Reference Manual of Dynamic Voltage Stability

Advanced Engineering Support Documentation

Dynamic Stability Reference Manual

Revision 5.7

© 2016 EasyPower LLC | 7730 SW Mohawk St, Tualatin, OR 97062 | Tel: 503-655-5059 | Fax: 503-655-5542

www.EasyPower.com

Table of Contents 1.0 INTRODUCTION TO EASYPOWER DYNAMICS .........................................................................................1 1.1 CONVENTIONS .....................................................................................................................................................3 1.1.1 Generators ..................................................................................................................................................3 1.1.2 Motors .........................................................................................................................................................4 1.2 THE DS SIMULATION TECHNIQUE .......................................................................................................................4 2.0 USING EASYPOWER DYNAMICS ...................................................................................................................7 2.1 ENTERING DATA ..................................................................................................................................................7 2.1.1 Data via the Library – Library Structure ....................................................................................................7 2.1.2 Data via the Library – Supplied Naming ....................................................................................................8 2.1.3 Data via the Library – Adding to Library ................................................................................................. 11 2.1.4 Data via the Library – Importing into Database....................................................................................... 15 2.1.5 Generator Data Dialog ............................................................................................................................. 16 2.1.6 Motor Data Dialog .................................................................................................................................... 19 2.1.7 ATS Data Dialog ....................................................................................................................................... 20 2.1.8 LV Breaker Data Dialog ........................................................................................................................... 21 2.1.9 Fused Switch/Contactor Data Dialog ....................................................................................................... 22 2.2 MODIFIED EQUIPMENT BEHAVIOR ..................................................................................................................... 23 2.2.1 Generators ................................................................................................................................................ 23 2.2.2 Motors ....................................................................................................................................................... 24 2.2.3 MCCs and Panels ...................................................................................................................................... 24 2.2.4 Behavior of UPS’ ...................................................................................................................................... 24 2.2.5 Transformer Tap Behavior ........................................................................................................................ 25 2.2.6 Protective Device Behavior ....................................................................................................................... 25 2.3 PF BALANCED SWITCHING FEATURE ................................................................................................................. 27 2.4 DS FOCUS ENTRY .............................................................................................................................................. 29 2.5 INITIALIZATION DETAILS ................................................................................................................................... 30 2.6 INTEGRATION TECHNIQUE ................................................................................................................................. 32 2.7 TIME STEP ISSUES .............................................................................................................................................. 32 2.7.1 Numerical Instability ................................................................................................................................. 33 2.7.2 Visual Appearance of Numerical Instability ............................................................................................. 33 2.7.3 Numerical Aspects of Induction Motors .................................................................................................... 35 2.8 ONELINE RESPONSE ........................................................................................................................................... 36 2.8.1 Normal Oneline Display ........................................................................................................................... 36 2.8.2 Stepping Oneline Display .......................................................................................................................... 37 2.9 TWO FORMS OF POWER FLOW ........................................................................................................................... 40 2.9.1 Swing Bus Power Flow ............................................................................................................................. 40 2.9.2 VCN Power Flow ...................................................................................................................................... 41 2.10 DYNAMICS OPTIONS ........................................................................................................................................ 41 2.10.1 Control Screen ........................................................................................................................................ 42 2.10.2 Double-Click Screen ............................................................................................................................... 44 2.10.3 Plot Output Screen .................................................................................................................................. 46 2.10.4 Arc Flash Screen ..................................................................................................................................... 47 2.11 PLOT DEFINITIONS ........................................................................................................................................... 48 2.11.1 General.................................................................................................................................................... 48 2.11.2 DS Plot Window ...................................................................................................................................... 55 2.12 SCRIPTS ........................................................................................................................................................... 64 2.12.1 Commands............................................................................................................................................... 64 2.12.2 Creating a Script ..................................................................................................................................... 66 2.12.3 Renaming a Script ................................................................................................................................... 69 2.12.4 Deleting a Script ..................................................................................................................................... 69

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2.12.5 Copying a Script...................................................................................................................................... 70 2.12.6 Edit a Script ............................................................................................................................................ 70 2.12.7 Running a Script...................................................................................................................................... 72 2.12.8 Stepping Through a Script....................................................................................................................... 73 2.13 SCENARIO MANAGER BEHAVIOR ..................................................................................................................... 74 2.14 PRINTING MODEL DATA SHEETS ..................................................................................................................... 75 2.15 STATUS BAR MESSAGES .................................................................................................................................. 79 2.16 REGISTRY CONTROL VARIABLES ..................................................................................................................... 79 2.16.1 SlewIterationLimit ................................................................................................................................... 80 2.16.2 IndMotVarThreshMag & IndMotVarThreshExp ..................................................................................... 80 3.0 EASYPOWER DS METHODS .......................................................................................................................... 81 3.1 SELECTING MODELS AND MODEL DATA............................................................................................................ 81 3.1.1 Generators ................................................................................................................................................ 81 3.1.2 Excitation Systems ..................................................................................................................................... 84 3.1.3 Governor Systems...................................................................................................................................... 89 3.1.4 Induction Motors ....................................................................................................................................... 89 3.1.5 Synchronous Motors.................................................................................................................................. 89 3.1.6 Typical Inertia Constants .......................................................................................................................... 90 3.2 PERFORMING MOTOR STARTING SIMULATIONS ................................................................................................. 91 3.2.1 Example Data Setup .................................................................................................................................. 91 3.2.2 Starting the Motor ..................................................................................................................................... 98 3.2.3 Defining Plots ......................................................................................................................................... 102 3.3 PERFORMING A BUS FAULT SIMULATION ........................................................................................................ 106 3.3.1 Example System....................................................................................................................................... 106 3.3.2 Perform First Bus Fault .......................................................................................................................... 109 3.3.3 Perform Second Bus Fault ...................................................................................................................... 113 3.3.4 Perform Third Bus Fault ......................................................................................................................... 115 3.3.5 Critical Clearing Review ......................................................................................................................... 117 3.4 STEP TESTING AN EXCITATION SYSTEM .......................................................................................................... 120 3.5 STEP TESTING A GOVERNOR SYSTEM .............................................................................................................. 121 3.6 DETERMINING MACHINE SATURATION ............................................................................................................ 123 3.7 PERFORMING A LINE-TO-GROUND FAULT SIMULATION .................................................................................. 125 3.8 ATS SWITCHING FOR EMERGENCY POWER...................................................................................................... 128 3.8.1 The Backup Generator ............................................................................................................................ 128 3.8.2 Example System and Data ....................................................................................................................... 128 3.8.3 Running the Simulation ........................................................................................................................... 133 3.9 DS QUICK ADVANTAGE METHODS .................................................................................................................. 135 3.9.1 Steady State Run Checks All Device Pickups, Proper CT Selection ....................................................... 135 3.9.2 Symmetrical Fault Simulation Check on Protective Device Selectivity .................................................. 135 3.9.3 Balanced Switching Fault Voltage Depression Check ............................................................................ 136 3.9.4 Balanced Switching Fault Contactor Action Check ................................................................................ 136 3.9.5 Fuse I2T Percentage to Blow to Predict Fuse Fatiguing ......................................................................... 136 3.9.6 Check Relay Travel to Predict Device Racing ........................................................................................ 136 3.9.7 Real-Time Simulated Arc Flash to Symmetrical Currents ...................................................................... 137 3.9.8 Balanced Switching Analysis for Switching of Any Device ..................................................................... 137 3.9.9 Run Power Flow with Motors Showing Correct PQ Loading ................................................................. 137 3.10 CHANGING FROM DROOP TO ISOCHRONOUS MODE ....................................................................................... 138 3.10.1 Diesel Generator Example .................................................................................................................... 138 3.10.2 Gas Turbine Generator Example .......................................................................................................... 141 4.0 MODELS ............................................................................................................................................................ 144 4.1 GENERATOR MODELS ...................................................................................................................................... 146 4.1.1 Round Rotor Synchronous Generator ..................................................................................................... 147 4.1.2 Salient Pole Synchronous Generator ...................................................................................................... 160 4.1.3 PV1G - Photovoltaic Inverter ................................................................................................................. 163

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4.1.4 WT4G - Wind Turbine with Inverter ....................................................................................................... 165 4.2 EXCITATION SYSTEM MODELS ........................................................................................................................ 167 4.2.1 Basler AVC1 ............................................................................................................................................ 172 4.2.2 IEEE Type 1 Excitation System ............................................................................................................... 174 4.2.3 IEEE Type 2 Excitation System ............................................................................................................... 178 4.2.4 IEEE Type AC1A Excitation System ....................................................................................................... 181 4.2.5 IEEE Type AC2 Excitation System .......................................................................................................... 184 4.2.6 IEEE Type AC2A Excitation System ....................................................................................................... 186 4.2.7 IEEE Type AC3A Excitation System ....................................................................................................... 189 4.2.8 IEEE Type AC4A Excitation System ....................................................................................................... 192 4.2.9 IEEE Type AC5A Excitation System ....................................................................................................... 195 4.2.10 IEEE Type AC6A Excitation System ..................................................................................................... 197 4.2.11 IEEE Type AC7B Excitation System ..................................................................................................... 200 4.2.12 IEEE Type AC8B Excitation System ..................................................................................................... 203 4.2.13 IEEE Type DC1A Excitation System ..................................................................................................... 206 4.2.14 IEEE Type DC2A Excitation System ..................................................................................................... 209 4.2.15 IEEE Type DC3A Excitation System ..................................................................................................... 211 4.2.16 IEEE Type DC4B Excitation System ..................................................................................................... 214 4.2.17 IEEE Type ST1A Excitation System ...................................................................................................... 217 4.2.18 IEEE Type ST2 Excitation System ......................................................................................................... 220 4.2.19 IEEE Type ST2A Excitation System ...................................................................................................... 222 4.2.20 IEEE Type ST3A Excitation System ...................................................................................................... 224 4.2.21 IEEE Type ST4B Excitation System ...................................................................................................... 227 4.2.22 IEEE Type ST5B Excitation System ...................................................................................................... 230 4.2.23 IEEE Type ST6B Excitation System ...................................................................................................... 232 4.2.24 IEEE Type ST7B Excitation System ...................................................................................................... 234 4.2.25 Inverter Q Control - For WT4G and PV1G Models Only ..................................................................... 237 4.2.26 Simple Excitation System ...................................................................................................................... 240 4.2.27 STAMFORD 1 Excitation System .......................................................................................................... 242 4.3 GOVERNOR MODELS ........................................................................................................................................ 244 4.3.1 Caterpillar Diesel 1 Governor System .................................................................................................... 245 4.3.2 Cummins Diesel 1 Governor System ....................................................................................................... 247 4.3.3 Gas Turbine Governor System ................................................................................................................ 249 4.3.4 Gas Turbine 2 Governor System ............................................................................................................. 251 4.3.5 Gas Turbine WD Governor System - Woodward .................................................................................... 256 4.3.6 Hydro Governor System .......................................................................................................................... 259 4.3.7 IEEE Hydro 2 Governor System ............................................................................................................. 261 4.3.8 IEEE Hydro 3 Governor System ............................................................................................................. 263 4.3.9 IEEE Steam 1 Governor System .............................................................................................................. 265 4.3.10 Pratt & Whitney PWFT8 Governor System........................................................................................... 267 4.3.11 Split Shaft Gas Turbine 1 Governor System .......................................................................................... 270 4.3.12 Steam Turbine Governor System ........................................................................................................... 272 4.3.13 WECC Gas Turbine Governor System .................................................................................................. 274 4.3.14 Woodward Diesel Governor System...................................................................................................... 277 4.3.15 Woodward Steam PID1 Governor System ............................................................................................ 279 4.3.16 Cummins Gas Engine 1 Governor System ............................................................................................ 281 4.4 PSS MODELS ................................................................................................................................................... 283 4.4.1 IEEE PSS1A Power System Stabilizer ..................................................................................................... 284 4.4.2 IEEE PSS2B Power System Stabilizer..................................................................................................... 286 4.4.3 IEEE PSS3B Power System Stabilizer ..................................................................................................... 289 4.4.4 IEEE PSS4B Power System Stabilizer ..................................................................................................... 291 4.5 MOTOR MODELS .............................................................................................................................................. 294 4.5.1 Double Cage Flux Induction Motor ........................................................................................................ 294 4.5.2 Synchronous Motor ................................................................................................................................. 308 4.6 MOTOR LOAD MODELS .................................................................................................................................... 311 4.7 PROTECTIVE DEVICE MODELING ..................................................................................................................... 312

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4.7.1 Fuses ....................................................................................................................................................... 314 4.7.2 Low Voltage Breakers ............................................................................................................................. 315 4.7.3 Relays ...................................................................................................................................................... 316 4.7.4 Under-Frequency Relay .......................................................................................................................... 317 4.7.5 ATS Model ............................................................................................................................................... 320 4.7.6 Contactor Model ..................................................................................................................................... 320 4.7.7 Under-Voltage Relay ............................................................................................................................... 321 4.7.8 Over-Voltage Relay ................................................................................................................................. 323 4.7.9 Inverter Blocking During Fault............................................................................................................... 324 5.0 MESSAGING ..................................................................................................................................................... 325 5.1 EXCITER MAX LIMIT MESSAGES ..................................................................................................................... 326 5.2 EXCITER MIN LIMIT MESSAGES ....................................................................................................................... 327 5.3 EXCITER GATE LIMIT MESSAGES..................................................................................................................... 329 5.4 GOVERNOR MAX LIMIT MESSAGES ................................................................................................................. 329 5.5 GOVERNOR MIN LIMIT MESSAGES .................................................................................................................. 330 5.6 GOVERNOR RUNTIME LOAD LIMIT MESSAGES ................................................................................................ 331 5.7 GOVERNOR INITIALIZATION LOAD LIMIT MESSAGES ...................................................................................... 331 5.8 SLEW RUN MESSAGES ..................................................................................................................................... 331 5.9 SLIP ESTIMATE MESSAGES .............................................................................................................................. 332 5.10 DATA ERROR MESSAGES ............................................................................................................................... 333 5.10.1 Generator Error Messages................................................................................................................... 333 5.10.2 Exciter Error Messages ......................................................................................................................... 334 5.10.3 Governor Error Messages ..................................................................................................................... 338 5.10.4 Description & Fix ................................................................................................................................. 340 5.11 MOTOR STARTING RUNTIME MESSAGE ......................................................................................................... 340 5.12 INITIALIZED MESSAGE ................................................................................................................................... 340 5.13 LOAD TRANSITION MESSAGES ....................................................................................................................... 341 5.14 SYNC MOTOR FIELD TRIPPED MESSAGE ........................................................................................................ 341 5.15 SYNC MOTOR FIELD TRIPPED ON REVERSE POWER MESSAGE ....................................................................... 341 5.16 SYNC MOTOR FIELD APPLIED MESSAGE........................................................................................................ 341 5.17 SOLUTION MESSAGES .................................................................................................................................... 341 5.18 REFACTOR MESSAGES ................................................................................................................................... 342 5.19 ENERGIZING GENERATOR IN OFFLINE CONDITION MESSAGE ........................................................................ 342 5.20 INDUCTION MOTOR POWER FLOW MESSAGES ............................................................................................... 343 5.21 PROTECTIVE DEVICE PICKUP MESSAGES ....................................................................................................... 343 5.22 PROTECTIVE DEVICE RESET MESSAGES......................................................................................................... 344 5.23 PROTECTIVE DEVICE TRIP MESSAGES ........................................................................................................... 344 5.24 RELAY TIME DELAY SATISFIED MESSAGE ..................................................................................................... 345 5.25 RELAY TRAVEL BACK MESSAGE ................................................................................................................... 345 5.26 RELAY UNABLE TO TRIP BREAKER MESSAGE ............................................................................................... 345 5.27 RELAY INSTANTANEOUS RESET MESSAGE .................................................................................................... 345 5.28 ATS TRANSFERRED MESSAGES ..................................................................................................................... 346 5.29 CONTACTOR DROPPED OUT MESSAGE .......................................................................................................... 346 5.30 EXCEEDED RESULT STORAGE MESSAGE ........................................................................................................ 346 5.31 NO PF SOURCE MESSAGES ............................................................................................................................ 346 5.32 DSTATES NOT SETTLED MESSAGES............................................................................................................... 347 5.33 DSTATES SETTLED MESSAGES ...................................................................................................................... 347 5.34 FAULTED MESSAGE ....................................................................................................................................... 347 5.35 FAULT REMOVED MESSAGE .......................................................................................................................... 347 5.36 ATS TRANSFERRED MESSAGE ....................................................................................................................... 348 5.37 CONTACTOR DROPPED OUT IN ISOLATED SUB-SYSTEM MESSAGE ................................................................ 348 5.38 RESULTS SAVED MESSAGE ............................................................................................................................ 348 5.39 DEVICE OPENED MESSAGE ............................................................................................................................ 348 5.40 DEVICE CLOSED MESSAGE ............................................................................................................................ 349 5.41 SIMULATION RUN TO MESSAGE .................................................................................................................... 349

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5.42 SIMULATION RUN FOR MESSAGE .................................................................................................................. 349 5.43 SIMULATION RESET MESSAGE ....................................................................................................................... 349 5.44 RUN SCRIPT MESSAGE ................................................................................................................................... 349 5.45 RUN SCRIPT WARNING MESSAGE .................................................................................................................. 349 5.46 CONTROL SETTING CHANGED MESSAGES...................................................................................................... 350 5.47 MOTOR LOAD MESSAGES .............................................................................................................................. 350 5.48 SIMULATION AUTO-STOP MESSAGE .............................................................................................................. 350 5.49 COMPLEX OPERATIONS ERROR MESSAGES .................................................................................................... 350 5.50 NUMERICAL INSTABILITY MESSAGE .............................................................................................................. 351 5.51 STEPPING MESSAGE ....................................................................................................................................... 351 5.52 SIMULATION COMPLETE MESSAGE ................................................................................................................ 351 5.53 DS FOCUS ENTRY ERROR MESSAGES ............................................................................................................ 352 5.54 DS FOCUS ENTRY MODEL ERROR MESSAGE ................................................................................................. 352 5.55 ATTEMPTING OPEN / CLOSE MESSAGE .......................................................................................................... 352 5.56 EXCITER / GOVERNOR STEPPING MESSAGES.................................................................................................. 352 5.57 COMPLETING SCRIPT MESSAGE ..................................................................................................................... 352 5.58 RESET ENCOUNTERED ERRORS MESSAGE...................................................................................................... 353 5.59 ARC FLASH MESSAGES .................................................................................................................................. 353 5.60 COMPLETING SCRIPT MESSAGE ..................................................................................................................... 354 5.61 POWER FLOW SCALING MESSAGE ................................................................................................................. 354 5.62 TIME STEP CHANGE MESSAGE ....................................................................................................................... 354 5.63 BUS / DEVICE / ATS NOT DEFINED MESSAGE ............................................................................................... 354 5.64 GENERATOR AVR UNDEFINED MESSAGES .................................................................................................... 355 5.65 GENERATOR AVR ACTION MESSAGES .......................................................................................................... 355 5.66 MOTOR SOFT START MESSAGES .................................................................................................................... 355 5.67 GENERATOR GOVERNOR SETTING MESSAGES ............................................................................................... 356 5.68 EXCITATION SYSTEM WARNING MESSAGES .................................................................................................. 356 5.69 SOLID STATE DEVICE BLOCKING MESSAGE .................................................................................................. 356 5.70 CONTACTOR MINIMUM VOLTAGE MESSAGE ................................................................................................. 357 5.71 RELAY TRIP SIGNAL SENT MESSAGES ........................................................................................................... 357 5.72 INVERTER TRIP SIGNAL SENT MESSAGES ...................................................................................................... 357 5.73 ZSI MESSAGES .............................................................................................................................................. 357 5.74 BREAKER DELAY SATISFIED MESSAGES ........................................................................................................ 357 5.75 INVERTER LIMIT ON INITIALIZATION MESSAGES ........................................................................................... 358 5.76 EXCITER VL SELECTED FOR LOW VALUE GATE MESSAGE ............................................................................ 358 5.77 PLUGIN DATA TRANSLATION ERROR ............................................................................................................. 359 5.78 PLUGIN INSTANTIATION FAILURE ERROR ...................................................................................................... 359 5.79 INVALID PLUGIN ERROR ................................................................................................................................ 359 5.80 PLUGIN IS MISSING ERROR ............................................................................................................................ 360 5.81 PLUGIN IS NOT INSTALLED ERROR ................................................................................................................ 360 5.82 MOTOR TORQUE VS. SPEED LOAD TABLE SIZE EXCEEDED ............................................................................ 360 5.83 IGNORING SOLID STATE BREAKER/SWITCH ACTION...................................................................................... 361 5.84 MODEL SET PARAMETER NOT DEFINED MESSAGES ...................................................................................... 361 5.85 MODEL SET PARAMETER MESSAGES ............................................................................................................. 362 5.86 NO SUCH PARAMETER MESSAGES ................................................................................................................. 362 5.87 CHANGING PARAMETER MESSAGES .............................................................................................................. 362 5.88 PARAMETER CANNOT BE SET MESSAGES ...................................................................................................... 362 5.89 DROOP AND ISOCH MESSAGES................................................................................................................... 363 5.90 GOVERNOR FAILED STEP TEST MESSAGE ...................................................................................................... 363

Note: Additional excitation system reference material reprinted with permission from IEEE Standard 421.5 – 2005, Copyright 2006, by IEEE. The IEEE disclaims any responsibility or liability resulting from the placement and use in the described manner.

