (such as sheath losses) appear in one section (for sheath losses in metal sheath section) and this description will be referenced in other sections (such as impact of AC voltages for sheath losses) rather than repeating the description twice. In this way any duplication of descriptions for calculation methods is avoided. The most widely used documents for current ratings are the IEC series of standards. The cable engineer with experience in current rating calculations will be more familiar with the aspects of a cable system as described in IEC 60287 (that is in terms of losses, thermal resistances and base assumptions). For these engineers a table in Appendix C has been compiled that contains a list of calculation methods missing in the IEC standards, indexed in a similar fashion to IEC 60287 with cross references to the appropriate section in Chapter 6.

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4.1

Symbols used

The symbols used in this Technical Brochure and the quantities which they represent are given in the list below. As much as possible, SI units have been used in this brochure, but where misunderstandings might be introduced, other units have been used. Because multiple references are quoted in this brochure, unavoidably sometimes similar symbols are used for different meanings. Where unclaries might arise as a result of this, the section number where the symbol is used is stated. Following the practice adopted in the IEC standard 60287, all cable component diameters are given in millimetres. When the formulae shown in the text require these dimensions to be given in metres, an asterisk is added to the symbol. For example, De denotes the external diameter of the * cable expressed in millimetres, whereas De denotes the same diameter expressed in metres.

Symbol

Description

Unit

A

=

Constant in section 7.2.1

-

A

=

Surface area in section 7.3.5.5

m

B

=

Constant

-

B

=

Connection matrix

-

C

=

Electrical capacitance per core

F/m

C1..C8

=

Thermal capacitance of a specific layer per unit length

J/K∙m

D

=

Difference between maximum and minimum air temperature

K

De

=

External diameter of the cable

mm

Dearth

=

Earth diameter (jacket, conduit, pipe)

m

Di

=

Outer diameter of layer I

mm

Dx

=

Diameter where average heat output is seen

m

E

=

Electrical stress in the insulation in section 5.3

MV/m

E

=

Column vector of filament longitudinal voltage drop

-

E

=

Column vector of conductor longitudinal voltage drop

-

F

=

Mutual heating effect factor

-

G

=

Geometry matrix

-

Gb

=

Geometric factor for backfill

-

I

=

Current in one conductor (r.m.s.value) in section 5.1

A

I

=

Column vector of filament currents in section 7.1.3

-

Ii

=

Average load of hour number i in section 5.1

A

Ic

=

Capacitive current for the cable

A

Icond

c

=

Conductor current

A

c

I

=

Column vector of total conductor currents

-

IL

=

Load current for the cable

A

Imax

=

Highest current of daily load cycle

A

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES th

In

=

Current for n harmonic, with n=1 for fundamental frequency

A

Iz

=

Thermal rated current

A

L

=

Burial depth of cable

m

Lc

=

Critical length

m

LF

=

Daily (24 hour) loss-load factor for the cables

-

N

=

Total number of heat producing cables, occupied conduits or pipes within the backfill

-

Nc

=

Number of equal cables

-

Np

=

Number of water cooling pipe pairs

-

NC

=

Number of conductors

-

PL

=

Active power at load receptor

W

Pk

=

Transmitted real power of cable k

W/m

Q

=

Quantity of water per unit length per pipe

kg/m

R

=

AC resistance of conductor at its maximum temperature

Ω/m

R’

=

DC resistance of the conductor

Ω/m

Rd

=

Matrix containing filament resistances in the diagonal and zeros outside the diagonal

Rn R1..R8

= =

-

th

Effective AC resistance of the conductor for n harmonic in section 5.3

Ω/m

Thermal resistance of a specific layer per unit length in section 7.4.3

K∙m/W

Router

=

AC resistance of outer conductor at operating temperature

Ω/m

SG

=

Apparent power at injection point

VA

T(t,x)

=

Ambient temperature at time t at depth x

K

TR

=

Thermal resistance of the insulation around the steam pipe/hot air pipe K∙m/W

Taverage

=

Average annual air temperature

K

Tij

=

Mutual thermal resistance between cables i and j

K∙m/W

T1

=

Thermal resistance per core between conductor and sheath

K∙m/W

T2

=

Thermal resistance between sheath and armour

K∙m/W

T3

=

Thermal resistance of external serving

K∙m/W

T4

=

Thermal resistance of surrounding medion (ratio of cable surface temperature rise above ambient to the cable losses per unit length)

K∙m/W

THD

=

Total harmonic distortion

-

U

=

Phase to phase voltage

V

U0

=

Nominal voltage (between conductor and sheath / screen)

V

W(t)

=

Heat loss during time t

W/m

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

Wconv

=

Wcond,w-o = Wconv,s Wconv,w Wconv,o

= = =

Convective heat transfer loss in section 7.3.5

W

Heat conduction transfer rate from the wall inner surface to its outside per unit length

W/m

Natural convection heat transfer rate between cable outside surface and the air per unit length

W/m

Natural convection heat transfer rate between the wall inside surface and the air per unit length

W/m

Natural convection heat transfer rate between the wall outside surface and the atmosphere air per unit length

W/m

Wd

=

Dielectric losses per unit length per phase

W/m

Wdist

=

Total heat loss for a cable carrying a distorted waveform

W/m

Wi

=

Total power dissipation of all the cables in a trough per meter after iteration i in section 7.2.3

W/m

Wj

=

Sum of Joule and dielectric losses of cable j in section 7.2.1

W/m

Wmax

=

Maximum heat loss during a load cycle

W/m

Wn

=

Total heat loss generated by all cable components for all frequencies

W/m

Wp

=

Heat generated by steam pipe or hot air pipe

W/m

Wrad,s-w

=

Thermal radiation heat transfer rate between the wall inner surface and the cable outside surface, per unit length

W/m

Thermal radiation heat transfer rate between the wall surface and surrounding objects per unit length

W/m

Wrad,o-sur = Wsol

=

Solar radiation absorbed by the wall surface per unit length

W/m

Wt

=

Total energy per unit length generated within the cable

W/m

WI

=

Total heat loss of the cable related to I R losses of that cable

W/m

WTOT

=

Total power dissipation of all the cables in a trough per meter

W/m

a

=

Thermal diffusivity

m /s

c

=

Specific heat capacity

J/kg∙K

cw

=

Specific heat capacity of water

J/kg∙K

h

=

Heat transfer coefficient

W/ (m ∙K)

i(t)

=

Heat generated by the cable per unit length in section 7.4.3

W/m

k

=

Thermal conductivity

W/K∙m

n

=

Number of conductors in a cable (or, when mentioned, in another space)

-

Frequency component (n=1 is fundamental frequency, n>1 is harmonic) in section 5.3

-

n

=

2

2

2

p

=

Perimeter of the trough that is effective for heat dissipation

m

sii

=

Geometric mean radius of filament I

m

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

sij

=

Geometric mean distance between filaments i and j

m

t

=

Time

s

t0

=

Length of period

s

t

=

Time since maximum air temperature occurred in equation 37

s

v1..v8

=

Temperature of a specific node vi(x,t) means temperature of node i at location x at time t

K

Ambient soil temperature

K

vo (ys)n

= =

th

Skin effect factor for the n harmonic th

-

(yp)n

=

Proximity effect factor for the n harmonic

-

x

=

Depth below the earth’s surface

m

α

=

Temperature coefficient of electrical resistivity in section 5.3

K

α

=

Sheath loss factor in section 7.4.3

-

β

=

Stress coefficient of electrical resistivity

m/MV

γn

=

Ratio of the n harmonic current to the fundamental current in section 5.3

-

-1

th

tan δ

=

Loss factor of insulation material

-

εr

=

Relative permittivity

-

θ

=

Difference between actual and reference temperatures in section 5.3

K

θa

=

Ambient air temperature above ground in section 7.2.3

°C

θck

=

Conductor temperature of cable k in section 7.2.1

K

θi

=

Temperature inside a trough after iteration i in section 7.2.3

°C

θk max

=

Maximum conductor temperature of cable k in section 7.2.1

K

θo

=

Temperature of the wall outside surface in section 7.3.5.5

K

θs

=

Temperature of the cable outside surface in section 7.3.5

K

θw

=

Temperature of the wall inner surface in section 7.3.5.5

K

θR

=

Temperature of the surface of the steam pipe or hot air pipe in section 7.2.1

K

θW

=

Temperature of the steam or hot air in section 7.2.1

K

θ0

=

Initial temperature inside a trough in section 7.2.3

°C

θ1, θ2

=

Temperature of media 1 and 2 in section 7.3.5.5

K

λ1

=

Sheath loss factor (ratio of the total losses in the sheaths to the total conductor losses, or ratio of losses in one sheath to the losses in one conductor)

-

Armour loss factor (ratio of the total losses in the armour to the total conductor losses, or ratio of losses in one armour to the losses in one conductor)

-

λ2

(λ1)n

=

=

th

Sheath loss factor for the n harmonic

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES th

(λ2)n

=

Armour loss factor for the n harmonic

-

λ' 1

=

Ratio of the losses in one sheath caused by circulating currents to the losses in one conductor

-

Ratio of the losses in one sheath caused by eddy currents to the losses in one conductor

-

λ”1

=

μ

=

Loss-load factor for a load cycle in section 5.1

-

μ

=

Permeability of the material (μ0∙μr) in section 7.1.3

H/m

μr

=

Relative permeability of the material (nonmagnetic materials have a μr of 1)

-

-7

μ0

=

Permeability of air, 4π∙10

H/m

ρ

=

Electrical resistivity in section 5.3

Ω∙m

ρ

=

Density in section 7.3.1

kg/m

ρfill

=

Thermal resistivity of backfill material in section 5.1

K∙m/W

ρi

=

Thermal resistivity of layer i in section 6.46.2

K∙m/W

ρnative

=

Thermal resistivity of native soil in section 5.1

K∙m/W

ρ0

=

Electrical resistivity at reference temperature in section 5.35.3.3

Ω∙m

τ

=

Total duration of a load cycle

s

ω

=

Angular frequency (2πf) with f=frequency

s

φ

=

Phase angle

°

Δθ

=

Permissible temperature rise of conductor above ambient temperature K

Δθij

=

Conductor temperature reduction of cable i due to cable j

K

Δθint

=

Conductor temperature reduction due to heating from neighbouring cables

K

Δθs

=

Difference between the cable surface temperature in air and ambient temperature

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K

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

4.2

Definitions

Description of technical terms and section references are given below. Term

Definition

Reference (Section)

Ampacity

The current carrying capacity of a cable. This is a term widely used in North America, and avoids any confusion that may result from the use of the word “capacity”

-

Bonding

Electrical connection of the cable metallic screen, influencing the current dependent losses in the screen or sheath

7.1.2

Keystone conductor

A conductor in which individual strands are pre-shaped, for example in a trapezoidal shape, in order to achieve compaction

-

Continuous rating

The unchanging continuous current at which the conductor or conductors of a cable will eventually reach a defined maximum temperature

5.1.1

Cross bonding

An arrangement in which the screens of the individual phase cables of a single circuit are electrically connected to another phase cable screen after a certain distance. This is repeated such that there are as many sections as there are phases in the circuit. The goal of this arrangement is to minimize sheath losses

Appendix E

Cyclic rating

The maximum current or VA rating of a cable, when the load is varied in a sequence of steps that are repeated cyclically. The cyclic rating will differ for different sequences and different cycle periods

5.1.2.1

DTS

Distributed Temperature Sensing

8.4.2

Dynamic rating

The current rating of an installed cable with real time varying parameters (for example load current, ambient temperature, thermal resistivity), taking into account the thermal time constants of the cable and it’s environment

5.1.3

Earthing

Electrical connection of the cable metallic screen, referring to the fault current path and the reference for the electrical stress in the insulation

7.1.2

Electrical section

Section of cable circuit where the cable screens are not electrically transposed onto another phase cable

7.1.2

Emergency rating

The permissible short term rating of a cable already loaded and at a steady state, taking into account the thermal capacitance and the thermal resistance of the installed cable system

5.1.2.2

Flat formation, flat configuration

A flat horizontal laying arrangement of usually three single cores cables. The cables may be touching or spaced apart, with the spacing usually defined

-

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FEM

Finite Element Method. A numerical method for determining current rating using discrete elements, as detailed in IEC TR 62095

8.3.3

Load factor

The total energy transferred over a defined period, expressed as a percentage, or a per unit value, of energy that would have been transferred should the load remain at its peak value for the entire period

5.1.2.1 (2)

Loss factor

The heat loss in a metal component of a cable other than the conductor, expressed as a per unit value of the heat loss in the conductor

6.4.1

Loss factor, dielectric

The current though a dielectric that is in phase with an alternating voltage applied across the dielectric, expressed as a per unit value of the current through the dielectric that is in quadrature with the same applied voltage. Also referred to as the dielectric power factor, the dielectric loss angle and tan δ

6.2.2

Loss-load factor

The total heat loss from a cable over a defined period, expressed as a percentage, or a per unit, of heat that would have been lost from the cable should the cable load remain at its peak value for the entire period

5.1.2.1 (3)

Milliken conductor

A conductor consisting of stranded sector-shaped segments, lightly insulated from each other, and laid up to form a single circular conductor

-

Proximity effect

An effect alternating conductor conductor. conductor

that occurs in adjacent conductors carrying currents, whereby the current distribution on a is altered by the current flowing in an adjacent This increases the effective resistance of the

6.1.1

Real time rating

A dynamic current rating calculation performed in real time. Input variables may be taken from on-line measurements

5.1.3

Serving

Protection of the metallic screen against mechanical damage and against corrosion. Also referred to as Over sheath, Outer sheath, External sheath and Jacket

3.1

Sheath voltage limiter

Device similar to a surge arrestor that is normally high resistance but allows transient currents to pass through it

-

Single point bonding

In an arrangement such that the at one end of the electrical section the cable screens are solidly bonded and earthed and at the other end of the route the cable screens are not electrically connected to each other or the earth (other than via a sheath voltage limiter)

-

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

Skin effect

An effect that occurs in conductors carrying alternating current, whereby the current density increases towards the surface of the conductor. This effect is different for different conductor materials, and increases the effective resistance of the conductor

6.1.1

Solidly bonded and earthed (1)

When referring to the cables at end of an electrical section, in an arrangement such that the screens are electrically connected together and earthed

-

Solidly bonded and earthed (2)

When referring to a cable system, in an arrangement such that the cable screens at both ends of the electrical section(s) in the cable system or part of the cable system are solidly bonded and earthed

-

Specially bonded

A special arrangement in which the cable screens of the cable system are electrically connected such that circulating currents are minimized

-

Starting points

Initial situation, data and conditions required in order to determine the current rating of a cable

-

Steady state rating

The rating of a cable operated at a load factor of 100%

5.1.1

Thermal time constant

The time taken for the temperature of a conductor in a cable system to change from an initial steady state value to 1/e of the change to a final steady state value, in response to a step change in the conductor current. This assumes an environment at an ambient temperature that cannot be changed

-

Time varying rating

The current rating of a cable where the load varies with time

5.1.2

Transient rating

The same as the emergency rating

5.1.2.2

Trefoil (formation, configuration)

A triangular laying arrangement of three single cores, or three single core cables. The cores or cables may be touching or spaced apart, with the spacing usually defined

-

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

5

Dut y As p e ct s in C abl e Rat ing C a lc ul at i ons

A cable system is energised with a specific voltage and carries a current so that it transmits power. The power that the cable system carries may vary with time. The voltage and current can be at a frequency, continuous or variable and may also contain harmonics. All these factors will impact the current rating of the cable system and these impacts are discussed in this section.

5.1

Loading (Current)

The cable system can be subjected to a number of different loading patterns, where the current can vary over a period of time. The simplest load pattern is the continuous loading pattern and many of the rating methods assume a continuous loading. More complex loading patterns can be modelled that match reality more closely, giving an increased peak current rating.

5.1.1

Continuous Loads

Typical calculation methods assume that the temperatures of the cable have reached steady-state conditions after a long period of continuous operation and this load pattern is known as continuous rating. For this loading pattern only the heat generated, the thermal resistances of the system and the constraining temperatures need to be considered. The thermal capacitances of each part of the cable system can be neglected. The current rating is typically calculated using the equivalent thermal model below.

T1

θc

I² R

T2

λ1

Wd Insulation

Conductor

T3

θa

λ2 Bedding

Sheath

T4

Serving Armour

Surrounding medium

FIGURE 29: THERMAL MODEL

The thermal model shown in Figure 29 leads to the equation described by Neher, J.H. and McGrath, M. H. (1957) and which can be found in IEC 60287-1-1:

    Wd 0.5T1  nT2  T3  T4  I    R  T1  nR1  1 T2  nR1  1  2 T3  T4 

0.5

(EQUATION 1)

The constant load pattern may be an assumption if the actual loading on a selected cable circuit is unknown in operation and conservatively assumes that the loading will have a worst-case cycle (that of continuous full-current loading). In practice except for specific cable applications (e.g. generator

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

leads, continuously operating equipment, etc.) this type of loading pattern is often conservative in many utility and industrial applications. Therefore, other loading patterns are considered in subsequent sections.

5.1.2

Time Varying Loading

Various loading scenarios other than continuous 100% loading may be considered in situations where the thermal capacitances of the cable system, including the thermal environment, are factored into the rating calculations. As with most current rating problems, two general methods may be used to analyse time varying loadings: either numerical or analytical. Numerical methods include finite elements but also include simpler methods such as the one published in CIGRE (1983-2). The method in CIGRE can effectively deal with time-varying loading by representing the physical cable system and its surroundings by a ladder network of thermal resistances in series and capacitances in parallel. Heat flow is assumed to be radial both inside and outside the cable and hence it is possible to divide the cable and the soil into a number of concentric layers corresponding to the elements in the ladder network. The radius of the soil to be considered will need to increase as the duration of the transient increases. The principle of superposition is used to properly deal with multiple cables. For long transients the method may need to consider image sources dissipating heat of an equal value but opposite sign to model the soil surface as an isotherm (Kennelly’s hypothesis). The method described in CIGRE (1983-2) which was initially proposed to single-core cables has recently been successfully applied to multicore cables by Colla (2013). These numerical methods can consider a number of loading patterns, including arbitrary loading patterns, which make them particularly suitable for long lasting transients such as the ones foreseen in offshore submarine cable systems. Analytical methods include the method published by Neher/McGrath (1957) for cyclic ratings and the methods in IEC 60853 that can be used in a number of different loading patterns. Time varying loadings can be categorized into four possible patterns as summarized in the following sections.

5.1.2.1 Cyclic After a 100% (constant) load pattern, the most fundamental loading scenario to consider is an indefinitely repeated load pattern. Using cyclic loads can reduce the required cable conductor size, but this should be examined case by case, see Pilgrim et al. (2014). This type of evaluation considers the long thermal time constant of the earth surrounding the power cable system and recognizes that the extent of heating that occurs in the soil will effectively be the average of the heat generated by the power cable during the load cycle. In practice, loading patterns vary, but a common load variation that has some consistency is usually associated with a 24-hour load cycle as illustrated in Figure 30.

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Per Unit Loading (amperes or MVA)

1.2

1

0.8

0.6

0.4

0.2

0

Time (hours) FIGURE 30: SIMPLE 24H LOAD PATTERN

The load factor is generally defined as the ratio of average load over a period of time compared to the maximum load over the same period of time. With known load values (either from system planners or recorded load data), the load factor may be calculated from the following equation (for a 24-hour cycle). The load factor relates the average loading pattern to the peak loading pattern, usually over a 24 hour load period.

24

I Load Factor =

Where: Ii =

i

i=1

(EQUATION 2)

24 I max

average hourly load [A]

For cable rating purposes, the heat output (or losses) emitting from the cable must be considered, so the ratio of average losses to peak losses must be known; the loss-load (μ) factor (also known as loss factor) can therefore be determined as follows: The loss factor is defined by:



1 Wmax  





 W (t )  dt

t 0

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(EQUATION 3)

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

This is usually approximated by: 23

=

I

2 i

(EQUATION 4)

i= 0

24 I

2 max

System planners may be able to offer a load factor but may not know the actual (or projected) loading for a cable circuit. Empirical relationships (Neher, J.H. and McGrath, M.H 1957) such as the following may be used to relate the loss-load factor to the load factor:

= 0.3(

) + 0.7(

)

(EQUATION 5)

Figure 31 illustrates the variation in load and loss-load factor for a 24-hour sinusoidal cycle. Do note that in case of other types of cycles, the relation between load factor and loss-load factor will be different.

1.2

Load / Loss 1

100% / 100%

Load Shape (per unit of peak current)

95% / 90% 0.8

89% / 80% 83% / 70%

0.6

76% / 60% 0.4

67% / 50% 0.2

54% / 40% 0 0

4

8

12 Time (hours)

16

20

FIGURE 31: VARIATION IN LOAD AND LOSS-LOAD FACTOR FOR A 24 HOUR SINUSOIDALCYCLE

There are two analytic approaches considering the cyclic loading pattern. The calculation procedures in IEC 60287 may be modified in one of two ways. As illustrated in the preceding Figure 31, the reader should be aware that if a loss-load factor is incorporated into the ratings, the calculated ampacity will be the peak current during the load cycle. 

IEC 60853-1 gives a cyclic rating factor, M (a value greater than or equal to 1.0) to the 100% load factor rating to consider the cycle nature of the load. Section 3 of IEC 60853-1 defines the calculation of the cyclic rating factor after first determining the thermal time constants of the cable and the surrounding environment. The method supports considering cycle ratings for periods of 24 hours or other durations. The method requires that some knowledge of the time at

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peak current be known in developing the factors (or assumptions as in Neher/McGrath can be made if these are not known). 

Neher/McGrath (1957) offered an alternative method for considering cyclic loading by making an assumption that the 24-hour load cycle closely followed a sinusoidal load shape (note: this is an important assumption). On this basis, peak losses are applied to cable components and the portion of the earth thermal circuit that are “near” to the cable while average daily (24-hour cycle) losses are applied to the thermal resistance values entering the ground beyond a diameter, Dx. Diameter Dx is determined based on the thermal diffusivity of the soil and is typically taken to be about 210 mm for most soils and regardless of the outer diameter of the cable, conduit or pipe. The earth thermal resistance is then determined using an equation of the form:

     2 L  4L2  D 2 n    DX  X T4   Fill  ln  LF  ln   2  DX   Dearth      Where: n ρ Dearth L Dx F LF Gb N

= = = = = = = = =

     lnF      Native   Fill N  Gb       

(EQUATION 6)

number of conductors within Dearth earth or backfill thermal resistivity [K∙m/W] earth diameter (jacket, conduit, pipe) [m] burial depth of cable [m] diameter where average heat output is seen [m] mutual heating effect factor daily (24-hour) loss-load factor for the cables geometric factor total number of heat producing cables, occupied conduits or pipes within the backfill

Other approximations of the fictitious diameter Dx corresponding to different shapes of the load cycle can be found in the book by Heinhold (1990).

The above methods for calculating cyclic ratings should only be considered for the buried portions of cable systems. For cables in tunnels, air, water or other non-solids, transient ratings are more complex and covered in Section 7.4. Cable systems with segments in free air will generally have a much shorter thermal time constant and, therefore considerations of cyclic rating for cables in air are generally not made, except at the highest voltages.

5.1.2.2 Emergency Emergency ratings (sometimes called “transient” or “contingency” ratings) evaluate the permissible loading on a cable system that is applied for a finite period of time. The increased ratings afforded for these conditions consider higher allowable cable temperatures (usually constrained by the conductor temperature) and also consider the thermal time constant of the cable and the surrounding earth. The duration (period) for these emergency ratings is sometimes associated with the local protocol. Common designations include:

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

LTE or “Long Time Emergency” – often associated with emergency ratings longer than 24 hours.



STE or “Short Time Emergency” – emergency ratings less than 24 hours in duration and sometime shorter than 4 hour or as little as 15 minutes.



DAL or “Drastic Action Limit” – these are very short duration emergency ratings usually less than 15 minutes in duration and often requiring that the operator of the cable system sheds load.

The rating durations are often dictated by manufacture’s recommendations, industry standards, mechanical or structural limits associated with a particular cable design. Regardless of the terminology, the rating calculations are based on a method that generally considers the temperature response of the cable system to a step change in load. IEC 60853-2 defines a procedure for evaluating the temperature response to a step change in load. The method involves considering the thermal time constant of the cable circuit and, separately, that of the environment. The effects of both parameters are a function of many parameters including the duration of the emergency. For cables installed in free air, the air environment has a much shorter time constant than the same cables buried in the ground. As a result, the only transient part of the analysis is the temperature response of the cable (alone) resulting in lower emergency ratings than for buried cables. For cables in tunnels, transient ratings are more complex and covered in Section 7.4. As put forward above, emergency rating calculations based on IEC 60853 assume a step change in the cable loading. The step change starts from a stationary loading situation with stationary temperatures. If this is not the case, emergency rating calculations will lead to erroneous results, not necessarily being worst case. As an example, the emergency rating cannot be combined with a cyclic rating calculation resembling daily load cycles.

5.1.2.3 Arbitrary Load Patterns The methods in IEC 60853 permit considerations of cyclic ratings and simple emergency load patterns in relatively simple installation arrangements. The methods approximate the cable into a one dimensional thermal equivalent circuit having two lumped circuits and this generally limits the use to the given durations and installations. As noted in IEC 60853, the method provided in CIGRE (1983-2) can be used to yield adequate accuracy for any time period. This may be necessary to overcome the limitations of IEC 60853 method. An example of arbitrary load pattern is shown in Figure 32 along with the attendant conductor 2 temperature of a 132kV 3x800 mm Cu submarine cable.

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FIGURE 32: TYPICAL GRAPH SHOWING CONDUCTOR TEMPERATURE (IN RED) VERSUS TIME DUE TO A TYPICAL WIND LOAD CURRENT (IN BLUE) IN A 132KV 3X800 mm 2 CU SUBMARINE CABLE. AMBIENT TEMPERATURE: 10 °C, BURIAL DEPTH: 1.5 m AND SOIL THERMAL RESISTIVITY: 1 Km /W”

5.1.2.4 Long Time to Reach Steady State Cable ratings for deep installations (generally 10 m for buried cables or depth greater than 1-2 tunnel diameters) must consider the large thermal capacitance of the ground that can result in very long time periods to reach temperatures close to the maximum operating temperatures. This is discussed further in Section 7.2.1.9.

5.1.2.5 “Short” (less than 5 second) Loading Patterns Another type of rating not generally associated with conventional calculations is the current carrying capacity of a conductor during fault conditions. The durations of these events are generally less than 1 second and typically less than 3-10 cycles. A common approach is to assume adiabatic conditions for the conductor, screen or metal sheath during the fault while recognizing the characteristics of the metal carrying the current and non-metallic cable layers that may be in contact with the metal (cable insulation, jacket, etc.). Adjustments to the values calculated using the assumption of adiabatic conditions can be made to take account of the heat loss to give more realistic values. Methods of calculation for both adiabatic and non-adiabatic conditions are shown in IEC 60949.

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Other parts of the cable system may also limit the maximum short circuit temperatures, for example some cable joints use soldered conductor connections and the typical limit for this type of connection is 160 °C, more information about temperature limits during short circuit situations can be found in IEC 61443.

5.1.3

Dynamic

Dynamic ratings are ratings that change depending on real time information. The current rating methods can generally be based on calculations used for arbitrary load patterns, particularly if the real time rating information is the same as the input parameters (or starting points) used in the calculations such as the ground ambient temperature. In some cases the real time measurements include values other than input parameters (for example the temperature of the cable surface). In these cases, the current rating calculations will need modification. A summary of dynamic rating techniques is given in Section 8.3.4.

5.2

Voltage

The voltage applied to the cable system has relatively few direct effects on the current rating of the cable. The main direct effect is for AC cables only, where the time varying electric field generated by the voltage will cause a dielectric loss in the insulation of the cable (see Section 6.2.2). Unlike heat losses that are related to the current in the cable, the voltage tends to be relatively constant when a cable is in operation, hence the heat loss generated is constant. Note that these losses can be fairly high in paper insulated extra high voltage cables. For very long cable circuits, the charging current losses, which are also voltage dependent, might limit the allowable real power that can be transmitted by the circuit (see Section 7.1.6). Referring to question 5.8 of the questionnaire: “Do you consider the impact of charging currents on the real power transfer in long cable systems?” around 34% of the respondents had taken account of charging currents although only around 30% of utilities had taken account of charging currents. A number of respondents commented that they did not have sufficiently long length circuits to need to take account of charging current. Of the comments regarding the method of calculation, many mentioned load flow calculations and many also mentioned that the frequency, capacitance, and length of the cable had to be taken into account. For DC cables the electric stress on the cable insulation is influenced by the resistivity of the insulation, which in turn is influenced by the temperature of the insulation. As the current rating of the cable affects the temperature of the insulation, this will affect the electric stress of the cable and, hence, the maximum operating voltage and the current rating of the cable are interlinked. Further details are given in Section 5.3.3.

5.3

Frequency and one, two and three phase systems

There are a number of different potential frequencies, voltages and currents that a cable system can operate at although typically the frequency is 50 or 60 Hz (power frequency AC). In some systems, direct current (DC) is used. The number of poles or phases that a cable system operates at can also vary.

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5.3.1

AC Frequency

The current and voltage in a cable system operating at power frequency will generate a time varying magnetic and electric field that will generate additional heat losses above the DC resistance losses in the conductor. These losses are: 

Additional AC losses in the conductor through skin and proximity effects (see Section 6.1.1).



Dielectric losses in the insulation (see Section 6.2.2).



Induced current, both eddy currents and circulating currents, in the metal sheath (see Section 6.4) and any other non-magnetic metal objects (see Section 7.2.1.7) near the cable system.



Magnetic hysteresis losses in the cable armour (see Section 6.6) and any other magnetic metal objects near the cable system.

IEC 60287 does not consider the magnetic coupling of all the cable conductors but presents the relevant equations for one two-phase or three-phase circuit only. This qualifies the accuracy of the conductor losses and hence current rating calculation but still demonstrates the tendency correctly. To get a first impression of the dependency on the frequency, Figure 33 has been prepared based on the following cable construction: A 110 kV XLPE cable with 630 mm² copper conductor, round compacted, thickness of insulation 18 mm, copper wire screen 35 mm², PE-outer sheath approximately 3 mm, overall diameter approximately 83 mm.

FIGURE 33: CURRENT RATING OF A GIVEN SYSTEM AS FUNCTION OF THE FREQUENCY

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

With different frequencies, current rating calculations have been conducted according to IEC. The parameters on the curves demonstrate which frequency depending effect has what influence on the entire system. In the diagram (Figure 33) the frequency is scaled on 50 Hz and the current rating is scaled too on its value at 50 Hz. The scaling of the variables in the diagram is done to ensure that qualitative dependencies only are shown in the diagram. Curve 3 demonstrates a cable with no screen losses by circulating currents due to the cross bonding measures and with the dielectric losses suppressed. So the losses of this cable are based on the DC conductor losses including skin effect and proximity effect. Curve 2 added the dielectric losses to the system and curve 1 shows the entire loss situation including circulating current losses in the screen. The tendencies in the entire diagram identify the screen losses due to solid bonding and skin effect as well as proximity effect as those loss sources which show a significant reaction on changes of the frequency. It is possible to influence those loss sources either by the bonding method of the screen or special improvement measures on the conductor construction (Milliken conductor). At least the loss structure is important to know. In case loss sources with a frequency up to 2 kHz have to be considered e.g. the bonding method of the screen decides which attenuation level of the signal can be expected.

5.3.2

One, two and three phase systems

The number of phases that a power system operates at can vary. Typically three phase systems are used at the voltages considered in this technical brochure. These phases will require a multitude of three cables to be placed in close proximity to each other and these other cables will cause mutual heating and may impact on some of the losses being generated (see Section 6.4.1). Generally current rating calculation methods are well developed for three phase systems. Two phase systems are also generally well covered with specific clauses in IEC 60287. There is, however, no method given to calculate specially bonded single core cables for two phase systems and the generalised method for calculating sheath losses given in Section 7.1.3.2 has to be used. At higher voltages, neutral currents are often small because the phase currents are generally balanced. If this is the case, the contribution to mutual heating from the losses in the neutral conduct(s) can often be neglected. Where this is not the case, IEC 60287 does not make any specific provision for determining the neutral current. When the neutral currents are known, the methods in IEC 60287 may be applied by treating the neutral cables as line heat sources with superposition and the effect can be subsequently taken into account. Single phase networks are used on railway systems and some distribution networks. The effects of time varying magnetic field described for three phase systems still apply, but additionally the return current must be considered. Since the return current can travel along any earthed path, it is typical to reduce the inductance of the intended return path to a minimum to ensure the return current travels along the intended conductor. This can be done by using a concentric conductor and the current rating for these is covered in Section 6.3.4. Alternatively a separate neutral return cable can be installed close to the phase cable. In this case, the methods used to calculate the current rating for a two phase cable system will be generally applicable although some approximations would have to be made since the phase and neutral cable will have dissimilar cable designs and the neutral cable will not generate any dielectric losses.

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5.3.3

DC Current Ratings

When DC is used on a power cable system, as opposed to AC, a number of sources of heat loss generated by the cable no longer exist (see AC losses in Section 5.3.1).This leads to a simplification of the equations derived, and these simpler equations are shown in IEC 60287-1-1. In addition the limitations due to charging currents as detailed in Section 7.1.6 are also irrelevant. As noted in Section 6.2.2, the electrical stress for AC cables depends on capacitive effects, which in turn depend on the permittivity of the insulation material. The permittivity is relatively stable under all operating conditions encountered by AC cables and hence the electrical stress in an AC cable is also relatively stable. For DC cables the electrical stress is dependent on resistive effects, which in turn depend on the resistivity of the insulation material. The resistivity is sensitive to temperature and this change in resistivity can change the electrical stress distribution within the cable. For example, when the cable is cold after just being energised, the resistivity of the insulation will be uniform throughout the cable. The electrical stress in the cable will then follow a similar pattern to AC cables (that is higher stress at the insulation close to the conductor). Once the cable has been energised for a length of time and carrying significant load current, the insulation closer to the conductor will be hotter than that at the edge of the cable. Generally the hotter the insulation material is, the lower the electrical resistivity becomes (additionally there is a dependency on the electrical stress). The electrical resistivity can be modelled using the following formula:

Where: ρ0 θ α β E

= = = = = =

(

)

(EQUATION 7)

resistivity at reference temperature [Ω∙m] difference in temperature between the actual and reference temperatures [K] -1 temperature coefficient of electrical resistivity [K ] electrical stress coefficient of electrical resistivity [m/MV] electrical stress in the insulation [MV/m]

Typical values of α and β may be found in CIGRE (2005), although it should be stressed that there may be subtle differences between appropriate values for different types of the same insulation. For further discussion on this theory, refer to Eoll (1975) or Jeroense (1995). Hence the voltage drop across the inner part of the insulation will be reduced and the stress at the outer edge of the insulation will increase. It is possible that under some operating conditions the stress will actually be higher at the outer part of the insulation, with a stress distribution opposite to that seen when the cable was cool. For some insulation materials, particularly mass impregnated non-draining (MIND) insulation, when the load on a cable is reduced, the resulting insulation cooling will form additional voids in the insulation. These additional voids will reduce the dielectric strength of the material. This link between the current being carried by the cable and the electrical stress and strength in the insulation can lead to additional rating constraints (other than maximum operating temperature), particularly for higher voltage DC cables. For these reasons, the assumption that the maximum current rating is limited by the values obtained by applying the methods of IEC 60287 is not correct for higher voltage DC cables, see Huang (2013) and Murata (2014).

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5.3.4

Other AC Frequencies

Power systems typically operate at frequencies around 50 Hz to 60 Hz. There may be some situations where the frequency being considered is not at these typical values, particularly in the case of harmonics (see Section 5.3.5). The frequency will have an effect on heat loss generated by the cable system. This will impact all the sources of heat loss generated by the cable. The AC resistance of the conductor will change due to the skin and proximity effect. The dielectric loss of the cable, the sheath loss and the armour loss are directly related to the operating frequency. Additionally, any heat generated due to metallic objects or parallel conductors are affected by the operating frequency. In general, as the frequency increases the losses generated will increase, all other things being equal. Where frequency has an impact on the calculation normally this is recognised with the term explicitly stated in the formulae. For the methods shown in IEC, this is the case. The methods generally assume that the frequency considered is approximately in the range 50 Hz to 60 Hz. IEC may be used for lower frequencies (16⅔ Hz, 25 Hz) as the impact of the frequency reduces and the resulting calculated current rating remains accurate.

