Engineering Method for Calculation of Short-Circuit

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Engineering Method for Calculation of ShortCircuit Mechanical Effects in HV Substations with A-Frame Arrangements using FEM CONFERENCE PAPER · JANUARY 2011

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CIGRÉ Canada Conference on Power Systems Halifax, September 6- 8, 2011

Engineering Method for Calculation of Short-Circuit Mechanical Effects in HV Substations with A-frame Arrangements Using FEM B. SEDAGHAT1, A. NABATCHIAN2 Monenco Iran Consulting Engineers Company1,2, MAPNA Group (IR)

SUMMARY There are many types of rigid tubular connection in HV substations. Tube conductors are used in situations that high current carrying is important like bus-bars. A-frame arrangement is the typical type of connection between different bus-bar height levels in the condition that tubular conductors cross each other. During short-circuits, electromagnetic forces are produced and mechanical stresses are applied on insulators and their clamps which hold tubes firm in their positions. Accurate determinations of the forces are important during design stage of a high voltage substation. T.P. Hermod Company had proposed new software for calculation of short-circuit mechanical effects on equipments in electrical substations. This software calculates the stresses based on IEC 60865 and IEEE 605 standards and does not cover A-frame arrangements. In this paper, an engineering method is proposed to calculate the resulting forces on supports. TPH software will be used for modeling and calculation of tension forces generated by tubes separately. Afterwards these forces are used as the inputs of Finite Element Method for calculation of the resulting forces on the supports. FEM calculations are done with the SAP software.

KEYWORDS A-frame, Electromagnetic force, FEM, HV substation, Mechanical stress, Short-circuit, Tubular conductor.

[email protected]

1. INTRODUCTION Rigid conductors, especially tubular types, are widely used in high current HV substation. The main reasons for that are high capacity of current carrying of tubular conductors and their mechanical strength in long spans. In the high voltage substations, it is so occurred that two different bus-bar height levels must be connected to each other. There are several methods for this type of connection. Yet, if tubular conductors crossed each other and are arranged in different levels, like what happens in 11/2CB substation arrangement, A-frame connections are applied. A-frame connections have two main benefits compared with other types of connections, they can carry electrical current properly and used as one of the supports for upper conductor. Fig. 1 shows the typical arrangement of A-frame in Shahrekord 400/63kV high voltage substation. On the other hand faults and short-circuits in substation can result in several damages in HV equipments. Short-circuit currents can made great electromagnetic forces. As can be observed from Fig. 1, if the short-circuit happens, both upper and lower conductor oscillate and mechanical forces are produced. Post insulators must withstand resulting forces of both conductors and supports must be designed based on maximum resulting forces [1]. Calculation of the forces for this type of arrangement is complicated and needs accuracy. The calculation method must be reliable and simple so it can be used during design stage of HV substations establishment. Standards IEC 865 (1,2) and DIN VDE 0103 contain calculation procedures for the assessment of mechanical short-circuit strength of straight, parallel rigid conductors [2]. In this paper these standards will be used only for calculation of resulting forces of each conductor separately. In This proposition, it is supposed that two level conductors are not connected to each other. So the resulting forces of each one of them cannot affect the other one.

Figure.1 System configuration and main parameters definition

The vector of forces will be used as the inputs of the FE method for calculation of final applied force on PIs. Distributed type of forces is applied and the calculations are done by the SAP software. This supposition is based on superposition principle. T.P. Hermod company have a five years investment on a comprehensive software, called “TPH Electrical Substations Comprehensive Software”, for designing of electrical substations up to 400kV voltage level [3]. One of the packages of the comprehensive software, called “T.P.H. HiVREM”, is used in this paper. Several standards are used to design this software such as, IEC 865, IEEE 605 and etc. Following that many appeals are executed for this software and several load combinations are added to the software. This package is used in several projects and the generated documents with this software are approved by well-known consultant companies. In this paper a new hybrid method based on the standards and FEM for calculation of the resulting mechanical forces on PIs in a-frame arrangement is proposed. This method will be applied to determine mechanical withstand level of PIs of the Shahrekord 400/63kV substation and the results of the calculation will be discussed.