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1.0 Introduction to EasyPower Dynamics Running dynamic simulations requires a new level of knowledge and understanding in power system simulation techniques from those most users of EasyPower have become accustomed to. If you are new to performing dynamic stability simulations, please review one of many texts by noted engineers such as Crary or Kundar that set the stage for use of EasyPower’s Dynamic Stability (DS) Engine. If you are familiar with stability simulations, then please take our advice, and read this manual to familiarize yourself with the methods used in EasyPower’s DS Engine. Due to the par excellent graphical interface of EasyPower, you may find running simulations a bit different than methods used in other industry software. We are certain however, that you will find the interface mature and well thought out. It was the DS Engine designer’s goal to make dynamic simulations in EasyPower as easy to run as possible. In the DS Engine, we include the following dynamic stability models: Generator Models    

Round Rotor Flux Synchronous Salient Pole Flux Synchronous PV1G - Photovoltaic Array with Grid Connected Inverter WT4G - Wind Turbine Generator with Grid Connected Inverter

Excitations System Models                  

Basler AVC1 IEEE Type 1 IEEE Type 2 IEEE Type AC1A IEEE Type AC2 IEEE Type AC2A IEEE Type AC3A IEEE Type AC4A IEEE Type AC5A IEEE Type AC6A IEEE Type AC7B IEEE Type AC8B IEEE Type DC1A IEEE Type DC2A IEEE Type DC3A IEEE Type DC4B IEEE Type ST1A IEEE Type ST2

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         

IEEE Type ST2A IEEE Type ST3A IEEE Type ST4B IEEE Type ST5B IEEE Type ST6B IEEE Type ST7B IEEE Type AC8B Inverter Q Control (for WT4G and PV1G models only) Simple Excitation System STAMFORD 1

Governor System Models                

Caterpillar Diesel 1 Cummins Diesel 1 Cummins Gas Engine 1 Gas Turbine Gas Turbine 2 Gas Turbine WD (Woodward) Hydro IEEE Hydro 2 IEEE Hydro 3 IEEE Steam PWFT8 (Pratt & Whitney) Split Shaft Gas Turbine Steam Turbine WECC Gas Turbine Woodward Diesel Woodward Steam PID 1

Power System Stabilizer Models    

IEEE Type PSS1A IEEE Type PSS2B IEEE Type PSS3B IEEE Type PSS4B

Motor Models  

Double Cage Flux Induction Salient Pole Flux Synchronous

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Protective Device Models       

Contactors - Automatic Drop Out Action ATS’ - Automatic Transfer Action All Protective Devices in EasyPower Power Protector – Relays, LV Breakers, Fuses Over-Voltage Relays Under-Voltage Relays Under-Frequency Relays Source Inverter Solid State Blocking for Faults

In later updates, the model library will grow even more. These models however supply a broad range of application, and should be most complete and with the greatest level of detail possible within a balanced positive sequence stability simulation. This includes the full detail of flux change in the machines, modeling of saturation, and full starting detail, including pulsating current and torque in the synchronous motor model.

1.1 Conventions Between groups of engineers and technicians within the U.S., there are numerous conventions used to describe electrical power systems. Groups like the IEEE and their sub-groups the Power Engineering Society and the Industrial Applications Society, have done their best to create a common convention to ease communication. Nonetheless, there are points of confusion. The goal of this section is to include a few notes on conventions used in the DS Engine, and the documentation. The conventions selected do not necessarily conform to any particular group, but are based on the designer’s experience and choice. In most cases, several other industry engineers were solicited for their view on a given convention.

1.1.1 Generators In the power system industry, there is (unfortunately) confusion in the use of the term “generator”, where it can represent the “electrical machine” that produces the electrical power, and in some cases (especially backup generators) the “total generation system”. The author has endeavored to write as clearly as possible, so that model components are clearly distinguishable. Whether exactly correct or not, we have elected to use the term Generation System to represent the combination of a Generator that generates electricity, the Excitation System that supplies the Generator’s field voltage, and the Governor System that supplies prime mover power and speed control to the Generator. From our Dynamics 101 notes, we have drawn a similar chart in Figure 1 to represent this structure.

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Thevenin Voltage

Terminal Voltage

Governor System Model P Mech Governor

Generator Model Internal Voltage

Prime Mover

Internal Impedance Ra + jX’’d

The Network

Field Voltage

Generation System

Field Current

Speed

Excitation System Model Terminal Conditions AVR

Power System Stabilizer

Amplifier

Exciter Terminal Voltage Feedback Terminal Conditions

Alternator

Figure 1. Generation System definition.

1.1.2 Motors For motors, we have a similar issue. Often “motor” is used to define the motor and the load, and any field excitation that is needed. Similar to the Generation System definition defined above, we have elected to define Induction Motor System and Synchronous Motor System as detailed in Figure 2 and Figure 3 below.

1.2 The DS Simulation Technique The DS simulation technique is a method that has been in existence for over 30 years. It basically assumes that: 

We are interested in time responses typically no smaller than a half cycle.



We are not interested in simulating the fast transient effect of the network.



We are interested in simulating the time response of machines and control systems.

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Thevenin Voltage

Terminal Voltage

T Mech Induction Motor Internal Voltage Internal Impedance Ra + jX’’d

Speed

The Network

Motor Load

Induction Motor System Terminal Conditions

Figure 2. Induction Motor System definition.

Thevenin Voltage

Terminal Voltage

T Mech Synchronous Motor Internal Voltage Internal Impedance Ra + jX’’d

Speed

The Network

Synchronous Motor System

Field Voltage

Motor Load

Fixed Field Voltage Terminal Conditions

Figure 3. Synchronous Motor System definition.

Thus, the network (overhead lines, cables, transformers, etc.) is not simulating any transient response due to the interchange between inductance, capacitance and resistance. The model is solved as if the instantaneous solution represents the present fundamental frequency network response. To illustrate the DS model and network interaction, we have supplied Figure 4. In this figure, we see the network (all modeled network items in EasyPower, including cables, transformers, capacitors, loads, etc.) being the central connective link between all DS machine models. Now on each time step of the simulation, a network solution is used to solve for the updated network conditions (bus voltages, line flows, machine terminal conditions, etc.). Likewise, on each time

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step, the DS models (generation and motor systems) update their internal conditions based on the network conditions, and thus supply an updated Thevenin voltage that is used to again update the conditions of the network on the next time step. This progressive behavior continues until the simulation terminates. And so, the network is the central connective tool to link all of the DS machine models together. In addition, all system perturbations occur in the network. On each half cycle, protective devices use the updated network conditions to alter (if needed) the connectivity of the network, by opening switch devices, dropping out contactors, and performing ATS transfers. Finally, the user can use scripts to open or close switching devices, force ATS transfers, open or close contactors, and apply bus faults during the simulation.

R

Relay Generation System

Generation System Fuse

The Network Motor System LVB

Motor System Contactor

Mo to r Sy s te

Motor System

m

Figure 4. Network and DS Model Connectivity.

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2.0 Using EasyPower Dynamics Using the EasyPower DS Engine will involve several aspects that a user of EasyPower is already accustomed to. These are: 

Entry of data into the database



Entry into an analysis focus



Performing the simulation



Printing out results or copying results into a report

This procedure is the same used in all foci of EasyPower, and thus we have introduced a new focus, the DS Engine focus. In the following sections we will explain the steps needed to get the additional data specified for performing DS and get a simulation up and running. We will also describe the new behavior of equipment now operating in a dynamic (time simulation) simulation environment. For example, in Power Flow, a motor is a load, and in Short Circuit it is a source. In DS, a motor behaves as both depending upon variations in terminal voltage of the machine. The motors response is also plotted in real time, rather than being a set of static values like amps, kW and kVar.

2.1 Entering Data All dynamics data entry is performed via convenient spreadsheets that accompany the Library and the individual equipment dialogs. In the Library, there is a DS category, and in the equipment dialogs there is a stability tab. To open a Library, click the EasyPower “e” and then Open Library, and select the Library you desire to view or edit.

2.1.1 Data via the Library – Library Structure The DS category entry in the Library has the following breakdown: Category – Group – Equipment – Manufacturer – Type For example, this could be: DS – Generation System – Generators – (Generic) – Std RR Within the Group and Equipment levels, we have the following available Equipment: Generation System Exciters Generators

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Governors Stabilizers Motor Systems Motors Running Loads Starting Loads Network ATS Contactors Transformers Utility Sources

Within each Equipment level, we can have many Types arranged by Manufacturer designation. Given the amount of data supplied by default in the DS portion of the Library, we will not list every Type and every Manufacturer here, however Figure 5 below gives an indication of how the Library is organized, and how you might add your own Manufacturer designation and Types.

2.1.2 Data via the Library – Supplied Naming In the Library that accompanies EasyPower DS, you will see a number of Manufacturers and Types entered for your use. Each of these entries is given a name, as well as located under a designated Manufacturer. Note that there is no hard-coded-reason why the present naming convention in the DS portion of the Library was used. The Library has the flexibility to accommodate many other naming schemes dependent only upon simple text entry for the Manufacturer or Type. We developed the naming convention as supplied here to have as much information about a device as possible visible in the Type names, so that when importing Library data into the equipment dialogs, selection would be easy. If desired (though not recommended), you may rename all of the Manufacturer and Type designations in your own copy of the Device Library. And, as shown in the next section, you can add to any existing Equipment or Manufacturer designation. For clarity, we supply the following definitions so that you have a better idea of what you are being supplied in the DS Library group. (Generic)

For each Equipment designation there is a Manufacturer labeled (Generic). In this designation, you will find listed all available hard coded model types, each listed with the “Std” prefix. The data supplied in this Library entry is truly “generic”, and we suggest that you review it closely before making use of it. We supply this (Generic) Manufacturer designation to clearly show what models the user has available.

(Plugin)

For each Equipment designation there is a Manufacturer labeled (Plugin). In this designation, you will find listed all available plugin model types. The data supplied in this Library entry typically supplies variations in tuning (fast,

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medium and slow for exciters and governors mostly) and at least one entry for each plugin model. Plugins are listed as a separate category since they are dependent upon the latest plugin dlls located in the “Plugins” folder in the EasyPower installation folder. Four dlls, Generators.dll, Exciters.dll, Governors.dll and Motors.dll are possible, and can be updated without an EasyPower “formal” update to gain the latest models made available by EasyPower engineers.

Figure 5. DS Group in Library open to show structure.

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Typical

This set of data for excitation systems and governor systems supplies three tunings (fast, medium and slow) for each hard coded model available in these two Equipment designations. We suggest performing an excitation system and governor system step test if you use this typical data, as the response will differ depending upon the generator (time constant and inertia) data that you use.

EPRI Synthetic This set of generator data supplies typical data that was taken from a report issued by EPRI in 1977. RR

This means Round Rotor.

SP

This means Salient Pole.

W in Governors This means Woodward. IM

This means Induction Motor.

Generator Types For the generator Types supplied in the Library, they have been supplied names with a specific meaning in each part of the name. This is defined to be: (Model)-(MVA)-(RPM)-(Year)-(Number) For example, RR-106-3600-1991-1 means:     

A Round Rotor generator Rated 106 MVA Rated 3600 RPM Built in 1991 The first one of these we had in our library of data

Droop

For the Woodward Diesel Governor model this designates the typical governor tuning uses the Droop setting.

Isoch

For the Woodward Diesel Governor model this designates the typical governor tuning uses the Isochronous setting.

Motor Types

For the motor Types supplied in the Library, they have been supplied names with a specific meaning in each part of the name. This is defined to be: (Model)-(HP)-(Sync RPM)-(NEMA Design)-(NEMA Code) For example, IM-100-1200-B-G means:  

An Induction Motor Rated 100 HP

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  

Rated 1200 RPM at no load NEMA Design B NEMA Code G

2.1.3 Data via the Library – Adding to Library Now that we have seen the layout of the Library, and the EasyPower naming scheme for the DS group, one logical question is, “how is data entered into the Library for my own equipment?” We will show this by example. Consider a new motor that is to be installed at your facility, and this motor data represents a large number of motors that will soon replace older motors near the end of their life. Therefore, including this motor in the Library will allow you to import it into any EasyPower database in the future. To properly determine double cage induction motor flux parameters, you will need to perform a motor parameter derivation. That method is explained thoroughly in two documents entitled, “Induction Motor Modeling – Part 1” and “Induction Motor Modeling – Part 2”. Refer to those papers to learn how to take manufacturer’s performance data, and generate detailed flux model parameters. With the derivation complete, the Motor Data Dialog – Stability Tab will have a complete set of data in its Motor spreadsheet. Use the following steps to add this data to the Library: Step 1 - If desired, create a new manufacturer Right click on Motors in the Motor System group, and a context menu will pop up as shown below. Click on “Insert New Manufacturer”.

Figure 6. Library Manufacturer insert.

The Library will create a new Manufacturer with a default name. Enter a name for the manufacturer. For this example, we used “My Plant”.

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Figure 7. Library name Manufacturer.

The Library tree should now look like this:

Figure 8. Library after Manufacturer insert.

Step 2 - Insert New Type Right click on “My Plant”, and a context menu will pop up as shown below. Click on “Insert New Type”.

Figure 9. Library Type insert.

The Library will create a new Type with a default name.

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Figure 10. Library name Type.

Enter a name for the Type. For this example, we used “Motor 1”.

Figure 11. Library after Type insert.

You have now successfully added a new motor entry in the Library. Now, make sure that “Flux Ind 2 Cage” is selected for the model (see Figure 12) since we are adding an induction motor. If you are ever needing to add a synchronous motor, select “Flux Sync” instead. Step 3 - Copy Data from Motor Data Dialog After a motor parameter derivation, the resultant derived parameters will reside in the Motor Spreadsheet in the left most spreadsheet in the Stability Tab of the Motor Data Dialog. Select all of the cells in that spreadsheet, and then press CNTL-C to copy the cell data to the Window’s clipboard. See Figure 13 showing the Motor Data Dialog.

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Figure 12. Library Model selection.

Figure 13. Motor Data Dialog selection of motor data.

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Step 4 - Paste Data into Library Now, go to the Library you have open, and paste the data into the new motor we just added to the Library. Right click on the first left most cell, and then click on “Paste cell(s)” (see Figure 14). You have now successfully added a new motor to the Library. Close the Library to save your changes.

Figure 14. Library paste of motor data.

2.1.4 Data via the Library – Importing into Database Data can be easily imported into any equipment dialog Stability Tab from the Library, by selecting the Manufacturer and Type (see Figure 15 for an example with the Motor Data Dialog), and then clicking on the Library Import button in the dialog. Library Import Button Once this is done, your new data is immediately imported and ready for use. This procedure is the same for all equipment dialogs that have DS models (generators, LV breakers, two winding transformers, ATS, fused contactors).

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Figure 15. Motor Data Dialog Library import.

2.1.5 Generator Data Dialog The Generator Data Dialog has two tabs of DS data; the Stability 1 Tab and the Stability 2 Tab (see Figure 16 and Figure 17). The Stability 1 Tab includes all model selection, data entry, and status for the:   

Generator Excitation System Governor System

The Stability 2 Tab at this time only has Power System Stabilizer (PSS) modeling. In a future release, we visualize adding Minimum and Maximum Excitation Limiters, or some other automatic control function to the Stability Tab 2. To define data for each of these components, we suggest first importing typical data from the Library for the model you select, and then modifying that data accordingly to match parameter values for your own equipment. In that way, if any parameters are left out in your data, you will at least have a beginning data set. For example, excitation system saturation is often left out of typical data sets. All models that can be specified in the Generator Data Dialog are documented in Section 4.0.

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Figure 16. Generator Data Dialog – Stability Tab 1.

Figure 17. Generator Data Dialog – Stability Tab 2.

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Each model system:    

Generator Excitation System Governor System PSS

can be enabled or disabled. Depending upon the enabled status, the model systems will behave in the following manner: Generator Model

Enabled. If the generator model is enabled and properly specified, then the machine data specified will transfer with the model specified into the DS Focus. The model is then initialized and prepared for simulations. Disabled. If the generator model is disabled, then all generation system models (Generator, Exciter, Governor, PSS) are ignored and no DS model is specified in the DS Focus. The generator is thus a fixed voltage source model in the DS Focus.

Excitation Model

Enabled. If the Excitation System Model is enabled and properly specified, then the data specified will transfer with the exciter model specified into the DS Focus. The model is then initialized according to the generator’s initial conditions (from resultant field voltage), and prepared for simulations. Disabled. If the Excitation System Model is disabled, then no exciter model is specified in the DS Focus. There is also no automatic field voltage control (resulting in no terminal voltage control). The generator is then being simulated with a fixed field voltage.

Governor Model

Enabled. If the Governor System Model is enabled and properly specified, then the data specified will transfer with the governor model specified into the DS Focus. The model is then initialized according to the generator’s initial conditions (from resultant mechanical power) and prepared for simulations. Disabled. If the Governor System Model is disabled, then no governor model is specified in the DS Focus. There is also no automatic mechanical power control (resulting in no speed control). The generator is then being simulated with a fixed mechanical power.

PSS Model

Enabled. If the PSS Model is enabled and properly specified, then the data specified will transfer with the PSS model specified into the DS Focus. The model is then initialized according to the generator’s and excitation system initial conditions and prepared for simulations.