5.3.5

Harmonics

The ideal AC wave shape is a pure sinusoid. In some cases, for example due to power electronics, the wave shape may become distorted. This distorted wave shape may be represented by a current and voltage of the fundamental frequency and then a number of harmonics with frequencies at a multiple of the fundamental frequency. A measure of total harmonic distortion is often defined as:

THD 



 n2

Where: γn =

2 n

(EQUATION 8)

th

ratio of the n harmonic current to the fundamental current

The total heat loss generated by each component of the cable, at the fundamental and all harmonic frequencies, can be shown to be the sum of the calculated heat losses for each frequency. As noted in Section 5.3.4, the methods to calculate heat losses generally include a frequency term in the calculation so it is possible to calculate the heat loss at each frequency. While it is possible to calculate the current rating by using the total heat loss for each component of the cable in the normal current rating methods, this can be time consuming. A simplification (as described by Anders 1997) can be made by assuming the total heat loss (Wn) generated by all the cable components for each frequency (where n=1 is the fundamental and n > 1 are the harmonics) is:



 n  1   1 n    2 n 

W n  I n 2 R ' 1   y s n  y p

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(EQUATION 9)

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Where: In R’ (ys)n (yp)n (λ1)n (λ2)n

= = = = = =

th

current for n harmonic [A] DC resistance of conductor [Ω/m] th skin effect factor for n harmonic th proximity effect factor for n harmonic th sheath loss factor for n harmonic th armour loss factor for n harmonic

This enables the calculation of an effective AC resistance of the conductor (Rn) for each frequency:





Rn  R' 1   ys n   y p n 1  1 n  2 n 

(EQUATION 10)

The total heat loss for a cable carrying a distorted waveform (Wdist) is the addition of all the heat losses for each frequency:

W dist 



I n 1

2

Rn

n

(EQUATION 11)

th

This can be rearranged by introducing the term γn, being the ratio of the n fundamental current to the fundamental current (I1):

W dist  I 1

2



 n 1

2 n

Rn

(EQUATION 12)

Additionally, the approximation is made that the heat loss of the cable will be the same both for the cable carrying the fundamental frequency only at maximum load (i.e. at full current rating I) and carrying the distorted maximum load, hence

I 2 R1  I 1

2



 n 1

2 n

Rn

(EQUATION 13)

And this can be re-arranged to give:

I1  I

R1 

R1   n Rn 2

n 2

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(EQUATION 14)

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The above equation can be used to estimate the maximum current of the fundamental frequency of a distorted waveform in conjunction with equation 10. It is apparent that knowledge of the relative magnitudes of each harmonic is required as the effective conductor resistance is different for each harmonic. Hence knowledge of the total harmonic distortion value (equation 8) alone is not sufficient. More information on the impact of harmonics is given in Hiranandani (1995), Sakis et al. (1992), Demoulias et al. (2007) and Donazzi (1987). Two further notes on harmonics are: 

Harmonics are typically damped by transmission in the power cable. With increasing length therefore the amount of harmonics present will change.



Harmonics will also be present in DC cables depending on the filtering present in the converter stations.

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6

C abl e As p ect s in C a ble R at ing C al cu la t io ns

The current rating of a cable system is influenced by the specific design of the power cable itself. Aspects regarding the cable design, as the conductor type, skin and proximity effects, insulation design and the effects of screens, sheaths and armours all influence the current rating and are discussed in this chapter.

6.1

Conductor

A cable conductor can be made up of different materials, generally copper or aluminium, and can have different constructions, for example solid, compacted circular or Milliken, see Figure 34.

FIGURE 34: OVERVIEW OF CONDUCTOR CONSTRUCTIONS

The majority of conductor materials and constructions are referenced in IEC 60287-1-1 although oval and aluminium segmental are not. Values for the skin and proximity effect are suggested in the next section. These different materials and constructions all affect the DC and AC resistance of the conductor. The calculation methods used are those found in IEC 60287-1-1 and given the symbol R’ for DC resistance and R for AC resistance at maximum operating temperature.

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6.1.1

Skin and Proximity Effect

The AC resistance of a conductor will be greater than the DC resistance of the conductor due to the skin and proximity effect. Solid conductors will be worst affected by the skin and proximity effect. The effect of strands in the conductor will disrupt the proximity effect. The skin effect is reduced only in Milliken conductors. Both effects mitigate the increase of the resistance in AC compared to DC. Some manufacturing processes, such as extrusion, may impact on the stranding, for example by compressing the strands together. Milliken conductors are specifically designed to maximise the disruptive effect of the strands and optimise the AC resistance of the cable. The disruptive effect of the strands can be further improved by increasing the electrical resistance between the individual strands using some form of surface treatment (oxidation or enamelling). The AC resistance is derived from the DC resistance through 2 coefficients, representing the skin and proximity effects. For the calculation of skin and proximity effects for Milliken conductors of extruded cables, the methods of calculation are given in IEC. CIGRE (2005-1) gives extensive guidance on calculating AC resistance for these conductor designs and for conductors with large 2 (>1600 mm ) cross-sections. Given the difficulty in performing calculations, the publication recommends that the AC resistance is measured during the type tests. When measured values are not available, the publication recommends that the classical IEC 60287 formula is used but with the coefficients revised with the values given in the publication. For oval and aluminium shaped conductors it is recommended that the values for round stranded conductors are used. In addition to the skin effect, the proximity effect has to be taken into account especially for threecore cables, single-core cables in trefoil or cradle formation for large cross section single core cables. For shaped conductors, a common feature of multicore cables, the proximity effect factor yp is smaller than for circular conductors. 6.2

Insulation

6.2.1

Thermal Resistance

Different materials will have different thermal resistivities and will hence have an impact on the thermal resistance of the cable between the conductor and sheath. This value is calculated in IEC 60287-2-1 and given the symbol T1. Care has to be taken with cables with corrugated sheaths to select the correct dimensions. Often there is more than one material layer between the conductor and sheath, but this is not generally taken into account by the model. Typically, the thermal resistivity of the insulation is used for the entire thickness between conductor and sheath. However, if there is a substantial layer with a higher thermal resistance, this should be accounted for by modification of the IEC 60287 calculation. Where the heat transport is still by thermal conduction, it is possible modify the calculation of T1 [K.m/W] accordingly to:

=

1 ∙ 2

∙ ln

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(EQUATION 15)

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Where: i = Di = ρi =

number of the layer between the conductor and metal sheath outer diameter of layer i [mm] thermal resistivity of layer i [K.m/W]

For thermal resistivity values of various materials, manufacturer values may be used for accurate results (refer to section 3.1). The modification of T1 given above does not take into account contact resistance between various layers nor any changes in thermal resistance of bedding material due to compression. In some cases, the heat transport may be more complex, for example this may occur for cables that have a substantial volume of oil or air (clearance) under the sheath, particularly corrugated sheaths. Methods to take account of this air or oil gap have included adding an empirically derived constant (not found in standards) to the calculated thermal resistance. Due to the difference in corrugation designs between manufacturers, it is difficult to recommend constants, see Brakelmann et al. (1991). Note that when the cables are hot, the clearance is usually reduced because of the thermal expansion of the insulation, which is beneficial to the heat transfer.

6.2.2

Dielectric Loss

The insulation of the cable can be constructed from different materials, for example XLPE, EPR, oil or impregnated paper. Different insulation materials will have a different relative permittivity and this will impact the capacitance and dielectric loss of the cable. These values can be calculated in IEC 60287-1-1 and the symbol for dielectric loss is Wd. The power cable is typically a long cylindrically symmetrical capacitor and the AC voltage initiates an AC current through the dielectric whose resistive part, responsible for all thermal changes, is represented by the tan δ of the insulation. Therefore, the equation for the dielectric losses Wd (W/m) is as follows:

= Where: ω C U0 tan δ

= = = =

(EQUATION 16)

angular frequency (radian /s) capacitance (F/m) phase to earth voltage (V) loss angle

The equations in IEC 60287-1-1 give methods to calculate the capacitance for circular conductors with co-axial screens only. For oval conductors, IEC 60287-1-1 recommends that the geometric mean of the minor and major diameters is used. Generally, other conductor shapes and belted cables are used at lower voltage where dielectric losses are smaller, so it is considered acceptable to use a suitable approximation. Besides the direct physical relation of voltage and dielectric losses there is a dependency of temperature on the dielectric losses via the tan δ connected to the properties of the insulation material itself. The following diagrams representing the dielectric loss factor for an insulation material illustrates this relationship.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES With higher temperatures, tan δ increases. Above 100 °C this becomes particularly pronounced, which means that in this situation a thermal runaway of the insulation may be initiated. With higher stresses, the beginning of this process moves towards lower temperatures. In general, this behaviour can also be found in paper insulated cables .

FIGURE 35: DIELECTRIC LOSS FACTOR VERSUS TEMPERATURE FOR VARIOUS STRESS LEVELS OF XLPE MATERIAL ‘A’

FIGURE 36: DIELECTRIC LOSS FACTOR VERSUS TEMPERATURE FOR VARIOUS STRESS LEVELS OF XLPE MATERIAL ‘B’

Under service conditions, the maximum operating temperature of XLPE insulation is set to be 90 °C (e.g. IEC 60502, IEC 60840 and IEC 62067) and for the dielectric loss factor IEC 60287 recommends a value of 0,001. Today’s XLPE insulated cables are operated at stress levels between about 6 kV/mm and 14 kV/mm and it is common practice under all testing conditions not to exceed a stress limit of 30 kV/mm. Therefore, now looking to the comparison of both materials in Figures 35 and 36, material B would not have been chosen for a highly stressed XLPE insulation.

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES It should be noted that the relative permittivity εr, which is hidden in the calculation of the capacitance has no significant dependency on the temperature and hence the electrical stress gradient of an AC cable is relatively static despite load and temperature changes within the cable. Ageing can affect the tan delta of power cables negatively. Older power cables are sometimes found to show a significantly increased tan delta, especially at higher temperatures. Of course, the increase of tan delta depends on many cable details making it difficult to generalize findings. The advice is given to establish the tan delta of a cable insulation material as a function of temperature in case significantly aged power cables are considered in an engineering study, or in case these aged power cables are loaded close to their original current rating.

6.3

Arrangement of Cores in a Cable

Although single core cables are most common, it is possible to have a number of cores and construct these in different arrangements within the cable. These different constructions will have an impact on the calculation of thermal resistances and losses. In case of multicore cables, conductors can be shaped. Shape also has an influence on losses.

6.3.1

Single Core Cables

The simplest construct is to have a single conductor contained within the cable and these are known as single core cables. However, a circuit will then consist of more than one phase cable or at least have a separate neutral cable and the circuit arrangement will have to be considered (see Section 7.1.1).

6.3.2

Multi-core Cables (including three core)

It is possible for some cable designs to contain more than one conductor and since power is generally transmitted using three phases, it is common to have 3 core cables, each core carrying a separate phase. For land cables, the typical construction is to have three cores, each core insulated for full phase to earth voltage, then laid up in a single common metal sheath. However, it is possible that each core has an individual sheath which is typical for submarine cables, see Figure 37. If the cable is a multicore construction, this will affect the thermal resistance of the insulation (T1) and possibly the thermal resistance between sheath and armour (T2) and methods of calculation are given in IEC 60287-2-1.

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FIGURE 37: THREE CORE 36KV SUBMARINE CABLE, EACH CORE HAVING AN INDIVIDUAL SHEATH

Sheath and armour losses will be lower than for single conductor cables and these are discussed in Sections 6.4 and 6.6 respectively.

6.3.3

Pipe type Cables

Losses for pipe-type cables are determined in accordance with equations from Neher/McGrath’s 1957 paper and were adopted by IEC 60287. Equations from IEC 60287-1-1, Section 2.4.3, “Losses in Steel Pipes”, should be used in the calculations. The user should note that the calculated equations are based on empirical work done in the 1950s and 1960s for typical cable pipe diameters up to 305 mm. The application of these equations to larger pipe sizes, including those that might be used as steel casings with extruded cables, should be done with caution as the empirical relationships may not accurately represent larger sizes of pipe. In particular, the Neher / McGrath paper refers to three single core cables placed inside the pipe in either a trefoil or cradled configuration. Thus, when the number of cables in the pipe is different, or the casing is relatively large compared to the cable diameter, or the cables are placed in other arrangements, the above approach cannot be used. Factors such as the magnetic permeability of the steel pipe (a quantity seldom known by the user) could influence the accuracy of the losses. Alternatively, electromagnetic finite element studies have to be used.

6.3.4

Concentric Cables

A concentric cable has a conductor around the core for a return path. These are typically used for single phase systems or for single core HVAC submarine cable circuits where specially bonded cable systems are not possible. Also DC cables may be of concentric type as is the case in an integrated return conductor cable, where the return conductor is installed around the core conductor. Two phase concentric cables are not directly covered by IEC 60287. The suggested method is to assume that the current in the outer conductor is equal to the current in the central conductor. The heat loss in the outer conductor can then be calculated and hence a revised sheath loss factor can be evaluated:

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1 

Where: Router =

R outer R

(EQUATION 17)

a.c. resistance of outer conductor at operating temperature [Ω/m]

Note: Normally for the outer conductor the AC resistance can be assumed to be the same as the DC resistance as the skin and proximity effect will be negligible. For the inner conductor the proximity effect can be assumed to be negligible although the skin effect will still need to be calculated. Any subsequent metal sheaths or armour layers can then be assumed to have no heat losses as the magnetic field outside the outer conductor generated by the cable will be negligible.

6.4

Metal Sheaths and Screens

There are a number of variations in cable design but almost all use some form of a metal earth return path for short circuit currents, charging current, circulating current and as screening for the electrical field in some cable constructions. Optionally, there may be a requirement to stop water entering the core of the cable or hold a fluid inside the cable system. Typical cable designs may use one or more of the following:     

Metal sheaths: extruded lead, copper, aluminium or stainless steel either plain or with corrugations Copper or aluminium wire screens Foil laminates Copper tapes Steel pipes with cable cores inside.

6.4.1

Metal Sheath and Screen Losses

For AC cables, the time varying magnetic fields will generate currents in the metal sheaths and screens. Formulae for a number of different cable designs and installations arrangements are given in IEC 60287. In IEC 60287 the currents generate a heat loss, represented by the loss factor λ1. These sheath losses consist of losses caused by circulating currents ( ) and eddy currents ( ), where:

 1   1'   1' '

(EQUATION 18)

The formula expresses the loss in terms of the total power in the conductor(s), and for each particular case it is indicated which type of loss has to be considered. For single-core cables in a solidly bonded cable system, only the loss due to circulating currents in the sheaths need normally be considered, although there are exceptions for large Milliken conductor cables. For single point bonded cable systems, there will be no circulating currents and for cross bonded cable schemes, circulating currents will only result if the minor sections are unbalanced.

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There are some cable designs or cable arrangements that are not covered by formulae in IEC 60287. In particular: 

The formulae for single core cables apply to single circuits or two flat spaced circuits only. However, the general approach for the latter case can be extended to more circuits in any phase arrangement.



A formula for the sheath loss for two phase cross-bonded systems is not given.



Cable constructions with multiple sheaths or screens are not considered (see Section 6.4.2).

For cable arrangements or designs not covered by other methods, the generalised methods described in Section 7.1.3.2 may be applied.

6.4.2

Multiple Sheaths and/or Screens

For cable systems that are solidly bonded and earthed, the sheath losses can be estimated by combining the calculation of all nonmagnetic metallic layers. The parallel resistance of the multiple layers can be used in the formulae given in IEC 60287, much in the same way as would be done for non-magnetic armour or reinforcement. For cable systems that are specially bonded and earthed, the majority of cable designs that have multiple sheaths or screens will have a copper wire screen as one of the layers. Cables with copper wire screens are considered in CIGRE (2005-1) and as the losses in a copper wire screen are negligible they need not be considered, leaving only the other layers to be considered. Where the methods above are not appropriate, the methods given in Section 7.1.3.2 can be used to calculate the sheath losses. Cables that use multiple sheaths and/or screens will generally have bedding layers between the sheaths and/or screens. The bedding will have a thermal resistance and this can be calculated in a similar fashion to the armour bedding (see Section 6.5). In most cases, it is desirable to add the resulting value to the thermal resistance of the cable external serving (T3) or armour bedding (T2) if it exists, but if the sheath loss of the inner layers are negligible, then the resulting value can be added to the thermal resistance of the insulation (T1).

6.5

Armour Bedding

The armour bedding will have a thermal resistivity and this is accounted for in IEC 60287. Where the armour is nonmagnetic, IEC 60287 suggests that the armour loss is combined with the sheath loss. The resultant loss should be treated as the sheath loss ( ) and no armour loss. The thermal resistance of the armour bedding (T2) is added to the thermal resistance of the cable external serving (T3). Note that this approach is not applicable to submarine SL-type cables with sheath/concentric neutral wires around each core and common nonmagnetic armour.

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6.6

Armour and Metal Pipes

Armouring, also called reinforcement, has a mechanical protection function for the given cable. Armouring can be either magnetic or not-magnetic. This section pertains to the magnetic armour losses. The armouring of the cable can be constructed from different materials, for example steel, bronze, copper, aluminium or stainless steel. Different armouring will have a different resistivity and different temperature coefficient and this will impact the overall loss of the cable. These values can be calculated in IEC 60287 as a fraction of overall conductor losses and the symbol for armour loss is λ2. Referring to question no. 5.6 in the questionnaire, ‘have you made any comparison between calculated and measured steel wire armour losses for 3 core cables?’, in total 7 respondents had reported measuring steel wire armour losses. Of these 5 were cable manufacturers, with the other two being a consultant and a utility. The following comments were made:   

IEC calculations too high Evaluation not complete Evaluation not complete, preliminary results IEC losses too high

2 responses 1 response 1 response

None of the comments found that the armour losses agreed with IEC calculations but only 4 comments were received.

Pipe type cables use steel pipes to contain the cores of the cable and the oil. These steel pipes will generate losses and empirical formulae to calculate these losses are given in IEC 60287. Since pipe type cables do not have any armour, the losses are given the same symbol (λ2). IEC 60287 gives formulae for some limited pipe dimensions and arrangements only. Where IEC is not applicable, an alternative may be to use finite element methods. Moutassem and Anders (2010) describe some of the issues. The temperature of the armour or pipe is a function of the current and, therefore, an iterative method is used for the calculation.

6.6.1

Armour Loss in Multicore Cables

Steel wire armour losses in three-core cables are described in the IEC standard 60287. Three types of cable designs are dealt with in the standard: steel wire armoured, steel tape armoured and SL type cables where each core in the three-core cable has a sheath and an overall magnetic armour. Two types of losses are created in the steel wire armour in a three-core ac cable, eddy currents losses and hysteresis losses, both induced by the magnetic flux. New measurements performed by one cable manufacturer on steel wire armoured XLPE cables of SL type with lead sheaths have shown that the IEC standard gives losses that are too high. No recent measurements have been found for cables with reinforcing tapes, or with flat wire armour. A report about armour loss in three-core submarine XLPE cables was presented at Jicable 2011 by Palmgren, D. et al. (2011). The measurement setup and the measured losses with and without armour are given in the report for two different XLPE cables of SL type.

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The first cable (Cable 1) is a 145 kV cable that has aluminium conductors with a cross-section of 2 815 mm and a single layer of mixed armour of steel wires and plastic wires. The number of steel wires in the armour is reduced in order to lower the cable weight and the power loss. Every second wire is replaced by a PE string of the same diameter as the steel wire. Table 5 shows the resulting loss factors for the sheath and the armour for Cable 1 as a function of the conductor current. The armour loss factor is current dependent and essentially smaller than the IEC value.

TABLE 5: 145KV SINGLE ARMOUR CABLE MEASURED LOSS FACTOR AS FUNCTION OF THE CONDUCTOR CURRENT

Icond [A]

326.1

431.9

640.7

846.7

1

0.1653

0.1680

0.1739

0.1798

2

0.1132

0.1355

0.1609

0.1870

2 (corrected to 90C conductor temp)

0.0872

0.1044

0.1245

0.1430

2 (according to IEC 60287)

0.2511

2

The second 132 kV cable (Cable 2) has solid copper conductors with a cross-section of 240 mm and double wire armour layers. Table 6 and Table 7 show the resulting loss factors for Cable 2 as function of the conductor current. The loss factors are given for one (Table 7) and two (Table 6) armour layers. The loss factors are current dependent and essentially smaller than the IEC values.

TABLE 6: 132KV DOUBLE ARMOUR CABLE MEASURED LOSS FACTOR AS FUNCTION OF THE CONDUCTOR CURRENT

Icond [A]

303.5

402.6

600.1

789.0

1 (two layers)

0.0992

0.1001

0.0998

0.1076

2 (two layers)

0.0655

0.0700

0.0779

0.0712

2 (corrected to 90C conductor temp)

0.0500

0.0535

0.0603

0.0538

2 (according to IEC 60287)

0.1541

TABLE 7: 132KV SINGLE ARMOUR CABLE MEASURED LOSS FACTOR AS FUNCTION OF THE CONDUCTOR CURRENT

Icond [A]

304.9

404.3

600.4

799.0

1 (one layer)

0.0966

0.0985

0.1007

0.1043

2 (one layer)

0.0597

0.0675

0.0816

0.0859

2 (corrected to 90C conductor temp)

0.0457

0.0515

0.0627

0.0649

2 (according to IEC 60287)

0.1790

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Additional measurements have also been performed on 400 kV three-core SL type cable with 1200 2 mm Al conductors and a single layer steel wire armour, see Table 8. The loss factor are current dependent and essentially smaller than the IEC values. The IEC 60287 standard gives an armour loss factor ( ) of 0.476.

TABLE 8: 400KV 3 CORE 1200MM2 AL SL TYPE CABLE WITH SINGLE LAYER STEEL WIRES ARMOUR, MEASURED LOSS FACTOR AS FUNCTION OF THE CONDUCTOR CURRENT

Icond [A] 1

302.2 0.3337

403.9 0.3272

597.0 0.3343

790.7 0.3366

2 2 (corrected to 90C conductor temp) 2 (according to IEC 60287)

0.3774 0.2402

0.4018 0.2560

0.4169 0.2658

0.4281 0.2722 0.476

Performed measurements give similar armour losses for single and double layer armoured cable. The similar loss factor could be explained by the fact that the inner armour layer acts as a magnetic shielding for the outer layer. The above measurements, made by one cable manufacturer, show that the derived losses in a steel wire armoured three-core SL type cable are approximately 60% of the losses according to the IEC 60287 standard. Other publications also underline the overly estimation of 2 for armour losses if calculated by IEC, see Pilgrim et al. (2014): the impact on the cable current rating being 6% less than accounted if the real armour losses are taken into account. Also Halto and Bremnes (2014) investigated the current dependent armour loss in three-core cables: The paper “Comparison of FEA results and measurements” shows experiments and FEM results that suggest that armour losses calculated by IEC are overestimated by a considerable amount. Results suggest in some cases hysteresis losses will be significant. It is recommended that additional measurements are made by other cable manufacturers in order to verify that a different design philosophy or another material selection does not result in any major influence on the losses. The most recent measurements show it is important to measure the losses on a suitable length of cable in order to achieve well measurable values and reach an acceptable level of accuracy. The measurement must be performed at rated current since the loss factor is current dependent. It is also recommended to do a comparative measurement with and without the steel wire armour, however it should be noted that the difference between these two measurements will not equate to the magnitude of the armour losses. This is due to the effect which the presence of the armour has on the conductor and sheath losses. A difference analysis will reduce the total error due to dimension variations between different cable samples and the measuring accuracy. No new measurements have been found for three-core cables with tape armour, it is therefore recommended that the formulas according the IEC 60287 standard are used for this type of cable. It must be noted that this section describes various measurements that showed losses different to that deduced from the IEC models. This implies that the current IEC models are in need of updating. In this case there however must either be enough reliable measurements to come to an empirical model, or there must be fundamental work to come to a sound physical model explaining the measurements conducted. Either route will take time, and during this time to come to improvements,

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the WG recommends to use the existing IEC standards (giving too high losses), unless one is absolutely sure about an alternative based on representative measurements.

6.7

Outer Covering

The outer covering or external serving as it is named in IEC 60287 (in North America the term jacket is used), is the outer component of the cable. It is typically a concentric even layer. It can be extruded or not, depending on the function and applications. It can be constructed from different materials e.g. PE, PVC, jute or polypropylene yarns. Lapped serving are typical of submarine cables in the so-called semi-wet design of this layer; there are no additional losses but it represents an additional thermal resistance. In the case of extrusion on a corrugated metallic sheath, an equivalent diameter has to be taken into account. Formulae for both cases and extruded over corrugated sheath covering are covered by IEC 60287-2-1. The thermal resistivity of various materials are reported in IEC 60287-2-1 but where a thermal resistivity of a material is not reported in the standards, a value should be either provided by the supplier or measured. For thin layers, such as semi-conducting layers for serving tests, the change in the overall thermal resistance will be small and hence the thickness of these thin layers is included in the outer covering. In case other layers present, such as fire protection material, these layers have to be included in the total thermal resistance of the outer covering.

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7

Ins t a ll at i on As p ect s i n C ab le R at ing C al cu lat ion s

7.1

Features Common to Many Installation Types

Many of the design aspects of a cable system (e.g. cable spacing) impact the current rating in the same way, even though the cable system may be installed in different ways (e.g. buried or in air). The impacts of these design aspects, or installation features, are covered in this section.

7.1.1

Cable Spacing / Arrangement

In addition to cable construction, circuit layout has to be taken into account. The two common cable arrangements are trefoil and flat configurations. In some cases, a cradled configuration (typical of three single core cables installed in a pipe) or open trefoil may be used. There are occasions, for example when installing cables in existing ducts, where the formation may not be a recognised one and installations in any arbitrary configuration are feasible. The configuration and cable spacing will affect the losses generated by magnetic fields, in particular the conductor (see Section 6.1) and sheath losses (see Section 6.4.1). Where the cables are installed in typical cable configurations, IEC 60287 provides methods to calculate these losses. Where the installation configuration is not standard, it may not be covered in IEC 60287 and, in these cases, the more generalised methods described in Section 7.1.3 may have to be used. The configuration of the cables will also affect the mutual heating between them. For buried cables, (see Section 7.2), a generalised method of calculation is given in IEC 60287. For cables installed in air (see Section 7.3) and similar installations such as tunnels, a variety of arrangements is considered by IEC 60287 but there is no generalised method.

7.1.2

Bonding of cable sheaths

The simplest method of bonding cable sheaths is to solidly bond them at each end of an electrical section. Typically the cable sheaths will also be earthed at solid bond positions to ensure that the sheath is at or near earth potential and hence that the voltage drop across the insulation is correct. Additionally the earth may be needed to act as a fault current path. An electrical section is, in this case, a section of cable circuit where no transposition of cable sheath has been made between the phase cables. For single core cables, this will result in circulating currents in the cable sheaths that will reduce the current rating of the cable. For single core cable circuits required to carry larger currents, it may be economic to use a special bonding scheme (such as single point bonding or cross bonding). Cable systems that use special bonding schemes or multicore cables will have either negligible or reduced circulating currents but there will still generally be eddy currents in the sheath that will need to be calculated. These circulating and eddy current losses are termed sheath losses and details are given in Section 6.4. For more information on bonding and earthing see CIGRE (2005-2) and IEEE (IEEE 575, “Guide for Bonding Sheaths and Shields of Single-Conductor Power Cables Rated 5 – 500 kV”).

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7.1.3

Multiple Parallel Circuits

When cable circuits are installed in parallel, one circuit will impact the other circuit. This impact will be directly, where the heat generated by the cable may heat the other cable circuit. These effects are considered in the installation specific sections of this document. Additionally, the magnetic field generated by one circuit will impact on the other circuit, altering the losses generated by the conductors and the sheaths.

7.1.3.1 Conductor ac Resistance When calculating the current rating of a cable circuit, the currents in parallel circuits will generate magnetic fields in the conductors of the cables in question that will cause some redistribution of the current within the conductor and an increase in its apparent AC resistance. This is a similar effect to the other phase cables within the same cable circuit and this is calculated as the proximity effect. However, given that generally the spacing between cable circuits is significantly greater than those between cables within the same circuit and that the proximity effect is generally small, the effect of parallel circuits on the AC resistance of the conductor of the cable can generally be neglected. If there is a concern that the current rating accuracy may be affected, the generalised computation method (filament heat source simulation) described in Section 7.1.3.2 can be used.

7.1.3.2 Impact on Sheath Loss for Specially Bonded Cable System When there are several circuits in a proximity to each other, the induced voltages and the corresponding eddy currents in sheaths caused by the parallel circuits should be considered. IEC 60287-1-2 gives methods to calculate sheath eddy current losses for two identical single core parallel cable circuits in flat spaced formation. However, the methods to calculate the sheath losses in IEC 60287 apply to limited circuit configurations and, in addition to being limited to two cable circuits, the methods to calculate eddy currents for single core cables are limited to three phase systems with flat or trefoil formations. Analytical methods for alternative arrangements can be derived, for example Jackson (1975), but can become very complex. An alternative generalised method to calculate losses due to induced voltages can be applied and is briefly described below. It should be noted that this method will not only calculate the losses generated by the eddy currents, but all the losses generated by induced currents such as circulating losses in the sheath and proximity effects in conductors. Such systems can conveniently be analyzed with the application of the filament heat source simulation (f. h. s. s.) method published by Anders (1997). The term conductor is used to denote any metallic component of the cable. Applying the method of filament heat source simulation, the conductors are replaced by a large number of smaller cylindrical sub-conductors or filaments. The number of filaments should be large enough so that the current density can be assumed uniform throughout each filament cross section. The size of the filaments is calculated such that the sum total cross-sectional area of the filaments equals the total conductor cross-sectional area. Helically wound wires are replaced by tubes with equivalent resistances.

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The expressions describing the electrical connections of the filaments are as follows:

Ic  B I

(EQUATION 19)

E Bt Ec

(EQUATION 20)

Where the superscript t denotes transpositions and: 1 1 . . . 1 0 0 . . . .  0 . . . . .  . B = connection matrix, B   .  . .  0

0 0

.

.

.

0

1 1 . .

. .

. .

. .

1 .

.

0

.

0 1

. .

0 0  .  . .  . 0  1 

=

column vector of filament longitudinal voltage drop, E   E1, E2 , .. ., En 

E

=

c column vector of conductor longitudinal voltage drop, E c  E1c , E c2 , . .. ENC

I

=

column vector of filament currents, I   I1, I2 , . . . , In 

I

=

c column vector of total conductor currents, I c  I 1c , I 2c ,... I NC

NC c n

= = =

number of conductors superscript referring to conductor quantities number of filaments

E c

c

t





t

t





t

The value of NC will depend on the number of cables per phase and on whether or not the cables have metallic armour or sheath. The presence of neutral cables and earth conductors will further increase NC. In above method it is assumed that there is no cross-filament current: the contact resistance is ignored. We can see that the connection matrix B is such that the sum of the filament currents in each conductor equals the total conductor current, and the longitudinal voltage drops in each filament of a conductor are equal to the conductor longitudinal voltage drop. Our aim is to express filament currents as a function of phase conductor currents and the geometry of the system. The longitudinal voltage drop in a filament is given by:

    E  R d  j 0 r G   I 2  

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Where:

G

=

 1 ln s  11 . geometric matrix, G    .  1 ln  sn1

ln

1 s12

.

.

.

.

.

.

.

1  s1n   .  .  1  ln  snn  ln

Rd

=

n  n matrix with vector  R1, R2 ,..., Rn  of filament resistances in the diagonal and

sii sij μ0 μr

= = = =

zeros outside the diagonal geometric mean radius of filament [m] geometric mean distance between filaments i and j [m] permeability of air, H/m relative permeability of the material, (μr =1 for nonmagnetic materials)

Since both E and I are complex quantities, their separate components must be determined. In effect, therefore, there are 2n equations and 4n unknown quantities to be found. After some manipulations, we obtain:

1

1 1         I  R d  j G B t BR d  j G B t  I c 2  2     

Where: μ =

(EQUATION 22)

μ0 μr

For systems where all the conductor currents are known, evaluation of the above equations represents the required solution. For systems in which total conductor currents are not known, calculations must be performed to determine the unknown values of the currents. These equations can now be used to determine the sheath and armour loss factors by suitably specifying the matrix boundary conditions. If the sheaths are solidly bonded, the sheath and armour filaments are solidly bonded. Equation 22 yields both the circulating and approximate eddy currents after observing the boundary conditions that the voltage drops in all sheath filaments are equal and the sum of all sheath filament currents is zero. If the sheaths are bonded at one end only, the filaments representing the sheath of each cable are bonded together, but not those belonging to different cables. The boundary conditions now require the sum of sheath filament currents in each cable be equal to zero. Thus, the eddy currents and standing voltages can be computed from the above equations. For solidly bonded systems, for example, we proceed as follows. Let us suppose that the first i-1 c entries in the vector I represent known cable conductor currents. From Kirchhoff’s first and second laws, we have:

c I 1c  I 2c  ...  I ic1  ...  I NC 0

(EQUATION 23)

c E ic  E ic1  ...  E NC  E 0  a constant

(EQUATION 24)

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Where: E0 =

the sheath longitudinal voltage drop [V]

Defining: 1      C  B  R d  j G B t  2    

1

(EQUATION 25)

We obtain:

 E1c   C11     .   .  .   .     .   . E c   .  i 1     E0   .  .   .     .   .     E0  CNC,1  0   1

C12

1

.

.

.

.

C1, NC   I1c    Ic    2    .       .    I ic1 .     .    .       .    CNC, NC   .   c  . 1   I NC  .

(EQUATION 26)

This constitutes a set of NC+1 equations in NC+1 unknowns. Some reduction in computational effort can be obtained by noting that the longitudinal voltage drops of the central conductors are not of interest. Similar equations can be set up for single-point bonded systems. The sheath voltages in this case are different and are to be computed. The loss factor for a particular conductor (a sheath, armour, or pipe) composed of filaments k to m is equal to:

m

I  I

2 R i i

ik

2 R j j

(EQUATION 27)

j

Where j is the index of central conductor filaments belonging to the same cable as the sheath or armour. The current represents the rms values. Please note that the f.h.s.s. method assumes that all the conductors are straight (and parallel). As it is, it is not directly applicable to the calculation of losses in the screen of single-core cables composed of a bundle of wires or in the metal screen of 3core cable (because of the twisting of the conductors).

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7.1.3.3 Impact on Sheath Loss for Solidly Bonded and Earthed Cable System When there are several circuits in a proximity to each other, the induced voltages and the circulating currents in sheaths caused by the parallel circuits should be considered. IEC 60287-1-3 gives methods to calculate sheath circulating current losses for any given formation.

7.1.3.4 Impact on Armour Losses The magnetic field from one circuit will modify the losses generated by the armour on another circuit. For multicore cables that are armoured, the spacing between the cores will be much smaller than the spacing between circuits, so the effect is likely to be negligible. For single core cables, in most cases the cables will be installed much closer together than the circuits so it is anticipated that the effect will be small and the effect can be neglected.

7.1.3.5 Thermal Impact of Multiple Circuits The thermal impact of circuits on one another will depend on how they are installed and hence are covered in the sections on each specific type of installation.

7.1.4

Multiple Cables per Phase

With a single cable per phase, it is reasonable to assume a balanced system in which the conductor currents are equal. When it is necessary to install a number of cables per phase in one circuit, the reactances of the sheaths and conductors are functions of their spacings from all the other sheaths and conductors. Because of this, not only will the impedance of the sheaths vary but also the impedance of each phase conductor may vary, depending on the relative positions of the cables. Hence, for cables in parallel, the current flowing in each conductor may be different, and the situation is often referred to as load sharing. This leads to the need to solve simultaneous equations for both the conductor and sheath currents. For example, for two cables per phase in a three-phase system, the six conductor currents and the six sheath currents must be found. In this case, a set of 12 simultaneous equations with 12 unknowns has to be solved, each equation having a real and an imaginary component. In general terms, for n cables per phase, 6n simultaneous equation must be solved. Additional equations may be required to set up the boundary conditions for voltages and currents. A general approach that should be used is set out in the IEC standard 60287, with details of the derivation of the equations in the standard given in Chapter 8 of Anders book (1997). This is not a task for manual calculations. Other aspects such as the thermal impact of cables on each other are similar to cable installations with multiple parallel circuits and these aspects are covered in the sections on multiple parallel circuits.

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7.1.5

Circuits Crossing

The impact of circuit crossings will be specific to the method of installation. For most installation methods the installation design is made to make the impact of the circuit crossing negligible but for buried installations (including subsea installations) it is not possible. Section 7.2 on buried installations covers circuit crossings.

7.1.6

Long Lengths (charging currents)

The power transfer capacity of a circuit is affected by long cable lengths. An increase in length causes increased charging currents in the cables, allowing for less real power to be transferred through the cables. Adding compensation shunt reactors connected at one or both ends of cable circuits mitigates the effect to some extent. As a general rule, in AC links compensation is necessary when the reduction of the active power is larger than 15%. In any case, it is required to do a system planning study which determines the quantity and type of compensation (one end, two ends, placed in the middle of the connection) and a system impact study which determines the impact of a cable on the rest of the power system. As a reference, CIGRE (2013-2) describes system technical performance study issues which are important for a power system with long AC cable lines. More detailed calculations about power transmission over long cable circuits can be found in Arrighi (1986) and Del Brenna (2004). A simplified approach is given in Section 7.1.6.1 and Section 7.1.6.2 but should be considered as indicative.

7.1.6.1 Critical Length The series inductance of an overhead line is about 2-3 times larger compared to an underground circuit but the shunt capacitance of an underground line is about 10-20 times larger. These factors depend on the geometrical configuration of the cable system and material properties of the cable. It is possible to define the concept of “critical length” and we can use the following simplified scheme considering only the capacitance of the cable to illustrate this concept.

FIGURE 38: REACTIVE POWER GENERATED BY A CABLE

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Where: Iz Ic IL PL SG

= = = = =

the thermal rated current for the line (steady-state) [A] the capacitive current for the cable [A] the load current [A] the active power at load receptor [W] the apparent power at injecting point [VA]

To feed a purely resistive load in a radial network with a given current trough an underground line, it is necessary to inject a higher current at the source to compensate for cable capacitance. The difference being the capacitive current generated in the line, in quadrature with the current in load. This is the charging current:

I z  I c2  I L2 2

(EQUATION 28)

With increasing length, the capacitive charging current will reach the value of the maximum allowable current of the cable, so the charging current accounts for all the available heat losses in the cable. This length is called the “critical length” (Lc) and occurs when the condition in the above equation occurs:

I z  Ic

(EQUATION 29)

The equation can be re-arranged to find the length at which the charging current is equal to the thermal rating of the cable:

I = Where: C = ω = U =

U ∙ω∙C∙L √3 ∙ 10

→ L =

I √3 ∙ ∙ 10 (m) ω∙C U

(EQUATION 30)

capacitance per unit length [μF/km] -1 angular frequency of voltage [s ] rms phase-phase voltage [kV]

It can be concluded that the critical length “LC” is determined by the system voltage and frequency and by cable rating which is determined by the conductor size, environmental and installation conditions and cable capacitance.