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2. MECHANICAL STRESSES When short-circuit occurs in substations, large currents flow in conductors which lead to a large amount of electromagnetic force. The electromagnetic force that occurs during short-circuit can be defined as the mechanical push or pull which is caused by the short-circuit and it’s magnetic field, and which is exerted on the conductors [4]. High multi-phase fault currents produce electromagnetic forces which cause the phase conductors to repel one another and swing ensues [5]. The tension force leads to some reactions on the terminals, insulators and supports of the equipments. These reactions are due to the elastic restoring forces set up in the above components [4]. The amount of tension forces is in relation with the following independent variables: Tubular conductor size and characteristics, span length, phase spacing, short-circuit current, and the duration of the current flowing [1]. These forces can be calculated according to IEC standard [1,6]. The system configuration and main parameters are shown in Fig. 1. In the following section, IEC methods for calculation of mechanical forces for rigid conductors during short-circuit have been presented. Further calculations for final result will be done by Finite Element Method.

2.1 ELECTROMAGNETIC FORCES In a HV substation with the main conductors arranged with the same center-line distances on the same plane, the maximum force acts on the central main conductor during a three-phase short-circuit can be obtained from Eq. 1 [1].

Fm 3 

0 3 l ( I p3 ) 2 am 2 2

(1)

Where, ip3 is peak short-circuit current in case of a balanced three-phase short-circuit, l is center-line distance between supports and am is effective distance between neighboring main conductors. And the maximum force acts on the central main conductor during a line to line short-circuit can be obtained from Eq. 2.

Fm 2 

0 l (I p2 )2 2 am

(2)

Where, ip2 is peak short-circuit current in case of a balanced three-phase short-circuit. Effective am between main conductors with the center-line distance a, in which the main conductors consist of single circular cross-sections is given by Eq. 3 [1].

am  a

(3)

Where, a is the center-line distance between conductors.

2.2 STRESSES IN RIGID CONDUCTORS The stresses in the conductors and the forces on the supports like PIs depend on the ratio between the relevant natural frequency of the mechanical system and the electrical system frequency [1]. If resonance happens, the stresses in the system may be amplified. If fc/f < 0.5 the response of the system decreases and the maximum stresses are in the outer phases [1]. Under the assumption that the conductor is rigid, the forces acting are bending forces and the general equation for the bending stress caused by the forces between main conductors are given by Eq. 4.

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 m  V  Vr   

Fm l 8Z

(4)

Where σm is bending stress caused by the forces between main conductors, Vσ is ratio of dynamic and static main conductor stresses, Vr is ratio of stress for a main conductor with and without three-phase automatic reclosing, Fm is force between main conductors during a short-circuit, Z is section modulus of main conductor and β is a factor which depend on the type and the number of supports. Fig. 2 and Fig. 3 show the simple overview of the upper and lower support arrangement of the proposed system in Fig. 1.

Figure.2 Upper Tube Support arrangement

Figure.3 Lower Tube Support arrangement

A single conductor is assumed to withstand the short-circuit forces when Eq. 5 is satisfied.

 m  qR p 0.2

(5)

Where, q is factor of plasticity and Rp0.2 is the stress corresponding to the yield point. The factor q shall be taken from IEC standard. In this study, for tubular conductors, q can be calculated by Eq. 6.

2S 3 ) D q  1.7 2S 1  (1  ) 4 D 1  (1 

(6)

Where, S is resultant spring constant of both supports of one span and D is outer diameter of a tubular conductor.

2.3 FORCES ON SUPPORTS OF RIGID CONDUCTOR The generated mechanical forces in rigid conductors are applied to supports of the conductors. The dynamic force Fd can be calculated from Eq. 7.