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Disabled. If the PSS Model is disabled, then no PSS model is specified in the DS Focus, and no PSS damping is included in the simulation.

2.1.6 Motor Data Dialog The Motor Data Dialog has a tab of DS data; the Stability Tab (see Figure 18). The Stability Tab includes all model selection, data entry, and status for the:   

Motor Starting Load Running Load

As noted for the Generator Data Dialog above, to define data for each of these components, we suggest first importing typical data from the Library for the model you select, and then modifying that data accordingly to match parameter values for your own equipment. In that way, if any parameters are left out in your data, you will at least have a beginning data set. For example, motor saturation is often left out of typical data sets. All models that can be specified in the Motor Data Dialog are documented in Section 4.0.

Figure 18. Motor Data Dialog – Stability Tab.

In the motor system, there is only one enable check box. This model status behaves as follows: Motor System

Enabled. If the motor system is enabled and properly specified, then the data specified will transfer with the models specified into the DS Focus. The models are then initialized and prepared for simulations.

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Disabled. If the motor system model is disabled, then all motor system models (Motor, Starting Load, Running Load) are ignored and no DS models are specified in the DS Focus. The motor is thus a fixed load model in the DS Focus, having no ability to supply any short circuit current contribution. By default, when a motor is initially specified, the Starting and Running Load are set to a Speed Squared model. This selection eliminates the need for specifying any additional data in the Motor Data Dialog. For details on specifying data for induction motors, refer to documentation:        

Induction Motor Modeling - Part 1 Induction Motor Modeling - Part 2 Induction Motor Modeling - Part 3 Induction Motor Modeling – Part4 Induction Motor Modeling - Part 5 Induction Motor Modeling - Part 6 Induction Motor Modeling - Part 7 Induction Motor Modeling - Part 8

These papers discuss a wealth of information that will guide you in the use of manufacturer’s performance data, performing flux parameter derivation, validating manufacturer’s performance data, and discussing details on grouped and single motor behavior. For details on specifying data for synchronous motors, refer to documentation: 

Synchronous Motor Modeling

2.1.7 ATS Data Dialog The ATS Data Dialog has a tab of DS data; the Stability Tab (see Figure 19). The Stability Tab includes all model selection, data entry, and status for the automatic transfer of an ATS in the DS Focus. To define data for the ATS, we suggest first importing typical data from the Library for the model you select, and then modifying that data accordingly to match parameter values for your own equipment. The ATS DS model is documented in detail in Section 4.0. In the ATS Data Dialog, there is only one enable check box. This model status behaves as follows: ATS DS Model

Enabled. If the ATS model is enabled and properly specified, then the data specified will transfer with the model into the DS Focus. The model is then initialized and prepared for simulations.

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Disabled. If the ATS model is disabled, then no automatic ATS action is simulated in the DS Focus. The ATS can, however, still be manually switched from the oneline, and switched in a DS Script.

Figure 19. ATS Data Dialog – Stability Tab.

2.1.8 LV Breaker Data Dialog Low Voltage Breakers have the ability to also function as a Contactor, and thus include a DS model of a contactor in their Stability Tab. The “Std Contact” model in the Library has typical settings. Replace these to match dropout behavior of your installed contactors. The “Enable Contactor Model” checkbox allows you to include or exclude action of an individual contactor. This model status behaves as follows: Contactor Model

Enabled. If the Contactor model is enabled and properly specified, then the data specified will transfer with the model into the DS Focus. The model is then initialized and prepared for simulations. Disabled. If the Contactor model is disabled, then no automatic contactor action is simulated in the DS Focus. The contactor can however still be manually switched from the oneline, and switched in a DS Script.

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Figure 20. LV Breaker Data Dialog – Stability Tab.

2.1.9 Fused Switch/Contactor Data Dialog Fused Switches have the ability to also function as a Fused Contactor, and thus include a DS model of a contactor in their Stability Tab. The “Std Contact” model in the Library has typical settings. Replace these to match dropout behavior of your installed contactors. The “Enable Contactor Model” checkbox allows you to include or exclude action of an individual contactor. This model status behaves as follows: Contactor Model

Enabled. If the Contactor model is enabled and properly specified, then the data specified will transfer with the model into the DS Focus. The model is then initialized and prepared for simulations. Disabled. If the Contactor model is disabled, then no automatic contactor action is simulated in the DS Focus. The contactor can however still be manually switched from the oneline, and switched in a DS Script.

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Figure 21. Fused Switch Data Dialog – Stability Tab.

2.2 Modified Equipment Behavior In DS, the power flow solution is “the” initial system condition criteria used for initializing all DS models. Due to the nature of stability, and the model’s equations, we find that a few adjustments are needed in the power flow solution technique to get an appropriate initial condition power flow. As noted in the next section, entry into the DS Focus includes solving the system power flow to establish our initial conditions. Thus after entry into the DS Focus, the user is presented with the solved power flow on the oneline of the system. The user may notice a solution that is not exactly equal to the solution in the Power Flow Focus. This is caused by a few subtle changes that are necessary to prepare the power flow initial conditions to line up with the needs of DS simulation methods and DS models.

2.2.1 Generators Generators are converted to internal Thevenin sources behind equivalent impedances, to represent the internal behavior of the machine and its interaction with the network. Thus, swing sources and power flow voltage control no longer exist. All automatic control is supplied by the generator’s excitation system and governor system, if they are included.

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2.2.2 Motors Due to the need for motors to be represented as active sources in DS, motors have a modified behavior in the power flow solution within the DS Focus. First, since the regular power flow does not contain the ability to model motors as Thevenin sources during balanced switching, motors are converted to a PQ generator internally. This means that the motor load is treated as a constant MVA load (instead of constant current or impedance as specified in the motor data dialog) during the DS Swing Bus Power Flow. This slight change could then cause a system to take a few more iterations to solve, and could present slightly lower voltages than those seen when solving the system in the Power Flow focus. NOTE: If the user notices that DS entry is not allowed due to lack of a power flow solution, there are induction motors being modeled and the system solves just fine in the Power Flow focus, try increasing the number of iterations in the Power Flow Options dialog. This can be accessed in the PF focus, under Tools. Then, try re-entering DS Focus. In addition, induction motors have an issue in matching var requirements determined by the machine equations with vars specified in the database. To properly initialize the motor, we have elected to ignore vars specified in the database, and match vars determined by machine equations. This then causes the need to repeat several power flow solutions (iteratively), as the machine equations are initialized to supply updated var requirements. Upon completion, the initial power flow solution will create a match between power flow voltage and var conditions, so that induction motor machine equation var requirements match the power flow. Finally, there are differences in how single and grouped motors are treated. Refer to “Induction Motor Modeling – Part 4”, for an in depth discussion of this behavior.

2.2.3 MCCs and Panels In the DS Engine, MCC’s and Panels have no ability to model dynamic motor response. Their motors specified will be treated as passive loads in the DS Engine. If motor starting is desired for a motor in an MCC, we recommend adding a single motor on a bus connected off of the MCC. Note also, that since the motors of MCCs and Panels are represented as passive, there is no short circuit contribution from them during a fault in DS. In a future revision, detailed modeling of MCC and Panel motors will be considered.

2.2.4 Behavior of UPS’ In the Power Flow focus, a UPS is modeled as a load on its primary, and a swing generator on its output. This falls in line with a UPS holding voltage and supplying power as needed, as long as it is operating within its rating. In the Short Circuit focus, a UPS has a fault contribution like a generator on its output according to entered data.

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In the DS Focus, a UPS is modeled as a fixed Thevenin voltage source on its output, and a load on its input. During a simulation, changes in the output loading are not reflected on the primary, and no voltage control occurs. We thus recommend not simulating switching actions on the secondary of a UPS, as they will provide no automatic voltage and power response, and the changes will not reflect onto the high side of the UPS. In a future revision, full UPS automatic control will be considered.

2.2.5 Transformer Tap Behavior Since transformer tap changing is typically timed in an actual system with a 20 to 60 second delay, transformer tap changing is disabled during a dynamic simulation.

2.2.6 Protective Device Behavior All Protective devices modeled in Power Protector are simulated in the DS Engine if appropriate data is supplied and the Power Protector feature is enabled (has been purchased). For users without Power Protector, no protective devices are transferred into the DS Focus. Modeling of protective devices includes:         

Fuses LV Breakers Relays Under-Frequency Relay Action Contactor Drop Out Action ATS Auto-Transfer Action Over-Voltage Relay Action Under-Voltage Relay Action Source Inverter Solid State Blocking Action for Faults

In all cases, for devices that include a minimum and maximum curve for device operation (for example, an uncertainty band or fuse min melt and max clear curve) the more severe max clear curve is used to determine when a device will be tripped. This will thus keep a fault condition on longer, and corresponds to a consistent tripping action that matches the EasyPower Arc Flash tool. More specifically, we note the following for each protective device: Fuses

Fuses are simulated using an accumulated I2T action. When current through a fuse causes the trip time to drop below 1000 seconds, I2T energy begins to accumulate. The I2T trip value is updated on each time step corresponding to the present current flowing through the fuse. When the accumulated I2T meets or exceeds the I2T trip value, the fuse is tripped (actually the EasyPower switch on the oneline is opened to simulate this).

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Note that the energy accumulated in the fuse is not reset during a given simulation. This memory action is performed since a typical dynamic simulation runs for 10 to 50 seconds, and we believe this is not long enough to allow any significant dissipation of heat from the fuse. From this memory action, multiple faults through a fuse can contribute to a faster fuse blowing action, which in reality would exist in the field. LV Breakers Low Voltage Breakers are simulated using a time accumulation method. When current through a LV Breaker causes the trip time to drop below 1000 seconds, then a timer is used (accumulating time) to trip the device as long as the current remains above the devices pickup setting. When the accumulated time exceeds the trip time at the current point on the devices TCC (specified and updated by the present current flowing through the device), the device will trip. The device instantaneously resets if the current drops below the pickup setting. Relays

Relays are simulated using time accumulation as a simulated induction disc turns. This assumes that digital relays are performing a similar action. Thus the device is simulating travel time and tripping in accordance to the time dial setting. When current through a Relay causes the trip time to drop below 1000 seconds, the disc simulator starts timing. When the time passing by meets or exceeds the trip time from the relays TCC based on present current through the device, the device will trip. If the current drops below the pickup setting before tripping, the device will simulate travel-back of the induction disc (again assuming digital devices will do the same). This travel-back assumes that the full travel-back of any relay is 60 seconds when on the maximum time dial, with this effect ratio’ed accordingly to other time dial settings. From this travel-back action, we are simulating memory, and thus are including the capability of a relay to trip faster on a second fault application.

UF Relays

Under-Frequency Relays use a single under-frequency setting and timer. When the bus frequency drops below the setting, and has stayed below for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the frequency goes above its setting. Under-Frequency Relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet.

Contactors

Contactors operate like the Under-Frequency Relay, and trip after voltage has dropped below its setting for the time specified. The device resets instantaneously.

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ATS

ATS’ only perform automatic operation from left (Normal) to right (Emergency) as seen on the oneline. Their behavior is as follows: Assuming we are originating on the Normal side, if the source is lost (voltage drops below the Trip Voltage setting for a time longer than the Delay on Start setting), the ATS is prepared for transfer. If the voltage on the Emergency side is above the ATS Required Voltage setting, then the transfer will continue. If not, the ATS remains on the Normal side. The ATS model does not presently simulate the Neutral position in its transfer. Therefore, if transferring, it stays on the Normal Source side until the Neutral Delay time and Mechanical Delay time are satisfied. To simulate the Neutral position, an additional bus would need to be simulated in the network, and that has not been implemented in the present version. The ATS will not auto-transfer-back if the Emergency Source is lost. The action presently modeled is a one-way transfer.

OV Relays

Over-Voltage Relays use a single over-voltage setting and timer. When the bus voltage goes above the setting, and has stayed above for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the voltage goes below its setting. Over-Voltage Relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet.

UV Relays

Under-Voltage Relays use a single under-voltage setting and timer. When the bus voltage goes below the setting, and has stayed below for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the voltage goes above its setting. Under-Voltage Relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet.

Inv Block

Inverters (when no DS data is specified) include a blocking action when the fault current (specified in the inverter data dialog), has stayed above 102% FLA for the time specified. Upon blocking, the inverter current injection is removed from the network model and the inverter does not interact with the grid.

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ability of performing simulations with a minimal set of DS model data, or for that matter, no DS model data. In the case where you have an EasyPower database with no DS models enabled, you can perform balanced switching. Balanced switching allows you to determine network conditions immediately after a network change has occurred. Since there are no DS models active, the resulting plot will take on a squarish nature (see Figure 22), where the conditions before the change represent the time T zero minus (To-) and the conditions after the change represent time T zero plus (To+). Such simulations are very useful if one desires to know network conditions immediately after a line opening (for example). Since all sources are modeled as Thevenin voltage sources, and all other motors and loads are passive, the difference seen will be one that reflects the sudden change, but will not represent the real-time response of the system. When first learning to use DS, we suggest doing a few balanced switching simulations to get familiar with the DS Focus, before specifying DS model data. 800.00

M-1 [kW]

M-1 [kVar]

-400.00

0.00

1200.00

M-1 [I Amps] -800.00

800.00

BUS-4 [V PU]

BUS-4 [V PU] M-1 [I Amps] M-1 [kW] M-1 [kVar]

0.8800

0.9600

EasyPower DS

0.0

0.6

1.2

1.8

2.4

3.0

3.6

4.2

4.8

5.4

6.0

Time (Seconds)

Figure 22. Balanced switching plot result.

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2.4 DS Focus Entry Upon entry into the DS Focus, your model is checked and set up to run a simulation. The simulation relies upon a tight link between the DS Engine and the Power Flow Engine, as all flows and voltages are dependent upon the network. Without a well-developed power flow case, DS Simulation is impossible or of no value. Make sure that your power flow case solves well, and accurately represents your network. Once clicked, moving into the DS Focus will: 

Not allow entry into the DS Focus if any dynamics data fields are partially completed, i.e. started but not complete. However DS Focus entry is allowed when there are sparse DS models or even no DS models, as the system will resort to passive load models for nonDS motors, and Thevenin sources for non-DS generators. In this way a user can spec only a single DS-motor, and run a fully detailed motor start case using short circuit impedance info for the source. Such is actually an accurate simulation for a system with no nearby (local) generation.



Solve the Power Flow case using a swing-bus power flow. If the case does not solve, the user will be alerted, and returned to the Database Focus.



Initialize induction motors alone if there are any. The system is then repeatedly (iteratively) solved as a swing-bus power flow and induction motor initialization updates motor terminal conditions in the power flow. This typically takes between 1 and 4 power flow solutions, and is reported in the message log.



Initialize all other defined models. Models use the conditions specified by the power flow to perform their initialization. If any models fail initialization, the user is returned to the Database Focus. Failure is typically due to power flow conditions that are unrealistic or through which the model is incapable of initializing. For example, such a condition might be having a load in the power flow on a motor specified at 180%. When the motor dynamics are initialized, the motor will most likely initialize into a stall condition on the wrong side of the torque speed curve. The motor is thus not able to supply the load, and will be operating at a ridiculously high slip.



If a motor is connected on a bus with zero voltage, or is disconnected from the system by its breaker, then the motor model will be initialized such that it is ready to start. Otherwise, the motor is initialized online.



Note that all static loads (and non-DS motors) are converted into constant impedance loads. This is the present load model used in the program. Future revisions may allow constant power and constant current load models, with eventual reduction methods when voltages drop below a pre-defined threshold. However, at this time, all static loads are converted to constant impedance. The reason for the conversion to constant impedance is due to the fact that the network solution is a direct solution, and is non-iterative. This supplies a great degree of robustness. The network solution under this condition will always solve. If loads however

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are modeled as constant current or power, the solution would have to iterate. This would then open up the possibility of divergence or minimal convergence under severe voltage depressions. It is known that utility systems necessitate this modeling flexibility, since often entire complex sub-systems are modeled with a simple static load. Thus the three model types supply a total power equation with a constant (constant Z), linear (constant I), and squared (constant power) capability. This affords the user load models that can be developed to closely represent the sub-system with just a static load. In industrial systems however, such static load modeling should have less need, as motors will be modeled as actual machines. Thus, constant Z load models (representing resistive heating, and incandescent lighting, etc.) are an accurate method when employed. 

Evaluate all model DStates. If any exceed a specified threshold (defined in the DS Options Dialog), then the user is alerted to review the DS Message Log to fix any problems. The user is allowed into the DS Focus, but we highly recommend that the DState violations be dealt with. Refer to “Message Log Messages” for help in determining appropriate actions to resolve any DState issues. Also, additional information is included in the “Models” section (Section 4) for each dynamics model available in EasyPower.



If all is well, the DS Focus is entered, and the user is able now to perform DS analysis.

2.5 Initialization Details When the case you are simulating goes through initialization, the power flow conditions specified at the terminal of machine models are used to initialize the machine models. Initialization of a machine model is thus performed assuming all differential states (DStates) are equal to zero. This should be so at steady state, as we are considering no movement in the model and thus, no changes (DStates are changes) are taking place. This allows us to work backwards through the machine equations and initialize all States. Next, for generators, their excitation systems and governor systems are initialized, given the machine has been initialized. This is our natural progression back through the model control flow. Excitation systems use generator field voltage and current to specify initial conditions, and governor systems use the machine’s mechanical power or torque. For generators at steady-state, we assume speed is at rated condition, and so mechanical power and torque are equal in the per unit data system. For induction machines, we take the machine’s mechanical power, and initialize the load model that specifies the Torque vs. Speed characteristic for the motor load. The process of moving back through the models appears fairly straight forward, and actually is so, with exception of a few models and load specification conditions that upset this simplicity. The first upset is saturation. Since saturation is a non-linear effect, we find that specifying the correct internal machine conditions necessitates an iterative approach, as the machine equations would generate a very complex algebraic solution. In fact the algebra does not lend itself to a direct solution, as squared and cubed terms appear and make the direct solution impractical.