7.1.6.2 Power Transfer for Long Circuits The maximum transmitted power in an underground radial link is dependent on the frequency, length and voltage across the insulation. However a large conductor can transfer higher loads than a smaller conductor can. Therefore the charging current becomes of less importance when the conductor area becomes larger, if the generated power is unchanged. With reference to Figure 38,

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the power transfer of a long cable system (assuming purely resistive loads and no compensation) can be found:

S =P +Q → P =

S − (ωCLU ∙ 10 )

(EQUATION 31)

As an example, we can apply the above equations for calculating the critical length of several underground lines with rated voltage of 20 kV and 400 kV, and different cross-sections of the cable (refer to table 9).

TABLE 9: CRITICAL LENGTH FOR 20KV AND 400KV CABLE SYSTEM

For lower voltages the critical length is longer when the conductor area is larger (due to Iz, higher ratings). At higher voltages as the conductor area increases the capacitance increases and counters the increase of critical length due to higher current ratings seen at lower voltages.

In Figure 39, the active power (at cos φ = 1) at the load point (PL) versus the length of the line is presented:

FIGURE 39: EFFECT OF LENGTH ON POWER TRANSMITTED BY A CABLE SYSTEM

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For actual systems as discussed above it is mandatory to do a system planning study which determines the actual current taking into account required load currents, charging current in the cable, and other reactive currents in the wider power system. It should be noted that the charging current will vary along the length of the cable route. The thermal bottleneck of the cable system may not be at the end of the circuit and the required current carrying capacity (taking into account both load and charging current) should be verified at the position that the thermal bottleneck occurs.

As DC cable systems have no charging currents the length of a DC cable system does not have the same considerations and this is an advantage of such systems.

7.1.7

Joints

It is possible under certain circumstances that joints can be the limiting factor for a cable system’s ampacity. The issue is dealt with on a case by case basis, and different methods have been applied for this purpose. The number of publications within the subject of ampacity calculations concerning cable joints is small and, therefore, many aspects seem not to be fully explored at present. Almost all of the publications are concerned with high voltage cables (above 100 kV) and most are concerned with directly buried cable systems or cable systems in air.

7.1.7.1 Single Isolated Joints Even though the number of research projects concerned with temperatures in cable joints is small, some researchers have investigated the thermal performance of single isolated cables with joints. It is acknowledged by most studies that the normal IEC standardised method cannot be applied to cable joints, as the standard does not consider longitudinal heat flow. Therefore, the thermal performance of a cable joint must be investigated in 3D (unless 2D rotational symmetry may be assumed) such as for example in Lyall (2004), Anders (2007), Moutassam (2007) and Liang (2008). It is confirmed in these studies that the conductor temperature in the cable joint is higher than in the rest of the cable, and, thus, the cable rating (if limited by the conductor temperature) may need to be evaluated on the basis of the temperature which will be reached in the joint. It should be noted that this joint operating temperature may not be the same as the maximum operating temperature for the cable itself and confirmation should be sought from the manufacturer. The studies utilise the thermoelectric equivalents (TEE, also denoted lumped parameters models) and finite element method (FEM) for the calculation of the dynamic thermal response of cable joints and the results are generally confirmed via laboratory experiments. The methods for the calculations are publically available and derating factors could possibly be developed for specific components by manufacturers who know the design of their components better than anyone else. It should be noted that the studies find that the thermal time constant is higher for the joint part of the cable than the rest, and thus temporary high loads may not be as severe for the joint as for the rest of the cable. The joints of 3-core cables are particularly difficult to handle. Anders and Coates in EPRI Bronze Book (2011) give the following thoughts to the analysis of cable joints.

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Ampacities for resin- or compound-filled three-core cable joints can be calculated using the calculation methods used for cables. However, unfilled heat/cold-shrink joints contain significant air voids. These voids restrict the heat flow from the conductors in the joint and are likely to cause the joint to run warmer than the cable. Analytical calculation methods for determining the thermal resistance across a complex heat path including air voids are not generally available. If there is a requirement to calculate temperatures in an unfilled three-core cable joint, it is recommended that finite element methods are used. Because the air voids in such joints are restricted, heat transfer by convection in the voids can be ignored, and only conduction across the air void is considered. The thermal resistivity of still air can be taken as approximately 40 Km/W. The increased insulation thickness in a joint leads to a higher internal thermal resistance than for a cable. However, the larger overall diameter leads to a reduction in the external thermal resistance. The balance between these two factors varies with cable and joint design as well as with cable size and installation conditions. For direct buried cables, the calculated ampacity for a joint may be 3% 2 2 lower than that for a 350 kcmil (~170 mm ) cable but 1.5% higher for a 1000 kcmil (~500 mm ) cable. When cables are installed in ducts, the joints are normally positioned at manholes. Heat transfer by convection is greater in a manhole than in a duct, and thus the ampacity in the manhole is higher than in a duct. Simple ampacity calculations for joints based on the methods used for cables do not take into account any longitudinal heat transfer. If the joint runs hotter than the cable, longitudinal heat transfer reduces the temperature in the joint. The calculation methods given by Whitehead and Hutchins (1938) or Brakelmann and Anders (2001) can be used. The temperature profile along a joint that is 1 m long is given in Figure 40 for a 350 kcmil and a 1000 kcmil cable. For this figure, it has been assumed that the ampacity of the joint, without considering longitudinal heat conduction, is 5% less than that of the cable and the cable is operating at full load. The temperature expected within the joints without longitudinal heat conduction is approximately 98 °C.

96 350 kcmil

Temperature, °C

95 1000 kcmil

94 93 92 91

Inside joint

outside joint

90 89 0

0.5

1

1.5

Distance from centerline of joint, m

FIGURE 40: TEMPERATURE PROFILE IN A JOINT (EPRI, 2011)

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These curves demonstrate that longitudinal heat conduction can reduce the temperature of a potential hot spot by 3 to 4 K. Additionally, special precautions can be taken to avoid overheating cable joints. These precautions could include:   

Use of materials with low thermal resistivity Increased spacing of joints compared to the relevant cable Improved thermal environment around the joints compared to the cables (manholes, forced cooling, etc.).

As mentioned above, due to their longer thermal time constants, joints present a higher short-term emergency overload capacity than the corresponding cable, as shown in Figure 41.

FIGURE 41: TEMPERATURE INCREASE IN A CABLE CONDUCTOR AND IN A JOINT DUE TO A STEP CURRENT CHANGE (EPRI 2011)

However, depending on the duration of the loading cycles, joints may present a gradual increase of conductor temperature in subsequent cycles (an example of a type test in air is shown in Figure 42).

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FIGURE 42: ‘EXAMPLE OF THE TEMPERATURE VARIATION IN A CONDUCTOR AND A JOINT FOR A CYCLIC LOADING (EPRI, 2011)

Lyall (2004) shows that the jacket temperature of the joint, due to the larger geometry, can be significantly lower than the jacket of the rest of the cable. This reference contends that the steady state rating is not limited by the joint. However, there are cases where the joint may prove to be the steady state rating limit, particularly where cooled installations and ventilated tunnels are concerned. It has not been possible to find general guidelines for calculating de-rating factors for single isolated cable joints, and a case by case approach must therefore be applied.

7.1.7.2 Multiple Joints One study, Pilgrim (2009), has been concerned with modelling three single phase cables with joints, and, therefore, this is the only study which has been found to deal with the mutual thermal influence of multiple cable joints in close proximity. The thermal performance of three single phase directly buried cables in flat formation in a joint bay was investigated by modelling the system with an extensive 3D FEM. It is found that, by allowing the axial spacing between cables to increase sufficiently at the joints, the cable joints will not be the thermally limiting part of the transmission line. Staggered joint bays were shown to allow for smaller axial spacing between the cables in the joint bay than when arranging the joints in parallel. It should be noted that all knowledge within this area relies on this single study, and thus verification of the problem may be necessary. Furthermore, Pilgrim (2009) does not include experimental validation, which may be necessary for further validation and implementation of the technique. Several of the studies are also concerned with including forced cooling of the joints in the models. It is generally shown that the ampacity can be increased by cooling, however Pilgrim (2009) finds that the ampacity of the normal part of the cable increases more than the joint part, and thus the

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conductor temperature of the joint may become the limiting parameter for cables forced cooled with parallel water pipes. With this background, it must be concluded that no generally available de-rating factors are available for jointed cables, and calculations must therefore be performed on a case by case basis.

7.1.8

Terminations

Although the construction of cable terminations is similar to that of cable joints, the manner in which they are installed usually prevents the use of the calculation methods used for cables being used for the thermal analysis of the terminations. Further discussion of this may be found in Electra 128 (CIGRE, 1990). Terminations are likely to be installed vertically in air, in air-filled boxes or in compound-filled boxes. A further factor that complicates the calculation of temperatures in terminations is heat transfer to, or from, connected equipment. This factor is likely to have a greater effect on the operating temperature of a termination than its design. When cables that are expected to operate at close to their maximum temperature are connected to equipment, a check should be made to ensure that any heat transferred into the equipment from the cable does not cause undue degradation of the equipment. Conversely, if cables are connected to equipment expected to operate at high temperatures, measures should be taken to ensure that heat transferred from the terminations of the equipment does not cause undue degradation of the cable insulation.

7.1.9

Metalwork

Metalwork (including baseplates of outdoor sealing ends) need to be considered and often the rule is, if a magnetic material is used, that there is a break in the material to stop a loop being formed around the conductor. Even if there is no loop, for buried installations there may be a reduction in current rating because eddy currents in the steel work might cause additional temperature rise in the cable system. In some cases there is a requirement to minimise the magnetic field of installations and this can reduce the current rating, see cigre (2013). The number of companies that reported they made calculations of the heat generated by induced currents in nearby steel plates, concrete reinforcing wires or parallel earth wires was 24, while the majority of 76 companies reported they did not (see Appendix B for details, question 5.3). The main method reported was FEM but a number of companies appeared to report methods that were not consistent with the question.

7.1.10 Short Lengths different to rest of Installation (longitudinal heat flow) In some installations, short sections of cable will be installed in a different arrangement than the rest of the route, and these short sections may limit the current rating of the entire circuit. Normally current rating calculations are made in 2 dimensions but for short sections heat may flow longitudinally along the cable circuits and an improved current rating may be obtained by considering this additional heat flow. An example is cable circuits crossing other cable circuits (see Section 7.2.1.3), where relatively easy to use methods of calculation have been developed.

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Pilgrim et al. (2009) shows an alternative approach in the evaluation of temperature distribution in a cable joint bay using the finite element modelling (FEM) during steady state load conditions. The method (FEM) however does not seem to be limited to the joint bay application, and all of the calculations shown in Anders (2005) should thus be reproducible by FEM. Furthermore FEM may create an easier overview when compared to Anders (2005) in the case of complex cable installations, see e.g. Chaaban and Leduc (2011). However the method of Anders (2005) is a simpler approach and obviously requires less computational effort while maintaining a high reliability. For nonstandard installation arrangements other than cable crossings, there is unlikely to be a simple current rating method and most of the time it is anticipated that FEM methods will have to be used. Pilgrim et al. (2014) shows with FEM how variable burial depth and ground topography (greater earth surface area than flat ground) allows an increase of around 4% rating when longitudinal heat flow along the cable and the ground is considered.

7.1.11 Parallel Metallic Paths (e.g. earth continuity conductor ) In some cases, parallel metallic conductors are installed close to cable systems. Typically this is the earth continuity conductor (ecc) for single point bonded systems (see ENA C55/4 1989) or screening cables intended to reduce induced voltages in other parallel cable circuits such as pilot cables. Earth continuity conductors are normally installed with transpositions at the mid-point of the cable sections to minimise any circulating current and in these situations the earth continuity conductor can be ignored for current rating calculations. In some cases, particularly duct blocks, it is not possible to install the earth continuity conductor with such transpositions and then it may be necessary to include the earth continuity conductor as part of the current rating assessment. This topic is very sparsely described in the literature. There are a number of published studies concerned with induced currents in e.g. pipelines, adjacent cable systems, etc. In one way or the other these studies are application of the basic electromagnetic equations, which for power lines most commonly are solved by the “Telegrapher’s equation”, “Lossy transmission line model” or “Finite element method” (or similar numerical methods), see Taflove and Dabkowski(1979-1), Taflove and Dabkowski (1979-2), Djogo and Salam (1997), Ferkal and Black (1996), Du and Wang (2010), Kovač et al. (2006) and Novák and Koller (2011). It is suggested that the reduction in ampacity is divided into two parts. Firstly, the currents in the parallel metallic path are determined and secondly these currents are converted into joule losses and the influence on the ampacity of the cable is evaluated. Methods of calculation as described in CIGRE TB 283 can be used to calculate the circulating current. Having determined the currents induced in the parallel metallic path, the losses should be fairly easy to estimate (based on the geometry and knowledge of the materials). When the losses are known, IEC60287-2-1 gives suggestion on how to calculate the derating of the power cable (clause 2.2.3.1) in the static case, and IEC60853-2 (see Anders (2005) for in depth description) in the dynamic case. The standard suggests that the ampacity of the power cable is determined by decreasing the allowed temperature rise which is caused by the induced losses in the parallel metallic path (the principle of superposition, for in depth description see Anders (1997). Alternatively, the dynamic thermal response can be evaluated by the finite element method.

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7.2

Buried installations (not tunnels)

This Chapter highlights all aspects of cable current rating calculations related to direct buried cables, cables installed in ducts, installed in surface troughs and horizontal directional drillings.

7.2.1

Common Aspects and Direct Buried installations

Installing cables in a trench, embedded in a sand or special backfill layer with good thermal properties around the cables, and normal soil on top is in many countries one of the most common installation methods. For AC systems, cables are installed in (close) trefoil formation, (touching) flat formation, with one or multiple circuits with mutual influences. This configuration differs from place to place, depending on the available space and influence of the environment area (thermal, vibrations, space and other conditions). Horizontal directional drilling is often used when it is impossible or inconvenient to carry out digging work, for example when crossing roads, rivers or vegetation. Horizontal directional drilling is carried out by drilling a hole from the surface or from a pit to the destination required. One pipe or a bundle of pipes is then pulled through the hole, making it possible to pull cables through the pipes at a later stage. Ducts are used to provide mechanical protection to cables, for instance at crossing roads or railways. Ducts are also in use for minimization of public nuisance by installing small duct sections and pulling in cables at a later stage. Duct laying configurations are similar to that of direct buried cables. For buried cables, the thermal resistance is formed mainly by the surrounding soil. The thermal resistivity of the soil not only depends on its composition (which can vary considerably along the cable run) but also on the current condition of the soil which, in turn, is influenced by the operation of the cable and the atmospheric conditions. The most important factor here is the moisture content of the soil; the dryer the soil, the higher its thermal resistance, refer to section 3.3. This section reviews two aspects dealing with the ampacity calculations for cables installed in multiple parallel circuits namely: the thermal impact, i.e., heat generated by other circuits and the induced currents.

7.2.1.1 Multiple Parallel Circuits: Thermal Impact Ampacity calculations of a single circuit or a group of cables are described in the IEC standard 60287-2-1. The treatment of a group of cables is described in the section dealing with calculations of the external thermal resistance of a cable of interest. The proposed approach is an application of the principle of superposition, assuming that each cable acts as a line source and does not distort the heat field due to the other cables. The effect of neutral and earth conductors can be calculated by including them in the appropriate loops. The method set out in the standard does not take account of any portion of the sheath circulating currents that may flow through the earth or other extraneous paths. The conductor currents and sheath circulating currents in parallel single-core cables are unlikely to be equal. Because of this, the external thermal resistance for buried parallel cables should be calculated using the method set out in section 3.1 of IEC 60287-2-1. Because the external thermal resistance and sheath temperatures are functions of the power dissipation from each cable in the group, it is

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necessary to adopt an iterative procedure to determine the circulating current losses and the external thermal resistance (see also Section 6.4.2 ). The method itself is based on the superposition principle, and is not applicable for those situations where the cable circuits are touching. The IEC 60287 series contains two standards providing tables and equations related to additional losses: IEC 60287-1-2 provides a method for calculating the eddy current losses in the metallic sheaths of single-core cables arranged as a three phase double circuit in flat formation. The method provides coefficients which are applied as corrections to the loss factors for the sheaths of one isolated three phase circuit. In practice this method should be used for most sizes of aluminium-sheathed cables and unusually large lead-sheathed cables. IEC 60287-1-3 provides a method for calculating the phase currents and circulating current losses in single core cables arranged in parallel, i.e., multiple cables per phase. The method can be used for any number of cables per phase in parallel in any physical layout. No literature was found on multiple parallel circuit thermal aspects. It is believed that the IEC 60287 provides sufficient guidelines to calculate the mutual influences between parallel installed circuits from a thermal and mutual losses point of view.

7.2.1.2 Unequally Loaded Circuits Ampacity calculations of a single circuit or a group of identical cables are described in the IEC 60287-2-1. The treatment of a group of cables is described in the section dealing with calculations of the external thermal resistance of a cable of interest. The proposed approach is an application of the principle of superposition, assuming that each cable acts as a line source and does not distort the thermal field due to the other cables. Two situations are dealt within the standard. The first, and most general type, is a group of unequally loaded cables of different construction, and for this problem the standard gives a general indication of the method only. The second type, which is a more particular one, is a group of equally loaded identical cables and, for this problem, a fairly simple solution can be derived, see Anders (1997). This section first reviews the IEC 60287 approach and then discusses a possible method for calculating the total ampacity of a group of unequally loaded buried cables. A general case of unequally loaded cables is considered.

Standard approach for ampacity of unequally loaded cables A typical power cable consists of a conductor, insulation, metallic sheath or screen, possible armour bedding, armour, and external serving layers. The main sources of heat generated by a cable are the Joule losses in the conductor, sheath/screen, armour, and pipe. In addition, some cables may produce substantial dielectric losses. This heat is dissipated through the various cable layers and the soil. The thermal resistances of the cable layers and its surroundings influence the rate at which the heat is dissipated, and hence the rise of the conductor temperature above the ambient temperature. This thermal interaction can be represented for the steady-state conditions by a lump-parameter thermal circuit that incorporates the thermal resistances of the cable layers and the soil, the Joule and dielectric losses, and the ambient and conductor temperatures. The thermal circuit is then solved to obtain the maximum conductor current, given the allowable insulation temperature. The

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solution for the current, I [A], is formulated hereunder, with a comprehensive derivation given in Anders (1997):

 A   int  I   B  

Where: A, B = Δθint =

0.5

(EQUATION 32)

constants dependent on the cable construction and laying conditions conductor temperature reduction due to heating from the neighbouring cables

Calculating Δθint for the ampacity equation of the cable of interest ‘i’ is obtained by summing up the thermal influences of all neighbouring cables, as given by equation 33. The thermal influence by each cable ‘j’ on cable ‘i’, Δθij, is calculated using equarion 34 by multiplying the heat produced by the cable ‘j’, Wj, and the mutual thermal resistance Tij between cables ‘j’ and ‘i’. Wj is the sum of the Joule and dielectric losses of cable ‘j’. Tij depends on the distance between the two cables and their depth below the earth’s surface.

 int 

n

 

ij

j 1 j i

ij  Wj Tij

(EQUATION 33)

(EQUATION 34)

Calculation of the mutual thermal resistance becomes somewhat more involved when the cables are located in a duct bank, backfill or a large casing. It is evident from equations 32 to 34 that in order to calculate the ampacity of a cable ‘i’, the currents of all the other cables must be known. However, these currents are not known a priori because the objective is to compute the ampacities of all the cables in the system. The application of equation 34 to every cable will result in a system of interrelated equations. In practice, these equations are solved iteratively. However, in many cases, the iterative method is not always convergent and does not guarantee the optimal cable loading. A recently postulated alternative is to express these equations as an optimization problem and then solve it to obtain the ampacities (Anders (2007)). This method is always convergent, and is summarized next.

Ampacities of unequally loaded cables as an optimization problem Because the ampacity of a cable is the largest current that it can carry while not causing its conductor temperature to rise above a specified maximum, the total ampacity of a group of cables is the largest sum of the currents that do not cause any of the cables to overheat. Using equation 34 for every cable, the resulting system of interrelated equations can be expressed, through algebraic manipulations, as an optimization problem with an objective function of maximizing the sum of all cable currents or the sum of the transmitted real powers Pk with the constraints of having every cable conductor temperature θck below a specified maximum θk max . The resulting formulation for

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optimization of the transmitted power, with a complete mathematical derivation is detailed in Moutassem (2007).

Maximize

P

k

k

subject to

(EQUATION 35)

 ck   k max for all k

An additional constraint should be added requiring that the currents of all three phases in a circuit be equal when a balanced system is specified. When some cables carry a specified current, these are excluded from the objective function in equation 35 but added as the equality constraints. This problem belongs to the class of continuous convex optimization problems. Such type of problems can be solved effectively using the barrier method algorithm or a similar interior point approach, see Boyd and Vandenberghe (2004).

7.2.1.3 Circuit Crossings This section reviews the ampacity calculations for cables crossing cables, direct buried or ducted, installed in soil with uniformly thermal resistivity or with multiple thermal resistivities. IEC Standard 60287-3-3 provides a method for calculating the continuous current rating factor for cables of all voltages where crossings of external heat sources are involved. The method is applicable to any type of cable. The method assumes that the entire region surrounding a cable, or cables, has uniform thermal characteristics and that the principle of superposition applies. The principle of superposition does not strictly apply to touching cables and hence the calculation method set out in this standard will produce an optimistic result if applied to touching cables. Furthermore, IEC60287-3-3 does not specify if the calculation method is applicable for cable installed in ducts or when the crossing circuits are installed in soil with multiple layers with differing thermal resistivity. Dynamic aspects are also not considered. IEC60287 does not provide an answer when:     

Crossing cables are touching Crossing cables are installed in ducts Crossing cables are installed in non-uniform soil with differing thermal resistivity Dynamic ratings of crossing cables are considered Soil dry out caused by moisture migration is considered.

Crossing cables are touching For crossing touching cables, the superposition principle is no longer valid and, since the mutual heating has to be considered in 3D, FEM should be used to determine the current ratings of the circuits.

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Crossing cables installed in ducts. If the ducts are filled with a solid mass, like bentonite, the same calculation principle can be applied as in IEC60287-3-3. However, the thermal resistance of the solid mass filling and the thermal resistance of the duct shall be added to the thermal resistance of the cable covering T3, multiplied by the number of conductors in one cable, and not to the external thermal resistance T4. In unfilled ducts, an air space is present between the cable surface and the duct internal surface. As known from IEC60287-2-1, the thermal resistance of this air space is, among other factors, depending on the average temperature in this air space. Because of the crossing, a temperature gradient is present in axial direction, causing an axial air flow in the air space due to convection. It can be assumed that because of this air flow, the temperature of the air space will be lower, resulting in a higher thermal resistance at that hot spot. The exact influence can be calculated numerically, but as a rule of thumb it is suggested to calculate the thermal resistance of the air space as if there is no crossing, to be on the safe side. Further calculation can be done in the same way as suggested for the filled ducts.

Crossing cables installed in soil with multiple thermal resistivities. Please refer to clause 7.2.1.5 of this report for obtaining an average soil thermal resistivity when multiple thermal resistivities are involved. It should be noted that the assumption of an average soil thermal resistivity may introduce error into the calculation, particularly where a wide range of thermal resistivity values is encountered.

Dynamic ratings of crossing cables The determination of de-ratings of crossing cable circuits with transient and cyclic loadings are described in Anders (2005). The described method determines the temperature rise caused by cyclic variation of losses in the external heat source at an arbitrary time τ assuming that the heat dissipated in the external cable is directly proportional to the square of the applied current.

Soil dry out caused by moisture migration The determination of de-ratings of crossing cable circuits with partially soil dry out because of moisture migration is described in clause 3.7 of Anders (2005).

Multiple crossing angles are considered. The method in IEC60287-3-3 is applicable for one or multiple cable(s) or heat sources for one crossing angle. If more than one crossing angle is observed, IEC60287-3-3 is still applicable: the deratings of the cables of belonging to the same crossing angle should be determined, thereafter the de-ratings of the cables belonging to the second crossing angle etc. This is an iterative process.

Consideration of screen longitudinal heat flow Metallic components in the cable, other than the conductor, will generate additional losses. Clause 3.5 of Anders (2005) indicates how the longitudinal heat flow in these components can be taken into account.

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7.2.1.4 Soil dry-out The thermal resistivity of the soil in which a cable is buried has a large effect on the rating of the cable. One important factor is the formation of dry zones around the underground power cables due to the migration of moisture along the temperature gradient. This migration of moisture occurs when the cable surface temperature is raised above a certain temperature limit, defined in IEC 60287 by the critical temperature rise. IEC 60287-1-1 Clause 1.4.2 gives a general steady state rating equation based on the two zone model taking into account the critical temperature and the thermal resistivity of the wet and dried-out soils. Clause 1.4.3 of the same standard gives a formula based on the limitation of the cable external temperature to the critical temperature. IEC 60853-3 provides formulae for transient ratings. Both IEC methods are limited to a single circuit only. Heinhold (1990) provides a calculation method for taking into account the backfill layer around the power cables and to determine the possibility of native soil drying out at the boundaries of the back fill layer. This method allows for multiple circuits. There have been a lot of discussions, conferences and papers about the topic of soil dry-out. The generally accepted physical description of the very complex system of heat and moisture transfer processes is the Philip/de Vries-model (PdV model), which describes the transport of water, water vapour and heat as functions of the gradients of temperature, moisture content and of gravity, depending on some external parameters as e.g. the distance to the groundwater level. The arising nonlinear partial differential equations are governed by a set of diffusion coefficients, which change their magnitudes over some decades in dependence on temperature and moisture content. Better information on these problems can be found in the KEMA/Heijdemij (1981) report and the works of Cigré Working Group B1-41. There are groups not accepting the two-layer-model for partial soil dry-out. Their argument is, that the time-dependent transport mechanisms in soil are not governed by temperatures, but by the gradients and thus by the direction of the heat flow density. Indeed, some tests for classification of soils with respect to “thermal instability” are defined in the USA to measure a “time to drying-out” of a soil as a function of the heat flow. The two-layer-model is widely adopted because of its simplicity and manageability. It could be shown, refer to Brakelmann (1984) by means of the Philip/de Vries-model, that the situation described by the two-zone-model with a critical isotherm may actually happen in nature, if somewhat advantageous soil parameters and conditions (e.g. remote groundwater level, low initial moisture content) are given. Extensive simulations by means of FEM and based on the PdV-model (Pilgrim et al. 2011) have shown the same results and conclusions. The two-zone-model drying-out is considered as the result of instability, but which can be contained by reducing temperatures and power flux densities at the border of the arising dry zone, and consequently avoiding a “thermal runaway”. So it is important that the assumed thermal properties of the dry zone and the surrounding wet zone (dry thermal resistance, wet thermal resistance and critical temperature rise) are selected on the safe side. The crucial advantage of the two-layer-model is that it allows current rating calculations in a quite simple way, even for complicated structures in the trench as groups of different cables with different load cycles, heat sources, crossings et cetera, refer to Brakelmann (1984). Please refer also to section 3.3 for additional information on this subject.

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7.2.1.5 Multiple thermal resistivity values (e.g. backfill) The earth portion of the thermal circuit accounts for more than 50% of the total cable system thermal resistance. A cable design must be based on accurate soil thermal parameters. Native soils may not always have the most preferable thermal properties, or may contain sharp materials that might damage the cable outer sheath. In such cases, selected sand or backfill may be applied around the power cables. Usually this backfill material does not have the same thermal properties as the native soil and this will have an impact on the cable rating. IEC 60287-2-1 provides a method (in Clause 2.2.7.3) based on the works of Neher and MacGrath (1957) with consideration of a cylinder equivalent to the actual backfill. The formula used for calculating the equivalent cylinder is of limited application range (ratio of dimension has to be lower than 1/3). El-Kady and Horrocks (1985) have extended the range of application of the “geometrical factor”. An interesting formulation is proposed by Slaninka and Morgan (1992): a method is described for calculating the external thermal resistance of a power cable buried in a backfilled trench or in thermally non-uniform soil of defined shape. The analysis is based on the multiple reflections of a line source of heat and its images. Cable configurations examined are: within or beneath a horizontal top layer of soil; close to the vertical boundary between dissimilar media; near or within a vertical layer sandwiched between two media; and within a backfilled trench Other alternatives are the use of conformal transformation as presented in CIGRE (1985). In some cases, it may be simpler to deploy finite element analysis, particularly where transients or multiple circuits are concerned. With the same approach other configurations could be studied, see for example Pilgrim et al. (2014) where FEM results allowed and increase of around 2% rating for cables installed in a non-uniform thermal resistance ground.

7.2.1.6 Water cooled cable systems Water cooled cable systems are not addressed in the IEC standards; however a number of installations exist. They offer an alternative to multiple cables per phase where the required rating cannot be achieved, even with the largest conductor sizes. The typical forced cooling methods are as follows: 

External cooling, where pipes of synthetic material containing circulating water are laid in close proximity to directly buried cables. This is most commonly rated using CIGRE (1979).



Surface cooling, where the coolant flows in direct contact with the cable external surface, which can be rated using CIGRE (1979).



Conductor cooling, where coolant flows along the central duct of the cable conductor. Usually the cooling fluid circulates in a closed circuit and is refrigerated at convenient sites along the cable route. As a general rule, the conductor operating temperatures are the same as for naturally cooled cables of the same type. Rating methods are presented in Anders (2005).

Those intending to use CIGRE (1979) should also note the erratum to the paper. Where transients and cyclic loads are to be considered, calculation methods were discussed in CIGRE (1986). The efficiency of forced cooling is higher for systems with reduced separation between cables and coolant, the best conditions occurring in the case of conductor cooled cable systems. In comparison

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with natural cooled cables, the orders of magnitude increases in transmissible power for the most typical forced-cooling methods are as follows (CIGRE 1979): 

40 / 50% for externally water cooled cables having cooling sections several km long.



40 / 50% for surface oil cooled cables with single core cables inside a common steel pipe, having cooling sections several km long.



100% for surface water cooled cables with 1 single core cable per (non magnetic) pipe having cooling sections several km long.

For both surface and conductor cooling, significant increase of the transmissible power may be achieved by returning the coolant along a suitable separate pipe. Special cooling methods exist for fluid-filled pipe type cables. They include oil circulation between two circuits or between a cable pipe and a return pipe to smooth out thermal hot spots as well as forced cooled installations when the oil is circulated through oil-to-air heat exchangers (chillers) or refrigeration cooling plants permitting upwards of 50% increases in ratings, see EPRI (1984). Other examples for such systems can be found in Koreman et al. (2006) and Vavra and Wanda (2006).

7.2.1.7 Non-cable Objects This section discusses the influence and consequence of non-cable objects in the vicinity of cable circuits and the impact these objects might have on the cable ampacity. The following non-cable objects are identified:  

thermal sources, like steam or hot-air pipes, or magnetic material thermal sinks, like high water table or water course, or water cooling pipes, sewages.

The IEC Standard 60287 does not specifically address these non-cable objects, which have an influence on the system rating due to high temperatures (steam pipe, hot air pipe) or low temperature (sewage, water pipe).

Steam pipe/ hot air pipe A method for calculating the influence of steam or hot air pipes on power cables is given in Clause 3.4.2 of Anders book (2005) and is described below: The heat generated by the steam pipe or the hot air pipe can be calculated with the following equation:

W =

[W/m]

(EQUATION 36)

Where: θR = temperature at the surface of the steam / hot air pipe [K] θW = temperature of the steam / hot air [K] TR = thermal resistance of the insulation around the steam / hot air pipe [K∙m/W] The steam / hot air pipe can be now represented as a single core cable where the outer diameter of the pipe (including the thermal insulation) is equivalent to the outer diameter of the single core cable.

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Ferromagnetic material The use of ferromagnetic material for EMF shielding of structures such as pipes and casings is increasing, Maioli (2007). The effect this ferromagnetic material has on the system current rating is complex and is normally calculated with dedicated software. An outline of the issues is presented in CIGRE (2013-1), which is a good first point of reference. For detailed calculations, finite element approaches may be required.

Thermal Sink (high water table, water course, water cooling pipes, sewages) As mentioned before, the current-carrying capacity of buried cables depends to a large extent on the thermal conductivity of the surrounding medium. The soil thermal conductivity is highly dependent on its moisture content Mochlinski (1976). The current rating of cable system installed nearby water courses or in soil with a high water table will be maximized due to the optimized thermal conductivity. Furthermore, the risk of moisture migration away from the cable will be limited, minimising the risk of thermal runaway. When including the beneficial impacts of such thermal sinks, it is important to consider whether the thermal sink will be continuously active throughout the life of the cable to avoid the risk of over-rating the circuit. For dedicated water cooling circuits, please refer to Section 7.2.1.6.

7.2.1.8 Method of Determining Ambient Temperature IEC 60287-3-1 contains an overview of common ambient temperatures for buried cables, subdivided into country and/or regions and seasonal influence. It should be noted that these values are applicable for ‘standard’ buried cables, limited to a minimum and a maximum buried depth. IEC 60287-3-1 gives no guidelines for regions not mentioned, for cable installed at shallow (3 m). In those cases where the air temperature is known, an estimation of the ambient temperature can be calculated with the annual average air temperature as input variable (Williams and Gold, 1976):

T(t, X) = T Where: Taverage D x a to t

= = = = = =

+D∙e

∙

∙

2πt π ∙ cos( −x∙ t a∙t

)

(EQUATION 37)

average annual air temperature [K] difference between maximum and minimum air temperature [K] depth below the earth surface [m] 2 thermal diffusivity [m /s] length of period [s] time since maximum air temperature occurred [s]

Note: when a measurement or accurate estimate of the thermal diffusivity is not available, the thermal diffusivity can be estimated according to Appendix D of IEC 60853.

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It should be noted that the soil nearby the earth surface is less homogenous and this may affect the soil temperature. It is also reported that the ambient temperature under roads (asphalt, paving stones) is higher than under bare land due to the solar radiation absorption by the covering layer on earth. The exact correlation between solar radiation and ambient temperature cannot be given, as rule of thumb, a 5 °C increase of the ambient temperature can be considered in these cases.

7.2.1.9 Very Deep Installations Burying cables at large depths is becoming more common these days as: 

Cables are installed in directional drillings up to 40 m laying depth for crossing rivers, rail tracks, motorways or suburban areas with minimal nuisance for public.



Cables cannot be installed at usual depths in urban areas as these are already congested with other infrastructure.

The questionnaire indicated that the number of companies reporting to use IEC calculations for this situation was 60, while 36 other companies reported to use non-IEC calculations. The majority of companies that used methods other than IEC did not specify the method used. Of those that did, FEM was the main method identified. Additionally, a number of companies identified changes from their normal current rating practice. These were using transient ratings, lowering the ambient temperature and reducing the soil thermal resistance. Cigre can give the guidelines below in the situation of deep buried cables. The current rating of deep installed cables is influenced by daily, weekly and even yearly load variations, these effect are not so profound for cables installed at usual depths. These effects are not considered by the IEC standards. Therefore, the standard IEC60287 approach might lead to pessimistic results and another approach for determining the current ratings calculations is needed. The IEC standard 60287-2-1 contains a statement about very deep installed cables: ‘For cable circuits installed at laying depths of more than 10 m, an alternative approach for calculating the current rating is to determine the continuous current rating for a designated time period (usually 40 years) by applying the formulae given in IEC 60853-2, taking into account as far as is practical seasonal variations in load and ground conditions, if any. Finite element modelling may provide a more versatile model for such a lifetime assessment. This subject is under consideration’. Various papers have been published on ratings of very deep installed cable. A good summary and guidelines can be found in Dorison et al. (2010). This paper provides equations and guidelines for deeply installed cables, taking into account daily, weekly and yearly cycles. Furthermore, the paper introduced the concept of ‘equivalent laying depth’, which makes it possible to use the continuous current rating calculations and avoid the more complex transient approach. For deeply installed directional drillings, the cable circuit crosses various soil layer which might have different thermal properties. For this situation: the guidelines in this report towards ‘multiple thermal layers’ shall be followed (clause 7.2.1.5).

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7.2.1.10

Variable Inter-axial Spacing

For single core cable circuits with sheaths solidly bonded at both ends and possibly at intermediate points, the circulating currents and the consequent loss increase as the spacing increases; therefore, it is advisable to use as close a spacing as possible. The optimum spacing is achieved by considering both losses and mutual heating between cables. It is not always possible to install cables with one value of spacing all along a route. IEC provides equations and guidelines how to cope with this situation, see IEC60287-1-1 clause 2.3.4. Loss increase as a consequence of variable inter-axial spacing does not apply to installations with single-point or cross bonding.

7.2.2

Duct installations including directional drillings

Cables are nowadays commonly installed in ducts. Ducts are often used in situations where power cables cross other infrastructures as roads, highways, rivers. Increasingly, ducts are also used to bridge areas where the underground is particularly crowded (full of other utility infrastructures), typically in urbanized or industrialized areas. Ducts often used for cable installation are made of PE or PVC in the case of horizontal directional drillings. For large dimensions, steel pipes are often used, typically for road crossings. Concrete ducts also exist, but are less common. Ducts are either filled or unfilled, though this classification may not be optimal. An unfilled duct is filled with air, while a filled duct may be filled with water or bentonite-like mixtures. There are various possibilities to accommodate cables inside ducts, for some examples, see Figure 43 and Figure 44.

FIGURE 43: TYPICAL CABLE INSTALLATIONS IN DUCTS

If ducts in ducts are used, typically the outer duct is filled with bentonite. There may be more, typically similar duct structures next or on top of each other (see Figure 44).

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Air / water Soil

15 m 5m

5m

FIGURE 44: TYPICAL CONFIGURATION OF MULTI DUCT ARRANGEMENTS

It is important to consider the mutual heating if multiple cables are installed in a single duct / drilling. When power cables are buried at normal depths of 1 to 1.5 meters in soils with normal thermal resistivities, a cable circuit spaced horizontally with a distance in the order of meters will have virtually no thermal influence anymore. However, if a circuit is installed at larger depths, this thermal influence is not negligible anymore and must be taken into account. Calculation of the effect of multiple cables can be performed by means of superposition as is also used in IEC 60287. In the case of inclined ducts, it is important to consider that the methods for determining T4. The IEC standards assume that a 1 m cable length equates to a 1 m length of ground surface for the heat to be dissipated from. This assumption is violated for inclined ducts, and the effect should be taken into account in the calculation of T4. For example: in case of a 45 degrees inclined duct, then 1 m of cable equates to 0.71 m of ground surface, and hence, T4 should be increased by a factor of 1.41.