Fd  VF  Vr    Fm

(7)

Where, the maximum values of VF and Vr and the value of α can be taken from IEC standard. The relevant natural frequency of a rigid conductor can be calculated from Eq. 8.

fc 

 l

2

EJ m

(8)

The values of γ and J can be obtained from IEC standard. The factors VF, Vσ and Vr are functions of the ratio fc/f, where f is the system frequency. Final results of the software were compared to the examples in [3,6] and the accuracy of the outputs based on IEC method were approved.

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2.4 FINITE ELEMENT METHOD Existing standards like IEC 865 so far do not offer methods covering calculation of the electromagnetic forces acting upon the conductors of more complex arrangements like a-frame. As was proposed, FEM is applied for calculation of the final resulting forces on conductor and supports. The Structural Analysis Program (SAP) uses FEM to calculate and analyze stresses in structures. This software is used to implement and analyze the stresses on conductor and supports in the proposed arrangement (Fig. 1). The calculation methods are detailed in [4]. The resulted forces from previous section are calculated based on three phase system, so the resulting force in each conductor also is affected by the other phases. This mutual effect is considered in the calculation of the forces according to IEC method. For modeling and implementation of the system in the FEM software it is needed to divide the system into several individual systems. From this point forward there is no need for analyzing the system in the three phase arrangement. In this study, conductors of each phase are located on the single support and are electrically and mechanically separated from the other phases. The three phase arrangement is divided into two individual systems: the Middle phase arrangement and the lateral phase's arrangement. Fig. 4 shows the implementation of the system in two situations. Characteristic of the system and type of the supports are shown in the Fig. 4 and detailed in Table 1.

Upper Conductor

Rigid Connection A-Frame

Slide Connection Support

Fix Connection Support

Lower Conductor

Legend Force Vector Direction

Figure.4 System implementation in SAP, Left figure: Middle phase arrangement, Right figure: Other two phases arrangement

3. ANALYZE AND DISCUSSION According to the previous chapters, short circuit forces on each tube conductor are calculated based on IEC simple calculation method individually. The proposed method is applied to the Shahrekord 400/63kV substation to determine the resulting forces on supports. TPH HiVREM software is used to calculate the forces in the actual condition of the site. The software can include wind, ice, damper and some other effects in the calculations. But in this paper, these factors are eliminated. The calculation results of the applied forces on supports of the conductors are shown in Table 2. The outputs of the TPH software are used as the inputs of the Structural Analysis Software. The direction of the forces is shown in Fig. 4. The electromagnetic forces are always orthogonal to the conductor axis [5,7]. In this study, resulted forces of A-frame legs during short-circuit are eliminated because the forces are relatively too small. The forces from Table 2 are applied to the implemented conductors' arrangement in SAP software. The parameters of the material, shape, formation and etc. of the upper and lower conductors are adjusted in the software and simulations for four combinations are executed.

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Table 1. System, conductors and supports characteristics Conductor (AlMgSi) Outer Diameter 200[mm]

Type Upper

Wall Thickness 6[mm]

Lower (middle phase) 120[mm]

6[mm]

Lower (longest lateral 120[mm] phase)

6[mm]

Span lenght 22[m] 13.25[ m] 15.5 [m]

Height to ground 13.5[m] 7[m] 7[m]

Support (PI) C8

Min. tensional breaking load 8000[N]

Min. torsional breaking load 4000 [Nm]

C12.5

12500[N]

6000 [Nm]

Vn / Vmax

Isc / duration

S.S Type

400kV/420kV

50[kA]/1[Sec]

AIS

Type

Table 2. Individual calculation results (TPH HiVREM Software Report) Type Upper Lower (middle phase) Lower (longest lateral phase)

Force on fix sup. 3671 [N] -

Force on rigid sup. 7868.42[N]

5719 [N]

3493 [N] 4570 [N]

-

6691 [N]

3466 [N] 4503[N]

-

Force between conductors 4748 [N]

Force on slide sup.

Electrical System

Fig. 5 shows the conductor deformation during short circuit. This figure shows movements and deformation of the tubes in an exaggerated manner. The final values for the resulted forces on supports during short short-circuit in worst combination are proposed in Table 3 and Table 4.