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Similar to power flow solutions, we then iterate within the model to find machine model States that create the same terminal conditions as specified in the power flow. This iterative approach is termed a “Slew Run”, as we are actually running a simplified and fast dynamic simulation in the model while updating particular States based on the error of the desired terminal conditions vs. what the model is calculating. Slewing is performed on round rotor generator and induction motor models, as each allows simulation of machine saturation. The second upset that causes a need for slewing is the fact that the induction motor model does not have a direct solution for initializing its States due to the interaction between the real and imaginary axes of the model. To explain this we would need to delve into the machine model and explain what the real and imaginary axes do. Suffice it to say, the modeling method is similar to the d and q axis modeling technique used in generator modeling, and we will stop there. However, we note that the induction motor model has complete cross coupled interaction between its real and imaginary components, even without saturation. For the round rotor generator model, however, the d and q axes can be initialized separately and will only interact when saturation is included. The third upset involves the inability of an induction motor model to match conditions specified in the power flow case. Power factor conditions for an induction motor in a power flow case are estimated. But in reality, the machine determines its reactive power based upon magnetizing impedance, internal machine impedances in the rotor and stator, machine slip, loading and saturation. We can only make the model match terminal real power (via slip), and must allow the machine model to tell us what the actual vars of the motor are, given the machine data used. This means that the resultant vars will most likely differ from those in the power flow case, and that we “cannot match” the power flow case vars for each induction motor. There are several ways to handle this issue. One method utilized in a well-known stability package adds a reactive or capacitive shunt to the motor bus (in the network model) which is equal to the difference between the power flow case and what the motor model requires. This has been used for many years, and thus appears to be an acceptable technique. With EasyPower, however, we have decided to forgo this method since it actually adds a “new” component to the system that really does not exist and thus compromises model accuracy. For example, if the motor model vars are greater than those in the power flow, we would have to add a capacitor to the bus where the motor is connected in order to compensate. We are convinced that this is simply unrealistic, given the customers we serve. The other software package noted above is used mostly by large interconnected utility systems. In such a case the system response is mostly determined by generators, excitation systems, and governors. Induction motor models have less impact on simulations by most users. However, EasyPower customers are predominantly industrial, and may have hundreds or even thousands of induction motors modeled in their case. Thus, the accumulation of this additional reactive fudge factor becomes a significant “change” to the real model. Because of these ramifications to the overall system model, we have elected to iterate the swingbus power flow, while the induction motor model re-initializes and updates its power flow terminal conditions. In reality, if the motor is modeled correctly by the machine model, then the

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vars will be different, and the system power factor will change based on the real motor vars. This then requires us to update the power flow solution accordingly. Table 1. Summary of Slew Actions in EZP.

Model

Slew in Init

Slew for Sat

Slew for No Sat

Sys PF Iter

Round Rotor Gen

Yes

Yes

No

No

Salient Pole Gen

No

No

No

No

Induction Motor

Yes

Yes

Yes

Yes

Synchronous Motor

No

No

No

No

2.6 Integration Technique The integration technique used in the DS Engine is simple yet elegant, and has been found to yield excellent results for many systems. The method used is a “Modified Euler” technique, and has the main advantage of increasing simulation accuracy as well as being a very fast method. Other more complicated integration methods may take double to triple the math operations per integration. When this is multiplied by the number of times that the integration algorithm is called during a simulation (i.e. on every time step and as needed in each model), the performance repercussions are clear. The Modified Euler technique uses an averaging technique with memory. This then means that one additional variable is needed in addition to the State and DState. This is called the Store value, and is involved in the integration equations for each time step as noted in the following equations. StoreNew  StoreLast Time  DState  t StateNew  StoreNew 

DState  t 2

2.7 Time Step Issues The time step used in a dynamic simulation is the lowest level fundamental value that moves a simulation through time. With it, you are defining: 

The ∆T or dt for numerical integration



The step size resolution of the simulation



Plot level detail

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2.7.1 Numerical Instability Due to the use of numerical integration to perform our simulation, the time step affects numerical stability of our simulation. This issue, which can rear its ugly head during a critical simulation, must be understood so that corrective actions can be taken by the user. So, how does numerical instability occur? It occurs when the time step is large to the point where control block feedback (for example, as seen in a single time constant block) is unstable. In simple terms, this happens when the time step is greater than a control block’s time constant. However, very complex systems may have “effective time constants” (formed by loops within the model) which cause the actual time constant during a simulation to be even smaller than the smallest observed time constant in any model. A good practice, then, is to never simulate with a time step greater than half the value of the smallest observable time constant.

2.7.2 Visual Appearance of Numerical Instability To see numerical instability and its effect on output, let us review the single time constant model discussed in the Dynamics 101 material. That block is shown in Figure 23, with its exploded view (to see the integration block) in Figure 24. The result of a step on the input to this system is shown in Figure 25. The simulation to generate Figure 25 was performed with a 0.1 second time step, and since the time constant T is equal to 1.0 second, this is a safe and accurate time step.

K 1  sT

Vi

Vo

Input

Output

Figure 23. Single time constant block.

Vi

K +

1 T DState

1 s

Vo

State

Figure 24. Single time constant block showing integrator.

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1.20

2.00 1.80 1.60 1.40

0.80

1.20 0.60

1.00

Input

DState & Output

1.00

0.80 0.40

0.60 0.40

0.20

0.20 0.00 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.00 10.0

Time (Seconds) Dstate

Output

Input

Figure 25. Results of step simulation on single time constant block – ∆t = 0.1 Sec.

However, if we were to increase the time step to say 0.8 seconds, we would see some numerical artifacts begin to appear. In Figure 26, we have such a simulation. Our time step is now so large, that we miss seeing the exponential curve of the dynamic response, and the jagged overshoot is definitely not part of the real result. Similarly, if we were to increase the time step to 1.8 seconds, we now see a definite problem with the simulation. Figure 27 shows the response with a 1.8 second time step. The jagged backand-forth response of the system is a clear indication of the numerical feedback loop of the single time constant model becoming unstable. The system even needs time to settle numerically. Here we have results that show a clear “signature” of numerical instability. If this is noticed in plot outputs, then a model in the system may have too small a time constant for the time step being used in the simulation. In more complicated systems, such as we have when simulating induction motors and generators, there are conditions where numerical instability occurs so severely, that jagged curves do not even result. In such cases, the model States move quickly to unstable and non-realistic values with high exponents. In such cases, the DS Engine has checks to shut down a simulation with such behavior before math errors are created that may cause severe repercussions, like an application crash to the operating system.

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1.40

2.00

1.20

1.80 1.60 1.40

0.80

1.20 0.60 1.00 0.40

Input

DState & Output

1.00

0.80 0.20

0.60

0.00

0.40

-0.20

0.20

-0.40 0.0

10.0

20.0

30.0

40.0

50.0

60.0

0.00 70.0

Time (Seconds) Dstate

Output

Input

Figure 26. Results of step simulation on single time constant block – ∆t = 0.8 Sec.

2.00

2.00 1.80 1.60 1.40

1.00

1.20 0.50

1.00

Input

DState & Output

1.50

0.80 0.00

0.60 0.40

-0.50

0.20 -1.00 0.0

10.0

20.0

30.0

40.0

50.0

60.0

0.00 70.0

Time (Seconds) Dstate

Output

Input

Figure 27. Results of step simulation on single time constant block – ∆t = 1.8 Sec.

2.7.3 Numerical Aspects of Induction Motors One of the places where numerical instability can appear first is the application of starting motors. Due to the small time constants in the rotor, and the effective time constants that are very small during starting, motors (both induction and synchronous) need small time steps during a starting simulation. For this reason, and since a majority of EasyPower users will be using dynamics to perform detailed motor starting simulations and responses, we have specified the default time step to one twentieth of a cycle. For 60 Hz systems, that would be 0.0008333 seconds.

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From this selection of a default time step, it is clear that there will be a significant performance hit on running any dynamic simulation. However, this is necessary due to the modeling detail used in the induction and synchronous motor models in the DS Engine. Both are full detail flux models, and can be used for running and starting motor simulations. If simulations being performed do not include motors or do not include motors in a starting condition, then one can increase the time step to shorten simulation computer run time. A typical time step used in systems with mostly generators is half a cycle.

2.8 Oneline Response As has been discussed earlier, the network as simulated in the Power Flow engine is the critical link between machine models. Because of this (and because of our user’s familiarity with the oneline display in the Power Flow Focus), in the DS Focus, the oneline and the resulting power flow solution have again been brought forth as central for simulation interaction and visualization. You will see this first-hand as you enter the DS Focus, where the oneline is presented with the results of the pre-simulation power flow solution. This solution is unique and has subtle differences from the Power Flow Focus solution (documented just above). Given that DS is a real-time simulation, there is a need to know what is displayed on the oneline and how it benefits the user in the DS Focus.

2.8.1 Normal Oneline Display The oneline display can be summarized as follows: 1. After entering DS Focus, the oneline displays the resultant power flow solution that represents the initial conditions of your simulation. As noted above, if induction motors are present, the results on the oneline may change slightly from results seen in the Power Flow Focus. 2. After a simulation is performed, the oneline displays the resultant network conditions present at the end of the simulation. 3. After right clicking on a switching device and selecting either “Open and Resolve PF” or “Close and Resolve PF”, the oneline is resolved and displays newly updated initial conditions for your simulation while including your selected switching device status change. 4. After resetting a simulation using the Simulation Reset button, the power flow resolves; the oneline displays the initial conditions of your simulation, taking into account whatever initial condition network changes you made in 3. Simulation Reset

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5. When a new script is selected from the Script Load drop down list box, the power flow resolves; the oneline displays the initial conditions of your simulation, taking into account whatever initial condition network changes you made in 3. 6. When DS Options are changed, the power flow resolves; the oneline displays the initial conditions of your simulation, taking into account whatever initial condition network changes you made in 3. Thus, while in DS focus, the user has the ability to change the steady-state initial conditions used to perform a simulation. You may ask “why?” Among other reasons, this feature is essential if one wishes to perform a quick and easy motor starting simulation. Typically, a user will enter a new focus with their system model set up as it is normally running. This means that the DS Engine is ready to run a simulation based upon the steady-state initial conditions that it has been supplied. But before starting a motor, it needs to be set offline, and the system needs to be resolved in order to supply a new steady-state condition. To accomplish this, one could go back to the DB Focus, open the motor breaker, re-enter the DS Focus, and then double click on the open motor breaker. A simulation will thus be triggered which runs steady state for a pre-set time (according to the DS Options dialog – Double Click settings), closes the motor breaker, and then runs to a pre-set simulation end time. From this example, we also see that the fundamental behavior of a double-click action on a breaker has changed in the DS Focus. In the Power Flow and Short Circuit Foci, a double-click action on a breaker changes the steady-state condition of the system (before solving the power flow, and before application of the fault). In DS, double-click actions perform simulations, similar to the Harmonics Focus. Double clicking on a bus in Harmonics causes a frequency scan to be performed. Double clicking on a bus in DS Focus causes a bus fault simulation to be performed. So, a method is needed to change the steady-state system in DS Focus, without having to go back and forth between DB and DS Foci. The method selected is that of right mouse clicking on the switching device, and selecting “Open and Resolve PF” or “Close and Resolve PF”. After that action, the system is resolved and set up according to the third method listed above. Now, for a newly opened motor breaker, for example, a simple double click on the breaker is all that is needed to start the motor.

2.8.2 Stepping Oneline Display One enhanced feature of the oneline, that we believe has not been done in any dynamic simulator to date, is the ability to see system wide network conditions during a dynamic simulation. To do this, however, one would need to freeze the simulation in time so that an update in the display can be made. This is accomplished through the stepping feature in DS. The stepping feature makes use of the following button: Simulation Step

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This button is similar to the Simulation Run button: Simulation Run but only runs the simulation up to a point in time defined by the Tools / DS Option / Step Run Delta Time. This parameter basically defines how long the simulation will run before it is paused, and updates the oneline with the condition of the entire network. Multiple presses of the Simulation Step button will thus propel you through the simulation (defined by the presently selected script) one moment at a time, while pausing and allowing you to view conditions in the entire network. For example, the default value of Step Run Delta Time is 0.1 seconds. Just after entering DS Focus or after a Simulation Reset, if the Simulation Step button is pressed with this setting, the simulation will run from 0.0 to 0.1 seconds, update the plot window for that brief time-span in the simulation, and then update the network conditions on the oneline. If pressed again, the simulation will run from 0.1 to 0.2 seconds, update the plot window, and then update the oneline window. This continues as you press the Simulation Step button until you reach the end of the simulation.

Figure 28. Example of system with script stepped several times into the simulation.

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We suggest trying this feature at least once to expose yourself to the concept of updated oneline results during a dynamic simulation. Users with a history of using other stability simulation software may skip over this feature, as it is unique and is not a standard offering in other DS software. The power of this feature is addicting, as you find how fast you can move around the oneline to observe system conditions during a contingency event at any frozen moment in time. An example of a system with a motor start simulation that is being stepped is shown in Figure 28. The Step Run Delta Time is set to 0.1 seconds, and so the simulation has been stepped several times to get to about 1.3 seconds. Notice the conditions of the system on the oneline, and how both temporary bus under-voltage and transformer overload are highlighted in red, according to the present settings in the Power Flow Options. Also, notice that the selected script is “Start Motor 3”, which was specifically written to start the motor at 1.0 second, and run to 3.0 seconds. The x-axis of the DS Plot Window is set to the maximum time found in the script. To see results for a step run simulation, plot channels must be defined. The example in Figure 28 has plot channels defined to monitor MCC-3 bus voltage, motor current and transformer current. A quick pan of the oneline up to the generator bus (Figure 29) shows that the system voltage is just fine at 0.985 pu at this time in the simulation.

Figure 29. Figure 28 panned up to the generators bus.

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2.9 Two Forms of Power Flow In the DS Focus, you will find that there are two forms of power flow solving at work. At all times after a time step’s power flow solution and oneline update, the form will be a Voltage Controlled Network (VCN) that is ready to perform further dynamic simulation. However, after a Simulation Reset or other resolve after a steady-state system change, the original Swing bus power flow is used to solve the system first, and then the swing bus power flow is converted to a VCN. The methods at work before the oneline is updated with results are: Entry into DS Focus:

Solve swing-bus PF Check induction motor vars Feed back updated motor vars to PF Convert to VCN Solve VCN Update oneline

Perform a Reset in DS Focus:

Reset all status to initial condition Solve swing-bus PF Convert to VCN Solve VCN Update oneline

Right Click Switching Device change:

Add breaker to initial condition list Solve swing-bus PF Check induction motor vars Feed back updated motor vars to PF Convert to VCN Solve VCN Update oneline

2.9.1 Swing Bus Power Flow As a review, we would note again that a swing bus power flow (as used in the Power Flow Focus), is the basis for determining the steady-state initial conditions for DS. The swing bus power flow is thus assuming: 

Generators and Utilities specified as PV are performing voltage control actions to accommodate system changes, and have settled.



Generators and Utilities specified as Swing are performing voltage control and governor control to accommodate system changes, and have settled.

Now, in reality, swing generators do not really exist. The actual power system is responding in real-time to supply load and maintain frequency. Even if you are not near a utility generator, and

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only see the utility supply as a feeder or step-down transformer, there is a generator (actually generators) somewhere responding to your increase and decrease in load demand for any given moment. A swing source is a convenient way of simulating a source that supplies whatever power is needed, and holds voltage at a user defined set-point. It is also necessary to solve an iterative power flow, since without a swing, we are over-constrained in our equations for a solution and will not be able to solve the system. We need at least one degree of freedom, or, a place where all of the “left over” power needs can be met (either supply or consume). The swing source provides this for us.

2.9.2 VCN Power Flow The VCN power flow is used in the stability simulation to allow machine models to update conditions, so that a new network condition can be determined for any given time step in a DS simulation. It uses a formulation of YBus (an admittance matrix formulation) to perform a direct solution. It is dependent upon the driving voltage sources supplied by the machine models to determine its solution (actually converted to Norton equivalent current sources, to properly interact with the YBus solution). As noted in other sections of the DS Operations Manual, this means that all loads are modeled as constant impedance. In a future version of the DS Engine, other load types may be allowed; however, that would necessitate an iterative solution on each time step (a well-known method). In the first version of the DS Engine we have chosen not to use the iterative network technique, since the main users of EasyPower are industrial in nature, and are not concerned with large interconnected utility networks, where such load models are needed. It is our goal in future releases to not require an iterative technique by including actual dynamic models that simulate a variety of loads. This would thus supply additional modeling detail for EasyPower users, and would guarantee a network solution on every time step. If an iterative solution is used, then conditions can arise where the network does not solve. The VCN solution network can be illustrated as shown in Figure 4 back in Section 1. In that figure we see the interconnected network of lines, cables, transformers, loads, etc., and then we see the interface points for the machine models. As the machine models update their driving voltages on each time step of the simulation, the voltages across the network are updated using a quick forward-back matrix calculation of the network model. For any change in the network, it must be re-factorized to include the change, so that we can again do fast forward-back computations.

2.10 Dynamics Options When in the DS Focus, the DS Options Dialog can be reached by clicking on DS Options. The dialog includes four main sections with settings that supply control over the DS Engine. Each setting is described in detail in this section.

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2.10.1 Control Screen The Control Section includes settings that control the foundational elements of a DS simulation, as well as control display and messaging (Figure 30). The settings are defined as follows: Simulation Run Control Solution Time Step

The defined time step, in seconds, of the simulation. The default value is 1/10th of a half cycle, and is set low on purpose, to create stable numerical conditions for induction motors under starting and spin-down conditions.

Step Run Delta Time

The time duration, in seconds, over which a simulation is run and then paused after the Simulation Step button is pressed. The default value is 0.1 seconds.

Enable all protective devices

If enabled (default), then relays, fuses and low voltage breakers will sense and trip in a simulation. For this feature to be active the user must own the Power Protector feature of EasyPower.

Enable contactor action

If enabled (default), then contactors will sense and trip in a simulation. For this feature to be active the user must own the Power Protector feature of EasyPower.

Enable ATS

If enabled (default), then ATS’ will sense and transfer in a simulation. For this feature to be active the user must own the Power Protector feature of EasyPower.

Include Stator Flux Dynamics Induction motor models

If enabled (not default), then additional stator flux dynamics (the time build-up of flux in the stator windings) are included for all induction motors in the simulation.

Message Log Control Log model messages at initialization

If enabled (default), then all initialization messages from DS models appear in the Message Log.

Log model messages during run

If enabled (default), then all run time messages from DS models appear in the message log.

Log protective device trip messages

If enabled (default), then all run time message from protective devices will appear in the message log.

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Figure 30. Dynamic Stability Options – Control Tab.

Initialization Control Maximum Allowed DState

The maximum allowed DState, in per unit, that triggers an initialization error message in the Message Log if exceeded.

Entering Stability Focus Automatically arrange windows

If enabled (default), then the Oneline Window, Message Log Window, and DS Plot Window will autoarrange all in view. You may also press the F8 key at any time to perform the same auto-arrange.

Show plot window

If enabled (default), then when DS Focus is entered the DS Plot Window will automatically appear. If not enabled, the DS Plot Window will automatically appear whenever a simulation is run or step-run.

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Show message log

If enabled (default), then when DS Focus is entered the Message Log Window will automatically appear. If not enabled, the DS Plot Window will automatically appear whenever a simulation is run or step-run.

2.10.2 Double-Click Screen The Double-Click Control Tab includes settings that control all of the double-click actions that are performed on the oneline (Figure 31). The settings are defined as follows: Generator’s Exciter Symbol to Step VRef Step

The step voltage, in percent, applied to the reference of the excitation system to be stepped.

Initial Terminal Voltage

The initial terminal voltage of the generator, in percent, used to initialize the generator machine model and the excitation system model.

Simulation End Time

The total simulation time length in seconds.

Delay Time Length

The time duration, in seconds, where the simulation runs steady-state before any actions are taken. After this time, the excitation system voltage reference (VRef) is stepped.

Generator’s Governor Symbol to Step Initial Load

The initial loading of the generator, in percent.

Load Step

The step load, in percent, applied to the terminals of the generator.

Simulation End Time

The total simulation time length, in seconds.

Delay Time Length

The time duration, in seconds, where the simulation runs steady-state before any actions are taken. After this time, the load on the generator’s terminals is stepped.

Breaker or Switch to Open Simulation End Time

The total simulation time length, in seconds.

Delay Time Length

The time duration, in seconds, where the simulation runs steady-state before any actions are taken. After this time, the switching device is opened.

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Figure 31. Dynamic Stability Options – Double-Click Control Tab.