7.2.2.1 Duct filling Material or Casing Grouting Material It is important to consider the duct filling material. The duct filling may be a solid or a solidifying substance as for example bentonite, or may be a fluid, such as air or water. In the former situation, a solid, heat transfer from the power cable is governed by conduction. This means that the heat transfer can be modelled with means as described in IEC 60287-2-1. If the duct is filled with a fluid, the situation is more difficult: 

Horizontal – air – closed at both sides Considering a horizontal cable system in a perfect horizontal duct filled with air, closed at both sides, the heat transfer will consist of contributions of purely radial conductive, convective and radiative heat transfer, of which the latter 2 are strongly temperature dependent.



Horizontal – water – closed at both sides A horizontal cable system in a perfect horizontal water filled duct, closed at both sides, can be considered in the same way, thought the properties of the fluid are of course significantly different.



Non horizontal In non-horizontal arrangements, the situation is significantly more complex because there will also be axial heat transfer next to the radial heat transfer which can have a significant effect. This means that the warmest locations are expected to be near the higher sides of the ducts.

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Air - open at one or both sides In situations where the duct is not closed, care has to be taken. If ducts are completely open and filled with air, there will be a heat exchange to the free air. However, a certain temperature difference is needed to overcome the flow resistance of the duct system to start this heat exchange process, meaning that this heat exchange will depend on a number of geometric parameters. Furthermore, if the ducts are open to free air, the ambient temperature of the free air, which is different from the ambient temperature of the soil around a buried power cable, must be considered. Vertical ducts of this type are discussed in Anders (1997).



Water – open at one or both sides If the duct is not fully closed, completely underground and there is water filling, the ducts can lose the water filling to their environment leaving an (unexpected) air gap. Also note height differences between the duct ends.

Example In this example, the temperature of a HV power cable in a water filled horizontal directional drilling at relatively low loading was monitored by means of DTS measurements. The drilling was made to a depth of 10-20 meters to cross a water way, and was a few hundred meters in length. At both ends of the drilling, hotspots were noted having a temperature of up to 10 degrees higher than in the direct vicinity outside the ducts. This effect may be originating from either the presence of air pockets at the termination points of the drilling, from a change in soil conditions, or from the fact that warmer water collects at the higher points in the drilling, or from a combination of both. The exact reasons are currently unknown and further measurements and analyses are needed to figure out the dominating effect. However, it becomes clear that in a case of water filled horizontal directional drillings, the current rating of the cable circuit may very well be limited at the termination points of the drilling, rather than at the deepest point.

Temperature in a horizontal drilling 35

5 5

30

4

4 3

20

3

15

2

22

Temperatuur [C]

Temperature [C]

4

25

3

2

2

10 1

1

1

1

5 1

0 9200

0

9300

0 0

9400

9500

9600

9700

Glass fibre length [m] FIGURE 45: TEMPERATURE IN A HORIZONTAL DRILLING

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00

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Heat transfer through the duct wall and beyond Typically ducts consist of a layer of solid PE or PVC material. This leads to a relatively simple calculation of the thermal resistance of the duct wall as described in IEC 60287. Some ducts consist of pipes with air enclosures inside the pipe wall. The thermal resistance of such a wall may be high if heat convection in the air enclosures is prevented. As a worst case approximation, stationary air with a specific thermal resistivity of 40 Km/W can be used when modelling the behaviour of such pipe walls. Outside a duct, often concrete or native soil is found which can be taken into account. Note that different soil layers with different thermal properties may be crossed in the case of horizontal directional drillings.

Guidelines for calculations of cable inside ducts filled with a fluid IEC guidelines exist for the situation of horizontal ducts. These calculations are based on a set of approximations detailed in Anders (1997). Not much literature exists describing accurate calculation techniques in the situation of inclined ducts as horizontal directional drillings. This remains to be an important gap for calculations as horizontal directional drillings are often filled with water or air. Only one paper (Defega, 2012) on the subject was identified which can provide a comparison between the different ways of representing air in a duct.

Guidelines which can be given in this situation are more general in nature: 

The heat transfer from cable to duct wall is governed by a combination of conduction, convection and radiation, which all have to be considered. The latter two processes are strongly temperature and geometry dependent. Inclination of ducts further complicates the calculations as the problem becomes three dimensional due to the axial heat transfer. Care is required in these situations.



Consider the possibility of air pockets in case of water filled ducts which may need to be avoided.



Note in this situation that the termination points may be the actually limiting situations to the current rating because of the above.



In case of air filled ducts which are open to free air, there may be some heat exchange to the free air, which can give both relief (release of heat) and pressure (additional ambient air temperature to take into account).

Guidelines for calculations of cable inside ducts filled with a solidifying medium Follow IEC 60287 guidance with larger depth and additional thermal resistance allocated for the filling medium and duct wall.

Cables in environments with non-homogeneous thermal properties The most common approach to handling non-homogeneous thermal properties is the use of the finite element technique or the conformal mapping technique in CIGRE (1985).

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Note the situation regarding inclined ducts crossing multiple layers of soil especially if there is a fluid inside these ducts (air, water). In this case, the possibility of axial heat transfer along the duct must be considered, refer to the previous section. In such a case, a deeper layer of soil with bad thermal properties may have an effect at another (higher) location along the drilling. Simply considering the radial heat transfer may be too optimistic. Multiple soil layers are discussed in Section 7.2.1.5.

ρ=1.2 ρ =0.8 ρ =1.7

FIGURE 46: A DUCT CROSSING MULTIPLE LAYERS OF SOIL WITH VARIOUS THERMAL RESISTIVITIES. WHERE IS THE LOCATION LIMITING THE CURRENT RATING?

7.2.2.2 Losses in Steel Casings IEC 60287-1-1 provides empirically-derived equations for calculating the Joule losses in steel pipes normally associated with pressurized pipe-type cables where the pipe diameter and cable phase separation are relatively small. These equations are based on experimental tests done in the 1950s on a particular line pipe (Morris, (1954), Katz (1978)) derived for the size of pipe, type of steel and typical current loading most common in the USA and select countries worldwide. The equations given are for two common configurations, cradled at the bottom of the pipe when the ratio of pipe inner-diameter to cable skid wire diameter is 1.6 or greater or triangular for when this ratio is smaller than 1.6, of the three cable phases in a pipe-type cable system. The empirical equations were developed from tests on a particular cable pipe with a given permeability. In practice, the permeability of steel line pipe varies both due to variation in the characteristics of the pipe but also due to handling during installation including welding, heating and bending that occur during installation. Single core cables are sometimes installed with groups of all three phases together in large-diameter steel casings, but the equations for pipe-type cables may not adequately describe the loss characteristics for these cable system types. For single core cables, a more practical formula is given in Kawasaki et al. (1981) as in practice the three single cores will lie in a formation somewhere between trefoil and cradle. Other references (“Designer’s Guide – Pipe AC/DC Resistance Ratio”, EPRI EL-3977-V1, 7832-3) permit a more precise consideration of the relative positions of the cables within larger casings and casing permeability than the empirical equations of IEC 60287). Another numerical approach is given in Kawasaki et al. (1981) and Mekjian and Sosnowski (1983). The reader should note that installing individual cable cores in ferromagnetic pipe can result in significant hysteresis losses that may exceed the losses of the individual cable conductor and metallic screen/sheath of the cable within; installing individual cables in carbon steel pipe should

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therefore be avoided. Pipe-type cable systems avoid this problem by using non-magnetic stainless steel pipes for each phase between the trifurcator and termination. In the course of preparing this technical brochure and administering the survey, approximately a quarter of respondents have calculated current ratings for cables installed in large steel conduits using various methods as follows:           

Software Calculated (method not disclosed) Finite element method (FEM) IEC60287, pipe type Use consultants IEEE paper Modified IEC B1-102 CIGRE 2008 IEC 60287 (applied to non-pipe cables) Paper by Moutassem and Anders Avoid use

5 responses 4 responses 3 responses 2 responses 1 response 1 response 1 response 1 response 1 response 1 response 1 response

From the methods identified, there appear to be a number of different approaches. This may indicate a lack of a credible standard method within the cable industry.

7.2.2.3 Multiple thermal resistances of Duct Bank Environments For cables laid in ductbanks, there may be multiple thermal resistances of the cable environment. Most importantly, the duct bank may have different thermal properties as compared to the cable environment. Calculations are possible with a correction factor (IEC and Anders (1997)), and in more complicated situations with multiple soil layers with conformal mapping CIGRE (1985) or finite element analysis. 7.2.3

Surface Trough and Shallow Installation

This section reviews several analytical methods, including some recent publications dealing with the current rating calculations for cables in surface troughs, unfilled troughs, or indeed shallow installed cables. Finite element methods have also been applied (see Pilgrim et al. (2012)) to solve the trough current rating problem but they are not reported here since standard partial differential equations are used and several commercial programs are available to deal with this subject. Where cables are installed in troughs, the trough lid is commonly flush with the ground and exposed to solar radiation. The troughs may be unventilated air filled, naturally ventilated air filled, force air cooled or filled with sand or other material. The troughs have the surface flush with the ground level. Figure 47 shows an example of a surface trough.

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FIGURE 47: EXAMPLES OF CABLES IN SURFACE TROUGH INSTALLATION

7.2.3.1 Filled surface troughs or shallow installations Current ratings for filled troughs can be generally calculated as though the cables were direct buried, provided that the thermal resistivity of the sand filling, the trough, and the surrounding ground can be taken to be the same. However: 

It is likely that any filling material in the trough will dry out and have a high thermal resistivity unless it is specially selected. Thus, the thermal resistivity of the various materials is likely to be different, and, hence, finite element methods would usually be used to calculate the external thermal resistance. An alternative approach is to use the partial drying method for buried cables, as provided in IEC 60287 or the method as described by El-Kady and Horrocks (1985).



The cable ambient temperature is likely to be affected more directly by solar radiation leading to higher ambient temperatures than for deep installations (Swaffield et al., 2008).



The ground may not be isothermal and hence the IEC calculation for thermal resistivity of the ground (T4) may no longer be correct (Swaffield et al., 2008).

For shallow installations the method involving creation of an artificial soil layer at the earth surface can be used. The method is described by King and Halfter (1983). The thickness of the artificial layer will depend on the earth surface and air ambient temperatures and its resistivity is the same as that of the native soil.

7.2.3.2 Unventilated and Naturally Ventilated Troughs The questionnaire revealed that around 40% of the respondents had calculated ratings for unfilled unventilated surface troughs although only 29% of utilities have calculated unventilated surface troughs ratings. Since cable manufacturers and consultancies deal with multiple utilities, it suggests that the 29% reported from utilities is a better indication of the use of unventilated troughs. The IEC 60287 method was the most used approach but a number of alternative methods were also used. More details can be found in Appendix B. Several methods have been published for determining the current rating of cables in an air-filled trough (IEC60287-2-1, Slaninka (1965)). Test work on the subject was reported by McCormick (1969). Both of the calculation methods base the current rating of a cable in a trough on the current

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rating of the cable in air, with an additional thermal resistance or temperature rise to take into account the effect of the trough.

The IEC 60287 method IEC standard 60287 sets out methods for calculating the current rating of cables under a range of different installation conditions. For cables in air-filled troughs, the method uses an empirical equation to calculate a temperature rise due to the trough. This temperature rise is added to the ambient air temperature to give a new “ambient” temperature. An ambient temperature correction factor is then applied to the tabulated, in-air ampacity. The IEC equation for the temperature rise due to the trough is:

 tr 

WTOT 3p

(EQUATION 38)

Where: WTOT = total power dissipation of all the cables in the trough, per meter [W/m] p = perimeter of the trough that is effective for heat dissipation [m] The equation is credited to Morello (1959). In his paper, he states that the empirical equation gives th good agreement with rating factors given in “IEE Wiring Regulations, 13 Edition, 1955”. No details of the derivation of the empirical equation are given in Morello’s paper. Morello (1959) gives a suggestion how the above equation can be applied in practice. An intuitive iterative approach starts with an initial guess for the temperature inside the trough θ0. This can be the air ambient temperature above ground, θa. Starting with this initial guess for the temperature inside the trough, the IEC standard method to rate the corresponding installation in free air can be applied. In general the total loss obtained for the corresponding installation in free air will not satisfy equation 38. However equation 38 can be used to compute a “better” second guess using:

i 1  i 

Wi 3p

(EQUATION 39)

With this new temperature inside the trough, the main iteration loop explained above is repeated. The air ambient is set to θ1 and the current I1 and the total loss W1 are obtained. One can check whether the new total loss W1 and the temperature inside the trough θ2=θ1+θa satisfy equation 38. As Purushothaman et al. (2012) point out, it turns out that this is almost never the case (Terracciano et al. (2012)). In fact the sequence of solutions Ti, Wi, Ii for any typical installation, will not converge to the set of final solutions for the inside temperature of the trough. Extensive experimentation with different cable installations and initial guesses has shown that the fixed point iteration described above rarely arrives at the correct results. The iteration frequently diverges or toggles between a high and a low value. The use of (de-)acceleration factors in the Gauss-Seidel method also proved to be ineffective. Although convergence is achievable with large de-acceleration factors for many examples, the convergence is slow and still not guaranteed. The above reference proposes successive relaxation to obtain consistently accurate solutions for the thermal rating of cables inside

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unfilled troughs. The method is based on equation 38, but the new value for the temperature inside the trough is computed as a linear combination of the previous value and the one computed.

Slaninka’s method In this method, the thermal resistance of the trough can be divided into three parts: from the base of the trough to ambient soil, from the sides of the trough to ambient soil, and from the top of the trough to ambient air. This approach allows different thermal resistivities to be used for the material surrounding each portion of the trough.

Anders-Coates method An extension of the Slaninka’s method was more recently published by Anders and Coates (2010). The method is based on an unpublished work that compares the calculated results with those obtained from test work reported by McCormick (1969) and gives good agreement. The approach uses an equation identical to Slaninka (1965) but the value of T0 includes not only a representation of the trough but also of the surrounding soil.

Naturally Ventilated troughs There is one publication by Pilgrim et al. (2012) using the finite element method for the current rating calculations for ventilated troughs. In such troughs lids are replaced by ventilated grilles. This reference shows that for a specific installation with about 50% of the surface being exposed to the outside air, by allowing full natural ventilation of existing covered troughs, the continuous rating could be increased by as much as 28% above the unventilated trough rating. Although its reliability has not been rigorously tested, an approach used in the UK has been to assume that the rating of such an installation would be 90% of the rating obtained by an IEC 60287 calculation for the cable being in free air.

7.2.3.3 Force Ventilated Troughs In this type of installation the cables are installed in troughs by cleats in air. The lid of the trough is solid and the air is circulated from one end of the trough to the other by means of a ventilation fan system. Current ratings for force ventilated troughs can use methods used for force ventilated tunnels. Another method which can be applied (and should give conservative values) may be found in Heinhold (1990).

When using either force ventilated troughs, or naturally ventilated troughs as described in Section 7.2.3.2, it must be noted that the rating calculated will be dependent upon the air flow being unrestricted. Depending on the location of the air inlets, or ventilated trough covers, it may be necessary to enforce a maintenance regime to ensure that inlets are not blocked by leaf litter of similar debris.

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7.2.3.4 Effect of Solar Radiation The methods given above take no account of solar radiation. However, McCormick (1969) states that if the trough is exposed to solar radiation, the ambient temperature used in the calculations should be increased by 9 °C. A review of the report shows that this value was determined from the results of tests on a shallow trough during a period when the intensity of the solar radiation ranged between 2 930 and 1020 W/m . The results from a trough 300 mm deep gave a temperature rise, due to solar radiation of 8 °C during the same period. It is proposed that an increase in ambient temperature of 8 °C should be applied to take account of solar radiation. The proposed temperature increase due to solar radiation is taken from measurements made in southeast England. As such, it is considered that it can be applied in Northern Europe, Canada, and the northern United States. For areas having a greater intensity and longer durations of solar radiation, it is suggested that temperature rise measurements are made (but it is considered unlikely that a temperature rise of more than 15 °C will be encountered due to solar gain. The studies performed by the authors (Anders and Coates, 2010) showed that the temperature rise on a cable 2 exposed to 1000 W/m of solar radiation can vary between 10 °C for cable in air and 17 °C for cable installed in a duct as compared to a shaded installation. Hence, the maximum value of 15 °C with the effect of solar radiation in a trough will be on a safe side in places with high solar intensity.

7.3

Installations in air

This section comments on the situation where cables are installed in free air, individually or in groups, supported by a structure. Information is provided for both the steady state and the transient situations. IEC standard 60287-2-1 describes a calculation method for the external thermal resistance (T4) of cables installed horizontally in free air, without or with solar radiation. The method includes an 1/4 iterative procedure for calculating (Δθs) , where Δθs is the difference between the cable surface and the ambient air temperatures. In section 2-2 of the same standard a calculation is provided for reduction factors, to be applied to the current rating for individual cables, for groups of cables in free air, without solar radiation. The method accommodates a maximum of 9 cables in a square formation, or 6 trefoil groups (2 vertical layers of 3 horizontal trefoils).

7.3.1

Transients

The transient temperature response of a cable to a step-function of current in its conductor (or conductors) depends on the combination of thermal capacitances and resistances formed by the constituent parts of the cable itself and its surroundings.

7.3.1.1 IEC approach For cables in air, generally the conductor temperature follows changes in load current sufficiently rapidly so that the usual daily cycles do not permit peak loads greater than the steady-state value or

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emergency rating although for large conductor sizes used on transmission circuits this may not always be the case. A suitable transient rating method in this case is given by IEC 60853-2 (2008). An explanation for this is that the heating speed in the air is 300 times faster than inside the XLPE insulation (see Table 10), because of the difference in thermal diffusivity. Therefore, in the thermal dynamic analysis, the thermal capacitance of air is negligible, and we only work with the static part, the thermal resistance.

TABLE 10: HEATING SPEED OF AIR VERSUS XLPE

Properties thermal conductivity k [W/K∙m] density ρkg/m3 specific heat capacity c [J/kg∙K] 2 thermal diffusivity akρ∙c [m /s]

Air

XLPE

0.03 1 1000 -6 30 x 10

0.3 1000 2000 -6 0.1 x 10

IEC 60853 contains a manual method for calculating the transient temperature response of a cable to a step function of current, while CIGRE (1983-2) gives a computer method. Both consider only the thermal resistance of the air.

7.3.2

Solar Radiation

IEC standard 60287, Section 2-1 in section 2.2.1.2 calculates the external thermal resistance (T4) for cables installed in free air, with solar radiation. The calculation is based on cables in air without solar 1/4 radiation (T4), excepting that the calculation of (Δθs) is modified to include an absorption coefficient, the local solar intensity and the cable diameter. A graphical method is also provided.

7.3.3

Cables cleated to walls

Common installations where cables may be cleated to walls include cable basements, culverts and “in-air” installations within substations. Cases where cables are cleated to walls within a tunnel are dealt with separately under Section 7.4. A number of cases of cables cleated to walls are covered by the IEC 60287 standard, through particular methods of calculating the cable surface heat dissipation coefficient, h. The standard current rating equation for cables in air is used with the appropriate value of h to compute the rating. A subdivision can be made between those cables which are cleated such that they are touching the wall and those where the cable is stood off the wall by at least 0.5 De (where De is the external diameter of the cable). Heat dissipation coefficients are given for a total of 8 cable arrangements which are separated from the wall by greater than 0.5 De, with the exceptions being single cables (greater than 0.3 De) and vertical touching cables (greater than one cable diameter from the wall). The data is based on the work of Whitehead and Hutchings (1939). A restriction is placed upon the cable external diameter, which must be less than 0.15 m, however, the vast majority of single core designs should fall within this range.

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Only two cases are given in IEC 60287 for cables which are clipped directly to a vertical wall, these being heat dissipation coefficients for single cables and three cables in trefoil. The restriction on * external diameter of the cables is given as De ≤ 0.08 m. No other methods are known for the calculation of larger diameter cables cleated directly to a wall, however such installations are considered to be rare. It should be noted that while the IEC method can cover multiple circuits, it does so for only a limited number of arrangements. In addition, for grouped arrangements it is assumed that all cables are of the same construction and are equally loaded.

7.3.4

Cable bridges

Installation of cables on bridges is a common method to cross rivers or other obstacles. The following installation configurations appear: 

Installation in open air, shielded or unshielded, refer to Section 7.3



Installation in a utility tunnel within the bridge, ventilated or non-ventilated, refer to Section 7.4



Installation in surface through, filled or unfilled. For this case, the calculation methods (Section 7.2.3) are too limited. The publication from McRae (1975), dedicated for cable in troughs on bridges, is a good guidance.

7.3.5

Riser Poles

Power distribution systems frequently consist of a combination of overhead lines and underground cables. In most cases, the underground cable system is connected to the overhead line through a short section of cable located in a protective riser. Also, each cable terminating at a substation is terminating through a vertical riser portion, which can be protected or not. Figure 48 shows a cross section of a submarine cable installed on a riser pole with a protective guard. The protective guard is often simply referred to as a riser. The current-carrying capacity of the composite system is limited by that segment of the system that operates at the maximum temperature.

FIGURE 48: CROSS-SECTION OF A SUBMARINE CABLE ON A RISER POLE (CRESS AND MOTLIS, 1991)

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From the questionnaire (appendix B, question 5.11) it appeared that around 35% of the respondents calculated the current rating of cables installed vertically exposed to solar radiation. Considering the importance of accurately rating power cable systems consisting of cables on riser poles, several mathematical models were introduced to represent such systems. All these models are based on writing the power balance equations. Construction of those equations is briefly discussed below. For cables installed in air, the significant modes of heat transfer are as follows: 1. By natural or free convection when no longitudinal induced flow is present 2. By forced convection by air flow along the cables 3. By radiation of the heat from the cable surface to the ambient air, walls, or covers.

Since conduction in air accounts for a small fraction of heat transfer in the installations under consideration in this Chapter, we will, in agreement with common practice, ignore this mode of heat transfer in further analysis. The convective heat transfer process in a riser is determined by the following factors: 1. The geometry of the riser, including its diameter and length. The size of the air gap between the cable and the internal wall of the riser will also be important in determining the extent of any convective behaviour 2. Venting conditions at the ends 3. The heat flux generated in the cable, which depends on the electric current and cable type 4. The environmental conditions such as temperature, humidity, solar radiation, wind speed, and others.

Thermal radiation is an important heat transfer mode in air-filled cable-wall systems. Thermal radiation transfers energy from the cable surface to the wall inside surface. This is different from convective heat transfer. Thermal radiation from the cable surface accounts for 40 - 60% of the total heat transfer (Keyhani and Kulacki (1985)). Thus, with free convection and air flow at low velocities, the proportion of heat removed by radiation is substantial and must be accounted for in calculations. The amount of heat transferred by radiation depends upon a number of factors, including surface temperatures and emissivity. To compute the rating of cables in air considered in this Chapter, the temperatures at various points of the thermal circuit are required. To obtain the required temperatures, a set of energy conservation equations has to be solved. In the next section, we will develop a general set of energy balance equations for a cable system surrounded by a wall, and the selection of appropriate coefficients will be discussed. Note: The effect of solar radiation on a vertically installed riser might be of importance. It will depend on the riser surface solar absorption coefficient, sun angle and the intensity of the solar radiation.

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7.3.5.1 Energy Conservation Equations This section deals with cables in vertical risers filled with air. The following assumptions are introduced to simplify the calculations: 1. The process is steady state 2. The length of the wall and the cable are large, so the heat transfer can be considered as one dimensional 3. The wall is opaque and the cable jacket material is radiatively gray and opaque; the air inside the protective wall is radiatively transparent The physical properties of all materials in the cable system are temperature dependent. The model takes into account the variation of physical properties with temperature.

7.3.5.2 Energy Conservation Equation for the Cable Outside Surface Considering the outside surface of the jacket under steady-state conditions, the conduction heat flux from its outer surface is equal to the heat loss through free convection and thermal radiation in the air between the cable surface and the wall. The energy balance equation takes the form

Wt  Wconv,s Wrad ,sw Where: Wconv,s = Wrad,s-w = Wt

=

(EQUATION 40)

natural convection heat transfer rate between the cable outside surface and the air per unit length [W/m] thermal radiation heat transfer rate between the wall inner surface and the cable outside surface, per unit length [W/m] total energy per unit length generated within the cable, where:

Wt WI Wd

(EQUATION 41)

7.3.5.3 Energy Conservation Equation for the Wall Inside Surface For the wall inside surface, the energy transferred by conduction through the wall material is equal to the energy transferred through convection and radiation on the inner surface of the wall. Thus, the energy conservation equation under steady-state conditions is

Wcond,wo  Wconv,w Wrad,sw

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(EQUATION 42)

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Where: Wcond,w-o

=

Wconv,w

=

conduction heat transfer rate from the wall inner surface to its outside surface per unit length [W/m] natural convection heat transfer rate between the wall inside surface and the air per unit length [W/m]

7.3.5.4 Energy Conservation Equation for the Wall Outside Surface In this section, we will consider cable installations which have air as a medium outside the wall. At the outside surface of the wall, the energy transferred through the wall material by conduction and the energy gain due to solar radiation are balanced by the convective and radiative energy losses to the atmosphere. Thus, the energy conservation equation is:

,

Where: Wconv,0

=

Wrad,o-sur

=

Wsol

=

=

+

,

+

,

(EQUATION 43)

natural convection heat transfer rate between the wall outside surface and atmosphere air, per unit length [W/m] thermal radiation heat transfer rate between wall surface and surrounding objects, per unit length [W/m] solar radiation absorbed by the wall surface, per unit length and time [W/m]. This quantity is only considered for installations exposed to solar radiation

7.3.5.5 Energy Conservation Equations – Heat Transfer The above equations are the basic energy conservation equations for the cable-riser system. There are three unknown temperatures;  s ,  w and  o , so this nonlinear system can be solved if the parameters are known. Full equations are developed in Anders (1997). There are several issues to be addressed when the parameters are entered. One issue relates to the calculation of the radiative heat transfer. There are well known expressions for single cable and the wall system. Usually, the radiation effect between the cables is ignored, but in the riser situation it might be of importance when three cables are located in one duct. Normally, a single cable is placed in a riser; hence, this issue is of a peripheral importance. The second issue of significant importance is how to compute the convective heat transfer losses. A general equation has a form:





Wconv  h 1   2 A

(EQUATION 44)

Where the temperatures between the two media 1 and 2 are sought and the two parameters A (surface area) and h (the convection coefficient) are required. In the riser application, three different convection coefficients need to be computed corresponding to convection between the cable surface and air in the duct, between the wall of the duct and the air in the duct and between the duct outer

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surface and the environment. The first two convection coefficients will depend on the venting conditions of the riser.

7.3.5.6 Convection Coefficients in Riser Applications In general, three situations can occur: the riser can be open at both ends, closed at one end only and, closed at both ends. In each of the cases, different approaches should be used. Case 1: Riser closed at the top and bottom An increasing number of applications in microelectronic packaging, nuclear engineering, and solar systems resulted in remarkable attention being focused on natural convection heat transfer inside confined spaces. The correlations for this case proposed by Anders (1997) are taken from Keyhani and Kulacki (1985).

Case 2: Riser open at the top and bottom Considerable research has been done on the laminar natural convection in open-ended vertical concentric annuli. Joshi (1987, 1988) studied the natural convection in an isothermal vertical annular duct and discovered that the heat transfer strongly depends on the radius ratio K = Dd / De. If K is less than 1.2, the solutions for annular ducts coincide with those for parallel plates. Natural convection in the air gap formed by two vertical parallel plates has been studied for many years and corresponding heat transfer correlations can be found in many publications. Al Nimr (1993) studied free convection in vertical concentric annuli and the dependence of the heat transfer rate on the radius ratio K. In practical applications for cable on a riser pole, the convective heat transfer coefficients were calculated based on Al Nimr’s results and the convection correlations for vertical slot formed by two parallel plates discussed in Raithby and Hollands (1985).

Case 3: Riser open at the top and closed at the bottom There are very few published data available for the heat transfer in this particular configuration. Hartlein and Black (1983) used the natural convection correlation for vertical plates to calculate the convection coefficient at the cable outside surface. They also applied the glycerin free convection correlation in open thermosyphons to calculate the heat transfer coefficient of air at the inside surface of the riser. An open thermosyphon is a device to transfer heat from a high-temperature region to a low-temperature reservoir or atmosphere. The simplest open thermosyphon is a vertical tube sealed at its lower end. The tube is heated by the high temperature heat source from which energy is transferred to outside by the natural convection of the fluid in the tube. In the model proposed by Anders (1997) the natural convection correlation for open thermosyphons is adopted to calculate the heat transfer between the riser inside surface and the gas, see Dryer (1978), Martin and Cohen (1954), Martin (1955).

The natural convection heat transfer correlation for vertical cylinders can be used for the outside surface of the cable (Morgan (1982)) and in the case of a forced convection the correlations described in Holman (1990) can be applied.

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Case 4: Riser closed at the top and open at the bottom This configuration design is uncommon, but it may unintentionally occur in practice. For such situation, the configuration can be treated as Case I: Riser closed at the Top and bottom. Finally, the question of the intensity of solar radiation modelling for riser installations should be addressed. This factor plays an important role in riser pole cable rating calculations and a comprehensive treatment of this subject can be found in Cress and Motlis (1991).

7.4

Tunnel installations

Cable tunnels have become increasingly popular in urban areas, as the convenience of installation and improved access to the cable often outweighs the high capital expenditure required for their construction. These installations can be classified into three types, based on the way in which they are cooled: 1. Naturally ventilated/unventilated 2. Forced air ventilated 3. Water Cooled (often also with some form of air ventilation). The survey results identified that 30% of users had undertaken rating studies for tunnels, with a wide variety of methods noted depending on the cooling type. This section of the report summarises the main methods which can be applied to cable tunnel ratings, identifying a number of issues which must be addressed by users when doing cable rating calculations in tunnels.

7.4.1

Naturally ventilated / unventilated tunnel installations

This section reviews the calculation methods applicable for tunnels which do not have forced air ventilation. At the time of producing this guide, no method exists within IEC 60287 for rating cables in tunnels where no longitudinal flow can be expected. We highlight here a number of alternative methods which do exist and could be suitable for use in simpler installations. Work is ongoing in the UK to produce a method which will be suitable for both steady state and transient simulations in more complex tunnel environments. Although IEC 60287 is capable of rating cable circuits installed in free air, the same methodology can’t be used for rating unventilated tunnels. The reason for this is that the calculation assumes that once heat leaves the cable surface, it dissipates into surrounding environment (via convection and radiation), but does not cause the temperature of the environment to increase. While this is acceptable for outdoor free-air installations, it does not hold true for an un-ventilated tunnel (or e.g. a cable cellar or joint bay) as the thermal energy may only leave the tunnel air by way of the tunnel wall. As the tunnel wall presents a large thermal resistance in most cases, substantial air temperature rises are to be expected. A number of methods have been published which are suitable for calculating steady state temperatures in simpler tunnels. These simpler tunnels can be classified as: 

Containing only identical cable circuits



The load cycle of all cable circuits is identical

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

The tunnel has a constant cross section and can be safely assumed to be at the same depth, surrounded by a thermally-uniform material



The heat transfer coefficients from all of the cable surfaces can safely be assumed to be the same.

Work by Weedy and El-Zayyat (1972-1 and 1972-2) in the 1970’s provides a thermal network model which can be applied to un-ventilated tunnels (denoted “free-cooling” by Weedy). Equations are given for convective and radiative heat transfer coefficients, with some experimental validation of results. A later review by Anders (1997) summarizes the main energy balance equations required and draws together the most appropriate heat transfer coefficients. Where the tunnel may be particularly deeply buried, it can be valuable to consider using an “equivalent laying depth”, as discussed in Dorison et al. (2010). A further method may be found in the text of Heinhold (1990).

7.4.2

Forced air ventilated tunnel installations

This section reviews the calculation methods applicable for tunnels with forced air ventilation, for which a new section of the IEC 60287 standard is presently being formulated. This update to the main international standard is based on a numerical method published in CIGRE (1992-1)) and CIGRE (1992-2). A brief review is provided on the situations in which this method will be applicable, with relevant assumptions highlighted for the user. In addition to the method of CIGRE (1992-1), a number of other numerical methods exist which may be appropriate depending on the level of detail required from the calculation. A brief review of these methods is provided here for the benefit of users with more complex tunnel systems. IEC standard 60287 sets out methods for calculating the current rating of cables under a range of different installation conditions. At the time of producing this guide, the new section relating to forced ventilated tunnels was under final review and is expected to be published in 2015. The methodology presented is largely based on the earlier work of CIGRE (1992-1), but with minor amendments to bring it into line with the terminology and calculation style used throughout the remainder of the IEC 60287 standard. Five main components of heat transfer are represented within the model, all of which are essential for the successful calculation of a rating for this type of installation. They include: 

Conductive heat transfer within the cable itself, using the familiar IEC 60287 thermal model to represent the cable



Heat transfer by radiation direct from the cable surface to the tunnel wall



Heat transfer by convection from the cable surface to the tunnel air



Heat transfer by convection from the tunnel air to the tunnel wall



Longitudinal heat transfer resulting from the flow of air along the length of the tunnel



Radial heat transfer by conduction through the soil.

Relations are given for both laminar and turbulent convection, with the assumed boundary between the two being at a Reynolds number, Re, of 2000 for the cable surface heat transfer and Re=2500

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for the tunnel wall transfer. The magnitude of the Reynolds number demonstrates the ratio of inertial forces (dominant in turbulent flow) to viscous forces (dominant in laminar flow). The equations are solved using a straightforward iterative process to obtain the steady state current rating. A method is given to obtain the cable conductor temperature at the hottest point, along with an air temperature profile along the tunnel length. Although the method is sufficient for the majority of cable tunnels, it is important to note the following restrictions: 1. All cables are assumed to be identical in terms of construction and loading 2. The tunnel geometry is assumed to remain constant along the length 3. Cable losses are assumed to remain constant with length, based on AC resistance at the maximum conductor temperature 4. Heat transfer (convection and radiation) from the surface of all cables is considered equal.

Should these assumptions be incompatible with the tunnel to be rated, it may prove necessary to use an alternative method. Similarly, should transient ratings be required, a full numerical method is the only option. It should be noted that the convection and radiation heat transfer from such cable systems must be considered carefully. In tunnels with lower ventilation rates, radiation heat transfer can become the dominant mode by which heat is transferred from the cable to the tunnel. The position of the cable within the tunnel may also influence the extent of the convection from the cable surface, thus the locations of the cable should be designed with this in mind. Where a given cable is particularly close to a wall, great care must be taken to avoid selecting an overly optimistic convection coefficient.

Electra 143 (CIGRE (1992-1)) The most commonly used numerical rating method for forced ventilated tunnels, according to the survey data, is that of CIGRE (1992-1) Electra 143. As the assumptions in the method are largely common with those of the IEC 60287 approach, they are not described in detail here. One additional restriction of this model is that the convection correlations given are valid solely for turbulent convection, thus it is important to check the magnitude of the Reynolds number if the air flow rate is low. The general approach is to calculate a temperature profile through one-dimensional slices of the (equivalent) cable and the tunnel, with each of these slices being linked longitudinally at the air node. By incorporating appropriate thermal capacitances at nodes within this model, it is possible to obtain transient temperature profiles, including those based on a steady state initialization. If such calculations are performed, it is important to choose a representative time step to ensure an accurate set of results.

Complex Tunnel Scenarios In a number of cases, the assumptions affecting the above methods prove excessively limiting. Perhaps the most common case is that where multiple independent cable circuits, of different construction and load cycle, exist within the same tunnel space. This is becoming more common, particularly where transmission and distribution utilities share the same tunnel space (Boone and De Wild (2007)). For such installations, it is necessary to model each individual cable circuit separately in order to ensure that the conductor temperature remains below the accepted limit. This can be

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achieved by making a series of amendments to the calculation of Electra 143, for instance as presented in Pilgrim et al. (2010). Although such approaches are more complex, they do permit complex tunnel scenarios and combinations of cable loadings to be evaluated; hence, they may be valuable when designing these systems. While it is also possible to use computational fluid dynamics (CFD) techniques to rate forced ventilated tunnel sections, existing evidence suggests that the additional data available from the calculation process is not sufficient to outweigh the increase in complexity of the calculation and the time taken to obtain the results. Some respondents to the survey indicated that this approach had been trialled, but it was not considered a standard approach. As cable tunnel networks increase in complexity, it becomes important to ensure that no small section is omitted from the rating calculation, as it may prove to be a limiting factor. An example of this is the riser shaft, which may be less than 50 m in length, but frequently contains very different heat transfer behaviour. Where the shaft has a significantly greater cross sectional area than the main tunnel, it should be noted that the linear air speed across the cable surface will be reduced, leading to a reduction in the convective heat transfer from the cable to the air. For tunnels where conductor temperature (as opposed to air outlet temperature) is the limiting factor, any length of cable installed in the outlet shaft is frequently the limiting section. This change in velocity must be accounted for in the evaluation of convective heat transfer coefficients. Al-Jallaf (2014) gives details of a custom thermodynamic computation model to calculate air flow, air temperature and air pressure, coupled with an ELECTRA model to calculate conductor temperature. Both natural cooling (using different shaft heights) and forced cooling are calculated.