Figure.5 Conductor deformation, Left figure: Middle phase arrangement, Right figure: Lateral phases arrangement

According to the final results and after applying safety factors it is concluded that the C8 type of Post Insulator is quit suitable to support upper tube and C12.5 type of Post Insulator is quit suitable to support lower tube under A-Frame. Table 3. FEM final results – Middle Phase (SAP Software Report) Type PI under A-F

Fx 4570 [N]

6460 [N] 3022 [N]

Resultant Force 8470 [N]

Fy

Fz

Table 4. FEM final results – Lateral Phase (SAP Software Report) Type PI under A-F

Fx 4539 [N]

7789 [N] 3427 [N]

Resultant Force 9645 [N]

Fy

Fz

Upper Tube PIs

0 [N]

4375 [N]

437 [N]

4396 [N]

Upper Tube PIs

0 [N]

4502 [N]

677 [N]

4553 [N]

Lower Tube PIs

3493 [N]

0 [N]

713 [N]

3565 [N]

Lower Tube PIs

3428 [N]

0 [N]

665 [N]

3492 [N]

4. CONCLUSION When short-circuits occur, a large amount of current flows through conductors. During short-circuits, electromagnetic forces are produced and mechanical stresses are applied on insulators and their clamps which hold tubes firm in their positions. The oscillations result in large tension forces on

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connected HV equipments. In this condition equipments’ insulators, terminals, clamps and supports must withstand mechanical stresses during short-circuit. There are many types of connections in HV substations. Tube conductors are used in situations that high current carrying is important like bus-bars. One of the common types of connection between different bus-bar height levels in the condition that tubular conductors cross each other is A-frame arrangement. Calculation of the forces of this type of connection is complicated. On the other hand accuracy of the results is vital during design of a high voltage substation. In this paper, a new engineering method for calculation of the resulting forces on the support in Aframe arrangement was proposed. The proposed method combines standard methods with Finite element method. The TPH Co. HiVREM software calculates the stresses based on IEC 60865 and IEEE 605 standards and does not cover A-frame arrangements. In this paper, the T.P.H. software was only used for modelling and calculation of tension forces generated by tubes separately. Afterwards these resulting forces were used as the inputs of the Finite Element Method for calculation of the resulting forces on the supports. FEM calculations were done with SAP software and proper post insulators are selected for appropriate positions.

5. ACKNOWLEDGEMENTS The authors would like to express their sincere thanks to Mr. Ghelichi and Mr. Sotoudeh from Transmission & Dispatching division of Monenco Company. The authors would also like to express their sincere appreciation to Monenco Iran company and MAPNA group for their technical and

financial support. BIBLIOGRAPHY [1] [2] [3] [4] [5] [6] [7]

Group of Authors, Short-circuit currents – calculation of effects (865-1), 2nd ed., vol. 1, IEC standard, 1993. Norbert Stein, Amir M. Miri, High-voltage substations with rigid conductors full-scale short-circuit tests and comparative FEM studies on connections with so-called elbow bends (International Conference on Optimization of Electrical and Electronic Equipment, OPTIM 2008. 11th, 2008.). B. Sedaghat, M. Esmi, M. Najjari, M. Lari, T.P.H. HiVREM software development report, 2nd ed. Technical Report, T.P.H. company, 2009. Group of Authors, CSI Analysis Reference Manual, Computers and Structures, Inc., 2008. M. B. Awad, H. W. Huestis, Influence of short-circuit currents on HV and EHV strain bus design, IEEE Transactions on Power Apparatus and systems, Vol. PAS-99, No.2, 1980. P. Group of Authors, Short-circuit currents – calculation of effects (865-2), 2nd ed., vol. 2, IEC standard, 1993. Mircea Iordanescu, Claude Hardy, Jean Nourry, Structural analysis and testing of HV busbar assemblies with rigid conductors under short-circuit conditions, IEEE Transactions on Power Delivery, Vol. PWRD2, No.4, 1987.

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