Breaker or Switch to Close Simulation End Time

The total simulation time length, in seconds.

Delay Time Length

The time duration, in seconds, where the simulation runs steady-state before any actions are taken. After this time, the switching device is closed.

ATS to Transfer Simulation End Time

The total simulation time length, in seconds.

Delay Time Length

The time duration, in seconds, where the simulation runs steady-state before any actions are taken. After this time, the ATS is transferred.

Bus to Fault Fault Resistance

The fault resistance, in ohms.

Fault Reactance

The fault reactance, in ohms.

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Simulation End Time

The total simulation time length, in seconds.

Delay Time Length

The time duration, in seconds, where the simulation runs steady-state before any actions are taken. After this time, the bus is faulted.

Fault Time Length

The time duration, in seconds, that the fault is left on the bus. The fault is applied after the Delay Time Length, and is removed after Fault Time Length has elapsed. If you desire to have protective devices perform all fault clearing, we recommend setting this value longer than the Simulation End Time, so that the fault is never removed from the bus over the entire simulation. If you set this value equal to the Simulation End Time, then the last time step of the simulation, and the resulting end-of-simulation network results displayed on the oneline will present the system with the fault removed.

2.10.3 Plot Output Screen The Plot Output Tab includes three settings that control plotting in the DS Plot Window (Figure 32). The settings are defined as follows:

Figure 32. Dynamic Stability Options – Plot Output Tab.

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Maximum plot size

The maximum number of points for each curve presented in the DS Plot Window, and the tabulation of data in the DS Plot Window spreadsheet. Note: if the simulation time step and simulation duration are set such that the total number of simulation time steps exceed the Maximum Plot Size, the DS Engine will automatically skip points so as not to exceed the Maximum Plot Size.

Copy results to clipboard

If enabled (not default), then all results defined either via auto-plot behavior or through user defined plot settings, are copied to the Windows clipboard in a tab delimited format, ready for pasting into Excel, or any other software that supports tab delimited data import from the clipboard.

Overlay Plot Curves

If enabled (not default), then the min and max scales of all plots (when in auto-scale mode) in the DS Plot Window are determined so that all curves are in a maximum view mode. In most cases curves will overlap somewhat. If disabled (default) then all min and max plot scales of each plot curve will be determined so that no overlap in the curves occurs. The plot is broken into vertical sections depending upon the number of curves.

2.10.4 Arc Flash Screen The Plot Output Tab includes three settings that control plotting in the DS Plot Window (Figure 33). The settings are defined as follows: Use Arc Flash Simulation for Faults

If enabled (not default), this will use IEEE 1584 arc flash equations to apply a fault, thus including fault current limiting action by the arc.

Arcing Current

This percentage is applied to the calculated arcing current and is typically used to simulate conditions with the 85% of bolted fault current method typically used in arc flash calculations.

Working Distance

This distance is used to calculate PPE from the arc flash results.

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Maximum Time

If the arc is not cleared by a protective device, then this time will be used to remove the arcing fault. Since applying an arc flash significantly increases the time it takes to perform a simulation during the arc, the value will allow you to curtail simulations that may never clear (i.e. if protective devices were not specified).

Figure 33. Dynamic Stability Options – Arc Flash Tab.

2.11 Plot Definitions 2.11.1 General DS software would be useless without the ability to plot machine response and many of the results that appear on the EasyPower oneline. In line with the other Foci in EasyPower, we have integrated result plotting in the DS Focus, made it update with results that mirror the oneline, and supplied the easiest methods possible to define what you desire to monitor and plot in your simulation. To access plot definitions, click on the Define Plots button. Define Plots Button

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When pressed, the Define Plots floating dialog will appear (Figure 34). This dialog has the following features: 

Allows up to 5 curves per plot.



Allows up to 9 plots.



Gives you access to the oneline for fast select of values to monitor.



Gives you access to resize and pan around the oneline for value selection.



Can be moved around as you desire.



Has drop down list boxes for making plot value definitions.



Has drop down list boxes that auto-fill with the correct equipment IDs to complete value selection faster.



Auto un-grays appropriate cells in the plot define spreadsheet according to the needs of each value to plot.

Figure 34. Define Plots dialog.

The following values are able to be plotted in a dynamic simulation, if the appropriate equipment is being modeled and is in existence and enabled.

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Table 2. List of Available Plot Values.

Equipment

Value

Units

Comment

Bus Bus Bus Bus Bus Bus Bus Bus

Voltage Voltage Fault I Fault I Angle Frequency Frequency AF Energy

pu kV pu Amps Degrees pu Hz Cal/cm/cm

If AF Fault Enabled

Network Dev Network Dev Network Dev Network Dev

Current Current kW kVar

pu Amps kW kVar

See Note 1 See Note 1 See Note 1 See Note 1

DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor DS Motor

Term Voltage Current Current Speed Speed Torque Load Torque Watts Vars kW kVar Angle Field Voltage Power Angle D-Axis Current Q-Axis Current Psi''d Psi''q

pu pu Amps pu RPM pu pu pu pu kW kVar deg pu deg pu pu pu pu

Sync Motor Only Sync Motor Only Sync Motor Only Sync Motor Only Sync Motor Only Sync Motor Only Sync Motor Only

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Equipment

Value

Units

DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen DS Gen

Current Current Speed Speed Torque P Mechanical Watts Vars kW kVar Field Voltage Angle Term Voltage Power Angle D-Axis Current Q-Axis Current Psi''d Psi''q VPSS AVR Out

pu Amps pu RPM pu pu pu pu kW kVar pu deg pu deg pu pu pu pu pu pu

Note 1:

Network Dev values are those that have no DS Model defined, and include:                  

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Comment

Machine Angle

Id Iq Flux ψ’’d Flux ψ’’q PSS Output Voltage

Capacitors Loads Shunts Filters Motors (Non DS Model) Generators (Non DS Model) Utilities UPS Breakers Switches Tie Breakers Tie Switches Cables Overhead Lines Two Winding Transformers Three Winding Transformers Busway Current Limiting Reactors

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For Non DS motors and generators, we mean that no model is defined in the Stability Tab of the motor or generator data dialog, and/or their Enable checkbox is not checked. All plot definitions are saved with your case. We suggest defining plots when you first enter the DS Focus, while you know that your system represents the conditions (equipment status) in the database. Define the plots as you want, and then press the File Save button while still in the DS Focus. Remember, if you press save while in an analysis focus, the case will include any temporary status changes you have made (right click action on switching device and pressing “Open and Resolve PF” or “Close and Resolve PF”). This is why we recommend making plot definitions immediately after you first enter. Plot Channel Scaling In the Plot Defines Dialog, there are columns that let you define the min and max plot scales for the value you desire to monitor. By default, the mode is “Auto” so that no extra work has to be done (i.e. setting the min and max scale). The DS Engine plot scale selection is excellent in “Auto” mode. However, if you desire to enter your own min and max scale values, un-check the “Auto” field for the appropriate curve, and set the min and max values to those that suit your needs. Note that you must un-check the “Auto” field, or the min and max values will not be remembered after a simulation. When the “Auto” option is enabled, the min and max scale values determined by the DS Engine after a simulation are transferred into the min and max values of the Plot Defines Dialog (replacing any values previously entered). Now, if you desire to enter you own min and max scale values, but don’t have an idea as to what they should be, we suggest first running a simulation that is typical of what you are working on with all curves defined with the “Auto” feature on. Then, after the simulation is run, open the Plot Defines Dialog to see the min and max values selected by the DS Engine. Replace the scales as you desire, with guidance from the scales supplied by the DS Engine. Selection Method 1 The first method of selecting values to plot, is directly from the Plot Definitions Dialog. On any of the five cells in the “Monitoring” column, click to get the drop-down list box of available plot values. Select one (Figure 35), and then proceed to fill in the rest of the enabled cells on the same row. For example (Figure 36), if Bus Frequency is selected, then in the “With ID” column, select the bus you desire to monitor.

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Figure 35. Plot value Selection Method 1.

Figure 36. Example of completing Selection Method 1.

Selection Method 2 The second method of defining plot channels involves a blending of the Plot Definitions Dialog with selecting actions on the oneline. After opening the Plot Definitions Dialog, select the plot you wish to define via the Plot Tabs at the top of the dialog. Next, right click on equipment items on the oneline to fill in each row (see Figure 37). All cells for the row are automatically defined, with the Auto-Scale feature enabled for that plot channel. Rows are filled in starting at the first available (blank) row. If you desire to replace a row, click on the “Monitoring” cell of the row you desire to replace, and then right click and select the equipment and value you desire to monitor. You will be prompted about over-writing the existing defined row. Note that while in the plot define mode, you can still pan and zoom (using mouse wheel actions) around the oneline. This makes defining monitored items quick, visual, and easy to associate with the oneline.

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Figure 37. Plot value Selection Method 2.

Ind Motor

Sync Motor

Bus

Network Dev

Generator

Figure 38. Plot Definition context menus for Selection Method 2.

Finally, to make sure that plot definitions are saved with the EasyPower database, click on the Save button. Save

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2.11.2 DS Plot Window The DS Plot Window is a fully functional plotting tool that allows for quick display of results, printing of the plots, and several other features. We supply here a list of those features as well as some specifics that will help you understand what you are seeing in the plot window. 

The plot window includes printing of any plot.



The DS Plot Window includes an Auto Plot Tab that automatically plots pertinent values depending upon the double-click action performed (clicking a motor breaker for example plots motor parameters). Refer to the next section for more detail.



The DS Plot Window is updated at the end of a simulation, or after the pause of a steprun simulation.



Plots are all created using the maximum number of points (defaults at 3000) supplied in the DS Options; but in reality, not exactly that number. Based on the simulation time step, the DS Engine determines the closest integer divisor into the number of simulated points to determine the number of points to be saved for plotting. They will not exceed the plot size defined in DS Options.



There will be slight differences between times where events happen in the message log (which is the actual time of the event) vs. times when changes appear on the plots themselves. This is due to the natural down-sampling action needed to keep the plot within the size defined in the DS Options dialog.



In addition to plot results down-sampling, the DS Engine automatically saves conditions on both sides of a switching event. Thus, at times, one might see places where there are two points with the same time, but two different values. This is due to saving results both before and after the network is resolved for a switching event.



For more definition, increase the number of points plotted in the DS Options dialog.



For all network components, plotted flow is calculated into the bus.



Plot ID Names are automatically generated for each value you desire to plot. Those names appear in the legend and on the Y-Axis of the plot.

Auto Plot For each double-click action that runs a simulation, an auto plot is generated (first tab in the DS Plot Window). The results plotted are pre-selected values corresponding to the double-click action. The auto plot is generated according to the guidelines presented in Table 3.

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Table 3. Auto Plot Pre-Defined Values.

Double-Click On

Plots

Units

Generator Exciter Symbol

Terminal Voltage Field Voltage AVR Voltage

pu pu pu

Generator Governor Symbol

Mechanical Power Speed

pu pu

Motor Breaker

Terminal Voltage Terminal Current Speed Torque

pu pu pu pu

Generator Breaker

Terminal Voltage Field Voltage Angle kW kVar

pu pu Degrees kW kVar

Breaker on Network Device

Bus Voltage nearest breaker Amps through device kW through device kVar through device

pu Amps kW kVar

Plot Printing Printing of plots in the DS Plot Window falls in line with capabilities in the Harmonics and Power Protector Focus. The main controls used to Print and Print Preview are the Print and Print Preview buttons. Print Print Preview After selecting Print or Print Preview, the Print Plot Dialog shown in Figure 39 will be displayed to prompt you with several choices for how you want your plots to appear. First, select the plots you desire to see under Print What. Under Scaling, you will find several fit-to-page options that change depending upon the number of plots you have selected to see.

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Figure 39. Print Dialog showing default page option settings.

For example, if you select four plots as shown in Figure 40, three scaling options allow: 

Fit to Page



Fit to ½ Page - Fits Two Plots per Page



Fit to ¼ Page - Fits Four Plots per Page

- Fits One Plot per Page

Once selected the plots will either Print or Print Preview as you have selected.

Figure 40. Print Dialog showing settings for four plots per page.

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Figure 41. Example plot window ready to print.

As an example, a plot as shown in Figure 41 is ready to plot. The Print Preview of this plot is shown in Figure 42. Once the Print Preview is displayed, there are options that allow you to look at more pages (on a multiple plot Print Preview), Zoom In, Zoom Out, Close the Print Preview window, and finally to Print what you have previewed. These fall in line with standard Print Preview features in many Windows applications. In Figure 43 we show the Print Preview that matches selections shown in Figure 40. Figure 43 is also shown in Landscape. If you desire to see your plots in Portrait, you will need to first open the Page Setup Dialog, shown in Figure 44. This can be found under File / Page Setup in the EasyPower menu.

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Figure 42. Plot during a print preview with default settings.

Figure 43. Print Preview with four plots per page.

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Figure 44. Page Setup Dialog.

Plot Zooming When reviewing your plots, at some point you will most likely desire to zoom in to a section for closer scrutiny. EasyPower DS allows both X and Y axis zooming using the plot display control.

The plot display control. Zoom Area

Allows you to select any portion of your plot using a rubber rectangle. First click on this button, and then left-mouse click and drag on the plot to zoom into the location you desire. An example of this action is shown in Figure 45 and Figure 46.

Zoom Out Full

To restore the plot window to its original fully zoomed out view, click on this button, or double click on the mouse scroll wheel, if you have one.

Zoom In 1.5x

Pressing this button will zoom in by 1.5 times.

Zoom In 1.5x

Pressing this button will zoom out by 1.5 times.

Data View

Shows and hides the spreadsheet data view where the curve data plotted is supplied in tabular form.

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Data Cursor

When pressed causes the cursor to also show digitized values as you move your mouse over the plot. The values are displayed in the legend.

Scroll Bars

Shows and hides the plot scroll bars.

Figure 45. Plot with Zoom Area shown.

Figure 46. Results of Figure 44 Zoom Area.

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Plot Horizontal Zooming When you desire to zoom into an event for more detail, but desire the vertical axis scales to remain fixed, left-mouse click and drag directly on the plot without clicking on any of the buttons documented in the last section. This will perform a horizontal (Time Axis) zoom. Figure 47 shows the black zoom range while it is being selected, and Figure 48 shows the result of this action in the plot window.

Figure 47. Plot with horizontal zoom being applied.

Figure 48. Results of Figure 46 horizontal zoom.

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Spreadsheet Data The DS Plot Window inherently includes all plot data values for ready access if you need it. To quickly access the data, pull the splitter bar (shown in Figure 49), to the right. This reveals the plot data, thus allowing spreadsheet-like select and copy functions. An example of selecting a section of data is shown in Figure 50. To copy the data, either press Ctrl-C on the keyboard, or use the Copy button. Copy

Splitter Bar

Figure 49. DS Plot Window showing spreadsheet data.

Figure 50. DS Plot Window showing selected spreadsheet data.

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2.12 Scripts Scripts in the DS Engine are used to define simulation actions. EasyPower DS has supplied a good amount of automatic simulation actions through quick double-click actions performed directly on the oneline (See Chapter 3). However, in a lot of situations, more simulation action detail is necessary to perform what is needed. For this case, the DS Engine allows you to create as many scripts as you want, each as long as you need. Scripts have these limits: 

They perform no auto-plot action, and so plot definitions must be made to see any results.



They are limited to the commands documented in the next section.



Script commands are time dependent and chronological.



To be run, they must be selected from the Script Load drop down list in the toolbar.



They can only be run one at a time.



They can only be created in the Script Edit Dialog.

2.12.1 Commands Table 4 lists all presently available script commands. Table 4. Script Commands.

Script Command

Type

Value1

Value2

Time

Fault Bus (R+jX) Fault Bus For (R+jX) Remove Fault

Network Change Network Change Network Change

R-Ohms R-Ohms

X-Ohms X-Ohms

Seconds

Run to Time Run for Time

Simulation Run Simulation Run

Close LV Breaker Close HV Breaker Close Switch Close Fused Switch

Network Change Network Change Network Change Network Change

Open Switch Open Fused Switch Open LV Breaker Open HV Breaker

Network Change Network Change Network Change Network Change

Transfer ATS

Network Change

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Script Command

Type

Value1

Enable Contactors Disable Contactors Enable Prot Devices Disable Prot Devices

Override DS Options Override DS Options Override DS Options Override DS Options

Set Time Step

Override DS Options

AVR to Manual AVR to Auto Step AVR

Alter AVR Mode Alter AVR Mode Alter AVR Mode

% Step

Set Governor Speed Setpoint

Alter Governor Mode

pu Value

Set Exciter Parameter Set Governor Parameter Set Generator Parameter Set Stabilizer Parameter Set Motor Parameter

Alter Model Data Alter Model Data Alter Model Data Alter Model Data Alter Model Data

Row # Row # Row # Row # Row #

Value2

Time

Seconds

Value Value Value Value Value

Notes: 1.

If the fault impedance is specified as zero, the impedance value will be automatically limited to 0.0 + j1.0 E-10 per unit Ohms. No smaller value is allowed.

2.

Only one fault may be applied at a time. If another fault application is attempted, it will be ignored, and the operation of fault removal will only correspond to the first fault application.

3.

Repeated ATS Transfers will toggle the ATS back and forth from Normal to Emergency connections.

4.

Changing the time step will have impacts on plot length and can trigger an error in cases where the plot length is too short. We suggest changing overall simulation time step in the DS Options Dialog.

5.

The pu Value specified when setting the Governor Speed Setpoint is dependent upon each governor model. Some specify speed as a pu change, where rated speed is 0.0, and others specify speed in pu where 1.0 is rated speed.

6.

Row # in the table above is the parameter row number starting with 1, as seen in the data spreadsheet of the Stability Tab for a generator or motor. For example, an IEEE AC1A excitation system has gain KA specified in row 7 of its parameter list. Use 7 as the Row # to change this exciters value of KA at run-time.

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7.

For all model parameter setting commands, values are hard set. This means that no special data integrity checks are performed to validate the parameter value, and it means that whatever value was there is replaced immediately at the time in the simulation that the change is being made. There are a handful of details and exceptions to consider: 

Models with saturation have the internal saturation variables updated if any saturation parameter is modified. Without this extra step, changing the saturation parameters would actually do nothing.



IEEET1 and IEEET2 exciter models include modifying KE at initialization to include effects of saturation. If KE is ever set at runtime, this initialization is not repeated, and KE is hard set overriding whatever value of KE was determined.



For the Woodward Diesel governor model, the last parameter, +1 specifies droop control and -1 specifies isochronous control.



For the Round Rotor and Salient Pole generator models, changing X’’d also changes X’’q to the same value.

2.12.2 Creating a Script To create a script, click on the Script Edit button while in DS Focus. You will be presented with the Scripts Dialog, as shown in Figure 51. In Figure 52, we see that if you have no scripts defined, there will always be a default “Steady State” script that simply runs a five second simulation with no switching actions. Often, running your system in steady state using this default script is a good check of your system’s initialization. If the curves plotted are practically flat through the entire simulation, then all models are most likely initialized into a good steady-state pre-event condition. Script Edit

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Figure 51. Scripts Dialog.

To add a script to the list of scripts in the Scripts Dialog, click on “New”. This will pop up the New Script Dialog as shown in Figure 52.

Figure 52. New Script Dialog.