7.4.3

Water cooled tunnel installations

In order to increase ampacity of cables in a tunnel, water cooling system can be adopted. Generally, water pipes in the tunnel, in many cases pairs of forward and backward direction, are utilized. They absorb heat and lower the air temperature in the tunnel. Their cooling value depends on temperature difference between air and cooling pipe (water), and a surface radiation thermal resistance. Such system can be examined by analysing an equivalent thermal circuit as shown in Figure 49 taken from ETRA (1998).

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ai(t) v1

R1

v2

R2

v3

R3

(soil section) R7

v4

R8

v6

v0

i (t) C1

C2

C3

C6 C4 (water cooling section; number:Np) R4 R5 R6 v 5F

ai(t) v1

R1

v2

R2

v3

R3

C5 i (t)

R4

C1

C2

R5

R6

v 5B

C3 C5

FIGURE 49: EQUIVALENT THERMAL CIRCUIT OF A WATER COOLED CABLE SYSTEM IN A TUNNEL

Where: R1 R2 R3 R4

= = = =

R5 R6 R7,8 C1 C2 C3 C4 C5 C6 v1 v2 v3 v4 v5F v5B v6 v0

= = = = = = = = = = = = = = = = =

thermal resistance per unit length of insulating material of cable [Km/W] thermal resistance per unit length of cable sheath [Km/W] thermal resistance per unit length of surface heat radiation of cable [Km/W] thermal resistance per unit length of surface heat radiation of water cooling pipe [Km/W] thermal resistance per unit length of water cooling pipe [Km/W] thermal resistance per unit length between water and water cooling pipe [Km/W] thermal resistance per unit length of soil section [Km/W] thermal capacity per unit length of conductor [J/Km] thermal capacity per unit length of insulating material [J/Km] thermal capacity per unit length of sheath [J/Km] thermal capacity per unit length of air in tunnel [J/Km] thermal capacity per unit length of water and water cooling pipe [J/Km] thermal capacity per unit length of soil section [J/Km] temperature of cable conductor [K] temperature of cable sheath [K] temperature of cable surface [K] temperature of air in tunnel [K] temperature of water in forward direction pipe [K] temperature of water in backward direction pipe [K] temperature of soil section [K] base temperature of soil [K]

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i(t) α Nc Np

= = = =

heat generated by the cable per unit length [W/m] sheath loss factor number of equal cables number of water cooling pipe pairs

Temperatures of a cable section are expressed as:

∂v (x, t) 1 v (x, t) − v (x, t) = i(t) − ∂t C R

∂v (x, t) 1 v (x, t) − v (x, t) v (x, t) − v (x, t) = αi(t) + − ∂t C R R ∂v (x, t) 1 v (x, t) − v (x, t) v (x, t) − v (x, t) = − ∂t C R R

(EQUATION 45)

(EQUATION 46)

(EQUATION 47)

Where (x,t) means values at position x along the tunnel and at time t. The temperature of the air in the tunnel is expressed as:

( , )

=

( , )−

1 − −

( , )

( , )− ( , ) − + + ( , )− ( , )

( , )− ( , ) + +

(EQUATION 48)

Temperatures of water cooling sections are expressed as:

∂v (x, t) 1 v (x, t) − v (x, t) dv (x, t) = +c ∙Q∙ ∂t C R +R +R dx ∂v (x, t) 1 v (x, t) − v (x, t) dv (x, t) = +c ∙Q∙ ∂t C R +R +R dx Where: Q = cw =

(EQUATION 49)

(EQUATION 50)

quantity of water per length per pipe [kg/m] specific heat capacity of water [J/kgK]

The soil temperature in a section is expressed as:

∂v (x, t) 1 v (x, t) − v (x, t) v (x, t) − v = − ∂t C R R Page 128

(EQUATION 51)

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It is difficult to solve equations 45 to 51 analytically and a differential approximation method by numerical calculation should be adopted.

7.4.4

Method of Determining Ambient Temperature

When rating cables installed in a tunnel, it is important to consider both the ambient temperature of the ground and, for forced-ventilated tunnels, that of the inlet air. Some reference information is provided in IEC 60287, as noted in Section 7.4.2. However this information is unlikely to be sufficient, thus guidance is given on the selection of ambient temperatures appropriate for tunnel operation. Some reference data on operating conditions is given in IEC 60287 Part 3 Section 3.1 “Reference operating conditions and selection of cable type”. Information is given for 15 countries, including appropriate soil ambient temperature and outdoor annually-averaged air temperature, although it should be noted that the types of data given differs slightly between countries and can cover very wide ranges. The importance of project specific data is also emphasized within the IEC document, which states “Attention is drawn to the fact that the information provided in Clause 4 is intended only as a guide for cable installation designers when data provided by a user is incomplete”. Wherever site specific data is available, it should be used in preference to the data given in IEC 60287-3-1. Selecting an appropriate value of ground ambient temperature is important for all tunnel rating applications. For un-ventilated tunnels, the only ambient temperature value required is that of the ground. The value should be selected to be representative of the temperature at tunnel depth, without the presence of the tunnel itself. Generally speaking, the temperature at tunnel depth is unlikely to be greatly affected by the season as the thermal resistance between the tunnel and ground surface is high, while the specific heat capacity of the ground is very large. For this reason, the selection of a single annually-averaged value of ground temperature is likely to be appropriate. Where tunnels are shallow buried, or where the air ambient temperature is known to have a very large annual range, a number of methods are available for calculating the year cycle of ground temperature at tunnel depth. Work undertaken in the United States provided measured data from weather stations across the country, with an equation then provided to calculate the temperature at the required depth (Kusuda and Achenbach (1965)). Similar equations were also published in Canada by William and Gold (1976). Although these publications refer to data from specific countries, the general methods they present should be valid across most of the world. Exceptions may need to be made for areas which suffer permafrost during winter, or for areas which swing from drought conditions to fully saturated soil, as the thermal diffusivity of the ground would vary substantially between seasons.

7.4.4.1 Notes on Air Ambient Temperature Choosing an appropriate value of ambient temperature for the air is much more complex than that of the ground itself, as the air temperature will typically exhibit substantial daily and seasonal variations. For an example discussing this further, refer to Boone and de Wild (2007). Fortunately, for a long forced-ventilated tunnel, the daily variations are often attenuated long before the tunnel outlet is reached. This occurs due to the exchange of thermal energy between the air and the tunnel wall by convection. It is important to note that there is no set length of tunnel for which the daily variation will prove insignificant, as the rate of attenuation is dependent upon the tunnel geometry and ventilation flow rate.

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For the purpose of calculating a continuous rating, it is necessary to choose a representative, average air temperature either for the year, or where significant variations are expected, for the season. Any such values will be site specific; thus local meteorological data should be sought. One note of caution must be highlighted concerning potential differences between the outdoor ambient temperature and that seen by the tunnel. If the ventilated system is configured as “forcedintake”, as opposed to “forced-extract”, any thermal losses from the fan and its associated drive system could be drawn into the tunnel. Where tunnels have particularly high air flow rates (and hence large fans), this additional heat can make a significant difference to the tunnel air inlet temperature and must be accounted for by increasing the ambient air temperature used in the rating calculation.

7.5

Submarine cable installations

Submarine cable installations are becoming more common, especially with the advent of offshore renewable power generation. This section reviews the common installation scenarios for these cables and makes recommendations for appropriate rating techniques.

7.5.1

Seabed burial installations

The current rating of buried submarine cables follows the same rules as for buried land cables. However, submarine cables usually have armour.

7.5.1.1 Buried submarine cable rating calculations The IEC does not give any specific recommendation for the calculation of the current rating of submarine cables buried in a seabed. The calculation of the current rating in this specific installation configuration can, however, be performed by adopting the methods according to the IEC 60287 series of standards for cables directly buried in the ground and considering the laying depth in the seabed, the seabed soil thermal resistivity and its temperature. The seabed soil characteristics have to be evaluated along the entire submarine cable route: those values can be extrapolated from historical data or measured in situ during a submarine seabed survey. A review may be found in Worzyk (2009), along with some example calculations.

7.5.1.2 Thermal Resistivity of the Seabed Soil The thermal resistivity of the seabed soil is a critically important starting point for rating calculations, as was noted in Section 3.3. It is a function of the soil base material, the dry density, the distribution of grain size, the compaction, the humidity and the content of organic materials. The influence of humidity, one of the most important factors for land based soils, can be disregarded in subsea soils because the soil is typically saturated. This is also valid for seafloors of tidal flats which fall dry during low water tides. Thermal resistivity values are shown in Worzyk (2009) for some different submarine soils: a thermal resistivity from 0.2 up to 2.5 Km/W is possible. Thermal characteristics of the sea soil are given for some countries in IEC-60287-3-1. The large distribution of these values implies that it is one of the

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most important objectives of the marine survey to measure the thermal resistivity of the soil along the cable route. The measurement of thermal resistivity values for soil is rather delicate. Soil samples taken from the intended installation site can represent the soil base material, grain size distribution, and, in case of submarine soil samples, the humidity content. However, the in-situ degree of compaction is difficult to reproduce in the laboratory. The degree of compaction might be different in virgin soil and in soil after cable laying and burial. The soil conditions in the vicinity of the submarine cable can also be inhomogeneous. It is important to create a complete picture of the soil conditions along the entire cable route before designing the cable system. The locations of the limited number of soil samples should be chosen so that the thermal properties of the cable route can be mapped in sufficient accuracy.

7.5.1.3 Ambient Temperature of the Sea Floor For the thermal design of buried submarine cables, the ambient temperature of the sea floor at the cable burial depth must be taken into account, as was noted in Section 3.4. The temperature of the sea floor varies with the water temperature above the soil-water surface. The daily variation of the water temperature influences the temperature in the sea floor only to some centimetres depth. The annual variation of the water temperature determines the soil temperature up to much deeper depths in the sea floor. With increasing depth, the ambient temperature in the sea floor will decrease in amplitude, while the peak value will be occurring later in the year. The annual sea floor temperature at a certain depth may be approximated as a sinusoidal variation over the year and is a function of the annual variation of the water temperature and the depth of cable installation (Worzyk, 2009). For every submarine power cable project the annual average temperature on the seafloor and the amplitude of the annual variation of the seafloor temperature should be identified. If they cannot be retrieved from long-term measurements, the estimated values should have sufficient safety margins.

7.5.1.4 Seafloor Conditions Changing with Time Seafloor conditions, which have been charted by survey operations, may alter during the cable’s lifetime: 

Coastal waters exposed to tidal currents are subject to strong and fast changes of the bathymetric structure



Spring tides and storms can cause erratic changes both in the soil composition and in the laying depth of submarine power cables



Changes by human activities such as dredging, dumping, etc.

These changes have to be surveyed and evaluated during the cable’s lifetime for every submarine power cable and where possible taken into account for the submarine cable design and calculation. A common issue is the impact of sand waves, which may cause the burial depth of the cable to vary significantly during the lifetime of the cable system.

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7.5.2

Cables Installed on the Seabed

Many submarine cables were laid unprotected on the seafloor (except for the immediate beach zone) until the 1990s. When appropriate subsea burial equipment became available in the 1980s, the burial of longer cable stretches became more common. Today, almost all submarine power cables have an external protection (burial or covered). Submarine power cables at very large depths are possibly still laid on the seafloor unprotected. The IEC does not give any specific recommendation for the calculation of current rating of submarine cables laid on the seabed. It has to be considered that a submarine cable laid on the seabed during its lifetime will be gradually covered by a layer of sand, algae, shells and/or other types of seabed sediments and vegetation. The thickness and the composition of this layer depend on a great number of factors such as sea floor geological composition, sea currents, presence of particular marine vegetation and so on. A possible approach to perform the current rating calculation in this specific installation configuration is to consider the cable as directly buried in the seabed with a burial depth equal to the estimated thickness of the sediment layer described previously and performing the calculation as described for cables buried in the seafloor. The thickness of the sediment can be conservatively assumed equal to 0.3 m. It should be noted that because sediment is likely to be of a relatively low density its thermal resistivity is likely to be higher than that of the true seabed.

7.5.3

Cables Installed in Free Water

IEC standards do not provide a method for the rating of cables installed in free water. A suitable means of assessing the rating would be via energy balance equations. This requires the application of a suitable convective heat transfer coefficient to describe the rate at which heat is lost from the cable surface.

For unburied submarine cables, the ambient temperature is simply the temperature of the seafloor water. It should be noted that the annual variation of seafloor water temperature varies significantly depending upon location, with some areas seeing almost constant temperatures while others may witness fluctuations of at least 10 °C. Relevant data for a specific submarine cable project can often be obtained from the national hydrographical institute or commercial survey companies. The highest summer temperature of the seafloor water is different in different years. Statistics list 10-years-high, or 100 years-high values. It is up to the decision of the cable owner/operator which of these values should be used in the context of the overall cable system design.

When the unburied cable is carrying load, its surface temperature can only be a few degrees over the ambient water temperature. This will largely depend upon the flow rate of the water, with still water being a worst case. Caution should be exercised if flowing water is assumed.

From the survey responses received, only a small number of respondents had considered this type of cable installation. The majority treated the cable as if it were shallow buried, while some used modified methods for cables in air. It is noted that it is very unlikely that sections installed in open water would prove limiting, hence many users neglected to explicitly calculate a rating for these sections.

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7.5.4

Submarine Cables installed in Risers (J-tubes)

The IEC does not give any recommendation for the calculation of current rating of submarine cables installed in J-tubes. Some published methods do exist in the literature and these are briefly reviewed here. It should be noted that the results of different methods do not always show good agreement, however the survey undertaken showed that these methods are in routine use in a variety of countries. Thermal network approaches have been used for J-tube ratings in the past, with the most common approach being that of Hartlein and Black (1983). This method is applicable to the following J-tube designs:   

Riser closed at both the top and the bottom Riser open at both the top and the bottom Riser open at the top but closed at the bottom

The method accounts for convection from the cable surface to the air, the air to the J-tube wall and from the J-tube surface to the ambient air. Thermal radiation between the cable surface and the Jtube and between the Jtube and the environment is included, along with the ability to include solar radiation and wind on the surface of the tube. It should be noted that the published method focuses on the J-tube thermal model. Within the J-tube model the cable can be modelled as done in other standard configurations. Experimental work was also undertaken by ERA Technology in the UK, leading to the publication of a technical report Coates (1988). This led to the creation of empirical equations with which to obtain the temperature of the J-tube. Similarly to the above referenced Hartlein & Black model, ERA 880108 does not include a cable model explicitly. The method can handle both sealed and open topped J-tubes, including the effects of solar radiation. In some circumstances it may be desirable to conduct finite element analysis (particularly if the air filled section of the tube is short, meaning that some longitudinal cooling can be expected). It should be noted that, while 3D finite element analysis is viable for J-tubes, it is relatively time consuming. If the air filled section of the tube is sufficiently long, the use of 2D finite element analysis is practical as a sufficient length of cable within the tube will be at the same temperature. This is underlined by the publication of Pilgrim et al. (2014) where a J tube 3D FEM result is presented and the work made comparisons with 2D and operational installation measurements, although the comparison work is not described. It is noted that the temperature is relatively constant along the J tube and hence a 2D model is likely to be effective.

7.5.5

Cable Protection Systems

Some specific cable protection devices used for the protection of submarine cables, such as bending stiffeners, could represent a local hot spot for the cable. As these hot spot regions are usually limited in size the current rating should be calculated taking into account the longitudinal heat flow along the cable. It is also worth noting that they may not represent a thermal limit on the cable route, if other areas (perhaps landfall sites or lengths of cable in J-tubes) are more limiting. Other possible thermal obstacles may include concrete mattressing and rock dumps, which may be used to protect cables at crossing points, see Figure 50-52.

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FIGURE 50: CONCRETE MATRESSES FOR PROTECTING SUBMARINE CABLES

FIGURE 52: CAST IRON SHELL PROTECTION OF A SUBMARINE CABLE

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FIGURE 51: SAND/CEMENT BAGS ON TOP OF A SUBMARINE CABLE CIRCUIT

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8

Us ing C al cu la t io n T ools and T ech niq ue s

A number of different tools can be used to calculate the current ratings of cable systems including hand or spreadsheet calculations, tables of pre-calculated values, bespoke software, and commercially available software packages. These tools can use a variety of calculation methods or techniques to estimate the current rating. The tools and techniques to estimate the current ratings of cable circuits can be divided into two general types as described below. 

Steady state and transient rating: current ratings that are calculated using starting points, such as ambient temperature, that are assumed (typically the worst case) as actual values are not known. These current rating calculations are referred to as either steady state or transient calculations (covering cyclic and emergency calculations) and are typically calculated before the cable system is actually operated. In the survey, 80% of utilities reported that they used emergency ratings (see question 3.4.1) and 40% reported using cyclic ratings (although 35% did not respond to the cyclic rating question, see question 3.3). It is assumed that all the utilities used the steady state rating.



Dynamic (or real time) rating: systems that use real time information about some of the starting points of the current rating calculation to enable some of the assumptions to be removed and generally provide a larger current rating, as the starting point assumptions are typically worst case assumptions. These systems are referred to as dynamic current rating systems and the current ratings are generally calculated as the cable system is being operated.

The increase in the availability of fibre optic based distributed temperature sensing systems for cables has stimulated the interest in dynamic rating systems. Additionally, the increase in the connection of renewable energy sources to the transmission network has led to an increase in the connection of intermittent energy sources and it is possible that dynamic rating systems can help to maximise the use of intermittent energy, while minimising the expansion of the transmission network, see CIGRE (2010). This section of the report describes some of the tools and techniques available to calculate steady state, transient and dynamic cable current ratings.

8.1

Steady State and Transient Rating Tools

The tools used to calculate current ratings will be influenced by the current rating model used. These techniques can generally be split into analytical or numerical approaches. Analytical techniques use the manipulation of mathematical expressions to produce equations that find the exact solution (typically after making a number of assumptions). Analytical techniques are characterised by finding the solution in a single step or in a limited number of iterations. Numerical techniques solve a problem using algorithms that use numerical approximations and typically involve a number of interlinked equations that need a significant number of iterations to obtain a converged solution. Analytical techniques involve a smaller amount of calculation and hence a greater range of tools are available to implement an analytical method. Some of the available tools are: 

Some users rely on tables of current ratings, see IEC 60502, 60055 (not maintained) and IEEE 835. Note that these standards are for cables up to a certain voltage level where the current rating has already been calculated using another tool. These tables can be specific to a cable

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installation or can consider a limited number of variations (e.g. depth, type of sheath bonding, ambient temperature). Tables have the advantage that they are easy to use and a table or ratings can be verified once and then relied upon. There is, however, the possibility of using the table incorrectly, particularly by users who do not fully understand cable systems. 

For a relatively simple cable installation, it is possible to use hand calculations with a calculator, the spreadsheet function of spreadsheets, or computer algebra systems. For hand calculations, each individual calculation step is performed by hand, making this method time consuming but with the benefit of allowing for unusual installation configurations to be considered. Spreadsheets or computer algebra systems allow hand calculations to be reused, or modification to the original calculation to be made. Hand calculations are generally verified by a second person repeating the calculation (or at least checking that similar results are given in tables). Spreadsheet calculation can prove difficult to verify, particularly when they are modified. Additionally spreadsheet programs are not well suited to the iterations that are generally needed for current rating calculations.



Bespoke current rating software (that is software written specifically for the user) uses a computer program specifically written to use a current rating technique, or number of techniques. The result may be a current rating or in some cases an intermediate result such a ground thermal resistance (T4) that can be used by another tool to calculate the final current rating. These can vary from simple programs that consider a limited number of cable system configurations and a limited number of current rating techniques to complex programs that consider a number of possible cable system configurations and can use a number of different current rating techniques. Computer programs are suited to performing iterative calculations, permit more complex calculations and can be verified more easily than spreadsheets. However more complex current rating software can still be difficult to verify, particularly if the results of intermediate steps cannot be readily accessed.



Commercial current rating software is similar to bespoke current rating software but is written by a third party and made available to a number of users. These current rating programs will tend to be more complex and have a larger number of cable system arrangement options available, using a number of different current rating techniques, and should be verified. These programs sometimes, however, do not document very well the techniques used to calculate the current rating and may make it difficult for the user to verify that the calculation is correct or appropriate, or what assumptions were made.

Numerical methods by definition involve a large number of iterative calculations and hence generally are performed by computer programs. These can be either bespoke or commercial programs. Typically a program will concentrate on a specific numerical technique and the programs are generally classified by the specific technique used. In some cases, the program may not actually calculate the current rating, but calculate a parameter of the current rating that is then used by another current rating technique using a different tool. Typically where fluids play a role, the empirical calculations will be increasingly difficult. In all of the above cases it is essential that the correct base parameters are used (like cable modelling, bonding, installation arrangements, etc.) and that the mathematical model used is appropriate (like the assumptions made by the mathematic model are valid, the boundary conditions correctly specified, the finite element mesh sufficiently detailed) for the cable system being studied. To this end the person carrying out the calculation must be properly trained in the calculation method.

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8.2

Dynamic (or real time) Rating Tools

Dynamic cable rating tools take a real time input to calculate the cable current rating. Since the calculation is generally only valid for a limited time period after it is performed, the tool has to repeat the complete calculation for the cable system at every specified time interval. To be useful to a system operator, the resulting cable current ratings should be integrated into a tool that calculates the current rating of the busbar to busbar system as defined in Chapter 2. Dynamic cable rating tools do not have to be adaptable to different cable systems as such a tool is linked to a specific cable system in a specific environment. However, they may have the ability to be adaptable to different cable systems so that the same tool can be used on more than one cable circuit. Dynamic cable rating tools can use a variety of different real time inputs and produce a variety of different outputs, as discussed further in the following sections. According to the survey carried out, many users have limited experience with using these calculation tools which can make it difficult to successfully set up the system and correctly interpret the results. Currently a working group of CIGRE WG B1.45 'Thermal monitoring of cable circuits and grid operators’ use of dynamic rating systems' is working on this topic. The context to start with this working group is the following: nowadays due to the more variable situations and increasing loads in the power grids, a dynamic rating system and various measured values aid the asset manager in making optimal decisions in planning investments in the High Voltage grid. Based on measurement a grid operator can on the one hand decide if a hotspot in network should be taken away to increase the capacity or if the hotspot should be managed with the dynamic rating system and on the other hand will know the load and overload possibilities in real time and for the coming hours.

8.2.1

Inputs

By definition a dynamic cable rating system must have some form of real time input. A number of inputs are possible and some dynamic rating systems can accept more than one real time input. In some cases the measurements may be at a single point such as a thermocouple while other measurements can be distributed such as distributed temperature measurements using fibre optics. A number of potential inputs are listed below. 1. Historic and actual loading: if the cable system has not been continuously loaded at the continuous 100% current rating, the cable will not be at its maximum operating temperature and the cable will be able to be loaded above the continuous 100% current rating for a period of time, typically using an emergency rating calculation (see Section 5.1.2.2). 2. Predicted or potential future loading: the transmission operator can inform the dynamic rating system of the expected future loading, or give a number of scenarios. 3. Historic and actual ambient temperature: these temperatures are measured away from the cable system. As with historic loading, historic lower ambient temperatures may lead to the cable not being at its highest operating temperature and a potential current rating increase may be available for a period of time typically using an emergency rating calculation (see Sections 3.5.2 and 5.1.2.2). 4. Predicted future ambient temperature: If a lower ambient temperature can be relied on to be stable over the period of the study, an additional increase in current rating can also be calculated for the period of time in question. In some cases, such as buried installations, the historic

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ambient temperature can be used as the basis of predicting the future ambient temperature. In other cases some other forecasting method may be available. 5. Other cable rating input parameters (historic and predicted): although the majority of dynamic cable rating systems use loading and temperatures as inputs, other cable rating starting points described in Section 3 could be measured, such as air velocity in a tunnel. 6. Historic and actual system temperature: these temperatures are measured close to the cable system and are influenced by its operation. The most useful would be a measurement of the conductor temperature but this is difficult to obtain as the conductor is at system voltage. Normally, temperatures measured are parts of the system that are at earth potential. The closest component to the conductor at earth potential is the cable metal sheath or screen and some cables are designed with built in temperature monitoring sensors at that location (normally optical fibre). A number of other system temperatures are possible including cable outer temperature, soil temperature close to a cable system, tunnel wall temperature, air temperature at the exit of a forced ventilated tunnel, air temperature in an unfilled trough, etc. These temperatures will be influenced by a number of different cable current rating input parameters and hence the use of these system temperatures is more complex.

As with all measurements, these inputs will be subject to errors. The dynamic rating system designer should be aware of the tolerance of the inputs to ensure that the results of the dynamic rating system are valid. These errors include errors in the values measured, response times, and spatial resolution and assumed location for distributed measuring systems. Any measurement equipment should have an accuracy specified and tested as part of a quality assurance programme. It should also be noted that an input parameter may also be required as an output for verification purposes. For example, it may be desirable to make use of ambient temperature data to provide a context to the ratings calculated by the system. Some intermediate steps may also be required for verification (for example, if the system estimates the soil thermal resistivity as an input to the rating calculation, it is important to verify that the measurements or calculations seem realistic. This is discussed further in Section 8.2.4).

8.2.2

Outputs

The functionality of a dynamic rating system can vary between systems and this difference will lead to different outputs from different schemes. Some systems are able to produce a number of different outputs, which are used at different times for different purposes. Available outputs from the dynamic rating systems are listed below. 1. Temperature output: The simplest output for a dynamic rating system is to calculate the present and the expected future temperatures, perhaps as a function of time. This output can be used to implement an alarm type function warning the user that the cable is being, or is at risk of being, overloaded. In a more complex system, the user can enter a desired future loading pattern and the system will calculate the estimated temperature at each point in time and warn of any potential pre-set limit being exceeded. 2. Maximum loading output: For this function, the dynamic rating system will calculate the future permissible current rating from the present moment, typically as a permissible current rating for a defined period of time. More flexible systems allow a future cyclic or arbitrary loading pattern to be specified by the user.

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3. Rating study output: Some dynamic rating systems can calculate cable ratings not only at the present moment, but also following certain scenarios in the future. This output is useful for system schedulers who need to plan for potential loading patterns to decide how the system should be configured in the next days or weeks, for example to decide outages on the system. 4. Some of the inputs into the dynamic rating system are predicted future values. In some instances the cable dynamic current rating system may calculate current rating starting points (such as ground thermal resistivity) from indirect measurement and use these to predict the value of that starting point. Care must be taken with how these predicted future inputs are treated. Some inputs can be treated as starting points in the calculation methods that do not change during the period of any study; for example buried ambient soil temperature may be considered stable over a day. However, some inputs may change in the future, for example air ambient temperature will vary over the period of a day, and any calculations must take account that these inputs are not stable. This can also be important if the dynamic cable rating system calculates current rating starting points, for example ground thermal resistivity that may change over the period of the study due to changes in the soil water content. In the extreme case, this can lead to the output of a dynamic rating system being a probabilistic in nature, giving a current rating, or group of ratings, to a given level of confidence.

A dynamic cable rating system should consider the rating for each part of the cable system, and of the busbar to busbar system. In some cable systems, different parts of the route will constrain the rating at different times. For example, a section of cable installed in air may have a higher continuous current rating than a buried cable section but the air section may limit some emergency ratings. A dynamic cable system rating should take account of all potential parts of the cable system that could limit the circuit rating.

8.2.3

Use of Cable Dynamic Rating System

For practical use by a system operator, the output of the dynamic cable rating system has to be integrated into a circuit dynamic rating system. The circuit dynamic rating system has to combine the predicted ratings of the cable with the predicted ratings of the other equipment and provide an overall circuit output. From the results of the survey (see Section 8.4.6) it would appear that most of the systems on offer are not integrated, while the majority of utilities who have dynamic rating capabilities have integrated, or are investigating integrating their system. Generally, transmission operators install dynamic rating systems to improve the current rating of the circuit. The two main scenarios where the current rating increase can be used are: 1. Time limited current rating increase: the dynamic rating system gives a temporary rating increase to the circuit that can be used by the transmission operator to schedule outages and generators in a more efficient manner. 2. Long term current rating increases: a dynamic rating system that gives a permanent rating increase allows the transmission operator to reduce the need for transmission circuit upgrades or for new circuits. Permanent rating increases are likely to be based on re-evaluation of current rating starting points, possibly moving away from worst case assumptions and moving to a probabilistic current rating.

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Where probabilistic current ratings are used, the transmission planning strategy has to be compatible with the use of probabilistic current ratings. For example, agreements with generators that allow the transmission operator to change the maximum energy that can be generated (typically tied to a more favourable commercial arrangement) will facilitate the use of dynamic rating systems. On the other hand, a system where generators are guaranteed a fixed connection rating will make a dynamic rating system less useful.

8.2.4

Verification and Testing of Cable Dynamic Rating System

There are no standard methods for verification or tests and there are not many papers regarding the verification or testing of cable dynamic rating systems and these papers generally use different methods (see Lyall et al. (2004), Liang and Li (2008)), Hennuy et al. (2014) and Chimi et al. (2014). Methods of testing can be using actual installations, laboratory tests, and computer simulations. These are described in more detail below. 

Actual installations: an existing cable system can be furnished with monitoring equipment and the dynamic rating system results compared with the measured values. With this method, it is not possible to measure the conductor temperature and the actual loads on the cable system are not generally under the tester’s control. It is not necessary to perform the test live and historic information can be used on the dynamic rating system. Majority of modern dynamic rating systems will have a module that adjusts some system parameters (e.g., soil thermal resistivity or its ambient temperature) to match the measured value, usually the sheath/screen or jacket temperatures.



Laboratory tests: a cable system, or simulation such as hot water pipes, is installed in the laboratory and the measured values compared with the dynamic rating system. In some cases, the test may be combined with another activity, such as a prequalification test. Depending on the test arrangement, it is possible to measure all relevant values and control the loading although laboratory tests will not take account of unanticipated real life factors. Again, the test does not need to be performed live and historic information can be used on the dynamic rating system.



Simulation: it is possible to run a thermal model of a simulated cable system (generally using the most complete thermal model available). From the simulation, input values for the dynamic rating system then can be recorded and used to obtain results from the dynamic rating model. The values calculated in the simulation and the dynamic rating system can be then compared. It is possible to alter parameters in the simulated cable system (particularly those not used as inputs in the dynamic rating) and understand how the dynamic rating system copes. This approach will be most useful where known cable temperature data is available. The simulation can then be run from a known starting point to calculate ratings at different points in time, allowing comparison with the predictions obtained from the dynamic rating system. In practice, this approach may still leave some uncertainties and a mixture of these 3 approaches is likely to provide the best result.

During the verification or testing, it is possible to investigate the impact of tolerances in input values due to measurement inaccuracies by repeating a test but altering the input within the known accuracy of the measuring device and evaluating any changes in the results from the dynamic rating system. A number of users reported, via the survey, that they had experienced problems with either accuracy or calibration of the systems, including a number related to DTS systems. The usage of DTS systems, for monitoring the actual distributed temperature along the cable route, is not a common practice, 27% of the responses experienced limitations with these systems, referring to:

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accuracy of the system unknown (13%), system not reliable/subject to failure (7%) and difficult to use/ inexperienced users (4%).

8.3

Calculation Techniques

Sections 8.1 and 8.2 have outlined some of the tools which are commonly used in the calculation of current ratings. When using tools, in particular third party software, it is vital to understand which methods the tool is using in order to avoid the use of inappropriate methods (leading to incorrect ratings). We briefly review here the calculation techniques most commonly used, providing references for the benefit of those readers requiring more in depth information.

8.3.1

Analytical

Analytical methods are the most commonly applied, particularly those based around the key IEC standards. The approach taken by analytical methods is to represent the cable circuit using an electrical analogue to the thermal problem. For steady state problems, a simple network is required, consisting only of thermal resistances (to represent the thermal properties of the cable components) and sources (to represent the electrical losses which generate heat). For the transient case, thermal capacitances must be added to represent accurately the time constant of the cable system in its given installation environment. This typically takes the form of a ladder network. For further information, refer to Anders (1997). The accuracy of the analytical methods can be very high for simple installations, particularly involving single core cables where the thermal resistance and capacitance of each layer may easily be calculated. For a number of cases, an exact analytical solution may not exist, meaning that some empirical data (data acquired for experiments) be required. Another alternative is to use the technique of conformal mapping to calculate the equivalent thermal properties. This is most commonly used for representation of the external thermal resistance in more complex buried cable arrangements, for example as discussed in Luoni et al. (1972). IEC has issued a Technical Report explaining how the finite element approach can be used for thermal analysis of a buried cable circuit, see IEC TR 62095 (2003).

8.3.2

Empirical

In some cases, the heat transfer from the cable is a mixture of conduction, convection and radiation between multiple surfaces and media. Historically, this has led to experimental tests being undertaken to determine appropriate ways of representing the heat transfer. A good example is that of cables installed in J-tubes (Coates (1988)). Provided the experimental conditions are a good match for those which the cable could be expected to see in service, empirical data can be used to rate cable systems with high levels of accuracy. Care should be taken in using experimentally obtained data or correlations, in order to ensure that the conditions under which the original work was conducted are a sufficiently close match for the intended application.

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8.3.3

Numerical

With the advent of more powerful desktop computing over the last two decades, cable engineers have begun to turn to numerical methods in order to deal effectively with more complex problems, in particular those where the assumptions required to produce an analytical solution would lead to the calculation being unrepresentative of the actual installation. We briefly introduce the applicable methods here – a full description of their operation and functionality is beyond the scope of this Technical Brochure. All of the methods described share a common principle, which is the need to discretize a set of partial differential equations across the solution area. This is typically achieved through the use of a mesh – a series of interconnected nodes spread across the geometry. The differences between the methods are typically related to the way in which the connections between each node are treated. 1. Finite Difference: the general principle of finite difference calculations is to approximate the derivatives of a partial differential equation (PDE) by linear combinations of function values at each node, i.e. an expression can be written to express the value of a variable (for instance temperature) at each node in relation to the values at the adjacent nodes. The mathematical form used to relate one node to another is typically that of the Taylor series. It is normal to use a uniform grid, which does present some difficulties in working with curved boundaries as are found with cable systems. The finite difference method has been largely superseded by the finite element method for carrying out rating calculations. 2. Finite Element: at a basic level, the principle of the finite element method is similar to the finite difference method, with a mesh being applied to a geometry to allow discretization of a PDE. The benefits of using finite elements are largely ones of flexibility – the mathematical techniques used to describe the relationships between each node permit a greater variety of element types, permitting much more complex geometries to be handled. Finite element methods are also better able to cope with non-linearity. Many engineers have applied finite elements to cable rating problems, particularly those where the installation environment around the cable is too complex to be handled with analytical methods (see IEC TR 62095, 2003) and Lesur et al. (2014). 3. Boundary Element: the boundary element method is generally suitable for solving PDEs relating to linear, homogeneous materials, although inhomogeneous media can also be accounted for. The boundary element method is less widely used than the finite element method, although it can still be applied for cable rating problems. 4. Computational Fluid Dynamics (CFD): CFD techniques are typically based upon finite volume methods (these can be considered as a 3D form of finite difference). Some researchers have applied these techniques to problems involving cables in air, for instance in air filled troughs or tunnels. The correct application of these techniques is extremely complex, particularly where the air flow may be considered to be turbulent. As such, CFD techniques are normally used only as a last resort where no other methods are found suitable, or as a comparator to simpler calculations.

8.3.4

Dynamic Rating Techniques

Dynamic rating tools may use a range of different techniques to calculate ratings, meaning that it is not possible to provide a comprehensive summary here. When designing or assessing a dynamic rating tool, the following areas should be considered: 

Base thermal models: many dynamic rating tools available to system operators at the present time make use of existing thermal models. A large proportion is based on IEC 60853 with others

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using the CIGRE Electra 87 method. A small number use bespoke algorithms, although these are generally intended for use on specific types of cable circuits. 

Treatment of input values: in order to calculate the rating dynamically, the system must take the relevant real-time measurement inputs (as noted in Section 8.2.1) and input them into the thermal model in a suitable manner. For the use in the base thermal models, these can be treated in two broad categories: o

Present time values that are assumed starting point parameters of the base thermal model: these values such as ambient temperature or thermal resistivity can be used directly by the thermal model. Care must be taken that these values remain constant for the time period that the output considers or that any changes are modelled.

o

Historic and actual system values that are derived parameters of the base thermal model: these values are intermediate values calculated by the base thermal models, such as cable surface temperature. Since these are intermediate calculations of the base thermal model it is not a simple matter to change the value in the model to obtain a new result. Instead these will typically show up as a difference between the calculated value in the base thermal model and the measured value. Some dynamic systems will adjust the assumed values of other rating parameters (e.g. thermal resistivity of the ground) to minimise the difference between calculated and measured values (see assumed values section below).



Treatment of assumed rating parameters: in a dynamic system the most accurate results would be obtained by measuring all the parameters used in the calculation but this is not practical. However, in at least one instance known to the authors of this brochure such measurements were undertaken (see Figure 53). As with other current rating calculations often the worst case value is used for any assumed parameter. However in some dynamic current rating systems, an actual cable system temperature (general the cable surface temperature) may indicate that some of the assumptions are incorrect and the system may adjust the assumed rating parameter. The trend in Figure 53 well illustrates this problem. The soil thermal conductivity decreases as the year progresses but is the measurements were to be taken at the beginning of the period only, the resulting ampacity values would be too high.



The method may account for historical behaviour, or may just undertake a forward calculation (using the base thermal model) from the present state. The most advanced methods also take account of predicted variation in the input parameters over the period of the forward calculation.

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1.4

Thermal conductivity (W/Km)

1.2

1

0.8

0.6

0.4

0.2

0 1-Aug

8-Aug

15-Aug

22-Aug

29-Aug

5-Sep

12-Sep

19-Sep

26-Sep

3-Oct

10-Oct

17-Oct

FIGURE 53: MEASURED SOIL THERMAL CONDUCTIVITY DATA OVER A PERIOD OF 3 MONTHS

The thermal conductivity (Figure 53) was measured at the depth of the cable in close vicinity to the circuit. The reduction of the conductivity values (increase in thermal resistivity) might have been caused by drying out of the soil.