Once you have entered a name for your new script and clicked on OK, you will be provided the Edit Script Dialog as shown in Figure 53. This dialog is where all scripts for DS simulations are written. Figure 53 shows the 5 columns of the dialog, where they are defined as: 

Command

Via drop down list of the Table 4 Commands



Equipment ID

Via drop down list of appropriated equipment IDs



Value 1

1st value if needed



Value 2

2nd value if needed



Time

Time value if needed

Refer to Table 4 above for all script commands along with definitions for values or times that are necessary.

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Figure 53. Edit Script Dialog with no script yet defined.

To define a script, use the drop down list box in each Command column cell (click on cell to see it) to first select your script command. Next, enter any IDs, values or times that are needed. Repeat these actions to define your script in chronological order. A completed script for a sequenced motor start is shown in Figure 54.

Figure 54. Edit Script Dialog with script entered.

Once you have defined all of your script commands and any other data needed, click on OK to close the Edit Script Dialog. The new name of your script will now appear in the Scripts Dialog, as shown in Figure 55. Click on “Close” in the Scripts Dialog to close your script creating and editing session.

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Figure 55. Scripts Dialog with new “Sequence Start” script.

Finally, to make sure your script is saved with your EasyPower database, click on the Save button. Save

2.12.3 Renaming a Script To rename a script while in the Scripts Dialog, select the script and then click on “Rename”. You will be prompted with a Rename Script Dialog as shown in Figure 56. Click on OK after you have entered a new name to make your change.

Figure 56. Rename Script Dialog.

2.12.4 Deleting a Script To delete a script while in the Scripts Dialog, select the script and then click on “Delete”. You will be prompted with a delete confirmation dialog as shown in Figure 57. Click on Yes to delete the script.

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Figure 57. Delete Script confirmation dialog.

2.12.5 Copying a Script To copy a script while in the Scripts Dialog, select the script and then click on “Copy”. You will be prompted with a Copy Script Dialog as shown in Figure 58. Click on OK after you have entered a name to copy the script into.

Figure 58. Copy Script Dialog.

2.12.6 Edit a Script To edit a script while in the Scripts Dialog, select the script and then click on “Edit”. You will be put into the Edit Script dialog, where you can make changes. You can also double-click on the script name in the Script Dialog to do the same. Once in the Edit Script Dialog, use the same edit actions discussed above in “Creating a Script” to make any changes to commands, IDs, values or time. To move commands up or down, select the row, and click on “Up” and “Down” to accomplish your desired placement for a given command. For example, to swap BL-4 and BL-1, so that BL-1 is closed first in our example script, first select row 6 as shown in Figure 59 (click on row 6 number).

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Figure 59. Row 6 in script selected.

Next, click on “Up” two times. The result is shown in Figure 60.

Figure 60. BL-1 moved up two rows by clicking on “Up” twice.

Now, click on the row with BL-3 (click on row 5 number), and click “Down” once. The result is shown in Figure 61.

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Figure 61. S-3 row selected and moved down one row by clicking on “Down”.

To delete a row in your script, select the row (click on the rows number) and then click on “Delete”. You will be prompted with a delete confirmation dialog. Click “Yes” to delete the row.

Figure 62. Delete script row confirmation dialog.

2.12.7 Running a Script To run a script, select it from the DS script select drop down list (see example in Figure 63), and then click on the Run button. The DS Engine will run your script through to the end, and once completed, will have plot results in the DS Plot Window (if defined), messages in the Message Log and the oneline will display network results for the last time step of the simulation. An example result of a script run is shown in Figure 64. Note how the motors are started at 1, 2, 3 and 4 seconds, and how the 2nd and 3rd motor overlap slightly in their start. To clear the plot, and reset back to initial conditions before the simulation, click on the Reset Simulation button. Run Simulation Reset Simulation

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Figure 63. Selecting “Sequence Start” script from DS Toolbar.

Figure 64. Results after “Sequence Start” script was run.

2.12.8 Stepping Through a Script To step run a script, select it from the DS script select list (see example in Figure 63), and then click on the Step button repeatedly to move through the simulation. Step Simulation

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After each press of the Step button, the DS Plot Window, Message Log and oneline will update, presenting results at the end of the step. Default step size is 0.10 seconds. An example of a step run result is presented in Figure 65. This was used to see voltage conditions in the network at the moment of lowest voltage during the simulation.

Figure 65. Results after having stepped through “Sequence Start” script part ways.

2.13 Scenario Manager Behavior The DS Focus has inherited all of the capabilities of Scenario Manager. The loading and defining of scenarios, of course, occurs in the Database Focus. For DS, the main items that are affected by Scenario Manager are plot definitions and script commands. Figure 66 below details the behavior of Scenario Manager as it impacts dynamic stability simulations. This follows the same conventions used throughout EasyPower.

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Base Case

Base Case Action Doesn’t Matter.

Scenario Addition?

Yes

Use Base Case with Scenario Addition.

No Use Base Case As Is.

Change Script or Plot Def in Base Case.

Scenario Change for Same Base Case Change?

Yes

Use Base Case with Scenario Change Overriding Base Case Change.

No Use Base Case with Base Case Change.

Scripts

Plot Defs

No Changes In Base Case.

Scenario Change?

Yes

Use Base Case with Scenario Change Overriding Base Case Change.

No Use Base Case As Is.

Delete Command (Script) or Item (Plot Def) in Base Case.

Scenario Change for Deleted Base Case Item?

Yes

Use Base Case with Scenario Change Overriding Base Case Change.

No Use Base Case As Is.

Figure 66. Behavior of Scenario Manager in Dynamic Stability.

2.14 Printing Model Data Sheets Model Data Sheets are essential when documenting data in your EasyPower model. They are printed and viewed quickly and easily. Data Sheets can only be printed and viewed in the DS focus. This method of was implemented since it not only supplies the data sheet while in that focus, but because it supplies a verification of what data was actually transferred from the Database Focus into the DS Engine. This may seem unimportant, but it is a vital check of data validity. The information that is used in a DS simulation needs to be the data printed in the Data Sheet. If there is any discrepancy between data seen in the Data Sheet and data thought to be entered in the Database Focus (in an equipment dialog), then we have an automatic check to help catch a programming error. This process enhances the stability and maturity of the DS Engine and its data transfer methods.

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There are three methods to print Data Sheets: 1. Right click context on oneline. 2. Oneline single item select, and then click the Data Sheet button. 3. Oneline multiple item select, and the click the Data Sheet button. These three methods are shown in Figure 67, Figure 68 and Figure 69. After performing the method, the Data Sheet Window will be displayed with the equipment Data Sheets you selected. This is shown in Figure 70.

Figure 67. Right mouse context selection method for Generator Data Sheets.

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Then click on Figure 68. File / Data Sheet menu single selection method.

Then click on Figure 69. File / Data Sheet menu multiple selection method.

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After the Data Sheet Window is displayed, you now have the ability to scroll through it, print and print preview. For ease of viewing, we suggest using the Print Preview feature to view each data sheet page. Clicking on Print Preview, and then selecting a two page display option will generate a view like that seen in Figure 71. While in Print Preview, you can page quickly through all data sheets in a single and two page view.

Figure 70. Data Sheet Window.

Figure 71. Data Sheet Window in Print Preview mode.

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Finally, to print the data sheets, select the Print button in either mode. The dialog shown in Figure 72 will prompt you for the pages to print, as well as the number of copies.

Figure 72. Data Sheet Print Dialog.

2.15 Status Bar Messages Status Bar messages appear under some simulation circumstances. The Status Bar messages currently defined are: 

Running "Bus Fault" on XX - Press PAUSE to Suspend



Running "Open Breaker Action" on XX - Press PAUSE to Suspend



Running "Close Breaker Action" on XX - Press PAUSE to Suspend



Running "ATS Transfer" on XX - Press PAUSE to Suspend

These messages will display in the Status Bar when the appropriate simulation is running, and only during the simulation.

2.16 Registry Control Variables Several control variables are left, for the most part, as unchangeable by the user. In other words, they are not included in the DS Options dialog. Due to the complexity of dynamics, and the possible need to change some of the internal settings of the engine, the following control variables are accessible via the Window’s Registry. To change these control variables, the exact name and type of the variable must be added to the EasyPower/Options list of variables in the Registry. Then the value can be set accordingly.

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2.16.1 SlewIterationLimit Name: Type: Default: Range:

SlewIterationLimit DWORD 12000 20 to 100000

The SlewIterationLimit variable is used to define the maximum number of iterations used in induction motor and round rotor slew runs at initialization. The default value is 12000. Typically the slew run completes in just 10 or 20 iterations, since additional feedback logic is included to get the model initialized quickly. However, the slew run could extend to many hundred or more iterations if a machine is initialized high on its saturation curve, or if near pull-out torque, where there is a chance of initializing at a stall condition.

2.16.2 IndMotVarThreshMag & IndMotVarThreshExp Name: Type: Default: Range:

IndMotVarThreshMag DWORD 1 1 to 1000

Name: Type: Default: Range:

IndMotVarThreshExp DWORD 4 0 to 20

When induction motors are initialized vars specified by the power flow and vars required by the DS model may not necessarily match. To correct for the difference, the swing bus PF is forced on repeat solutions to match the vars required by the model. The full swing power flow solution is run until the difference between the power flow vars and the DS model vars fall below: Var Mismatch pu =  IndMotVarThreshMag  10-IndMotVarThreshExp

The default value is thus: 1.0 x 10-4 or 0.0001.

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3.0 EasyPower DS Methods 3.1 Selecting Models and Model Data Selecting dynamics models is not as easy as selecting the appropriate cable or overhead line conductor in EasyPower. This is a simple fact based upon the level of detail that is being simulated in the DS Engine. We have attempted, in the software and here, to make the model selection process as simple as possible. By reading through this section we hope you will learn to discern what represents a good or exact match, and where some simplifications can be accepted.

3.1.1 Generators The user is responsible for inputting machine data that is supplied for their generator. Machine data is specific to a user’s installed generator. Care must be taken to obtain machine data that represents the machines being modeled. Generator impedances must be unsaturated. Unsaturated values are essential to modeling a machine properly, as the model introduces saturation itself in real-time. In data sheets, saturated values are noted with an additional “v” subscript: X’’dv for example Unsaturated values are noted with a plain subscript or with an additional “i”: X’’d or X’’di for example Generators should be selected based on the two generator types used predominantly in the industry; Round Rotor and Salient Pole machines. A round rotor generator is constructed from a solid iron rotor, and is associated with high speed. That is, the units are typically two or four poles and have speeds of 3600 and 1800 rpm respectively. Salient Pole generators are constructed with a rotor that is not solid iron, where the rotor poles are laminated and placed on the perimeter of the rotor. A salient pole unit is associated with low speed, typically below 1800 RPM. Low speed hydro units are always salient pole. If you are uncertain if your generator is round rotor or salient pole, a review of the unit’s test data can typically help. Due to the rotor design, salient pole units do not include X’q or T’qo constants. There are several ways to arrive at the necessary data for modeling a generator. We supply four common methods here in order of highest accuracy first. 

Manufacturer’s Test Data. This data is generated from tests performed at the manufacturer’s facility, and should be part of a new generator procurement. Though extra cost is incurred, such testing is highly recommended and what we would consider a

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mandatory item when purchasing a new generator. In this day and age of computer simulations, there is no excuse for not obtaining Manufacturer’s Test Data. 

Field Test Data. For generators where only Manufacturer’s Typical Data or other Typical Data is available, field testing can be performed to generate all data items noted above. This testing relies upon access to the unit for breaker tripping under various loading conditions. A complete analysis of test data is needed to complete the data derivation. The combination of field testing work and analysis is not trivial, and can incur a significant cost. Under some circumstances (equipment limitations, modes of operation, and sensitivity to interruptions), testing cannot be completed to generate all necessary parameters. Thus a blend of field test and typical data may result. If a complete test can be adequately performed, Field Test Data is as good as or better than Manufacturer’s Test Data.



Manufacturer’s Typical Data. This data is typical of a generator’s type and size, and often has a historical basis. This data can have significant error based on generator design and the vintage nature of the typical data.



Typical Data. This data is generally formulated from two sources: 1) other similar generators where there is detailed manufacturer’s data, and 2) data based on a summarizing of many units into a typical response. In all cases, typical data for a generator should only be used in sensitivity simulations (where you are trying to get a feel for the dynamic response of your system) or as a last resort if you have exhausted all other avenues.

Round Rotor Generator The round rotor generator has the following parameters: Parameter Rated MVA Rated Efficiency Rated Speed Rated Voltage Rated Current Rated PF Ra Xd Xq X’d X’q X’’d = X’’q Xl T’do T’qo T’’do

Units MVA Percent RPM Volts LL Amps pu pu pu pu pu pu pu Seconds Seconds Seconds

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Armature Resistance D-Axis Synchronous Reactance Q-Axis Synchronous Reactance D-Axis Transient Reactance Q-Axis Transient Reactance D & Q-Axis Sub-Transient Reactance Stator Leakage Reactance D-Axis Transient OC Time Constant Q-Axis Transient OC Time Constant D-Axis Sub-Transient OC Time Constant

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T’’qo E1 E2 S( E1 ) S( E2 ) H D Note:

Seconds pu pu pu pu kW-Sec / kVA pu

Q-Axis Sub-Transient OC Time Constant First Voltage to Define Saturation Second Voltage to Define Saturation Saturation at E1 Saturation at E2 Combined machine and prime mover inertia Machine damping, normally = 0

OC - Open Circuit

These are standard machine quantities, and are based upon a sub-transient level detail flux model. All machine data shown above is mandatory for modeling the round rotor generator properly. Salient Pole Generator The salient pole generator has the following parameters: Parameter Rated MVA Rated Eff Rated Speed Rated Voltage Rated Current Rated PF Ra Xd Xq X’d X’’d = X’’q Xl T’do T’’do T’’qo E1 E2 S( E1 ) S( E2 ) H D Note:

Units MVA Percent RPM Volts LL Amps pu pu pu pu pu pu Seconds Seconds Seconds pu pu pu pu kW-Sec / kVA pu

Armature Resistance D-Axis Synchronous Reactance Q-Axis Synchronous Reactance D-Axis Transient Reactance D & Q-Axis Sub-Transient Reactance Stator Leakage Reactance D-Axis Transient OC Time Constant D-Axis Sub-Transient OC Time Constant Q-Axis Sub-Transient OC Time Constant First Voltage to Define Saturation Second Voltage to Define Saturation Saturation at E1 Saturation at E2 Combined machine and prime mover inertia Machine damping, normally = 0

OC - Open Circuit

Again, these are standard machine quantities, and are based upon a sub-transient level detail flux model. All machine data shown above is mandatory for modeling the salient pole generator properly.

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EasyPower Supplied Data In the EasyPower Library, a host of actual detailed and typical machine data is specified, falling in the category of Typical Data. Refer to this data to obtain typical values as well as to get a feel for the range that can be expected for each parameter. To gain a bit more insight into the latter, Figure 73 and Figure 74 are supplied below; these plot impedance and time constant data for the round rotor generator data supplied in the EasyPower Library.

3.1.2 Excitation Systems Defining an excitation system falls into similar methods as generator data, with some significant differences. First, the model (type of excitation system) needs to match the type of controls being used in the actual excitation system. Second, the model needs parameters that match the response of the unit in the field. With generators, due to construction practices, we basically have two synchronous types: round rotor and salient pole. With excitation systems, unfortunately, we can have hundreds of different model types, and then each can be tuned in an infinite number of ways. The parameters of an excitation system are a blend of physical constants and variable tuning parameters, whereas generators are all physical parameters based on construction. Older analog excitation systems use potentiometers, jumpers, DIP switches, taps, etc. to tune the system. New digital excitation systems allow digital settings of parameters in various ways. In general, there are three methods for defining an excitation system. Method 1 – Match Model Diagram and Match Tests To select a proper excitation system model, the first and best method (Method 1) to guarantee simulation accuracy is to match the block diagram of the excitation system model with that specified by the manufacturer, and then match response with actual field tests. Unfortunately, the manufacturer often will not supply such a block diagram that is built for “stability simulation purposes”, and field testing for generating stability simulation data is often not considered appropriate use of money. However, this is the best approach. Once the block diagram is matched, then the constants of the model need to be selected to “tune” the model to match the response in the field. If you have not had a formal machine parameter derivation performed on your units (where both the model and the parameters are specified to match actual field tests of the generator and excitations system) then you must rely upon the manufacturer to supply you those constants.

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Xq

3.000

3.000

2.500

2.500

2.000

2.000 Per Unit

Per Unit

Xd

1.500

1.500

1.000

1.000

0.500

0.500

0.000

0.000 0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

0.0

20.0

40.0

60.0

80.0

MVA

1.000

1.000

0.900

0.900

0.800

0.800

0.700

0.700

0.600

0.600 Per Unit

Per Unit

120.0

140.0

160.0

180.0

100.0

120.0

140.0

160.0

180.0

100.0

120.0

140.0

160.0

180.0

X'q

X'd

0.500

0.500

0.400

0.400

0.300

0.300

0.200

0.200

0.100

0.100 0.000

0.000 0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0.0

180.0

20.0

40.0

60.0

80.0 MVA

MVA

X''d

X''q

1.000

1.000

0.900

0.900

0.800

0.800

0.700

0.700

0.600

0.600 Per Unit

Per Unit

100.0 MVA

0.500

0.500

0.400

0.400

0.300

0.300

0.200

0.200

0.100

0.100

0.000

0.000 0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

0.0

20.0

40.0

60.0

MVA

80.0 MVA

Figure 73. Plot of Round Rotor Generator data in the EasyPower Library – Xd, Xq, X’d, X’q, X’’d, X’’q.

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RA

1.0000

0.020

0.9000

0.018

0.8000

0.016

0.7000

0.014

0.6000

0.012

Per Unit

Per Unit

XL

0.5000

0.010

0.4000

0.008

0.3000

0.006

0.2000

0.004

0.1000

0.002

0.0000

0.000 0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

0.0

20.0

40.0

60.0

80.0

MVA

12.000

1.200

10.000

1.000

8.000

0.800 Per Unit

Per Unit

120.0

140.0

160.0

180.0

100.0

120.0

140.0

160.0

180.0

100.0

120.0

140.0

160.0

180.0

T'qo

T'do

6.000

0.600

4.000

0.400

2.000

0.200

0.000

0.000 0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

0.0

180.0

20.0

40.0

60.0

80.0 MVA

MVA

T''qo

T''do 0.100

0.100

0.090

0.090

0.080

0.080

0.070

0.070

0.060

0.060

Per Unit

Per Unit

100.0 MVA

0.050

0.050

0.040

0.040

0.030

0.030

0.020

0.020

0.010

0.010 0.000

0.000 0.0

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100.0

120.0

140.0

160.0

180.0

0.0

20.0

40.0

60.0

80.0 MVA

MVA

Figure 74. Plot of Round Rotor Generator data in the EasyPower Library – XL, RA, T’do, T’qo, T’’do, T’’qo.

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As an example to Method 1, we show Figure 75 below; an excitation system model supplied by a manufacturer. The block diagram of the AVR (automatic voltage regulator) shows a series of blocks with time constants and limits. This unit is digital. The generator for this excitation system is also brushless. This then led us to choose an excitation system model that simulated the blocks and limits of the AVR as closely as possible, with the addition of blocks to model the brushless aspect of the generator. The model selected was the IEEE AC6A excitation system shown in Figure 76. This selection brings up an obvious shortcoming with the proper simulation of brushless generators where we need to include field feedback effects in the excitation system model. This is discussed in detail in the section on the IEEE AC6A excitation system model. As can be seen in Figure 77, additional effort was put forth to match the actual field response of the excitation system with the IEEE AC6A model. In the figure we see an almost exact match of the field test response to the model simulation response for an open circuit step test.

Figure 75. Excitation system AVR (automatic voltage regulator) block diagram.

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VRef VAMax

VT



1 1  sTR 





1  sTK  KA 1  sTA 

VT VR Max

1  sTC  1  sTB 





 

1 sTE

 

VT VR Min

VAMin I N  0.433

FEX  0.75  I

0.750  I N  1.000

FEX  1.732 1  I N 

I N  0.750



EFD

0

FEX  f  I N 

VE S E VE 

FEX  1  0.577 I N

0.433  I N  0.750

VE

2 N

VH Max

1  sTJ  1  sTH 

FEX  0



KH











0

IN 

KE



VFE LIM

K C I FD VE

KD

I FD

Figure 76. IEEE AC6A Excitation System Model.

1.06

Terminal Voltage in pu

1.04

1.02

1

0.98

VT Test 0.96

VT Sim

0.94 0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

Time Seconds

Figure 77. Simulation vs. Test for 10% Open Circuit Step Change in AVR Reference.

Method 2 – Generic Model and Match Test This then leads to Method 2 of selecting an excitation system model. As long as the primary components are being simulated in the model, any model may be selected as long as its tuned response matches the response of the actual field test. This has been a method used historically, where many excitation systems were simulated using the standard IEEE Type 1 excitation system model. To this day, many units simulated in the U.S. interconnected east coast simulation case are done so with an IEEE Type 1 model which does not model specific detail of the excitation system.

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Method 3 – Generic Model and Generic Data Finally, it has been proven through experience that simulating some form of excitation system, which has acceptable response, is always better and more accurate than performing a simulation without any excitation system model at all. When excitation systems are commissioned and maintained in the field, they are tuned to meet an industry standard response. The criteria for response varies for the electrical systems that a particular unit is connected to, but the response typically falls within a standard open-circuit overshoot and response time. Because of this, most units are tuned well. Thus selection of an excitation system model, when no other information may be obtained, can be performed using an excitation system model (with a typical tuning) that appears to have the most important aspects of the installed system. The EasyPower Library includes typical tunings for all supported excitation systems. This includes a slow, medium and fast response based on pairing it with a round rotor generator with typical data. Though we recommend simulating with only the model and data that match your system, you can get an idea of system behavior by using the Library provided excitation system tunings.

3.1.3 Governor Systems Governor system models simulate the power output of the prime mover as well as the governor control action in response to a desired set-point and machine speed. Thus, the output of a governor model is mechanical power. As with the excitation system models, the three methods noted apply in exactly the same way.

3.1.4 Induction Motors In EasyPower, the level of detail modeled in the induction motor model necessitates a level of parameter detail that many may be unaccustomed to. A detailed flux model needs machine impedances and time constants similar to that of a synchronous generator. To generate this data from manufacturer’s performance data please refer to several papers written specifically for this purpose:        

Induction Motor Modeling - Part 1 Induction Motor Modeling - Part 2 Induction Motor Modeling - Part 3 Induction Motor Modeling - Part 4 Induction Motor Modeling - Part 5 Induction Motor Modeling - Part 6 Induction Motor Modeling - Part 7 Induction Motor Modeling - Part 8

3.1.5 Synchronous Motors As noted for induction motors, in EasyPower, the level of detail modeled in the synchronous motor model necessitates a level of parameter detail that many may be unaccustomed to. A detailed flux model needs machine impedances and time constants similar to that of a synchronous generator. To generate this data from manufacturer’s performance data please refer to:

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

Synchronous Motor Modeling

3.1.6 Typical Inertia Constants Typical inertia constants should only be used when doing sensitivity studies, or when there is absolutely no way to obtain actual data. This data however must be used with great caution, and several simulations should be performed with different values if typical data is used to discern the impact of the typical values used. The following inertia constant equations were supplied by Conrad St. Pierre. Listed below are approximate motor and load inertia constants. These values do not include any motors which have special designs for high inertia loads and starting torques. In general, the motor inertia tend to follow the standard motors. Approximate values are: Synchronous Motors:

H = 0.202  pf   HP 

Small Slow Speed Engine Drive Generators:

H = 0.35  kVA 

Squirrel Cage Induction Motors:

H = 0.14  HP 

Wound Rotor Induction Motors:

H = 0.28  HP 

0.15

0.15

0.15

(kV)0.07

(kV)0.07

(kV)0.07

0.15

(kV)0.07

The following table is supplied from a list of motors from a generating facility. Table 5. Actual induction motor data for large generating facility (H is in last column).

Rated HP 4500 350 300 800 250

Rated Rated Volts Efficiency 4000 0.940 4000 0.920 4160 0.927 4000 0.937 4000 0.915

Rated PF 0.880 0.890 0.902 0.898 0.875

Rated KVA Calc 4056.6 318.8 267.5 709.0 232.8

Rated Amps Calc 585.5 46.0 37.1 102.3 33.6

Rated Amps 580.0 46.0 38.0 104.0 34.0

Rated RPM 1190 1775 1770 3561 1775

Synch RPM 1200 1800 1800 3600 1800

Rated Slip Calc (pu) 0.008333 0.013889 0.016667 0.010833 0.013889

Locked Locked Locked Pull Rotor Rotor Locked Rotor Out Current Current Rotor Torque Torque (Amps) (pu) PF (Mech pu) (Mech pu) 3480 6.000 0.150 0.60 1.75 282 6.130 0.320 1.00 2.00 208 5.474 0.310 1.21 2.27 543 5.221 0.219 0.80 2.60 201 5.912 0.330 1.00 2.00

Total Inertia Inertia H WR2 (kW-secs) (lbs-ft)2 KVA 5000.00 0.4014 168.60 0.3833 115.56 0.3112 149.10 0.6134 138.60 0.4313

250 600 900 7000 2000

4000 4000 4000 4000 4000

0.915 0.930 0.930 0.961 0.946

0.875 0.855 0.890 0.900 0.880

232.8 562.7 810.8 6035.3 1791.5

33.6 81.2 117.0 871.1 258.6

34.0 81.0 117.0 870.0 259.0

1775 3565 1180 3575 1785

1800 3600 1200 3600 1800

0.013889 0.009722 0.016667 0.006944 0.008333

201 407 800 5220 1554

5.912 5.025 6.838 6.000 6.000

0.330 0.218 0.300 0.150 0.150

1.00 0.80 1.00 0.70 0.70

2.00 2.50 2.50 2.25 2.00

261.00 115.90 1040.00 3095.00 1050.00

0.8123 0.6021 0.4108 1.5075 0.4295

400 800 600 500 250

4000 4000 4000 4000 4000

0.910 0.919 0.931 0.935 0.915

0.870 0.780 0.870 0.878 0.884

376.8 832.2 552.4 454.2 230.5

54.4 120.1 79.7 65.6 33.3

53.2 120.0 80.0 66.0 32.5

1760 322 1180 3570 3570

1800 327 1200 3600 3600

0.022222 0.016112 0.016667 0.008333 0.008333

355 660 480 370 200

6.673 5.500 6.000 5.606 6.154

0.280 0.200 0.300 0.258 0.300

1.00 0.70 1.10 0.91 0.80

2.10 2.00 2.25 2.40 1.75

418.72 12525.00 760.00 240.00 92.50

0.7918 0.3589 0.4406 1.5490 1.1765

200 150 250 155 200

460 440 460 460 460

0.950 0.925 0.936 0.925 0.962

0.940 0.890 0.865 0.900 0.895

167.0 135.9 230.3 138.8 173.2

209.6 178.3 289.0 174.3 217.4

209.0 178.0 289.0 169.0 218.0

3575 1770 1180 1780 1785

3600 1800 1200 1800 1800

0.006944 0.016667 0.016667 0.011111 0.008333

1459 1133 1707 992 1445

6.981 6.365 5.907 5.870 6.628

0.259 0.420 0.300 0.200 0.200

1.44 1.10 1.73 1.10 1.44

2.82 2.00 2.30 2.00 2.40

64.60 56.80 238.20 48.12 70.00

1.1370 0.3012 0.3313 0.2526 0.2961

150 250 150 200

440 460 440 440

0.930 0.925 0.930 0.962

0.880 0.830 0.880 0.895

136.7 242.8 136.7 173.2

179.3 304.8 179.3 227.3

179.0 295.0 180.0 242.0

3560 1175 1775 1770

3600 1200 1800 1800

0.011111 0.020833 0.013889 0.016667

1085 2065 1133 1445

6.061 7.000 6.294 5.971

0.200 0.450 0.420 0.200

1.10 1.10 1.10 0.70

2.00 2.00 2.30 1.44

252.20 165.60 47.20 2.40

5.3788 0.2166 0.2503 0.0100

© EasyPower LLC 2016

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3.2 Performing Motor Starting Simulations Motor starting simulations are one of the most common tasks performed by industrial power engineers that do power system simulations. The abundant use of motors, and thus a need to start them, can clearly be seen. Because of this, fast double-click actions have been included in EasyPower DS so that such simulations can be performed quickly and easily. To perform a motor starting simulation, you must first have a motor defined with a dynamic model (induction or synchronous) selected, and a load model specified for starting and running load. All parameters for the model must be defined to properly simulate your motor. Refer to these papers in regards to getting to this point:         

Induction Motor Modeling - Part 1 Induction Motor Modeling - Part 2 Induction Motor Modeling - Part 3 Induction Motor Modeling - Part 4 Induction Motor Modeling - Part 5 Induction Motor Modeling - Part 6 Induction Motor Modeling - Part 7 Induction Motor Modeling - Part 8 Synchronous Motor Modeling

As an alternative to performing an induction motor derivation for parameters, you can select a motor from the EasyPower model library that comes close to matching the motor you desire to model. Note that using this data, however, is only an approximation of what your actual motor may do. We recommend this method when: 

You desire to do preliminary or investigative simulations with typical data.



You have no other alternative, as the manufacturer is unable to supply you with adequate motor performance data. In this case, we suggest using several different motors, to bracket your simulations (to define the extremes of what could be expected).

3.2.1 Example Data Setup As noted just above, we will not supply the details here of working with motor performance data, and deriving motor parameters. Instead, we will use existing data in the EasyPower Library for our example. This data was actually generated from a detailed review of manufacturer’s motor data and a parameter derivation using EasyPower’s Induction Motor Parameter Derivation Tool supplied with TMS and DS (located within the Motor Data Dialog). Our example system is shown in Figure 78. That oneline shows a motor that has just been added to our small system, with no data yet defined.

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BUS-1

12

kV

UTIL-1 100000 MVA 150 (X/R) 100000 MVA 150 (X/R)

BUS-2

0.

48

kV

TX-1 1 MVA 12 - 0.48 kV 5.75%

BL-1

M-1 ** HP Induction 16.7%

Figure 78. Oneline of small system for motor starting example.

Double click on the motor to open the Motor Data Dialog as seen in Figure 79. Change the motor HP to 100 HP.

Figure 79. Set motor HP.

Click on the Short Circuit tab, and click on “Calculate” to fill in the X/R Ratio.

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Figure 80. Set default motor X/R.

Now click on the Stability tab to define a DS Model for the motor. The page will look like the left one in Figure 81. Click on “Enable Motor Model” to tell the DS Engine that a model is defined, so that the DS Model can be defined.

Figure 81. Enable DS motor model.

Select a motor manufacturer from the Library.

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Figure 82. Select motor manufacturer.

Select a motor type. Since we entered 100 HP, and left the motor at 1800 RPM, select IM-1001800-B-G. This is a 100 HP induction motor with an 1800 RPM synchronous speed, NEMA Design B and NEMA Code Letter G.

Figure 83. Select motor type.

Click on the Library import button: Library Import

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This will import the data from the Library into the Motor Data Dialog. You will be prompted to overwrite power factor and efficiency in the Motor Data Dialog data in the Specification tab. Click on “Yes”, since the DS Motor is being used as our total definition for the motor. If you have entered other data that corresponds to the actual motor nameplate, we suggest clicking on “No”. However, note that you now have inconsistency between the DS Model data machine parameters and the defined PF and Efficiency. If you enter the Parameter Derivation tool with the inconsistency, you could create a totally erroneous derivation. When performing a derivation, all motor parameters must be consistent. Induction Motor Parameter Derivation

Figure 84. Click “Yes” to overwrite PF and Efficiency.

After clicking “Yes” in the prompt, the Motor Data Dialog will appear like that in Figure 85. The red highlighted cells (denoting missing data) are now gone, and all fields in the Motor spreadsheet are filled in from the Library.

Figure 85. Motor Data Dialog after clicking yes.

The motor’s torque vs. speed curve can be reviewed by clicking on the Induction Motor Parameter Derivation button. The tool will display as shown in Figure 86, when the “Step 2” tab is selected. Click on “Cancel” to exit the review so that no changes are made to the motor parameters. During review, the window can be resized to improve viewing.

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Figure 86. Induction Motor Parameter Derivation Tool in Step 2 for motor review.

By default, the time at which the motor transitions from Starting to Running Load is 200 seconds. This large value basically forces the motor to only use the Starting Load for its simulation. If you have a load transition that you wish to model in your simulation, modify Ld Trans Str (Load Transfer Start Time) and Ld Tran Rmp (Load Transfer Ramp Time) to suit your simulation needs. Scroll the Motor spreadsheet down near to the end, and modify these values to 3.0 and 0.1 respectively. This will produce a transfer from Starting to Running Load 3.0 seconds after the motor start, and the load will ramp from Starting to Running in 0.1 seconds.

Figure 87. Scroll down and set “Ld Trans Str” and “Ld Tran Rmp”.

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Note that by default, DS Motor Models will use the Speed Squared load model for the Starting and Running Load. This is done on purpose, so that a quick simulation can be performed without entering any detailed load torque data. The Speed Squared load model is also the model of choice for many types of fans and pumps. If this model is not accurate for your motor, then use the Torque vs. Speed Load Model, and enter your own curve. Click on “Model” under the Starting Load Model, and select the “T vs. Speed” model. A spreadsheet with one row will appear. Fill in the first row as shown in Figure 88. A second row will automatically be added. Continue filling in the spreadsheet until it matches Figure 88.

Figure 88. Select and define torque vs. speed starting load.

Click on “OK” to close the Motor Data Dialog. All of our additions and changes will be saved back into the Database. To save this new data, click on the “Save” button, or File / Save. The oneline is now updated (Figure 89), and shows us that we have DS data in our motor, by drawing a rotor in the middle of the motor symbol. This allows you a quick assessment of whether or not a motor is DS ready.

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UTIL-1 100000 MVA 150 (X/R) 100000 MVA 150 (X/R) 12

BUS-1

kV

TX-1 1 MVA 12 - 0.48 kV 5.75%

0.

BUS-2

48

kV

BL-1

M-2 100 HP Induction 16.7%

Figure 89. Oneline after click on Motor Data Dialog “OK” button.

3.2.2 Starting the Motor Enter the DS Focus by clicking on the DS Focus button. DS Focus Upon entry, the system will be solved with a power flow, and will display as shown in Figure 90 (if the DS Option “Automatically Arrange Windows” is checked). To start the motor, we first need to take it offline (common sense dictates that the motor must be offline to start it). This is done by right mouse clicking on the motor breaker, and selecting “Open and Resolve PF” (Figure 91). This will open the breaker, and resolve the power flow using the standard swing bus power flow used in the Power Flow focus, so that new initial conditions are created for this new network condition. All conversions back into the VCN network solution mode are made, and all model initializations are completed as well.

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Figure 90. First entry into the DS Focus.

Figure 91. Open the motors breaker with right mouse context action.

Conditions after resolving are now presented as seen in Figure 92. This pre-event power flow represents conditions just before the motor is started, and is used to perform the complete initialization of the DS Motor and Load model.

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1. 00 0

@

0.

0.000 0.000 (0.000) (-0.000)

BUS-2

0

UT IL-1

12.000 T X-1

0. @ 1. 00 0

BUS-1

0.000 (0.000)

0

0.480

OPEN

M-2

Figure 92. Updated conditions after opening motor breaker.

To produce a simulation with a convenient time scale, change the simulation run time by opening the DS Options Dialog, under Tools on the menu (Figure 93). Set the “Simulation End Time” under the Double Click Control tab and “Breaker or Switch to Open” and “Breaker or Switch to Close” to 5.0 seconds. Click on “OK” to update the settings and close the dialog.

Figure 93. Change DS Options to 5 second simulation for any breaker action.

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To start the motor, double click on the motor breaker. This activates a simulation where the motor breaker is toggled closed. The simulation performed is defined in the DS Options dialog Double Click Control tab to first run steady-state to 1.0 second (“Delay Time Length”), then close the motor breaker (the one we double clicked on), and then to finally run to 5.0 seconds. The results of the simulation (Figure 94) are updated in the DS Plot Window, Oneline Window and Message Log Window. The plot is shown from beginning to end for a set of default “auto” channels as defined in the section on the DS Plot Window in this manual. Auto plot channels supply fast results with minimal setup. The Oneline Window shows the network conditions at the end of the simulation. The Message Log Window lists all messages logged by various models and script commands.

Figure 94. Conditions after left mouse double click on motor breaker.

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3.2.3 Defining Plots If the default “auto” plot channels are not adequate, specific values to plot can be defined independently. To do this, click on the Define Plots button. Define Plots The Define Plots Dialog as shown in Figure 95 will appear. In this case, no plots have previously been assigned, and so it is blank. To define plot channels, there are two methods, both of which are discussed in detail in the section on Plot Definitions. This example uses Method 2, where quick selections can be made directly off the oneline.

Figure 95. Define Plots Dialog.

Once the Define Plots Dialog is open, plot definitions can be made by right clicking on equipment, and selecting the value to plot. In Figure 96, the bus has been right clicked on, and per unit voltage selected. The plot channel in row 1 will automatically be filled in, as shown in Figure 97.

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Figure 96. Right mouse click context action on motor bus.

Figure 97. Plot Define Dialog after selecting “Plot Voltage (pu)”.

Continue defining motor channels by right clicking on the motor, and selecting “Plot Current (pu)” as shown in Figure 98, with results to the Plot Definition Dialog shown in Figure 99.

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Figure 98. Right mouse click context action on motor.

Figure 99. Plot Define Dialog after selecting “Plot Current (pu)”.

Continue further with “Motor Speed”, “Motor Torque” and “Load Torque” to fully populate the Plot Definitions Dialog as shown in Figure 100.

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Figure 100. Plot Define Dialog after three more motor parameter selections.

Now, close the Plot Definitions Dialog by clicking on “OK”, and save the plot definitions by clicking on the Save button. All definitions made are saved with the EasyPower database. Finally, to re-run the motor starting simulation with the new plot definitions, click on Reset Simulation, and then double-click on the motor breaker. The results for our new plot definitions can be seen by clicking on the Plot 1 tab in the DS Plot Window, as shown in Figure 101. Comparing Figure 94 and Figure 101, we see that by monitoring the bus voltage instead of the motor terminal voltage (which starts at zero volts when offline), we can see the resulting voltage dip more readily.