8.4

Discussion of Survey Results

The results of the survey in this section look at the questions that are to do with measurement techniques and tools. Where comments were requested and given these have been summarised and grouped together. In some of the surveys there were blank responses, sometimes indicating questions were not applicable to the company or sometimes missed out in error. For some of the analysis presented below, this means that the results (in particular the number of comments) do not add up to the totals reported.

8.4.1

Emergency Rating methods

Table 11 shows the number of companies that consider emergency ratings (refer to question 3.4 of the questionnaire).

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TABLE 11: THE NUMBER OF COMPANIES THAT CONSIDER EMERGENCY RATINGS

Result Company type Cable manufacturer Consultancy Utility Other Total

Considered 22 12 44 6

Not considered 0 0 11 2

Blank 0 1 3 0

Total 22 13 58 8

84

13

4

101

The results in Table 11 show that all the cable manufacturers and all the consultancies that responded to the question could calculate emergency ratings. The majority (76%) of Utilities considered emergency ratings. Of the companies that reported using emergency ratings (84 companies), the method of calculation reported is shown in Table 12. Note that since more than one method may be used by a company, the total number of methods used is greater than 84.

TABLE 12: THE METHOD OF EMERGENCY CALCULATION AS REPORTED

Result Emergency rating method

Yes No IEC 60853 53 30 Rating ratio 13 70 Automatic (e.g. real time rating) 12 71 Other 31 52 The other rating methods reported fell into the following general categories  Method not given (max temp. referred to) 7 responses  Calculate: method not disclosed 5 responses  Customer requirement 5 responses  External software 4 responses  Real time rating 2 responses  JCS 0501:2002 2 responses  CIGRE B1-209 1 response  Method not given 1 response  As specified by supplier 1 response  Blank 1 response

Blank 1 1 1 1

The results show that the majority of companies used IEC 60853. It is interesting that none of the companies report using CIGRE (1983-2) computer method although this may be implemented in software and the companies reporting use of a computer did not report the method used by the software.

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8.4.2

Method of Calculation of Steady State Current Ratings

A number of different tools can be used to calculate steady state current ratings and the table below shows the number of companies that use each type of tool (refer to question 5.1), see Table 13.

TABLE 13: THE STEADY STATE CALCULATION METHOD USED

Result Calculation method

Yes Hand or spreadsheet 57 Rating tables 33 In house (IEC Neher/McGrath) 57 Commercial (not FEM) 33 FEM 25 Other 15 The following “other” methods were identified:  Commercial 4 responses  In house (method not disclosed) 4 responses  Hand / spreadsheet 2 responses  In house (JCS0501) 2 response  In house (CIGRE B1-102) 1 response  In house (finite difference) 1 response  In house (forced cooling) 1 response  Rating tables 1 response

No 30 44

Blank 14 22

30 51 56 51

14 17 20 35

The majority of other methods identified were in house methods that did not use IEC or Neher/McGrath although it appears some “other” methods identified were identified in error (e.g. commercial or rating tables already is an option). Note that more than one “other” method could be identified leading to more methods identified than companies reporting “other” in Table 38. The results for question 5.1 suggest that the majority of companies perform current rating calculations themselves. These are either by hand, spreadsheet or in house computer program, or a combination of these. It should be noted that the survey may be biased in that the companies performing their own calculations were more likely to reply to the survey. However, it does suggest that there are a large percentage of companies that use current rating standards directly.

8.4.3

Comparison of Calculated and Measured Cable Temperatures

Around 40% of the respondents had compared calculated temperatures to measured cable temperatures for continuous ratings (details come from question 5.5, and are shown in Table 14).

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Result Company type Cable manufacturer Consultancy company Utility Other Total

Yes 7 5 22 6

No 13 6 37 2

Blank 2 0 1 0

40

58

3

The following comments were made:  DTS  Good results  Laboratory  DTS and thermocouples  Need transient models  Steady state never reached  Bad results  Measurement made at hot spots  Dynamic rating system used  At street crossing (big difference once)

8 responses 4 responses 6 responses 2 responses 1 response 1 response 1 response 1 response 1 response 1 response

The majority appeared to use a DTS system. Some noted that steady state conditions were not achieved and that a transient current rating or dynamic rating system was required. While most did not comment on the success of the measurement, where a comment was made, generally good results were reported but there was some that either reported bad results, or suggested difficulties.

8.4.4

Transient Rating Methods

Table 15 gives the number of companies that calculate transient ratings (question 6.1).

TABLE 15: THE NUMBER OF COMPANIES CALCULATING TRANSIENT RATINGS

Result Company type

Calculated

Not calculated

Blank

Total

Cable manufacturer Consultancy Utility Other

16 8 24 6

5 3 30 2

1 2 4 0

22 13 58 8

Total

54

40

7

101

The results in Table 15 show that the majority of utilities do not calculate the transient ratings themselves. However, most of the other respondents do so.

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Of the companies that reported using calculating transient ratings, the method used is reported in the following table:

TABLE 16: TRANSIENT RATING CALCULATION METHODS USED

Result Emergency rating method

Yes No In house, IEC 31 17 In house, CIGRE 11 27 Commercial program 25 17 Other 13 23 The other rating methods reported fell into the following general categories  In house, JSC 2 responses  In house, modified IEC 2 responses  In house CIGRE B1-209 2012 1 response  In house, own method 1 response  In house, numerical method 1 response  In house method 1 response  In house CIGRE 1 response  Rating factors 1 response  Dynamic rating system 1 response  FEM 1 response

Blank 7 13 10 15

A number of respondents are using their own methods, although many appear to be based on existing standards.

8.4.5

Limitations or Difficulties with Cyclic or Emergency Ratings

Of the companies asked, 24 of respondents had reported limitations or difficulties (question 6.3). Many of the comments appeared to relate to dynamic (or real time) rating systems and these comments have been left out:       

Complex calculation Short/variable loadings (IEC 60853 not applicable) Convection not modelled for air installations Moisture migration not modelled in IEC 60853 Not clear deep HDD calculation is accurate Calculation results not used as not integrated Thermal resistivity not static

6 responses 2 responses 1 response 1 response 1 response 1 response 1 response

A number of companies commented on the complexity of the calculation.

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8.4.6

Cyclic or Emergency Ratings fully Integrated into the Network or Stand-alone

Only 13 of the companies including 5 utilities (9% of such companies) reported on question 6.4 to use a fully integrated system. There were, however, 46 (46%) blank responses, of which utilities provided 31 (56% of utilities).

8.4.7

Real Time Temperature Monitoring Systems

Of the companies surveyed, 46 reported using a real time temperature monitoring system, with 38 reporting they did not and 17 not answering question 7.1. The minority of 13 reported using their own developed system. The number of companies reporting using a commercial DTS system was 52. It is noted that this is more than the number of companies reporting using a real time temperature monitoring system and some specifically reporting they did not have a real time temperature monitoring system. This may be as some companies were using the DTS systems for real time rating systems.

8.4.8

Position of the Optical Fibre Sensor for DTS Monitoring Systems

The companies were asked the location of the optical fibre sensor if they used DTS monitoring systems (question 7.2). Table 17 shows the results of the question.

TABLE 17: LOCATION OF DTS SENSOR

Result Company type

Yes

No

Inside cable, cable screen 41 21 Cable surface 38 20 External parallel conduit 33 33 Other 8 33 Where the location was other, the following locations were identified:  Inside conductor 2 responses  Inside the surrounding medium 1 response  Middle of cable trefoil 1 response  In the armour 1 response

Blank 36 40 42 57

There are a number of different locations, with some companies using different locations depending on the specific installation. There did not appear to be a predominant location although the cable screen or attached to the cable surface appeared to be the most common.

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8.4.9

Use of Fixed or Mobile DTS Systems

The companies were asked if the DTS monitoring systems they had installed were connected permanently to the same circuits or if the DTS system were used on a temporary basis (question 7.2). The majority of users (39 companies) connected the DTS system permanently, 20 companies used mobile/temporary connections, 3 used both types. One company responded that it did not have any DTS system and 38 companies left the answer blank.

8.4.10 Overall Accuracy Check for the DTS System The companies were asked if the overall accuracy of the DTS system was checked (question 7.3). Table 18 shows the results.

TABLE 18: THE NUMBER OF COMPANIES THAT CHECKED OVERALL ACCURACY OF A DTS SYSTEM

Result Company type

Yes

No

Blank

Cable manufacturer Consultancy Utility Other

11 4 15 3

5 4 20 2

6 5 23 3

Total

33

31

37

It appears that most companies check the accuracy of their DTS. The company was asked to provide the results of the check and these are shown:  Good accuracy 6 responses  Compare DTS to thermocouples 3 responses  Generally acceptable (within 2 °C) 1 response  Problems with longer lengths 1 response  Lab tests 1 response  System and distance dependent 1 response  Not possible to check accuracy of conductor temperature 1 response  Time lag between conductor and measurement 1 response

In general, good accuracy was reported although some users reported problems, particularly with longer lengths. Users also noted that the conductor temperature was generally not measured or easily deduced.

8.4.11 Limitations or Difficulties Experienced with DTS Monitoring Systems The number of companies that reported limitations or difficulties is shown in Table 19 (question 7.3).

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES TABLE 19: THE NUMBER OF COMPANIES THAT REPORTED LIMITATIONS OR DIFFICULT EXPERIENCES

Result Company type

Yes

No

Blank

Cable manufacturer 2 10 10 Consultancy 5 4 4 Utility 13 14 31 Other 6 0 2 Total 26 28 47 While about the same number of companies reported limitations or difficulties as did not, when split by company type, there is considerable variation. The limitations or difficulties reported were:  Unreliable equipment 6 responses  Does not measure conductor temperature 5 responses  Difficult to use 2 responses  Cost 1 response  Difficult to calibrate over the required operating temperature range 1 response  For cables in air, surface temperature measurement uncertain 1 response  Communication problems 1 response  Unstable software 1 response  Calibration difficult 1 response  Sensitive to different fibres 1 response  Accuracy 1 response

There appear to be three main themes: unreliable systems, difficult to use (or interpret conductor temperature), and accuracy/calibration problems. These subjects will be further considered in the CIGRE WG B1.45 ‘Thermal monitoring of cable circuits and grid operators’ use of dynamic rating systems’.

8.4.12 Number of Companies using Real Time Current Rating Systems The number of companies using real time current rating systems is shown in the table below (question 8.1).

TABLE 20: THE NUMBER OF COMPANIES USING REAL TIME CURRENT RATING SYSTEMS

Result Company type Cable manufacturer Consultancy Utility Other Total

Yes

No

10 5 15 1 31

12 8 36 7 66

The majority of companies do not use real time current rating systems. There is a significantly larger number proportion of cable manufacturers and consultancies using (it is assumed offering) real time

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current rating systems than utilities, assumed to be actually using such systems. In many of the comments it was noted that while many companies do not use a real time current rating system at present they are considering or working on implementing a real time current rating.

Of the companies that used real time current rating systems, the number of companies using a system developed by their company is given in Table 21.

TABLE 21: THE NUMBER OF COMPANIES USING OWN DEVELOPED REAL TIME CURRENT RATING SYSTEMS

Result Company type Cable manufacturer Consultancy Utility Other Total

Yes

No

6 3 2 1 12

4 2 14 0 20

The majority of utilities that have a real time current ratings system do not develop the system. In contrast, the majority of cable manufacturers and consultancies use (it is assumed that this means offer a system) a system that is developed by the company.

Of the companies that used real time current rating systems, the number of companies using a commercial real time current rating system is given in Table 21.

8.4.13 Use of Optical fibre (DTS) System as Input to Real Time Current Rating System Of the companies that use a real time current rating system, the majority 25 reported using an optical fibre DTS as the input to the real time current rating. There were 7 (22%) that reported not using an optical fibre DTS and 3 (9%) left a blank entry on question 8.2.

TABLE 22: THE NUMBER OF COMPANIES USING COMMERCIAL REAL TIME CURRENT RATING SYSTEMS

Result Company type Cable manufacturer Consultancy Utility Other Total

Yes

No

4 1 14 0 19

6 4 2 1 13

As expected from the results in Table 21, the majority of utilities using a real time rating system use a commercial real system and the majority of manufacturers and consultants do not.

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Note that one utility reported using both own developed and commercial systems, while 2 companies reported they used a real time current rating system but did not identify either an own developed or commercial system. Hence, the results in Table 21 and Table 22 do not add to up to those shown in Table 20.

8.4.14 Use of Safety Factors in Real Time Current Rating System Of the companies that use a real time current rating system, 7 reported using a safety factor (question 8.3). The safety factors reported were:   

Early alarm below maximum operating temperatures As specified by the client Same safety factor as static (10 °C reduction when soil condition not known)

3 responses 2 responses 1 response

8.4.15 Number of Integrated and Standalone Real Time Current Rating Systems The number of real time systems that are fully integrated and standalone is reported below (question 8.4).

TABLE 23: THE NUMBER OF INTEGRATED AND STANDALONE REAL TIME CURRENT RATING SYSTEMS

Result Company type Cable manufacturer Consultancy Utility Other Total

Integrated

Standalone

Blank

1 1 8 0 10

7 4 7 1 18

2 1 2 0 5

Of the companies that reported using real time current rating systems, the majority use standalone version. However amongst the utilities 50 % of the current rating systems are integrated with another utility (6%) stating that they were studying integrating the real time current rating system. Of the companies that were not utilities, it is assumed that they were offering real time current rating systems and the majority of these were standalone systems. It should be noted that some companies had both integrated and standalone systems.

8.4.16 Limitations or Difficulties Experienced with Real Time Current Rating Systems Of the companies that reported using a real time current rating system, the number of companies that reported limitations or difficulties is shown in Table 24 (question 8.5).

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES TABLE 24: THE NUMBER OF COMPANIES THAT REPORTED LIMITATIONS OR DIFFICULT EXPERIENCES

Result Company type Cable manufacturer Consultancy Utility Other Total

Yes

No

Blank

2 3 2 1 8

5 1 11 0 17

3 1 3 0 7

Although in general only 8 companies reported limitations or difficulties with real time current rating systems, 3 out of 4 consultants reported limitation or difficulties. The limitations or difficulties reported were:    

Reliability of measurement / monitoring systems Accuracy Use in control room Rating estimation at low load

6 responses 1 response 1 response 1 response

The majority of limitations related to the measurement / monitoring systems, mainly a concern of the accuracy of the measurement, sometimes in specific locations such as ducts blocks, although the reliability of the measurement equipment was also a concern. Another concern noted was the ability of the control room to use current ratings that would change over time.

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9

Con clu s ion s and R e c omm end at ion s

This technical brochure provides guidance to experts calculating the current rating of new or existing cable circuits. Starting points for cable rating studies, the rating calculations themselves, and the calculation tooling have all been considered. The WG hopes to have contributed to the topic of current rating calculations by providing clarity on how a current rating study can be performed for a power cable whatever its situation. By providing these guidelines, it is also hoped that companies worldwide will use similar approaches to deal with similar problems, so that in the long run, also solutions to the most difficult problems become available. The major conclusions are reported, and recommendations both to users and Cigre SC B1 are given. A first aspect to be noted in this section is that system failures due to overloading of power cables is rather rare. It appears that the moderate loading of the majority of the cable systems in use is the most important explanation to this finding. This means that in case of significant load (profile) changes in the future, we may be coming much closer to the limitations of the current rating of power cable systems than we are today. Given the ongoing developments in renewable energy and energy usage, the working group therefore believes that the topic of current ratings of power cables is only increasing in importance. Secondly, within cable projects cable rating evaluation studies will always come at a certain limited accuracy. There should be a margin in cable rating calculations which is dependent in this accuracy and therefore also on the exact project phase. The working group recommends that this margin in rating calculations is consequently discussed and agreed between parties in any cable project. Reference is made to Section 2.3 of this brochure. Considering the starting points for rating calculations, it is concluded that most starting points are currently being assumed, rather than measured or investigated. Assuming starting points easily lead to uncertainties of tens of percent’s in the cable’s current rating. Consequently, the user is recommended to measure or investigate the relevant starting points rather than to estimate or assume them. In order to have a well-defined cable current rating, there must be an even balance in between the accuracy of starting points, calculation methods and calculation tools. Although calculation methods typically already have an accuracy down to a few percent, this is not a realistic expectation for the starting points, although these are at the basis of every cable rating study. Therefore, the working group strongly recommends paying attention to measuring / investigating starting points. Information on how to improve the definition of starting points can be found in this document, but the working group also identified that an overall document on practical ways to determine the thermal resistivity of soils (which strongly vary in multiple aspects over the world) or the dry out behaviour of soils is currently not available in international literature. The working group recommends Cigre SC B1 to consider drafting such an overall document. Cable rating calculation methods are available to deal with many different situations. This technical brochure contains many different calculation methods, guidelines, and hints additional to existing IEC standards, to help the user in selecting the right method to perform a cable rating calculation. The WG is under the impression that the calculation methods presented in this technical brochure cover the vast majority of cables and installation methods, and provide a constructive procedure towards an answer. It is noted that the WG was not able to provide a detailed method in every situation. Sometimes, there is simply too little international experience available to come to a good solution. In

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those cases, the WG has provided more abstract guidance and hints on the way to come to a proper calculation as much as possible. In some situations, it is believed that there is an important need to develop better calculation methods. Experts are encouraged to publish their methods regarding those situations in international literature, so that in some years from now, the cable community can come to more precise calculations. The following situations are believed to be calling more strongly for the attention of experts, although this technical brochure contains significant wording on each of them: 

The current rating of HVDC cables. Especially the dependency of heat losses on detailed material characteristics needs to be known better, together with the temperature dependency of the electric field in the insulation material. Refer to Section 5.3.2.



The effect of oil / air gaps or pockets in cables with e.g. corrugated sheaths should be detailed. Given the wide usage of cables with corrugated sheaths, there is a need to understand the effect of these substantial oil / air filled clearances in the cable design on the current rating, preferably leading to a verified physical model. Refer to Section 6.2.1.



There is evidence available that the armour losses of three core submarine cables is smaller than what is currently calculated based on existing methods, implying that these existing methods should be improved. In order to come to this (and to a higher rating of submarine cables), more investigations of different companies are needed. Refer to Section 6.6.1.



Only a little experience (measurements, investigations, calculations) is available regarding the current rating of joints and terminations. It is helpful to increase the information on this subject in order to be able to derive, for any cable circuit, the limitations to the stationary and dynamic current rating coming from these accessories. Refer to Sections 7.1.7 and 7.1.8.



Where cables are installed in inclined air or water filled ducts (e.g. horizontal directional drillings) and especially in combination with layered soils, the heat transfer from the power cable to the far environment becomes very complex, calling for detailed investigations in order to determine the governing heat transfer equations. Refer to Section 7.2.2.

Regarding calculation tools available to perform rating calculations, this technical brochure contains descriptions of the calculations methods used. The amount of tools available has been increasing with multiple transient and dynamic rating tools. Also the user’s reflection on these tools is given within this brochure. It was found that dynamic rating systems and transient ratings are slowly attracting more attention, although at present the majority of companies do not use dynamic rating tools yet. The most important recommendation which can be made regarding calculation tools, is that the user needs to verify the calculations of the tool before using it. Despite some tools being used frequently, and by multiple companies, it is generally unclear exactly how a calculation is performed by the calculation tool. Given the many different installation situations and cable designs which exist, and for which a strict IEC based calculation is not even possible (refer to the many examples in this technical brochure), the user should verify how the situation is treated by the calculation tool. The assumptions made and the formulae used must be applicable, but these are not gathered in any standard. For dynamic or transient ratings, verification becomes even more important as the dynamic behaviour significantly complicates the models and their output. As it is rather difficult to verify calculations of calculation tools, especially when these tools provide transient or dynamic ratings, or real life situations which are not precisely covered by IEC, the WG considers helping the cable community by setting up a uniform calculation verification protocol, which can be used to ensure a correctly working software within a certain (limited) domain.

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10

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Arrighi, R. (1986), “Carrying capacity of AC high Voltage systems with internal insulation over long distances”, CIGRE report 21-13 1986 Bejan, A. (1993), “Heat transfer”, John Wiley & sons, ISBN 0-471-50290-1 Boone, W. and De Wild, F. (2007), “HV Power Cables Installed in Multi Purpose Tunnels, a Challengeable Option”, Jicable 2007, Versailles, France, June 24-28 Boyd, S. and Vandenberghe, L,( 2004) “Convex Optimization”, Cambridge, Cambridge University press, 2004 Bremnes, J. J., Evenset, G. and S. R, (2010), “Power loss and inductance of steel armoured threecore cables: comparison of ‘2.5D’ FEA results and measurements”, CIGRE session, Paris, France, paper B1-116 Brakelmann, H. (1984) “Physical principles and calculation methods of moisture and heat transfer in cable trenches”, ETZ report 19, page 1-93, VDE- verlag GmbH, Berlin u. Offenbach, 1984 Brakelmann H., Honerla, J., and Rasquin, W. (1991) “Thermal Resistance of Cables with Corrugated Sheaths” ETAP Vol 1, No. 6 pp 341 - 346 Brakelmann, H. (1999), “Reinforcement of Power Cables Crossing Thermally Unfavourable regions,” ETEP, vol. 9, no. 3, pp. 199-202 Brakelmann, H. and Anders, G. (2001), “Ampacity Reduction Factors for Cables Crossing Thermally Unfavourable Regions,” IEEE Transactions on Power Delivery, vol. 16, no. 4, pp. 444-448 Cress, S.L. and Motlis J. (1991), "Temperature Rise of Submarine Cable on Riser Poles", IEEE Transactions on Power Delivery, Vol. 6, No. 1, pp. 25-33 Carslaw H.S. (1945), “Introduction to the mathematical theory of the conduction of heat in solids”, Dover publications, New York Chaaban, M., and Leduc, J. (2011), “Reduction in Current Carrying Capacity due to Cables th Crossing,” 8 International Conference on Insulated Power Cables – Jicable’11, Versaille, France, paper id: c.8.4 Chimi, E., Heimbach, B., Bader, J. and Luternauer, H. (2014), “Pilot project for cable capacity monitoring using optic fibre cables and prognostic software in the city of Zurich”, Cigre 2014, Paris, France, paper B1-208 CIGRE (1979), “The calculation of continuous ratings for forced cooled cables”, Electra, vol. 066, with erratum CIGRE (1982), “the conditions govering the drying-out of soil around power cables”, Electra, vol 84 CIGRE (1983-1), “Forced cooling of cable joints and terminations”, Electra, vol. 90

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CIGRE (1983-2), “Computer method for the calculation of the response of single core cables to a step function thermal transient”, Electra, vol 87 CIGRE (1985), “The calculation of the effective thermal resistance of cables laid in materials having different thermal resistivities”, WG2 of CIGRE SC 21, Electra, no 98 CIGRE (1986), “Forced cooled cables. Calculation of thermal transients and cyclic loads”, Electra vol. 104 CIGRE (1987), “The calculation of continuous rating for forced cooled high pressure oil filled pipe type cables”, Electra vol. 113, including erratum: Electra vol. 119 (1988) and addendum: Electra 135 (1991) CIGRE (1990), “The steady state thermal behaviour of accessories for cooled cable systems”, WG 8 of CIGRE SC 21, Electra no. 128 CIGRE (1992-1), “Calculation of temperatures in ventilated cable tunnels – Part 1”, WG8 of CIGRE SC 21, Electra, no 143, pp 39-59 CIGRE (1992-2), “Calculation of temperatures in ventilated cable tunnels – Part 2”, WG8 of CIGRE SC 21, Electra, no 144, pp 97-105 CIGRE (1992-3), “Methods for calculating cyclic ratings for buried cables with partial drying of the surrounding soil”, Electra vol. 145 CIGRE (1992-4), “Determination of a value of critical temperature rise for a cable backfill material”, Electra vol. 145 CIGRE (2004), Technical Brochure 250, “General guidelines for the integration of a new underground cable system in the network”, WG B1.19 CIGRE (2005), “Addendum to recommendations for tests of power transmission dc cables for a rated voltage up to 800kV”, Electra, vol. 218, pp39-45, February 2005 CIGRE (2005-1), Technical Brochure 272, “Large cross section and composite screens design”, WG B1.03 CIGRE (2005-2), Technical Brochure 283 “Special bonding of high voltage power cables”, WG B1.18 CIGRE (2008), Technical Brochure 358 “Remaining life management of existing AC underground lines”, WG B1.09 CIGRE (2010), Fröhlich, K. “Cigre technical activities – strategic directions 2010-2020”, Electra no 249, April 2010 CIGRE (2013-1), Technical Brochure 559, “Impact of EMF on current ratings and cable systems”, WG B1.23

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CIGRE (2013-2), Technical Brochure 556, “Power system technical performance issues related to the application of long HVAC cables”, WG C4.502 Coates, M. (1988), "Rating Cables in J-tubes", Leatherhead: ERA Report 88-0108 Colla, L. and Marelli, M. (2013), “Dynamic rating of submarine cables – Application to offshore windfarms”, in proc of EWEA Offshore, Frankfurt, Germany Cress, S.L. and Motlis J. (1991), "Temperature Rise of Submarine Cable on Riser Poles", IEEE Transactions on Power Delivery, Vol. 6, No. 1, pp. 25-33 Defega, M.Z., Lehtonen, M. and Millar, R.J. (2012), “Comparison of Air-Gap Thermal Models for MV Power Cables indside Unfilled Conduit”, IEEE Transactions on Power Delivery (2012), volume 27, issue 3, page 1662-1669 Del Brenna, M., Donazzi, F., Mansoldo, A. (2004), “Long length EHV underground cable systems in the transmission network”, CIGRE session 2004, paper B1-304 Demoulias, C., Labridis, D. P., Dokopoulos P. S. and Gouramanis K. (2007), “Ampacity of Low_Voltage Power Cables Under Non-sinusoidal Currents”, IEEE Transaction on Power Delivery, Volume: 22, Issue: 1, pp. 584-594 Donazzi, F., Occhini, E., Eng, C. and Seppi, A. (1979), “Soil thermal and hydrological characteristics in desgning underground cables”, IEE proceedings, Vol. 126, June 1997 Dryer, J. (1978), "Natural Convective Flow Through a Vertical Duct with Restricted Entry", International Journal of Heat and Mass Transfer, Vol.21, pp. 1344-1354 Djogo, D. and Salam, M.M.A. (1997), “Calculation of inductive coupling from power lines to multiple pipelines and buried conductors,” Electric Power Systems Research, vol. 41, issue 1, pp. 75-84 Donazzi, F., Carpinelli, G. and Valenza, D. (1987), “On the low and medium voltage cables sizing problem in presence of current and voltage non-sinusoidal waveform”, L’Energia Eletrica, vol 64, no. 5 Dorison, E., de Kepper, B., Protat, F., Gurkahaman, A. and Masure, L., (2003), “Current rating of cables installed in tunnels”, Proc. of Jicable 2003, Versailles, France, paper C8-1-6 Dorison E., Anders, G. and Lesur F., (2010), “Ampacity calculations for deeply installed cables”. IEEE Trans. on Power Deliver”, Vol. 25, No. 2, pp. 524-533 Dorison, E. and Anders, G., (2011), “Current rating of cables installed in deep or ventilated tunnels”, Proc. Of Jicable 2011, Versailles, France, paper C8-3 Du, P.Y. and Wang, X.H. (2010), “Electrical and thermal analyses of parallel single-conductor cable installations,” IEEE Transactions on industry applications, vol. 46, no. 4, pp. 1534-1540

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El-Kady, M.A. and Horrocks, D.J. (1985), “Extended values of geometric factor of external thermal resistance of cables in duct banks”, IEEE Transactions on Power apparatus and Systems, PAS104, no 8, pp. 1958-1962 El-Shaarawi and Sarhan, A., (1981), "Developing Laminar Free Convection in a Heated Vertical Open-ended Concentric Annulus", Industrial & Engineering Chemistry, Fundamentals, Vol.20, No.4, pp. 388-394 ENA C55/4, 1989, “Insulated Sheath Power Cable Systems” Eoll, C. “Theory of stress distribution in insulation of high-voltage dc cables: part II,” Electrical Insulation, IEEE Transactions on, Vols. EI-10, no. 2, pp. 49-54, June 1975 EPRI (2011), “EPRI Underground Distribution Systems Reference Book”, Electric Power Research Institute EPRI (2011), Presentation of Henk Geene at the IEEE ICC 2009 fall meeting EPRI (1984), “Designer’s handbook for Forced-Cooled high-pressure oil-filled pipe-type cable systems”, EPRI EL-3624, July 1984 ETRA (1998), Electric Technology Research Association report, Vo. 53, No. 3 (1998) “Ampacity design for underground cables”, Japanese language Ferkal, K., Poloujadoff, M. and Dorison, E., (1996), “Proximity effect and eddy current losses in insulated cables,” IEEE Transactions on Power Delivery, vol. 11, no. 3, pp. 1171-1178 GB 50217 (2007), “Code for design of cable of electrical work”, translated Chinese standard, issued in October 2007, in force April 2008 Groeneveld, G.J. et al. (1984), “Improved method to calculate the critical conditions for drying out sandy soils around power cables”, IEE proceedings, vol. 131, Pt C n02 – 1984 Hatlo, M.M. and Bremnes, J.J.(2014) “Current depend armour loss in three-core cables; comparison FEA results and measurements”, Cigre 2014, Paris, France, paper B1-306 Hartlein, R.A. and Black, W.Z. (1983), "Ampacity of Electric Power Cables in Vertical Protective Risers", IEEE Transactions on Power Apparatus and Systems, Vol. PAS-102, No.6, pp. 16781686 Heinhold L. (1990) “Power Cables and Their Applications – Part I”, Siemens, Germany Hennuy, B., Leemans, P., Mampaey, B., Burceanu, M. and van Slycken, J. (2014), “Belgian philosophy and experience with temperature monitoring of cable systems by means of distributed temperature sensing techniques and future PD monitoring techniques” Cigre 2014, Paris, France, paper B1-203 Hiranandani, A. (1995), “Calculation of ampacities and Sizing of Line and Neutral Conductors in the Presence of Harmonics”, Annaul Meeting of Industry Society, Orlando, Florida, USA

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Holman, J.P. (1990), "Heat Transfer", McGraw-Hill, New York Houwelingen, D. van and Rossum, J. van (2007), “Re-evaluation of 150kV cable capacity”, Proc. of Jicable 2007, Versailles, France, paper 2007-B4-5 Huang, Z. Y., Pilgrim, J. A., Lewin, P. L.., Swingler, S. G. and Tzemis, G. (2014) ., “Thermal-Electric Rating Method for Mass-Impregnated Paper-Insulated HVDC Cable Circuits”, IEEE Transactions on Power Delivery, 30 (1), 437-444 ICEA P-32-382-2007, “Short-circuit characteristics of insulated cables”, 2007 ICEA P-45-482-2007, “Short-circuit performance of metallic shields & sheaths”, 2007 IEC standard 60055, “Paper-insulated metal-sheathed cables for rated voltages up to 18/30 kV (with copper or aluminium conductors and excluding gas-pressure and oil-filled cables”: 

IEC standard 60055-1 (2005), “Paper-insulated metal-sheathed cables for rated voltages up to 18/30kV (with copper or aluminium conductors and excluding gas-pressure and oil-filled cables) – Part 1: Tests on cables and their accessories” IEC standard 60055-2 (1981), “Paper-insulated metal-sheathed cables for rated voltages up to 18/30kV (with copper or aluminium conductors and excluding gas-pressure and oil-filled cables) – Part 2: General and construction requirements”



IEC standard 60287, “Calculation of the Continuous Current Rating of Cables (100% load factor)”: 

IEC standard 60287-1-1 (2014), “Electric Cables - Calculation of the current Rating – Part 1: Current rating equations (100% load factor) and calculation of Losses – section 1: General”



IEC standard 60287-1-2 (1993), “Electric Cables – Calculation of the current rating – Part 1: Current rating equations (100% load factor) and calculations of losses – Section 2: Sheath eddy current loss factors for two circuits in flat formation”



IEC standard 60287-1-3 (2002), “Electric Cables – Calculation of the current rating – Part 1: Current rating equations (100% load factor) and calculations of losses – Section 3: Current sharing between parallel single-core cables and calculation of circulating current losses”



IEC standard 60287-2-1 (2015), “Electric Cables – Calculation of the current rating – Part 2: Thermal resistance – Section 1: Calculation of thermal resistance”.



IEC standard 60287-2-2 (1995), “Electric Cables – Calculation of the current rating – Part 2: Thermal resistance – Section 2: A method for calculating reduction factors for groups of cables in free air, protected from solar radiation”



IEC standard 60287-3-1 (1999), “Electric Cables – Calculation of the current rating – Part 3: Sections on operating conditions – Section 1: Reference operating conditions and selection of cable type”



IEC standard 60287-3-2 (2012), “Electric Cables – Calculation of the current rating – Part 3: Sections on operating conditions – Section 2: Economic optimization of power cable size”

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES 

IEC standard 60287-3-3 (2007), “Electric Cables – Calculation of the current rating – Part 3: Sections on operating conditions – Section 3: Cables crossing external heat sources”

IEC standard 60502, “Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um=1,2 kV) up to 30 kV (Um=36 kV)”: 





IEC standard 60502-1 (2009), “Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um = 1,2 kV) up to 30 kV (Um = 36kV) – Part 1: Cables for rated voltages of 1 kV (Um = 1,2 kV) and 3 kV (Um = 3,6 kV).” IEC standard 60502-2 (2014), “Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um = 1,2 kV) up to 30 kV (Um = 36kV) – part 2: Cables for rated voltages from 6kV (Um = 7,2 kV up to 30 kV (Um = 36 kV)” IEC standard 60502-4 (2010), ““Power cables with extruded insulation and their accessories for rated voltages from 1 kV (Um = 1,2 kV) up to 30 kV (Um = 36kV) – Part 4: Test requirements on acce3ssories for cables with rated voltages from 6 kV (Um = 7,2 kV) up to 30 kV (Um = 36 kV)”

IEC standard 60724 (2008), “Short-circuit temperature limits of electric cables with rated voltages of 1 kV (Um=1,2kV) and 3 kV (Um = 3,6 kV)” IEC standard 60840 ed4.0 (2011), “Power cables with extruded insulation and their accessories for rated voltages above 30 kV (Um = 36 kV) up to 150 kV (Um = 170 kV) – Test methods and requirements” IEC standard 60853, “Calculation of the cyclic and emergency current rating of cables”: 

IEC standard 60853-1 (1985), “Calculation of the cyclic and emergency current rating of cables – Part 1: Cyclic rating factor for cables up to and including 18/30 (36) kV”, including Amendment 1 (1994) and Amendment 2 (2008)



IEC standard 60853-2 (1989), “Calculation of the cyclic and emergency current rating of cables – Part 2: Cyclic rating of cables greater than 18/30 (36)kV and emergency ratings for cables of all voltages”, including Amendment 1 (2008)



IEC standard 60853-3 (2002), “Calculation of the cyclic and emergency current rating of cables – Part 3: Cyclic rating factor for cables of all voltages, with partial drying of the soil”

IEC standard 60949 (1988), “Calculation of thermally permissible short circuit currents, taking into account non-adiabatic heating effects including Amendment 1 (2008)” IEC standard 60986 (2008), “short-circuit temperature limits of electric cables with rated voltages form 6 kV (Um = 7,2 kV) up to 30 kV (Um = 36 kV)” IEC standard 61443 (2008), “Short-circuit temperature limits of electric cables with rated voltages above 30 kV (Um= 36 kV)” IEC standard 62067 ed2.0, “Power cables with extruded insulation and their accessories for rated voltages above 150kV (Um = 170 kV) up to 500 kV (um = 550kV) – Test methods and requirements”

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IEC standard 62095 (2003), “Electric cables - Calculation for current ratings – finite element method” IEC Technical Report 62095 (2003), “Calculation of current rating - Cable current rating calculations using finite element method” IEEE standard 835 (1994), “IEEE Standard - Power Cable Ampacity Tables”, IEEE Press Jackson, R.I. (1975), “Eddy-current losses in unbounded tubes”, Proceedings of institution of Electrical Engineers, vol. 122, no 5, pp 551-557 Jeong, S., Nam, K., Choi, S., Ryo, H. and Lee, J., (2004), “Analysis on the Longitudinal Temperature Derating Factor of Power Cables Surrounding Dissimilar Soil Materials Region,” In Proc. 2004 International Conference on Power System Technology – POWERCON 2004, pp. 1463-1468 Jeroense, M. and Kreuger, F., “Electrical conduction in hvdc mass-impregnated paper cable,” Dielectrics and Electrical Insulation, IEEE Transactions on, vol. 2, no. 5, pp. 718-723, October 1995 Jivet, I. and Dragoi, B. (2008), “Performance analysis of direct digital synthesizer architecture with amplitude sequencing”, WSEAS transactions on Circuits and Systems, vol 7, 1 Joshi, Himanshu M, (1987) "Fully Developed Natural Convection in an Isothermal Vertical Annular Duct". International Communications in Heat and Mass Transfer, Vol. 14, No.6, NovDec 1987, pp. 657-664 Joshi, Himanshu M. (1988) "Numerical Solutions for Developing Laminar Free Convection in Vertical Annular Ducts Open at Both Ends", Numerical Heat Transfer, Vol. 13, No. 3, pp. 393-403 Katz, C. et al. (1978), “ Progress in the Determination of AC/DC resistance Ratios of Pipe-Type Cable Systems” , IEEE Transactions on Power Apparatus and Systems, Vol PAS-97, No. 6 Kawasaki K., Inami, M. and Ishikawá, T., (1981), “Theoretical considerations on eddy currents losses in non-magnetic pipes for power transmission”, IEEE Transactions on power apparatus and systems, Vol. PAS-100, no 2, pp. 474-484 KEMA/Heijdemej, “Moisture migration and drying-out in sand round heat dissipating cables and ducts”, Arnhem, 1981, additional: workshop “Current rating of buried cables in relation to thermal properties of soil”, Arnhem 1985 Keyhani, M. and Kulacki, F.A., (1985) "Natural Convection in Enclosures Containing Tube Bundles", in "Natural Convection", edited by KaKac,S. et al., Hemisphere Publishing Corporation. New York King, S.Y., Halfter, N.A., (1983) “Underground Power Cables”, Longman, London, United Kingdom Koopmans, G. and Kuiper, J. (1990), “The critical temperature for drying-out of soils around power cables as a function of local conditions”, Kema scientific & technical reports, 1990

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Koreman, C.G.A., Aanhaanen, G.L.P., van Rossum, J.C.M., Koning, R.F.F., Boone, W. and de Wild, F. (2006), “Development of a new 380kV double circuit XLPE insulated cable system in the Netherlands”, Cigre 2006, Paris, France, paper B1-107 Kovač, N., Sarajcev, I. and Poljak, D., (2006), “Nonlinear-coupled electric-thermal modelling of underground cable systems”, IEEE Transactions on Power Delivery, vol. 21, no. 1, pp. 4-14 Kusuda, T. and Achenbach, P. (1965), “Earth Temperature and Thermal Diffusivity at Selected Stations in the United States”, National Bureau of Standards Research Report 8972 Lesur, F., Mirebeau, P., Mammeri, M. and Santana, J. (2014), “Innovative insertion of very long AC cable links into the transmission network” Cigre 2014, Paris, France, paper B1-301 Lian, Y.C. and Li, Y.M. (2008), “On-line dynamic cable rating for underground cables based on DTS and FEM. WSEAS Transactions on Circuits and Systems” 2008, Vol. 7, 4, pp. 229-238 Luoni, G., Morello, A. and Holdup, H. (1972), “Calculation of the external thermal resistance of buried cables through conformal transformation”, Proceedings of the Institution of Electrical Engineers, vol. 119, 5, pp 575- 586 Lyall, J.S. Brooks, J. and McKeown, D., (2004), “A dynamic rating technique for underground power cables”, Australasian Universities Power Engineering Conference (AUPEC 2004) Maioli P. (2007), “Passive loops technique for electromagnetic fields mitigation: applications and theoretical considerations” Proc. Of Jicable 2007, Versailles, France, paper A.8.4 Martin, B. and Cohen, M. (1954), "Heat Transfer by Free Convection in an Open Thermosyphon Tube", British Journal of Applied Physics, Vol.5, pp. 91-95 Martin, B. (1955), "Free Convection in an Open Thermosyphon with Special Reference to Turbulent Flow", Proc. of Royal Society, Vols. 230, no. 1183, pp. 502-530 Mekjian A. and Sosnowski, M. (1983), “Calculations of alternating current losses in steel pipes containing power cables”, IEEE Transactions on Power apparatus and systems, Vol. PAS-102, No.2 McCormick, D. G. (1969), “Cable Ratings in Concrete Troughs”, ECRC report R219. McRae, B.P., Dowd, G. and Flanagan, P. (1975), “The performance of underground cables when laid in concrete bridges”, The electricity commission of new South Wales Transmission Division Mochlinski, K. (1976), “Assessment of the influence of soil thermal resistivity on the ratings of distribution cables”, IEE, vol 123, no1 , pp 60-72 Moore, G.F. (1997) “Electric Cables (HANDBOOK)”, Oxford ; Malden, Mass. : Blackwell Science Morgan, V.T. (1982), "The Thermal Rating of Overhead-Line Conductors Part I. The Steady-State Thermal Model", Electric Power Systems Research, 5, pp. 119 - 139

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Moreau, C. and Courset, L. (2007), “Current ratings of cables in plastic ducts”, Proc. of Jicable 2007, Versailles, France, paper B8-4 Morello, A. (1959), “The Calculation of the Current Flow in New Power Transmission Cables”, L’Elettrotecnica, Vol. 46, No. 1, p.2, January 1959 Morris, M. and R.W. Burell (1954), “Current-Carrying Capacity of Pipe-Type Systems under SteadyState and Transient Cyclical Loading Conditions”, AIEE Transactions on Power Apparatus and Systems, June, pp. 650-660 Moutassem W. (2007) “Optimization procedure for rating calculations of unequally loaded power cables”, M.A.Sc. Thesis, University of Toronto Moutassem, W. and Anders, G.J. (2010) “Calculation of the eddy current and hysteresis losses in sheathed cableles inside a steel pipe”, IEEE Trans. On Power Delivery Vol 25 No 3, pp 20542063 Murata, Y., Watanabe, C., Itou, Y., Sasaki, H., Katakai, S. and Watanabe, M. (2014) “Practical application of +/-250kV DC-XLPE cable for Hokkaido-Honshu HVDC link”, Cigre 2014, Paris, France, paper B1-110 Nakamura, S., Morooka, S. and Kawasaki, K., (1992), “Conductor temperature monitoring system in underground power transmission XLPE cable joints,” IEEE Transactions on Power Delivery, Vol. 7, Issue 4, pp. 1688-1697 NBS report 8972 (1965), “Earth Temperature and Thermal Diffusivity at Selected Stations in the United States”, National Bureau of Standards Reports Neher, J. H., and McGrath, M. H. (Oct. 1957) “The Calculation of the Temperature Rise and Load Capability of Cable Systems”, AIEE Transactions, Part III, Volume 76, pp 752–772 Novák and Koller, L. (2011), “Influence of phase order on losses and outer magnetic field of grouped underground cables,” IEEE/PES Power Systems Conference and Exposition (PSCE), pp. 1-6 Palmer, J.A., Degeneff, R.C., McKernan T. M. and T. M. Halleran (1993) “Pipe Type Cables Ampacities in the Presence of Harmonics”, IEEE Transactions on Power Delivery, Vol. 8, No. 4, pp.1689-1695, Page 19 of 20 Palmgren, D., Karlstrand, J. and Henning, G., (2011), “Armour loss in three-core submarine XLPE cables”, Proc. of Jicable 2011, Versailles, France. 2011-A7-4 Pavlovsky, M. and Bauer, P. (2002), “Cable selection and Shunt compensation for Offshore Windparks”, Delft University of Technology Pilgrim, J.A. Swaffield, D., Lewin, P. and Payne, D., (2008), “An investigation of thermal ratings for high voltage cable joints through the use of 2D and 3D finite element analysis,” Conference record of the 2008 IEEE international symposium on electrical insulation, pp. 543-546

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Pilgrim, J.A. Swaffield, D., Lewin, P., Larsen, S. and Payne, D., (2009), “Assessment of the impact of joint bays on the ampacity of high-voltage cable circuits,” IEEE Transactions on power delivery, Vol. 24, No. 3, pp. 1029-1036 Pilgrim, J.A., Swaffield, D., Lewin, D., Larsen, P., Payne, D. and Waite, F., (2010), “Rating Independent Cable Circuits in Forced-Ventilated Cable Tunnels”, IEEE Transactions on Power Delivery, vol. 25, no. 4, pp 2046-2053 Pilgrim, J.A., Swaffield, D., Lewin, P., Swingler, S., Waite, F. and Payne, D. (2011), “Impact of moisture migration on the current rating of high operating temperature cables”, proc. of Jicable 2011, Versailles, France, C.9.6 Pilgrim J.A., Lewin, P. Senior, Larsen, S., Waite, F. and Payne, D., (2012), “Rating of Cables in Unfilled Surface Troughs”, IEEE Trans. on Power Delivery, Vol. 27, No. 2, pp. 993-1001 Pilgrim, J.A., Catmull, R., Chippendale, P.L., Lewin, P., Stratford, P. and Tyreman, R. (2014), “Current rating optimisation for offshore wind farm export cables”, Cigre 2014, Paris, France, paper B1-108 Raithby, G.D. and Hollands, K.G.T. (1985), "Natural Convection", in "Handbook of Heat Transfer", edited by Rohsenow, W.M. and Hartnett, J.P., McGraw-Hill, New York Ruiter, J.P. and Thus, A.W. (1984), “Cooling of oil-filled cable joints using heat pipes,” IEE Proceedings Generation, Transmission and Distribution, Vol. 131, Issue 7, pp. 340-348 Sakis Meliopoulos, A.P. and Martin Jr, M.A (1992), “Calculation of Secondary Cable Losses and Ampacity in the Presence of Harmonics” , IEEE Transactions on Power Delivery, Vol. 7, No. 2, pp. 451-459 Sande, E. van de, and Hamer, B.J.G. (1979), “Steady and transient natural convection in enclosures between horizontal circular cylinders (constant heat flux)”, Intl. J. Heat. Mass. Tranfer, Vol 22. pp 361-370 Slaninka, P. (1965), “Thermal Resistance of a Cable Channel.” Bull. Vuki, Vol. 18, No. 5, pp. 212– 221 Slaninka, P. and Morgan, V.T. (1992), “External thermal resistance of power cable in non-uniform soil”, Vol 139, no 3, pp. 117-124 Swaffield, D.J. et al. (2008), “Methods for rating directly buried High Voltage Cable Circuits”, IET Generation, Transmission & Distribution, Vol 2, issue 3, pp. 393-401 Taflove and Dabkowski, J. (1979-1), “Prediction method for buried pipeline voltages due to 60Hz ac inductive coupling Part I - Analysis,” IEEE Transactions on Power Apparatus and Systems, vol. 98, issue 3, pp. 780-787 Taflove and Dabkowski, J. (1979-2),“Prediction method for buried pipeline voltages due to 60Hz ac inductive coupling Part II – Field test verification,” IEEE Transactions on Power Apparatus and Systems, vol. 98, issue 3, pp. 788-794

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Tang, K., Paton, D., Bucea, S., Mashio, S., Muramatsu, Y. (2014), “330kV XLPE cable specific testing protocol requirements”, Cigre 2014, Paris, France, paper B1-102 Terracciano, M., Purushothaman, S., de Leon , F. (2012), “Thermal analysis of cables in unfilled troughs investigation of the IEC standards and a methodical approach for cable rating”, IEEE Transactions on Power Delivery, vol. 27, issue 3, pp. 1423-1431 Vavra, J. and Wanda, M., (2006), “400kV Vienna – the Vienna 400kV North input”, Cigre 2006, Paris, France, paper B1-101 Wald, D., Nyffenegger, H., Orton, H. and Anders, G. (2011), “Improved cooling of high voltage cables”, Proc. of Jicable 2011, Versailles, France, paper C.10.4 Weedy, B.M., and Perkins, P. (1967), “Steady-state thermal analysis of a 400 kV-cable through joint” Proceedings of Institution of Electrical Engineers, Vol. 141, Issue 1, pp. 109-115 Weedy, B.M., and El-Zayyat, H.M. (1972-1), “The Current Carrying Capacity of Power Cables in Tunnels”, Paper T72 505-6, IEEE PES Summer Meeting, San Francisco, California Weedy, B.M., and El-Zayyat, H.M. (1972-2), “Heat Transfer from Cables in Tunnels and Shafts”, Paper C72 506-4, IEEE PES Summer Meeting, San Francisco, California Wild, F. de, Boone, W., Geest, H. van der, Smit, J. (2007), “Dynamic rating systems in general and in a hybrid 150kV transmission system”, Proc. of Jicable’07, Versailles, France, paper 2007-A6-5 Williams G. P. and Gold, L. W. (1976), “Ground Temperatures”, Canadian Building Digest 180 Wormer, C van (1955), "An Improved Approximate Technique for Calculating Cable Temperature Transients", AIEE Trans., vol. 74, pp.277 -281 Worzyk, Th. (2009), "Submarine Power Cables: Design, Installation, Repair, Environmental Aspects", Power Systems (2009) Zhang, D., Werle, V. and Jung, J. (2014), “The first HVAC and HVDC grid connection projects for wing power integration in German North Sea: experience, challenge and outlook”, Cigre 2014, Paris, France, paper B1-105

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Ap p end ix A: Q u e st i o nna ir e ( Empt y)

Note that name and address have been blanked.

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Questionnaire on Cable Rating starting points and calculation methods

Introduction This questionnaire has been sent to you by XXXXXX, convenor of CIGRE Working Group B1-35, to collect information regarding starting points for cable rating calculations as well as to collect information regarding the cable rating calculation methods currently used in your company for the engineering of high voltage power cable systems (both AC and DC).

The most important goal of the CIGRE Working Group B1-35 is to prepare a guide for cable rating calculations. This guide comprises three sections: a section on how we can best establish the starting points for a cable rating study, a section on how we can perform a cable rating calculation if other sources (e.g. IEC) do not provide an answer, and a section on how we can best perform a stationary, dynamic or on-line rating cable rating calculation.

In order to prepare a useful guide for you, as one of Cigre’s customers, we currently request your input information. It will help us to pinpoint the most important problems in the field of cable ratings, and it will enable us to share best practices in order for all to learn and improve. Therefore, please help us in our work on cable rating calculations by completing the questionnaire!

Your answers will be analyzed and compared to the answers of other utilities, but the final result will be made anonymous. Only to ensure correct interpretation of your input, we request your contact details in the questionnaire.

The time needed to complete the questionnaire will be about 2 to 4 hours. You can simply answer the questionnaire digitally, just by adding text to this file. Feel free to add any comment or attach any document you want.

Thank you for your effort!

XXXXX Convenor of Cigre Working Group B1-35 on Cable Ratings

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Contact information th

Please send the completed questionnaire on or before April 19 to Mr. XXXXX either via e-mail to XXXXXX, or via normal mail to:

XXXXXX

Personal details For reference purposes and for possible clarifications only, please complete your name and contact details:

Name

:

Company name

:

E-mail

:

Telephone

:

Address

:

City

:

Postal Code

:

State

:

Country

:

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Questions Note: Cross boxes, select option or complete text fields to give your answer. 1

Your Company and Cable rating practice

1.1

What kind of company are you belonging to? -

1.2

a utility a cable manufacturer a consultancy company other please specify:

What is the method used in your Company for cable rating? IEC methods (60287 and 60853 series)

Please select

Other(s), please specify: Please select Please select Please select

1. 2. 3. 1.3

Who is performing cable rating in your company? -

1.4

internal tenders / cable manufacturers consultants other please specify:

At what stages are you performing cable rating? -

feasibility / basic design tendering documents / specifications detail design / design review verification with installation feedback updates in case of modifications along the route reassess rating of existing cables other please specify:

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1.5

On which type of lines are you doing cable rating calculations? -

1.6

1.7

All above a certain rated voltage please specify: depending on the importance within your network please specify:

On which HV cable types are you doing cable rating calculations? -

general single core cables three cores cables armoured cables

Please select Please select Please select Please select

-

submarine cables DC cables

Please select Please select

Laying configurations What typical methods are used in your Company? -

direct buried in filled buried troughs in unfilled buried troughs in direct buried ducts in concrete encased ducts (duct bank) in free air in air in tunnel horizontal directional drilling other, please specify:

Please select Please select Please select Please select Please select Please select Please select Please select Please select Please select

Laying configurations for 3 single core cables: -

trefoil touching phases trefoil non touching phases ‘L’ position in duct banks Flat formation

Please select Please select Please select Please select

Installation depth (direct buried): -

do you install cables less than 0.4 m depth? do you install cables between 0.4 and 2 m depth? do you install cables between 2 and 10 m depth? do you install cable very deep (more than 10m) ?

What is the typical land use on the top of the cable? (e.g. pavement, tarmac, grass etc):

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Please select Please select Please select Please select

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

2.

Parameters related to the surrounding conditions

2.1

Soil/ Seabed Ambient temperature Note: according to IEC 60287 / Neher Mc Grath definitions, the ambient temperature is the temperature of the surrounding medium under normal conditions, at a situation in which cables are installed, or are to be installed, including the effect of any local source of heat, but not the increase of temperature in the immediate neighbourhood of the cables due to heat arising therefrom.

What is your practice regarding this parameter ? Site measurements (1)

Please select

If occasional/rare, when (e.g. submarine)

Assumed values (2) If occasional/rare, when (e.g. below

Please select

132 kV)

(1) Site measurements Please give details on your measurement method (how many, where on the route, at what depth, measuring equipment, when/which period, etc.)

(2) Assumed values Note : it is understood that assumed values are excluding the effect of any local source of heat.

Yes

No

Yes

No

Do you use seasonal values? Hot season

Do you use regional values for soil? What are your assumed values (please detail per season and region/installation where applicable)? If necessary use separate sheet if the table does not allow correct data entry.

Region A °C Region B °C Region C °C Seabed °C

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Cold season °C °C °C °C

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

How did you set these values?

2.2

Soil/Seabed Thermal resistivity

What is your practice regarding this parameter? Site measurements (1)

Please select

If occasional/rare, when (e.g. submarine)

Please select

Assumed values (2) If occasional/rare, when (e.g. submarine)

(1) Site measurements Please give details on your measurement method : -

Frequency of the measurements Location of the measurements What parameters do you measure How you deduce your worst case for engineering purposes ?

Yes

No

Yes

No

(2) Assumed values Do you use seasonal values ? Do you use regional values ?

Dry season

Wet seas on

K.m/W

K.m/W

K.m/W

K.m/W

K.m/W

K.m/W

K.m/W

K.m/W

Region A What are your assumed values (please detail per season and region/installation where applicable)? If necessary use separate sheet if the table does not allow correct data entry.

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Region B Region C Seabed

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

How did you set these values?

2.3

Soil Drying out: Do you consider soil drying out in your cable rating calculations? Yes, always No, never Yes but under conditions (please detail: depending on cable type, installation conditions, operating conditions etc ..)

When using soil drying out, what are the typical values you use for the following parameters :

K.m/W K.m/W

Thermal resistivity of the dried soil; Thermal resistivity of the moist soil

K.m/W

Others (please specify)

K.m/W

°C Critical temperature of the soil and temperature of the boundary between dry and moist zones

How did you set these values (if any)? If you measure it please give details of the method.

(seasonal values if any)

Yes

No

Thermal resistivity

Yes

No

Grain size distribution

Yes

No

After a possible drying out period do you consider a “resting” time to allow re-hydration of the surrounding soil? 2.4

Backfill and surrounding material properties What parameters of usual material surrounding the cable do you specify :

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Compaction

Yes

No

Yes

No

Others (please specify)

Do you make any control on the rest of materials?

backfill

Please detail: 2.5

Influence of other heat sources

How do you take into account influence of other heat sources in your cable ratings? By adding a margin to ambient temperature (please indicate typical margin value)

Yes (

By using de-rating tables or similar tools

No °C)

Yes

No

Yes

No

Yes

No

Yes

No

(please provide details)

By calculating the exact influence (please provide details)

Not taken into account Other (please provide details)

3.

Operating parameters

3.1

Do you use IEC maximum temperature as conductor normal operating temperature? If not, or if there are exceptions to this rule, please detail your practice and value.

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3.2

Where does the temperature limitation come from? -

3.3

Conductor temperature Metallic sheath temperature Cable surface temperature Air temperature (for tunnel)

Yes Yes Yes Yes

No No No No

Load factor

What is your practice regarding this parameter? -

Not considered Case per case calculations (based on IEC 60853) Assumed values Others, please specify:

In case of assumed values please give details and typical values. 3.4

Emergency

What is your practice regarding emergency? -

Not considered Case per case calculations (based on IEC 60853) Assumed ratio to normal operating ratings Automatic (real time rating, etc.) Others please specify:

(1) (2)

(1) Case per case calculations parameters min / Emergency Durations considered:

What is your practice regarding maximum conductor temperature at the end of emergency? Please detail:

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What are the typical values of density and specific heat capacity you use for : -

Dried soil Wet soil Concrete Others (please details)

(2) Assumed Coefficients to normal operating ratings

kg/m3 / kg/m3 / kg/m3 /

J/kg.°C J/kg.°C J/kg.°C

kg/m3 / kg/m3 /

J/kg.°C J/kg.°C

min /

min /

/

/

Yes

No K.m/W)

Yes Yes Yes Yes Yes Yes

No No No No No No

Yes

No

Durations Corresponding assumed coefficients 4

Others

4.1

Bottleneck mitigation What are your practice to increase cable rating at bottlenecks? -

-

-

Special backfill (Please indicate target thermal resistivity) Cooling systems : - Water cooling system - Natural ventilation - Forced ventilation - Air conditioned (thus: active cooling) Consider axial thermal Flux Change in laying configuration please indicate how:

-

4.2

Others please specify: Feedback from your cable rating experience What are the most usual thermal design limitations? (conductor/sheath temperature, soil dry out, surrounding conditions, operating conditions etc.)

Do you face other limits/regulations which influence cable ratings? (environmental aspects like EMF or temperature increase, vicinity with other equipment etc.)

If your Company experienced cable breakdowns

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due to over-ratings could you give some details (overloading, mistake in original cable rating calculations, modification of the environment, others):

Comments & additional starting points for calculations which are missing in this questionnaire?

What is your recommendation dealing with starting points for cable rating calculations?

5

Steady state rating

5.1

Do you perform steady state calculations yourself : By hand or spreadsheet?

Yes

No

With rating tables?

Yes

No

Yes

No

With commercial available program (not FEM)?

Yes

No

With Finite Element (FEM) program?

Yes

No

Other (please specify)?

Yes

No

Yes

No

Yes

No

Yes Yes

No No

With in-house software Neher/McGrath?

5.2

Do you use calculations?

a

safety

based

margin

on

in

IEC

the

or

rating

If yes: -

do you use a lower conductor temperature? do you use a reduced normal rating or a lower pre-emergency load? Other? please specify:

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5.3

Do you calculate heat, generated due to induced currents, in steel plates, concrete reinforcement or parallel earth wires?

Yes

No

Yes

No

Yes

No

Yes

No

Yes

No

Yes

No

Yes

No

Yes

No

Yes

No

If yes, how do you calculate: 5.4

Do you use standard IEC calculations (only) for deep buried cable system beyond 5 meter, e.g directional drillings? If no, how do you calculate:

5.5

Have you made any comparison between calculated and measured cable temperature to check if the calculations are correct? If yes, please specify:

5.6

Have you made any comparison between calculated and measured steel wire armour losses for 3-core cables? If yes, please specify your findings:

5.7

Do you calculate cable rating for unfilled unventilated surface trough in general? If yes, how do you calculate:

5.8

Do you consider the impact of charging currents on the real power transfer in long cable systems? If yes, how do you calculate?

5.9

What calculation methods do you use for tunnel installations not covered in Cigré publication Electra No 143?Think for example about multiple cable circuits, natural ventilated, vertical shafts etc.

5.10

Do you calculate current rating for cables in riser poles (J-tubes)? If yes, how do you calculate:

5.11

Do you calculate current rating for vertical cables exposed to solar radiation? If yes, how do you calculate:

5.12

Do you calculate current rating for cables in large steel conduits? If yes, how do you calculate:

5.13

Do you calculate current rating for cables in open

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water (not embedded)?

Yes

No

If yes, how do you calculate: 5.14

Where are the most important needs for improvement regarding steady state rating?

5.15

What do you do when IEC or Neher/McGrath does not provide an answer?

6.

Dynamic rating (cyclic or emergency time dependent rating)

6.1

Do you perform dynamic rating calculations yourself?

Yes

No

Yes

No

If yes, how do you perform these calculations: -

-

6.2

with in-house software based on IEC/Neher McGrath? with in-house software based on Cigré?

with commercial available program? With another method? please specify:

Do you use any safety margin in the calculations (Think for example about a lower temperature or limited time durations)? If yes, please specify:

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6.3

Did you experience limitations or difficulties with the used dynamic rating calculations?

Yes

No

If yes, please specify: 6.4

Is the dynamic rating system fully integrated in your network system or is it a stand-alone program / system?

7.

Real time temperature monitoring system

7.1

Do you use real time temperature monitoring systems? -

7.2

Fully Integrated Stand Alone

No Yes, an own developed system, e.g. PT100 Yes, a commercial available DTS system Yes, another system please specify:

If you use a glass fibre temperature monitoring system (DTS), what is the glass fibre position? -

inside cable, cable screen cable surface external parallel conduit other please specify: Permanent

Is the DTS system used permanently connected to the same cable circuit or is it used on a temporary basis among different circuits?

Mobile/Temporary

Yes

No

Yes

No

Have you checked the overall accuracy of the DTS system? If yes, please specify the findings: 7.3

Have you experienced limitations or difficulties with the currently used temperature monitoring system? If yes, please specify:

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8

Real Time Current Rating System

8.1

Do you use a Real Time Current Rating system for any cable circuit?

8.2

-

No Yes, our own developed system please specify system:

-

Yes, a commercial available system please specify type of system:

Do you use a fibre optic( DTS) system as an input for the Real Time Current Rating System?

Yes

No

Yes

No

In both cases, please specify:

8.3

Do you use any safety margin in the Real Time Current Rating System? If yes, please specify:

8.4

8.5

Is the Real Time Current Rating System fully integrated in your network system or is it a standalone system?

Fully Integrated Stand Alone

Have you experienced limitations or difficulties with the currently used temperature monitoring system?

Yes

No

Yes

No

Yes

No

If yes, please specify: 9

Others

9.1

Do you have any additional observations regarding calculations methods or dynamic rating system? If yes, please specify:

9.2

Did you make any comparison between calculated and measured steady state or transient temperatures? If yes, please specify:

9.3

What recommendations could you give to other users considering steady state or dynamic rating calculations?

Thank you for your time!

For sending the questionnaire, see introduction

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Ap p end ix B: Q u e st i o nna ir e – In c lud ing R e pli e s Su mm a r y

Note: Where company names or persons names are given, these names have been changed to ‘XXX’. Questions 1

Your Company and Cable rating practice

1.1

What kind of company are you belonging to?

Kind of company Kind of company A utility A cable manufacturer A consultancy company Other

1.2

Number of replies 59 replies 22 replies 12 replies 8 replies (4 Universities)

What is the method used in your Company for cable rating?

Method used for cable rating Method IEC methods (60287 and 60853 series) Other(s)

1.3

Blank

Always

Often

Occasional

Rare

Never

39

40

11

2

6

References were given to commercial cable rating software

Who is performing cable rating in your company?

Who performs cable rating Internal Tenders / cable manufacturers Consultants Other

Blank 8

Yes 89

No 4

22

45

34

38

24 8

39

Others specified are:   

Current ratings are mainly calculated for HV Cables based on installation conditions specified by clients University Some sub-contracting but always check with our own calculations

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Confirmation by cable manufacturer Consultants set the guidelines, Engineers adopt them to the practical situation Designing team Developers and supporting specialists Own developed program based on IEC.

1.4

At what stages are you performing cable rating?

At what stages are cable rating calculations performed Stage Feasibility / basic design

Tendering documents / specifications Detail design / design review Verification with installation feedback Updates in case of modifications along the route Reassess rating of existing cables Other

Blank 9

Yes 83

No 9

12

69

20

10

76

15

13

56

32

12

67

22

15

61

25

6

Others specified are:  

On line cable monitoring Assessment of temporary enhancement requests for operational purposes making use of known better ambient conditions N/A (It depends on customers) For research We perform cable rating at the time of designs proposals/or to do feasibility studies. We use to work join cable manufactures, whom generally furnish power cables, accessories and service installations. The cable manufacturers usually are responsible to perform ampacity calculations and define the cable rating Real time ratings.

  



1.5

On which type of lines are you doing cable rating calculations?

Types of lines on which cable rating calculations are done Types of line All Above a certain voltage Depending on the importance within your network

Blank 22 31

Yes 58 40

No 21 30

54

9

38

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The voltage specified in case of a voltage above which calculations are done is:                  

415V 6 kV 11 kV (6x) 33kV (5x) 46kV (2x) 50kV (3x) 60 (3x) 63 kV 66 kV (3x) 69 kV (2x) 72 kV 88 kV 110 kV (6x) 132 kV 138 kV 150 kV 154 kV 275 kV.

1.6

On which HV cable types are you doing cable rating calculations?

HV cable types on which cable ratings are calculated Cable Types HV cables, general Single core cables Three core cables Armoured Submarine DC

1.7

Blank 13 2 5 7 24 23

Often 74 94 40 27 17 10

Occasional 7 4 20 20 17 14

Rare 4 1 15 27 18 18

Never 2 0 21 20 25 36

Laying configurations

What typical methods are used in your Company? What is the typical land use on the top of the cable? (e.g. pavement, tarmac, grass etc):

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Typical laying configurations per continent – North America Laying configuration Blank Always Often Occasional Rare Never Direct buried 4 5 4 2 Filled buried troughs 1 2 4 2 6 Unfilled buried troughs 2 1 5 1 7 Direct buried ducts 5 6 2 2 14 Concrete encased ducts 1 In free air 1 4 6 1 3 In air in tunnel 1 1 5 5 3 HDD 4 2 4 2 3 Other 1 2 Other laying methods reported for North-America: Buried pipe type cables (1xoften) and submarine cables (2xoccasional )

Typical laying configurations per continent – South America Laying configuration Direct buried Filled buried troughs Unfilled buried troughs Direct buried ducts Concrete encased ducts In free air In air in tunnel HDD Other

Blank

Always

Often 2 1 2 2 2 1 1

Occasional 1 1

Rare 1 2 1

Never

1 2

2

1 2 1 4

1 1

Typical laying configurations per continent – Europe Laying configuration Blank Always Often Occasional Rare Never 36 Direct buried 5 5 2 Filled buried troughs 3 10 16 12 7 Unfilled buried troughs 2 9 18 10 9 Direct buried ducts 2 31 6 4 5 Concrete encased ducts 2 20 13 8 5 In free air 1 14 17 11 5 In air in tunnel 11 20 12 5 HDD 5 17 19 5 2 Other 1 2 1 Other laying methods reported with occurrence: J-tube (1xoften), steel pipes shielded (1xoccasional), cables on bridges (1xoccasional), sub-lake ducts (1xoccasional), cable crossings (1xrare), Buried pipe TYPE cables (1 x often) and submarine cables (1 x occasional).

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Typical laying configurations per continent – Africa Laying configuration Direct buried Filled buried troughs Unfilled buried troughs Direct buried ducts Concrete encased ducts In free air In air in tunnel HDD Other

Blank

Always

Often 2

Occasional

Rare

Never

1 1

1 1 1

1 2 2 1 1

1 1

Typical laying configurations per continent – Asia Laying configuration Direct buried Filled buried troughs Unfilled buried troughs Direct buried ducts Concrete encased ducts In free air In air in tunnel HDD Other

Blank

Always

2 2 2 1 2 1

Often 15 8 3 16 9 8 13 5

Occasional 4 8 3 11 7 9 7

Rare 6 7 8 1 3

Never 2 2 2 1 2 3

4

7

Rare

Never

5 5

2 1

1 3 3

1

Typical laying configurations per continent – Oceanic Laying configuration Direct buried Filled buried troughs Unfilled buried troughs Direct buried ducts Concrete encased ducts In free air In air in tunnel HDD Other

Blank

Always

Often 7

1 1

Occasional 1 1

8 4

1 1 1

1 4

2 4 2 4

Laying configurations for 3 single core cables: Laying configuration for 3 single core cables Laying configuration Trefoil touching phases Trefoil non touching phases L’ position in duct banks Flat

Always

Often 65 29 14 61

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Rare 6 26 18 12

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Installation depth (direct buried): Installation depth (direct buried) – North America Laying depth Blank Often Occasional Rare Never Less than 0.4 m depth 3 4 8 8 Between 0.4 and 2 m depth 4 3 Between 2 m and 10 m depth 5 4 4 2 Very deep: >10m depth 2 6 6 1 One response with following remark: ‘standard is 3 ft to top of duct bank. Due to urban congestion, often 5-6 ft to top is required.’ Typical land use on the top of the installed cables in North America:          

Roadway 3 responses Pavement 3 responses City streets 3 responses Grass 3 responses Granular fill or native soil 1 responses Green spaces, etc. 1 responses Pavement and tarmac 1 responses Any type of land can be accounted for as long as we know its thermal resistivity. 1 responses All possible surfaces 1 responses Varies greatly from marine installation to urban area to green field 1 responses

Installation depth (direct buried) – south America Laying depth Blank Less than 0.4 m depth Between 0.4 and 2 m depth Between 2 m and 10 m depth Very deep: >10m depth Typical land use on the top in South America:    

Often 3 1

Tarmac , pavement , concrete surfaces , Tarmac Pavement, asphalt Pavement or grass

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Occasional

Rare

1 1

1 2 1

Never 4

2

1 response 1 response 1 response 1 response

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

Installation depth (direct buried) – Europe Laying depth Blank Less than 0.4 m depth 2 Between 0.4 and 2 m depth 2 Between 2 m and 10 m depth 2 Very deep: >10m depth 2 Typical land use on the top in Europe:          

Often 1 45 12 4

Occasional 5 1 18 9

Rare 12

Never 8

16 19

14

Tarmac/asphalt/roads Pavement Grass Agricultural Soil / sand / peat Concrete Gravel / shingle Tiles Drilling under roads All types

18 responses 17 responses 15 responses 10 responses 5 responses 4 responses 2 responses 1 response 1 response 1 response

One remark by the responder: the ground temperature is increased by 5 till 10 °C when tarmac is used.

Installation depth (direct buried) – Asia Laying depth Less than 0.4 m depth Between 0.4 and 2 m depth Between 2 m and 10 m depth Very deep: >10m depth Typical land use on the top in Asia:        

Blank 2

Often 1 21 3

3 3

Occasional 1 1 8

Rare 6 1 8 11

Pavement Grass Tarmac / asphalt Concrete / cement Interlock tiles Vehicular road N/A(It depends on customers) And bridge

Never 14 1 2 10

14 responses 6 responses 5 responses 2 responses 1 responses 1 responses 1 response 1 response

Installation depth (direct buried) – Oceanic Laying depth Blank Less than 0.4 m depth 1 Between 0.4 and 2 m depth Between 2 m and 10 m depth 1 Very deep: >10m depth 1 Typical land use on the top in Oceanic:   

Often

Occasional

Rare 1

Never 6

8 2

3

2 4

3

Pavement Tarmac / roadway Grass

5 responses 3 responses 3 responses

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Installation depth (direct buried) – Africa Laying depth

Blank

Often

Less than 0.4 m depth Between 0.4 and 2 m depth Between 2 m and 10 m depth Very deep: >10m depth Typical land use on the top in Africa:   

Occasional

Rare

Never 2

2 2 2

Pavement Grass Tarmac

2 responses 2 responses 1 responses

2

Parameters related to the surrounding conditions

2.1

Soil/ Seabed Ambient temperature

Note: according to IEC 60287 / Neher Mc Grath definitions, the ambient temperature is the temperature of the surrounding medium under normal conditions, at a situation in which cables are installed, or are to be installed, including the effect of any local source of heat, but not the increase of temperature in the immediate neighbourhood of the cables due to heat arising therefrom.

What is your practice regarding this parameter?

Soil/ seabed temperature – assumed or measured Blank Always Often Measured 3 1 9 Assumed 6 7 73 Occasional/Sometimes/ rare reasons for measured:              

Occasional 21 7

Sometimes 5 2

Submarine Provided by customer/utility Reassessment of existing cables Buried cables Combined with thermal resistance testing along route Important high profile circuits Base on the rule of GB 50217(2007), the average earth temperature in the hottest month is chosen as surrounding temperature of laid place. River crossings, with thermal borings Reference temp. And in case of on line monitoring Confirmation of worst case scenario In some land where normal values are unknown In critical situation Service tunnel locations

Rare 21 3

11 responses 5 responses 4 response 3 responses 2 responses 2 response 1 response 1 response 1 response 1 response 1 response 1 response 1 response 1 response

Occasional/Sometimes/ rare reasons for assumed: 

No data available

10 response

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(1) Site measurements Please give details on your measurement method (how many, where on the route, at what depth, measuring equipment, when/which period, etc.)

Details given:          

   

              

A few thermo-couples are installed, but have not been used for rating purposes Usually assumed worst case summer conditions for depth and location Thermocouples placed at terminating substations at depth of cable and +/-5 ft (1.5 m)) both above and below depth of cable Work with a consultant to determine along route, depth of proposed cables Thermocouples, PT 100 in depth of 0,5 to 2 meters, OF measurement of a non loaded cable. For on line monitoring, near measuring points (in case no optical fibre measurements). Submarine, based on annual temperature profiles Never, this is generally done by the Utilities and in many cases using the optical fibre with one DTS Assumed value 35 °C During thermal resistance surveys at nominally 1.2 m depth Due to a long period heat waves during the summer seasons of 2008 and 2009. This coincided with the design stage of the most recent 275 kV cable installation which resulted in soil temperature measurements being taken during the hottest part of the day Temperature measured at 500 mm, 900 mm and 1.2 m deep at selected trial holes (eg proposed joint bays) Measured at trench depth at one or two locations only For big schemes geotech studies undertaken during development stage these include soil sampling. During project more taken At approximately 500 m intervals in the cable route, one @0.5 m depth, one @0.8 m depth and third one on the trench floor at about 1.2 m depth. This is carried out to investigate thermal characteristics of native soil in the cable route to accommodate in design for verification of cable ampacity. To be on safer side all the measured soil temperatures were well below 25 °C, hence we have assumed ambient soil temperature of 25 °C Discrete thermocouples or increasingly DTS Seabed surveys, depending on route difficulties Site measurements not carried out by EA Technology To measure thermal resistivity of soil, temperature of soil is measured. Example of deep laying case Measurement point: 1 Position: near planning position Depth: depending on laying depth (selectable values: 2 m, 5 m, 10 m, 15 m and 20 m; decided by measurement device specification) Sensor: thermocouple in a needle probe (transient probe method) Period: not decided (more than three times, more than 2 days’ interval) Case by case We use results of the site measurements and not perform it Thermocouples placed at 10 cm deep and at 70 cm deep at 2 meters of the cables We take information from customer’s specification or IEC values IEEE & ASTM standard

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   

       

Open trench several measurements along the route and throughout the day/night "Temperature measurements (DTS) will often be installed in a period after commissioning of the wind farm to approve the design of the cables. Ambient temperature will be available in no/low load periods The fibre is included in the subsea cables but in separate duct along onshore cable routes Experience from previous cables with DTS installed Probes in selected points (possible hot spot) along the route at about 1 m depth. Period depends on many factors Normally the particular conditions such as soil ambient temperature are established in the project specifications by the utility or the customer; We only checked by region and we take as reference the maximum and minimum temperature reached in the year We have measured the seasonal variation at typical HV cable burial depths to give a real-time ambient temperature approximation 0.5 m，away from surface；0.5 m，away from cable；ambient temperature is recorded by automatic measuring instruments Measuring equipment: Fiber Optic Temperature Measurement depth:0.5 m, 1 m, 1.5 m, 5 m Thermocouples installed away from the cables at cable depth. There are a few in our country, leading to an understanding of the ambient temperature seasonal variations Several over the route, thermal probe We have used soil temperature measurements using thermocouples placed at different depths to record seasonal data, cable depth, maximum ground temperature in Winter and Summer With FEM we rely mainly on the ambient air temperature rather than the soil temperature Every time the soil thermal parameters are measured. At least at three depth levels using digital equipment.

(2) Assumed values Do you use seasonal values? Do you use regional values for soil?

Soil / seabed temperature – use of seasonal and/or regional values Use of seasonal values Use of regional values

Blank 9 9

Yes 52 40

No 40 52

What are your assumed values (please detail per season and region/installation where applicable)?

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45 40 35 30 25 20 15 10 5 0

Typical soil temperature range (in °C) for hot conditions per country

50 40 30 20 10 0 -10 -20 -30 -40 -50 Typical soil temperature range (in °C) for cold conditions per country

45 40 35 30 25 20 15 10 5 0

Typical seabed temperature range (in °C) for hot conditions per country

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30 25 20 15 10 5 0

Typical seabed temperature range (in °C) for cold conditions per country

60 50 40 30 20 10 0

Typical tunnel / gallery temperature range (in °C) for hot season conditions per country

60 50 40 30 20 10 0

Typical tunnel / gallery temperature range (in °C) for cold season conditions per country

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How did you set these values?

Answers given:                                        

Detailed data from the 1950s Assumed / some measured Previous in situ measurements A three year earth ambient study Use certain values based on location (inland vs coastal) 31 °C near coast, 25 °C inland Hot season temperatures are 3 °C warmer under pavement. Soil temperatures decrease with depth and become more consistent between seasons History and operating experience Historic measurements, thermocouples installed in empty ducts We perform on every circuit a soil investigation on base of K.m/W, dry-out, soil fractures, etc. Region A: common practice, region B: common practice for deep installed cables L>8 m Based on long term annual temperature profiles where available, with verification by onsite measurements As per client specification Statistical analysis based on meteorological public company data French RTE specifications 'Cahier des charges général - Lignes souterraines HTB" According to IEC 60287-3-1 Singapore's temperature We consider soil temperature as 30 °C and ambient temperature as 40 °C Usually temperatures fall within following ranges in India Ground temp. 30 to 40 °C Ambient air temp. 40 to 50 °C Assumed value of 35 °C for all Oman BOM ground temps at 2'6" over 45 years Direct data from Bureau of Meteorology Originally used IEC287 values for Australia (25 & 15 °C) but after field tests confirmed higher values (especially under asphalt) have revised upwards Accepted norm for Australian values Past practice. Tunnel installations treated separately From occasional measurement Use values from IEC standard Studies carried out many years ago considering a range of typical UK conditions Use existign BS document that holds mean temperatures at 1m depth along with summer and winter varfiations for UK (NB seen and used it before, cant find the number right now) Values mainly based on NG TS 2.05 Values are supplied by customers and are occasionally different to the above UK standards From measurement data Region A: 1.2 m or below, Region B: 4.0 m or below JCS 0501 or Electric Technology Research Association 53-3. JCS 168 E 1995 It is besed on literature Depend on customer's specification JCS 0501:2002 For the highest temp

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              

Region A : Europe Region B : Asia or Africa Seabed : Europe Tunnel/Gallery : AsiaR Region A values of soil temperatures in west Europe from 1,5 m to 5 m depth Ambient soil temperature depends on burial depth; these values were set based on literature studies and soil studies : 20 °C below 1m , 15 °C between 1m and 4m , 10 °C more than 4m Our soil temperature value for duct banks is 25 °C They are the result of measurements and statistic values of different specifications. Values normally used in Portugal We usually take customer’s information on this topic, and we take always the worst case do perform the calculations Legal procedure about HV lines Meteorological data 3 month average Assumed standard values in Denmark Region A: normal cable trench Region B: deep drilling The temperature in seabed is site dependent. Ranges for two sites are enclosed in the schedule Based on geotechnical report from 1980’s. DTS measurements from a non-energized cable system showed higher values on land, therefore this parameter is under revision" Experience Values are set on the base of Historical/Literature value According on the type soil material and geographic location we select values of the thermal resistivity of soil taken from reference tables of IEC 60287 These are for 1.1 m burial depth not close to heated cellars. If built up area, we don't give the benefit of the cooler temp. We use an adjusted sinusoidal time dependence. Note, this is just for research purposes. As far as we are aware, the utilities generally assume a constant ambient temperature of 15 °C in Finland Average of values under the conditions present in the company Based on data of "XXX" According the atmosphere condition Users request The values are used in the area of Greece - in the case of seabed, we consider 15 °C for depths over 15 m and 25 °C for smaller From studies carried out several years ago in Ireland Use of fixed values minimum 10 °C and maximum 35 °C Customer specified, IEC 60287-3-1 or from "Application Guide AG 31-008" Based on historical temperatures or informed by clients. Data are supplied by customers By site measurement of surrounding temperature at least one year Numerous regions around the world. Values used according to customer specifications or taking from IEC 60287-3-1 when no other information is given. According to IEC 60287-3-1 § 4.13 for Switzerland Projects provide the information Values are for NL, and are dependent on application. For engineering the highest values in the area are used, for realistic calculations, real measured values are used

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Customers provide this value as an input based on the typical seasonal or regional values of soil ambient temperatures available in their area By multiple measurements in other places We use average ait temperature of -4 °C in December (peak load) and +21 °C in July It is difficult to set one value per season as it depends on the expected laying depth Based on SANS 10198-4.

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2.2

Soil/Seabed Thermal resistivity

What is your practice regarding this parameter?

Soil / seabed thermal resistivity – assumed or measured Blank Always Often Occasional Sometimes Measured 4 4 20 24 4 Assumed 7 2 69 10 5 Given reasons if occasional/sometimes/rare is mentioned for measured values:       

Done for all new projects Done for new submarine On customer request For critical site conditions (congested areas) When route is close to being finalised Reassessment of existing connections Installations using directional drilling at deep depth

Rare 23 4

16 responses 9 responses 5 responses 3 responses 1 response 1 response 1 response

Given reasons if occasional/sometimes/rare is mentioned for assumed values:         

No data available Small projects, lower voltage class Only for research purposes, in tender and pre-tender stage Limited project budget If advised/requested by customer Soil near rivers, sand earth surface Adjust somewhat by soil type if identifiable Circuit diversions The values are chosen depending of the site conditions for other links

1) Site measurements Please give details on your measurement method:

Frequency of the measurements Answers given:  

At least every 300-450 m Every 500-1000 ft

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Never 22 4

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Typically, contract with a soil thermal testing specialist to perform a soil resistivity study in conjunction with geotechnical soil study at least every manhole location at various depth intervals around proposed installation depth Periodic (every 500-1000 ft) Strongly depend on cable route and surroundings Every 100-250m Average each 500vm along route Route survey with thermal resistance measurements every 500 m max Approx. every 100 m interval along the cable route At every 50 mts. Along proposed cable route before laying Through the route at every 250 m, average of multiple readings, this followed by laboratory test 250-500 m Thermal resistance measurements are carried out every 100m for cable runs > 1km. smaller intervals are used for smaller runs. If a thermal resistance measurement is found that is considered higher than expected measurements are taken 25m either side to establish boundary of that soil condition One off test during project design at critical locations along route. Soil samples sent interstate for testing (Brisbane) at various moisture content levels. Not tested installation. Worse case assumed for ratings and laying arrangement Once off during pre-design Measured at trench depth at one or two locations only In trench wall 500 mm above trench. For tender purposes assumed to be every 100 m. Actual dictated by change in soil type Soil thermal resistivity measured values were used for designing the cable rating. At approximately 500 m intervals in the cable route in situ thermal resistivity At assumed hot spots at Zone subs and transmission stations For major submarine projects measurements are taken at regular intervals along the route Seabed surveys Dependent on project, finding worst case soil conditions (eg only larger grain size, no fines) Measurements done when site survey indicates poor backfill material and the samples sent to laboratory Example of deep laying case More than three times, more than 2 days’ interval Case by case Detail design "Once/twice across cable route measuring thermal resistivity Every drilling, for submarine: every km Done by the clients At each meter depth up to max depth of drilling at each side (end) of the drilling is a soil sample taken 3 point on every 200 m 3-10 samples depending on the length of the cable route Site measurement is typically performed along the land route and/or in sections that can represent a thermal bottleneck for the cable (e.g. landfall) Normally the particular conditions such as soil thermal resistivity are established in the project specifications by the utility or the custom; We use a procedure to measure the thermal resistivity of soil established in IEEE standard 442-1981.The frequency of measurement depends on whether the particular project have not established the values

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Some years ago I made extensive site measurements for MV and HV also with moisture dependence. Worst case - soil or backfill sample in oven for 24 hours at 108 deg. C Choose some random points in the area , then measure with four-electrode method Only one measurements during the civil works Temperature of soil and temperature of different cable sheaths We sometimes take samples of lean mix concrete duct surround material, particularly from new suppliers. Soil measurements are taken only in areas where thermal resistance is a particular concern The measurements are performed for each new line to check the design. Location: critical points of the lines where there is another source of heat near the cable Measure the soil thermal resistivty in about 1 week in the soil far away from cables heat resisting coefficient choose the biggest parameter as the result Provided through subcontractors if needed We take samples along the cable route, every few 100 m, depending on the geology. We analyse the samples in our labs to get typical soil data, which we use to establish the thermal parameters and proctor density. We measure: grain distribution, density, moisture content, proctor density, water retaining properties. We use established models depending on the soil type to deduce the thermal parameters from this set of information, which relates very accurately. Worst case situation is deduced from analysing the groundwater table at site, and performing calculations to acquire the thermal parameters at the lowest groundwater table occuring in the past We have actually incorporated thermocouples and RTD to measure temperatures at anticipated depth and also measured soil thermal resistivity when we undertake such work. When such opportunities are not available then a worst case case used on archived data Once at the beginning of the installation Usually one set of measurement per circuit as many as possible and wherever there is suspicion that the soil parameters can limit the cable load Once per project. Measurement required if source of type of soi changes.

Location of the measurements

Answers given:           

Thermal probe at 1 and 2 m depths Depends on geotechnical information Along route At various depth of the cable trench Upper and lower layer of trench Trial pits at burial depth Cable centreline at burial depth Within 5 m of cable centreline At anticipated thermal hot spots In trench wall 500 mm above trench. For tender purposes assumed to be every 100 m. Actual dictated by change in soil type One @ 0.5 m depth, one @ 0.8 m depth and third one on the trench floor at about 1.2 m depth. Further collecting at least 1 off undisturbed tube sample from each location at 0.8 m depth and enough disturbed bag samples sufficient to prepare at least two additional mould in the

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laboratory. This is carried out for thermal dry-out testing in the laboratory. The thermal resistivity value at 1% moisture content for soil immediately around the cable/conduit (450 mm x 450 mm) was considered to investigate the cable rating. This is referred as dry zone. Similarly, the thermal resistivity value at knee point for general ground soil was assumed. The knee point is identified as point on the thermal dry out curve where there is a rapid rise in thermal resistivity for little change in moisture level For every soil type along the route Position: near planning position Case by case Condition due to the passage of the route Once/twice across cable route measuring thermal resistivity Every drilling, for submarine: every km Location at crossings Laboratory measurement on soil samples from cable level At each side (end) of the drilling soil samples are taken ; along the submarine cable route Usually at 1,5 m, 1 m and 0,5 m depth Samples in different sections of the route. seabed, landfall, field, bug, etc. Special thermal resistance samples in deep drillings or crossings and area with gravel or bog (organic material) We use a procedure to measure the thermal resistivity of soil established in IEEE standard 4421981.The frequency of measurement depends on whether the particular project have not established the values Along the trench At several levels above the cables Source of blanket and bedding soil.

What parameters do you measure? Answers given:                

Geothermal samples at 1.25 m and 2.5 m depths In situ thermal resistivity and moisture content for dry-out characteristic In situ and thermal dry out Dry/wet thermal resistivity and dry-out temperature Thermal resistivity wet and dry critical temperature Thermal resistance value in situ test and in laboratory (up to 0% moisture content) Thermal resistance (Km/W) Thermal resistance, moisture content. Temperature during measurement Thermal resistance and moisture content Thermal resistance and moisture content Thermal resistance, moisture content and density Thermal resistance, moisture content and density Thermal resistance vs moisture content,compaction Thermal resistance on site conditions and dried out, measure moisture content at same time As per NGTS 2.05, dry density, particle size, void ration, thermal resistance Thermal probe method, only dry values relevant

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Temperature (transient probe method: heater and thermocouple are installed in a needle probe, thermal resistivity is obtained from relation of heat quantum, temperature and distance) Case by case Temperature rise when a certain amount of heat that caused heat source This has to be done by a third party Humidity, porisity, conductivity Thermal resistivity wet soil, dried out soil; porosity; water saturation Saturation degree Porosity Density Thermal resistivity Humidity, specific gravity, thermal resistivity in dry and wet condition, porosity, degree of saturation Thermal conductivity m*K/W for soil moisture (as found) m*K/W for dry sample % moisture Probes in the soil, during limited time duration, in few points, measuring T, Thermal Resistivity. Worst case from historical data Resistivity and diffusivity, verifying the amount of water in the soil, soil density (dry and with water) Thermal resistivity and stability Thermal resistivity most often As per SANS 10198-5.

How you deduce your worst case for engineering purposes? Answers given: 

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New installations; 1 measurement / 1.6 km; measured thermal resistivity and ambient temperature. Frequency: varies from project to project; location: as close to final design route as can get Frequency: 27 samples in 9.6 km; in situ thermal resistivity and temperatures at various depths; worst case is the deepest point along route Every 15 mins to 30 mins. Collected by thermocouples which are written to SCADA or archival file Send samples for soil thermal resistivity lab tests Highest thermal resistivity value Consultant recommendations Determine max. conductor temperature based on measured values Critical analys of results Dryout curves If dryout can be avoided, use measured value x1.2. If dryout can not be avoided, dryout value x1.2 Worst case thermal resistance Thermal resistance at critical moisture content Highest thermal resistance values used to determine conductor size

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Worst case of soil conditions with full or partially dried out soil Worst case assumption: ampacity increasing is examined, by adopting such as insulated wire stranded, or water cooling system Case by case Worst case related to soil plus safety margin Average value of the local soil; but depends of cases. Calculation with worst case conditions (dried out soil) We take and average, and we look the tendency of measured values Position and depth of sample Soil description Worst thermal resistivity location Worst case - combination of depth, resitivity and moisture Worst case based on engineernig judgement.

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(2) Assumed values Do you use seasonal values? Do you use regional values?

Soil/ seabed thermal resistivies – use of seasonal and/or regional values (question 2.2) Use of seasonal values Use of regional values

Blank 6 7

Yes 33 40

No 62 54

What are your assumed values (please detail per season and region/installation where applicable)?

8 7 6 5 4 3 2 1 0

Typical soil thermal resistivity range (in K.m/W) for dry seasons per country

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3,5 3 2,5 2 1,5 1 0,5 0

Typical soil thermal resistivity range (in K.m/W) for wet seasons per country

3,5 3 2,5 2 1,5 1 0,5 0

Typical seabed thermal resistivity (in K.m/W) applied values country

How did you set these values? Answers given:          

0.9 °C-m/Watt assumed 1957 Neher/McGrath paper Somewhat temperate climate (assume summer worst case), but coastal areas are winter peaking and may consider seasonal issues in future Conservative typical values from industry references. If utility doesn't have tests in the same area, they assume 1.0 to 1.2 °C -m/Watt Historic No typical values, K.m/W values varies significantly even in a few kilometers Rule of thumb, IEC and/or soil surveys Measurements in the 70 °C French RTE specifications “Cahier des charges général - Lignes souterraines HTB"

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According to IEC 60287-3-1 Through complied data Assumed value is 1.5 Km/W Assumed soil thermal resistance 1.2 to 1.5 Km/W when it is not specified by the client/user Historical soil tests in Sydney Region IEC287 and average from knowledge of local testing which confirms this value. Assumed standard nominal resistivity for Australian conditions Soil testing and past practice Based on measurements across regions If a thermal resistance value is not specified by the utility or is not measured, then for budgetary purposes only a thermal resistance value is assumed. Studies carried out many years ago considering a range of typical UK conditions Dry season based on 1.2 outside 50 °C isotherm and 2.7 inside 50 °C isotherm Assume worst case scenario eg 2KM/W with CBS or 3Km/W with poor soil conditions From NGTS Based on land values, software has been created for submarine cables. The user can put his/her own values in From measurement data Region A: above the groundwater level, Region B: below the groundwater level JCS 0501 or Electric Technology Research Association 53-3. JCS 168 E 1995 It is based on literature. Depend on customer's specification JCS 0501:2002 By measurements and assumption The worse case is used. Based on experienced values ; controlled backfill 1 Km/W 1,0 K.m/W for most soil or controlled thermal backfill; 2,5 Km/W for dried soil (above 50 °C) for land cables These values were set based on literature studies and soil studies Our value for the soil is: 1 K.m/W They are the result of measurements and statistic values of different specifications. We take the values given on customer’s specs or IEC values if it’s not required the measurement A historic typical value We require a certain value for the the backfill (sand) when it is delivered. Thermal resistivity for soil is measured in critical projects and values used in other projects A = Normal farmland, B = Marsh Danish assumed values Onshore we are using worst expected values or make special back fill if the section with high thermal resistance is a limited length General onshore value in 1m burial depth between 1.0 and 1.4 Km/W Fields 1.0 in general but is expected to be better Cable design to fit the complete cable route without limitation. Submarine is based on experience from system with DTS installed Land is based on literature We are involved in various international projects in different areas of the world, typically at tender and execution stage we use mainly data provided by the clients

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If nothing is specified by the client (typically in early project stage or feasibility study stage) we can refer to values specified in IEC 287-3-1 where applicable or make some assumptions based on mean ambient temperature data issued by local institutions where available From experience If historical data are not available the Dry-season value (1,5) is conservative for majority of cases. In case of rocks or other known problematic soil, values are increased According on the type soil material and geographic location we select values of the thermal resistivity of soil taken from reference tables of IEC 60287 These are just examples - region A graded crushed rock or sand backfill, region B native soil - in Finland we are more concerned with moisture migration than seasonal moisture variation Consulting values normally used around the world Average of values under the conditions present in the company "Regional" values depending on the type of soil: sand/clay: 0,75 Km/W, peat 2,0 Km/W Information received by installers/utilities and literature - in the case of seabed, 0.7 K.m/W applies for larger depths of 15 m. For smaller depths, we consider 1.2 K.m/W From investigations carried out several years ago Most of our region is wet and we use the design value of 1 °C.m/W Customer specified or IEC 60287-3-1 Based on historical soil resistivities or informed by clients Data are supplied by customer By measurement in different spot in a region at least one year Numerous regions around the world. Values used according to customer specifications or taking from IEC 60287-3-1 when no other information is given According to IEC 60287-3-1 § 4.13 for Switzerland; region C is in case of rocky soil Depends on the location on earth and the situation in the field, and the project and purpose. Typical for NL are a thermal resistance of 0.75, but in reality everything between 0.4 and 3.0 is found Customer provide the value Experience Usually we assume rho of 90 for the soil and 50 for the concrete I use measurement and drying curve for setting all values based on local South African standards (SANS 10198-4).

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2.3

Soil Drying out

Do you consider soil drying out in your cable rating calculations?

Consider soil drying out

Consider soil drying out

Blank

No, never

Yes, always

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Known poor soils We typically attempt to put our cables at or below the water table, which for most of Florida is high New lines get soil dry-out curves; 13% moisture content on average (red clay will not dry out more than that and get 40 in / 1016 mm of rain / year) Assume that there is typically a 0.5-1% moisture content Yes, we install thermal backfills where feasible and consider them to retain a certain amount of their moisture based on backfill dry out curves, depth, and water table. Also, thermal dry out curves of the soil are obtained during the soil resistivity study Cable type, installation conditions, mostly for high capacity circuits Depending on the lowest water table If allowed/specified by client When data is available from measurements and/or cable ratings are critical Usually not used for generation cable connection (no overload) This is considered when we have to calculate the overload with a long duration (>5 min) Depending on the project location Direct or direct duct buried installation We normally specify the design of the trench such that the 50 °C isotherm is contained within the controlled backfill. If it can be, only the dry out thermal resistance of the backfill is considered. If the 50 °C can’t be contained within the backfill then the dry out of the soil is considered Special designs for major 66kV high capacity cables and we have soil tested at various moisture contents. In general we assume 5% moisture content will apply. Not for operational purposes Design FTB around cables to ensure interface between soil & backfill 70 °C), installation and operating conditions I understand that considering the soil properties it is necessary calculations using "Conformal Transformation". Moisture migration /apparent resistivity ( soil + backfill) XXX recalculated the current rating of XLPE-cables based on a maximum sheath temperature of 45 °C instead of a maximum conductor temp. of 90 °C, assuming that a maximum sheath temp of 45 °C never leads to drying out of the soil Installation conditions, multiple circuits, full loading Soil dry out has not been a problem in Ireland. We get rain here all year round! For underground cables laid in conditions with seldom rainfall and surface temperature is above 50 °C Depending on the customer specifications. Only when required When the calculation of cable surface temperature is higher than 50 °C Depending on client request, and depending on the situation Under pavement and near a heat source In the rare case of direct buries installation. The problem is not encountered in our typical duct bank installations Whenever the cables are in direct contact with native soil and where there is indication that the cable surface temperature exceed certain value In substation Special installations We do not operate XLPE cables above 70 °C (continuous) in order to prevent drying gout of soil.

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When using soil drying out, what are the typical values you use for the following parameters: Thermal resistivity of the dried soil; Thermal resistivity of the moist soil; Others (please specify)

8 7 6 5 4 3 2 1 0

Soil drying out: typical values used for thermal resistance (in K.m/W) for dried out soil, per country

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3 2,5 2 1,5 1 0,5 0

Soil drying out (in °C): typical values used for thermal resistance (in K.m/W) for wet soil, per country

80 70 60 50 40 30 20 10 0

Soil drying out: typical values used for critical isotherm (in °C), per country

How did you set these values (if any)? If you measure it please give details of the method: Answers given are:         

We take in situ samples for thermal resistivity and temperature. The dry-out curves are drawn and thermal resistivity values corresponding to 3% dry-out and complete dry-out values Soil lab tests (geotechnial survey); then take soil samples based on geotech survey. If sea soil is uniform, then do fewer tests Consultant recommendation Measured in laboratory on soil samples Common practice, soil survey's From measurement results Adopted median value for various soil 2.5 Km/W is the classical value for dry sand (from measurements) 55/60 based on Electra Depending on customer requirements

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Our soil condition is always wet so we go by details mentioned in item 2.2 50 °C isotherm based on a research paper Historical data passed down (some previous CIGRE research on this) We have used the thermal resistivity value at 1% moisture content for soil immediately around the cable/conduit (450 mm x 450 mm) which is referred as dry zone. Similarly, the thermal resistivity value at knee point for general ground soil was assumed Used values that were measured in the UK for typical soils Generally accepted temperature for UK, partly confirmed by XXX study These are the typical assumptions of others UK standard No comment The same as 2.2 By measurements and assumption XXX Cable handbook third edition These values were set based on literature studies and soil studies ; measurement methods : IEEE “Guide for Soil Thermal Resistivity Measurements” – IEEE Std 442 – 1981 ( 2003 ) ; ASTM – Determination of thermal Conductivity of Soil and Soft Rock by thermal needle probe procedure – ASTM D 5334-05; “Détermination d’une valeur d’échauffement critique pour les matériaux de remblai de câbles » - Electra N° 145 – Décembre 1992 IEC literature Assumed Danish values According to IEC recommendation as far as I remember Comment to the below. resting time is only used for few cases and as back up if the load fluctuation and max load exceeds the expected time (eg. 7 days) - which is not expected to happen ever. Primary a question of guarantee that no damage to the cable will ever occur; issue during transfer of cable system to a transmission owner Geotechnical report from 1980´s Bibliography These are rough values that have given the best fit when modelling moisture migration models to recorded temperatures around a cable scale heating tube we have constructed - we set very long time constants (3 months) for the return of moisture From historical calculations Among others by means of consulting XXX of XXX Literature Not appropriate 1 °C.m/W - moist soil 2 °C.m/W dried soil Electra No. 104/IEC 60287-3-1 Site measurements This value will be measured in experiments in this September IEC 60287-3-1 § 4.13 (for direct buried, in case of permanent load) We use our previously conducted lab experiments on different types of soil. Depending on the soil water retaining properties, the Tcrit will vary significantly. Depending on compaction and grain size distribution, and the soil type, the dry thermal resistance may become very high (e.g. in peat areas) Thermal probe and laboratory measurements We have used DTS to identify such zones and then deployed temperature sensors to monitor soil temperatures IEC

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Based on rho/moisture drying curve obtained in the lab IEC guidance.

After a possible drying out period do you consider a “resting” time to allow re-hydration of the surrounding soil?

Consider resting time to allow re-hydration of the soil (question 2.3) Resting time considered

2.4

Blank 39

Yes 10

no 52

Backfill and surrounding material properties

What parameters of usual material directly surrounding the cable do you specify?Do you make any control on the rest of backfill materials?

Backfill and surrounding material properties Item What parameters of usual material directly surrounding the cable do you specify?

Parameter Blank Yes Thermal resistivity 4 89 Grain size distribution 13 47 Compaction 10 57 Others 23 (see note 1) Do you make any control on the rest of the backfill 14 42 (see note 2) materials? Note 1: other parameters specified for material directly surrounding the cable:          

FTB Sieve dimensions for granular backfill Compaction level at optimum moisture content Thermal resistance at a specific / minimum moisture content Reference to standard/ specify material Excluding materials (vegetal soil ) Minimise cement content below 1% Dry relative density Depend on customer's specification Diffusivity

No 8 41 34 45

3 responses 2 responses 2 response 4 responses 4 responses 1 response 1 response 1 response 1 response 1 response

Note 2: The following additional information is given when control is given on the rest of the backfill materials:         

Compaction level Thermal resistivity On specification provided by others Grain size distribution Moisture content Soil composition No organic material CBS and / or bentonite Voltage class depending

16 responses 12 responses 7 responses 5 responses 5 responses 4 responses 4 responses 2 responses 1 response

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2.5

Influence of other heat sources

How do you take into account influence of other heat sources in your cable ratings?

Influence of heat sources Method By adding a margin to ambient temp Use of de-rating tables Calculating exact influence Not taken in to account Other By adding a margin to ambient temp:      

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Blank

Yes

No

20 20 8 42 53

30 26 69 4 7

51 55 24 55 41

+ 5 °C + 10 °C +15 °C +20 °C A "point" heat source added to the model For new lines as needed consultants determine the final other known heat sources. For existing lines, ratings have to account for potential heat source Depending on crossing and type (steam, duct bank, etc.) Temperature increase from heat pipes

8 responses 6 responses 1 response 1 response 1 response rating incorporating not been adjusted 1 response 1 response

By using the de-rating tables:     

Standard (IEC, VDE, JCS) Software Provided by manufacturers De-rating of conductor temperature (-10 °C) 20% de-rating for parallel circuits in the same trench

8 responses 4 responses 2 response 1 response 1 response

By calculating exact influence:       

IEC60287 or local standards Commercial software FEM Reference to literature Assume similar loading and use IEC If parameters are known Done by others

14 responses 13 responses 9 responses 4 responses 3 responses 3 responses 2 responses

Note: one responder states that the influence of parallel circuits is calculated exactly, for heat pipes, 10 to 20 °C is added to the soil temperature. Ta is subtracted from the maximum temperature of the cable conductor.

If other is selected:  

Maintain separation to ensure thermal independence Dependent on separation and asset, e.g. solid bonded gas pipe, ac interconnector, dc interconnector, sometimes assume a temperature boundary from the existing asset but at further detailed engineering we may ask the asset owner for their calculations or calculate ourselves

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To adopt heat pipe and thermal insulation board (from XXX report 180533) Site measurements of surrounding temperature Standard rating values are calculated for a max burial depth of 3 m and assume no other heat source in the vicinity of the cables at a distance of less than 3 m ; other heat sources are taken in account at detail design stage together with all project-related installation parameters Keep a distance between cable and other heat sources, distance is 1000 mm when laid in parallel, and distance is 500 mm when crossing.



3

Operating parameters

3.1

Do you use IEC maximum temperature as conductor normal operating temperature?

If not, or if there are exceptions to this rule, please detail your practice and value.

Use of IEC maximum conductor temperature IEC maximum conductor temperature used

Blank

Yes

No

0

86

15

Practice detailed:                    

Use AEIC as normal operating temperature Use AEIC standards 90-100 °C, indicated by the cable manufacturer Use manufacturer's data except for TX tails Yes, except for 11 kV and 33 kV where a lower phase conductor temperature is used to allow improved fault rating in the copper wire screen 90 °C for XLPE and 70 °C for oil filled Mainly except for tunnels where air temperature may be the limiting value JCS, allowable conductor temperature is 90 °C, which is the same as IEC JCS 168 E 1995, it is based on literature. JCS 0501 : 2002 OF:80～85 °C,CV:90 °C JCS 0510:2002 For XLPE cables we consider 90 ºC as the maximum temperature. Normally we specify a lower operating temperature to have a margin for a upgrade In order to assess realistically power losses we sometime consider the temperature and not the maximum Approx 60 °C Max 50 °C on cable surface to avoid dryout zones Conductor temp in submarine cables. Surface on land Well, for planning purposes, we generally use 65 °C for XLPE, which tends to side re. moisture migration, but if looking at existing installations, we may use

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future network real conductor

be on the safe 90 °C but with

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES



 





conservative moisture migration modelling - once again, we are researchers - the utilities tend to err on the safe side! XXX recalculated the current nominal rating of XLPE-cables based on a maximum sheath temperature of 45 °C instead of maximum conductor temp. of 90 °C, assuming that a maximum sheath temp of 45 °C never leads to drying out of the soil. This has been done in order to obtain similar calculation settings both for PILC and XLPE cables. Sometimes in very difficult situations, lower temp is considered for safety reasons (ie avoiding moisture migration etc) Not always because for reasons of economy (cost of losses) and/or margin of safety, our customers in Switzerland often ask us the values of permissible current for a maximum conductor temperature 60 °C or 75 °C instead of 90 °C for XLPE cables Exceptions are clients request, windfarms (sometimes higher temperature), older power cables (e.g. SCFF, Gas filled: sometimes lower max temperature due to increased dielectric losses not accounted for otherwise) We follow IEC excepting for XLPE insulated cables, were we limit the max conductor normal operating temperature to 70 °C (not 90 °C) this is to limit drying out of surrounding soil as well as to limit technical losses.

3.2

Temperature limitation

Where does the temperature limitation come from?

Origin of temperature limitations Part -

3.3

Reply Conductor temperature Metallic sheath temperature Cable surface temperature Air temperature (for tunnel)

Yes: 94 replies, No: 3 replies, Blank: 4 Yes: 16 replies, No: 59 replies, Blank: 26 Yes: 33 replies, No: 46 replies, Blank: 22 Yes: 39 replies, No: 44 replies, Blank: 18

Load factor

What is your practice regarding this parameter?

Current practice considering load factors Practice

Reply

-

Yes: 32 replies, No: 33 replies, Blank: 36 Yes: 40 replies, No: 17 replies, Blank: 45

-

Not considered Case per case calculations (based on IEC 60853) Assumed values Others

Yes: 27 replies, No: 19 replies, Blank: 56 Yes: 28 replies, No: 29 replies, Blank: 45

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Specified others:       

A load factor was determined by analysing all cables in the system Measured We assume 0.75 LF for most cables; will use 1.0 LF for generator leads and other specific lines where 1.0 LF is required. Past load history (load factor corresponding to 50-95% percentile, i.e., 0.81 to 0.91 In special cases may use line specific values Study profiles of windproduction or generators Normally no load factor, but can depend on client requirements regarding loads and ratings



According to French rules we talk about form factor which is 0.9 for 60/90 kV and 0.95 for above 220 kV

  

All circuits are designed for 100% load factor Actual worst case weekly (summer & winter) load curves used We have a target load and aim to carry load 100% of time or design/rate a cable for a dynamic loading Not normally used unless have multiple cable installations in same area - usually at distribution voltages It depends on customers Depend on customer's specification Related to wind energy infeed for submarine power cables Daily cycling LF = 0,7 We also use FEM In some project an estimate previous load to state the cable temperature has been used; followed by at long period of max load Based on the required values of load factor of the utility We basically use transient algorithms, developed for real-time application Load factor of the substation being connected In cooperation. XXX introduced (de-)rating factors as a compensation for a cyclic cable load instead of a continuous cable load. Factors of 1-1,5 were calculated for load designated as "households", "industrial/mixed" and "individual customers" Usually for safety reasons but also by customer demand, the calculations are carried out at load factor 1 Customer specified User specifies this value. Then, the program can perform cyclic rating calculations either as per IEC or as per Neher McGrath Neher/McGrath modification of T4 Provided by System Planning department We calculate this parameter based on the daily load profile of the feeders Based on load pattern supplied by a customer For cables up to and including 36 kV When planning new networks, we always use a load factor of 1 (conservative approach to cable loading).

          

        

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In case of assumed values please give details and typical values. Details given:                          

3.4

Use sample of heaviest loaded circuits and then ran loss factor calculations and assume worst case design Typically 75% 0.75 - 0.85 depending on area; 1.0 for data center load Typical factor of 80% for mixed circuit; higher for generator leads Not really applicable since most of our cable connections are for generation units (load factor 1). For very special cases we calculate according to IEC Depends on load cycle ranges from 0.5 to 1.0 Flat - 1 , Industrial - 0.84, Mixed - 0.76, Domestic - 0.67 Standard daily load cycles are sometimes used Most UK cables operate at 100% load factor Power line: 1.0, other line: 0.65 From measurement data Power line(from power plant) etc:1.0 Other line:0.6 JCS 168 E 1995 It is based on literature. 0,6 0.5-0.7 0.6-1.0 0.8(design value) Permanent rating with load factor 100% and cyclic rating with load factor 0,81 are standard considered It’s not commonly required, and it’s typical a value of 0,8 1 75% minimum (reference - "ISO XXX Planning Procedure") 100% 0.7 According to data provided by our customers. Typical values used frequently in Switzerland: Load 10 h 100% / 14 h 60% or 10 h 100% / 14 h 70% Power plant - 1.0 Transmission - 0.85 Distribution - 0.75 Wind farm - 0.6 Solar farm - 0.45.

Emergency

What is your practice regarding emergency?

Number of companies that consider emergency ratings Company type Cable manufacturer Consultancy Utility Other Total

Considered 22 12 44 6 84

Result Not considered 0 0 11 2 13

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Blank 0 1 3 0 4

Total 22 13 58 8 101

A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES

Method of emergency calculation reported Emergency rating method Yes IEC 60853 Rating ratio Automatic (e.g. Real time rating) Other

53 13 12 31

Result No 30 70 71 52

Blank 1 1 1 1

Given replies when selecting “others”:                            



Calculate Most lines do not have emergency ratings We follow Independent System Operator's guidelines, i.e., LTE, STE, and DAL ratings At 230kV for XLPE, try not to run them over 90C (IEC tests to +/-5C of normal rating); concerns about softening of cross-linked insulation Use AEIC standards XXX DTCR Customer specified Not really applicable since most of our cable connections are for generation units (load factor 1). For very special cases we calculate according to IEC As specified by cable manufacturer Calculate Emergency rating not applied to our 66kV cables. We permit 120 °C max conductor temp for 11kV and 33kV XLPE and 80 °C for PLY Conductor temp limited to 90 °C XXX A plan is to use DTS sensing and switch off turbines if temperature limit exceeded XXX software from XXX Near real time method using past & future loads at 30 min intervals XXX software from XXX Based on JCS (about allowable temperature for short time and short circuit condition) To adopt short time allowable temperature It depends on customers. Case per case calculations (based on JCS0501:2002) Manual operation considering real time thermal rating Depending of the client requirements in accordance with the cables possibilities for overload (time/temperature) Own development Paper B1-209 Cigre 2012 Depending on customer rules and specification Assuming a maximum temperature of emergency depending on the type of insulation for a limited time Long and short capacity durations - (temperature max : ICEA S-108-720) In cooperation with XXX of XXX, XXX introduced (de-)rating factors as a compensation for a cyclic cable load instead of a continuous cable load. These factors are also applicable in emergency conditions < 24h. Factors of 1-1,5 were calculated for load designated as "households", "industrial/mixed" and "individual customers" Usually max. 25-30% overload

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A GUIDE FOR RATING CALCULATIONS OF INSULATED CABLES     

Write programme to calculate the capacity in emergency Internal calculation program existing long standing (details not available) General calculation routine based on IEC 60853. We analyse various scenarios of circuits loss and the dispatching of the load on other nearby circuits As we use 70 °C conductor normal operating temperature, the 90 °C rating is reserved for emergencies/contingencies (24 hours). The 130 °C rating is an even further "absolute" max emergency rating allowed for short (8 hours max) durations (never exceed).

(1) Case per case calculations parameters

Emergency Durations considered:

number of companies

12 10 8 6 4 2

da ys 15

x< =

5 da ys <

x< = 5

da ys < 2

< da y 1

da ys

da ys 2 x< =

24 = x<