Figure 101. Conditions after double click on motor breaker, and selecting “Plot 1” tab.

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3.3 Performing a Bus Fault Simulation Simulations that involve a fault in the network are one of the most common simulations when performing dynamic stability work. This is due to the many effects that faults can have on a power system. Similar to a motor start, running a bus fault simulation has been assigned to a fast double-click action for performing simulations with little set up. This method of performing a bus fault is discussed here in detail.

3.3.1 Example System One common effect of a bus fault is a machine acceleration action that results when depressed voltages occur. In such a condition, a depressed system voltage on a generator bus can cause a reduction in delivered power from the generator (as power is the product of voltage and current at the appropriate angle). When the generator cannot deliver that power, and the prime mover continues to supply mechanical power (unhindered, as the governor response is comparatively slow), the unit accelerates, causing the angle of the machine to move away from the pre-fault angle. The longer the fault duration, the more the machine angle changes. And so, upon removal of the fault, the system dynamically responds to the angle excursion, attempting to return to a condition where machine angles and power transfer balance. Our example system to illustrate how to perform a bus fault simulation is shown in Figure 102. For our example, we are going to fault BUS-2 three times, with increasing fault duration. Since we are performing bus faults using fast double-click actions, the fault will be applied and cleared according to settings in the DS Options. We are thus simulating a fault on BUS-2 that is located on a short feed with no load. The fault is cleared according to the settings in the DS Options.

GEN-1 1000 MVA 18.6% 31.5% 10%

BH-1

7 MW 3 MVAR

kV BUS-2

BH-3

12

kV BH-2

12

BUS-1

GEN-2 10 MVA 18.6% 31.5% 10%

BH-5

BH-4

1-1/C-350 kcmil CU, 9000', [Conduit]

Figure 102. Bus fault example system.

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Our example system is composed of two generators separated by a long cable. A load is also included. GEN-1 is a very large generator simulating the utility system. It is 1000 MVA and has a very large inertia (H = 1000). GEN-2 is a 10 MVA Gas Turbine. Both GEN-1 and GEN-2 are using the same generator, exciter and governor data, with the only differences being size and inertia. The data for this system is shown in Figure 103, Figure 104 and Figure 105. The large inertia in GEN-1 will keep speed from having a significant change, and thus from having an impact on machine angle. By definition, the angle of a machine’s rotor is the integral (or accumulation) of speed. If we look at the system from a synchronous perspective (where rotor angle is fixed, and always returning to the same deflection on each rotation) then speed deviation away from synchronous speed will cause angle excursions.

Figure 103. GEN-1 Data.

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Figure 104. GEN-2 Data.

Figure 105. Cable data.

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3.3.2 Perform First Bus Fault To begin, enter the DS Focus with the example system. Before running the simulation, we suggest defining plot channels according to the settings shown in Figure 107. If you have not learned how to set up plot definitions, refer to Section 2.11 Plot Definitions in this manual to learn how to specify them. In addition, modify DS Options in the Plot Output tab so that all results are copied onto the Windows clipboard for immediate pasting into Excel (Figure 108).

Figure 106. System after entry to DS Focus.

Figure 107. Plot channels defined.

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Figure 108. DS Option change to copy all results to Window’s Clipboard.

After making sure there are no initialization errors, and after reviewing the initial power flow for correctness, double click on BUS-2. According to the definitions in the DS Options, the activated simulation will run steady-state for 1 Second, fault BUS-2 for 0.1 Seconds, clear the fault and then run the simulation to 6.0 seconds. The results for this simulation are presented in Figure 109. In Figure 109, note how the DS Engine automatically assigns bus voltage and bus fault current as smart channels for the DS Plot Window “Auto Plot” tab. Thus, applying a bus fault will generate a plot even if no plot definitions have been made. Click on the Plot 1 tab in the DS Plot Window (Figure 110) to review the results plotted for our plot definitions. Though not immediately discernible, notice that the machine angle increased during the fault. After the fault is removed, the rotor angle quickly begins to turn around, moving towards a new settling point to balance the system power transfer.

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Figure 109. Results after double-click action on BUS-2.

Figure 110. Results after first double-click action on BUS-2, looking at Plot 1.

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Now, open Excel, select the upper left cell (A1), and click on Paste to insert the results of our simulation. The results include all plot channels defined, as well as the auto plot channels. According to our settings in the DS Options dialog, the number of points per column will be at or under 3000. Scrolling the window down will reveal 2405 points.

Figure 111. First paste action in Excel.

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3.3.3 Perform Second Bus Fault For our next bus fault, we will increase the fault time to 0.2 seconds. Open the DS Options dialog, and under the Double-Click Control tab, and under the Bus to Fault group, change the Fault Time Length to 0.2 Seconds.

Figure 112. Increase fault length to 0.2 Seconds in DS Options.

To perform our second bus fault, simply double click on BUS-2. The results of this action are shown in Figure 113.

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Figure 113. Results after second double-click action on BUS-2, looking at Plot 1.

As in our first fault run, go to Excel (where we already have our previous results), and add the results of our second bus fault simulation. Select cell H1 and click on paste. The results will look like those in Figure 114.

Figure 114. Second paste action in Excel.

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3.3.4 Perform Third Bus Fault For our third and last bus fault, we will increase the fault time to 0.3 seconds. Open the DS Options dialog, and under the Double-Click Control tab, and under the Bus to Fault group, change the Fault Time Length to 0.3 Seconds.

Figure 115. Increase fault length to 0.3 Seconds in DS Options.

To perform our third and final bus fault, simply double click on BUS-2. The results of this action are shown in Figure 116.

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Figure 116. Results after third double-click action on BUS-2, looking at Plot 1.

As in our first and second fault run, go to Excel (where we already have our two previous results), and add the results of our third bus fault simulation. Select cell O1 and click on Paste. The results will look like those in Figure 117.

Figure 117. Third paste action in Excel.

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3.3.5 Critical Clearing Review Now that we have the results of our three fault cases, it would be prudent to overlay the results so that we can assess the impact on our system. To do this in Excel, click on the column headers as shown in Figure 118. Then, click on the Chart Wizard button to bring up the dialog shown in Figure 119.

Figure 118. Selection of columns of data for plotting machine angle.

Figure 119. Excel prompt after clicking on Chart Wizard in Excel.

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Select the XY Plot option, and lower right method of plotting shown in Figure 119. Click on “Finish” to complete and view the plot. After a bit of formatting, color changes and column header changes, the result can look like the picture shown in Figure 120. Copying the actual plot out of Excel and into this document, we get the Meta File plot as shown in Figure 121.

Figure 120. Results in Excel after some plot formatting and column header updates.

In Figure 121, we see an increasing angle excursion and dynamic swing with the increase in fault time length. This response is typical, and shows that fault clearing time is essential to keep systems stable.

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140.00

120.00

Angle (Degrees)

100.00

80.00

60.00

0.1 Sec 0.2 Sec 0.3 Sec

40.00

20.00

0.00

-20.00 0.00

1.00

2.00

3.00

4.00

5.00

6.00

Time (Seconds)

Figure 121. Excel plot copied into this document as Meta File.

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3.4 Step Testing an Excitation System To step test the excitation system of a generator, after entering the DS Focus, double click on the generator excitation symbol (see Figure 122) next to the generator.

Generator Excitation Symbol

Figure 122. Generator Excitation Symbol.

If we use the same system documented in the Bus Fault section just above, results will be as shown in Figure 123. In the simulation, we double clicked on the GEN-2 excitation symbol. Note that an auto plot is generated showing machine terminal voltage, machine field voltage, and the excitation system’s AVR voltage.

Figure 123. Results of excitation system step test for GEN-2.

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The results of an excitation system step test are defined under the following conditions: 

Generator with excitation system is isolated, and in an open circuit condition.



Voltage conditions are set to match the pre-step terminal voltage setting defined in DS Options.



Simulation delay and length are specified in DS Options.



The amount of step to the reference voltage is also defined in percent in the DS Options.



All prime mover affects are forced not to move.

3.5 Step Testing a Governor System To step test the governor system of a generator, after entering the DS Focus, simply double click on the generator governor symbol (see Figure 124) next to the generator.

Generator Governor Symbol

Figure 124. Generator Governor Symbol.

If we use the same system documented in the Bus Fault section just above, results will be as shown in Figure 125. In the simulation, we double clicked on the GEN-2 excitation symbol. Note that an auto plot is generated which plots machine speed and prime mover mechanical power.

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Figure 125. Results of governor system step test for GEN-2.

The results of a governor system step test are defined under the following conditions: 

Generator with governor system is isolated onto a single bus system with a load.



Voltage conditions are forced at rated terminal voltage throughout the simulation. This keeps voltage changes from affecting the loading conditions on the machine.



Machine and governor system power conditions are set to match conditions specified in DS Options. This is accomplished using the single bus load and then initializing the models normally.



Simulation delay and length are specified in DS Options.



The amount of step change to the load is also defined in percent in the DS Options.

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3.6 Determining Machine Saturation Saturation is used in EasyPower DS in many places. These include: 

Round Rotor Synchronous generator saturation.



Salient Pole Synchronous generator saturation.



Induction motor saturation.



Synchronous motor saturation.



Excitation system “exciter” saturation.

Thus, determining what values to use for each of these conditions is important. As noted, for each of the models where saturation is included, four values are typically needed. These are, and represent: 

E1

First per unit voltage off sat curve, typically 1.0



E2

Second per unit voltage off sat curve, typically 1.2



S(E1) Per unit saturation at E1



S(E2) Per unit saturation at E2

To determine these values from manufacturer’s performance curves, we have supplied an example curve in Figure 126, and two equations. Use this method to define values of saturation in all of the EasyPower DS Models.

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1.2

E Term

1.0

B1.2

A1.2

B1.0

Field Current

A1.0

Figure 126. Generator saturation curve.

E1  1.00 E2  1.20

© EasyPower LLC 2016

S  E1   S 1.0  

A1.0  B1.0 B1.0

S  E2   S 1.2  

A1.2  B1.2 B1.2

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3.7 Performing a Line-to-Ground Fault Simulation The DS Engine is a positive sequence simulation engine that simulates only the balanced nature of a power system. Therefore, a direct application of a Line-to-Ground fault is not possible. However, excellent results can be obtained by using a common method used across the industry that “simulates” the same system impact as a line to ground fault from a positive sequence perspective. That method employs application of a restricted fault to generate a positive sequence voltage depression of 67% at the point of the fault. To apply this method, first add a temporary motor to the bus you desire to fault in the Database. We suggest a small 1 HP motor. Next, enter power flow and solve the case. Double click on the motor to do a motor start, set its scaling to 0.0%, set the locked rotor multiplier to 1.0, and set the starting power factor to 1.0%. Make sure the kVA/HP is also set to 1.0. Next, set the motor HP to near the value of the upstream source kVA rating. If, for example, the upstream transformer is 2500 kVA, set the HP to 2500. Push the motor start Go button. The voltage on the bus will solve to a new value. Keep iteratively increasing or decreasing the motor HP until the bus voltage reaches 0.67 pu. When you reach that value, you have now determined the amount of load impact impedance that is necessary to simulate a line-to-ground fault in the positive sequence. To convert the motor start values to reactive ohms (we are assuming the fault is purely reactive, a good and reasonable assumption), use the following equations:

Z Base 

 Base kVLL 

2

System MVA Base

Ohms

  Motor HP X Fault     Z Base  Ohms  System Base kVA 

For example, in the EasyPower sample case Bigger, use the motor on bus SWG-5. The bus is 4160 V and is supplied by a 1.0 MVA upstream transformer. From the base voltage equation, we get:

Z Base 

 Base kVLL 

2

System MVA Base

 4.16   10

2

 1.73 Ohms

Now, entering the power flow, and using the motor on the bus to do iterative motor starts (as described just above), we find 6100 HP needed to drop the voltage to around 67%. Figure 127 shows the Temporary Motor Data Dialog, and Figure 128 shows results on the oneline for both pre and post motor starting.

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MCC

-5 .7 @ pu

538.899 A

201.670 A 324.854 A

MCC

-6 .0 @ pu 0. 67 1 227.167 A

0.160 MW 0.068 MVAR

-6 .2 @ pu 0. 66 7

227.167 A

-1 2. @ pu 0. 90 4

324.854 A

0

0.092 MW 0.064 MVAR

538.901 A

-5 .9 @

0.030 MW 3.047 MVAR MSHp = 6100 MSPF = 1%

MCC

-7.2% 325 / 350 A

0.310 MW 0.132 MVAR

pu

pu

@

201.671 A

-1 1.

8 MCC

0.179 MW 0.125 MVAR

BL-9

MOTOR GRP

0. 90 9

770.520 A

6 -1 1. @ 0. 91 1

pu

0.388 MW 0.240 MVAR

BL-10

10.1% 771 / 700 A

MOTOR GRP

0. 67 7

SWG-5 BL-11

BL-9

770.518 A

288.285 A

BL-10

0. 67 2

BL-11

BL-12

0. 91 9

pu

BL-12 SWG-5

288.286 A

5779.255 A

@

-1 1.

5

1649.319 A

Figure 127. Temporary motor data for motor starting.

MCC

MCC

0.228 MW 0.089 MVAR

0.117 MW 0.046 MVAR

Figure 128. Oneline results for Bigger, Pre-Start Left, Post-Start Right.

Using the above equation:   Motor HP  6100  X Fault     Z Base     1.73  10.56 Ohms  10000   System Base kVA 

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Now, to simulate a line-to-ground fault in the DS focus on bus SWG-5, simply apply the fault using zero ohms of resistance and 10.56 Ohms of reactance. If you plot the SWG-5 voltage during the simulation, you should see a voltage depression down to around 67% during the fault. As a practical matter, if you used a temporary motor on a bus to generate XFault per the method defined here, don’t forget to remove the motor you just added to your system. It is a temporary motor only used to help you get the equivalent short circuit impedance that simulates the line-toground fault impact to the positive sequence network.

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3.8 ATS Switching for Emergency Power Automatic transfer on loss of power is used extensively around the world. And so for EasyPower users, simulating such behavior is central to the reason why the DS feature was added to the software. To facilitate making these simulations as easy and accurate as possible, the EasyPower DS Engine includes an ATS model that automatically senses loss of power on its Normal source, and transfers to an Emergency source. Of course, the detailed induction motor flux model, auto contactor drop-out, transformer inrush model, quick plot definitions and scripting add even more power and accuracy to an already complete set of simulation capabilities.

3.8.1 The Backup Generator In the DS Engine, no generator spin-up capability is included. This may be added as a feature in the future; however, simply having the generator on line on the Emergency source, and waiting to transfer into it, is completely acceptable. And so, since the generator is in an isolated condition before transfer, it needs to be specified in the Power Flow as a Swing source. Review of the generator data below will confirm this. Now, simulating the spin-up of an emergency generator is actually not that difficult, given additional development effort is expended for this. It does, however, necessitate: 

Additional automatic control similar to that which applies the field for a starting synchronous motor.



Starting the engine, and simulating the details of a diesel startup. This would most likely require the addition of a motor torque vs. speed characteristic, to properly simulate the spin up of the combined generator and engine inertia.



A pass or fail check on whether the generator is ready.

Again, all of this is possible in a dynamic simulation; however the need for this detail is not that essential for simulating the response of the system, since load should be transferred onto the emergency generator when it is ready. Controls that might fail to bring up the generator will fall into a level of detail rarely (if ever) simulated in a dynamic simulation. In reality, these controls and the generator will either succeed or fail. To simulate a failed generator start, simply simulate a case with no transfer to a generator (i.e. take the generator offline). To simulate a successful generator start, have the generator online and ready, in a condition ready to receive load.

3.8.2 Example System and Data To illustrate a simulation with automatic transfer action, the system shown in Figure 129 was assembled. Data for each of the equipment items is supplied in Figure 130 to Figure 134 below. This includes the emergency generator, motors M-1 and M-2, transformer TX-2, contactor BL-7, and the ATS. For this simulation we have included the following detail:

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

Auto transfer of the ATS. ATS will only transfer from Normal to Emergency (left to right). Time to transfer, upon loss of the Normal source, is about 4.75 Seconds.



Auto contactor drop-out action on motor M-2. This contactor will drop out when the voltage drops below 75% for 0.1 Seconds. Our script restarts this motor at 7.0 Seconds.



Transformer inrush action at 6 times FLA on TX-2. When TX-2 is re-energized, it draws inrush current, which impacts the voltage response of the generator.

12

kV

UTIL-1 10 MVA 15 (X/R) 10 MVA 15 (X/R)

UTIL

FS-1

EMERG GEN 0.5 MVA 18.6% 31.5% 5%

GEN

2-1/C-350 kcmil CU, 200', [Conduit]

48

kV

0.

BL-4 BL-3

BL-5

0.

MAIN

48

kV

TX-1 750 kVA 12 - 0.48 kV 5%

BL-6

BL-11

2-1/C-350 kcmil CU, 200', [Conduit]

5 kW 3 kVAR

48

BL-2

0.

LOAD

kV

2-1/C-350 kcmil CU, 200', [Conduit]

A

BL-7

BL-10

M-2 50 HP Induction 16.7%

125 kW 100 kVAR

0.

20

8

kV

TX-2 50 kVA 0.48 - 0.208 kV 3%

BL-1

OFFICE

BL-9

20 kW 15 kVAR

BL-8

M-1 15 HP Induction 16.7%

Figure 129. Oneline of system with ATS.

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Figure 130. EMERG GEN data.

Figure 131. TX-2 stability data.

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Figure 132. ATS stability data.

Figure 133. Motor M-2 data.

Figure 134. Motor M-1 Data.

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In addition to the data definitions, once DS Focus was entered, we also defined a script and several plots channels in order to perform and view our simulation respectively. The plot channels defined are shown in Figure 135, for plots 1 and 2. This includes the response of the generator and the response of the load bus. If you have not learned how to set up plot definitions, refer to section 2.11 Plot Definitions to learn how to specify them.

Figure 135. Plot Definitions.

The script for our simulation has been labeled “Drop Source”, and has been created using the script editor (Figure 136). This script includes 0.5 seconds of steady-state, loss of the ATS Normal source, running to 7.0 seconds after loss of the source, restarting motor M-2, and running out to 10.0 Seconds. If you are unfamiliar with creating a script, refer to section 2.12 Scripts in this manual for more information.

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Figure 136. Script “Drop Source”.

3.8.3 Running the Simulation To run the simulation, first enter the DS Focus with the fully defined system. If you have not made the plot definitions and script noted just above, do that first before running the simulation. Click on the Save button to save your definitions. Next, select the defined script “Drop Source” from the drop down list on the DS toolbar, as shown in Figure 137. Once selected, click on the Run button. The result of the simulation will be displayed, as shown in Figure 138.

Figure 137. Selection of script “Drop Source”.

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Figure 138. Results of dropping source, Plot 1.

In Figure 138, we see the response from channels defined in Plot 1. In Figure 139, we can also see the results for the same simulation, but for definitions made in Plot 2. From both of these plots we get insight into how the system responds after a loss of source and then automatic transfer to the emergency generator. In Figure 138, the generator terminal voltage shows a significant impact placed upon the generator due to transformer inrush, application of static load (lighting and other loads), and the 20 HP motor start. The excitation system is shown to have an excellent response. The motor M-2 restart also impacts voltage, but not as severely as conditions just after the transfer. In Figure 139, we see the LOAD bus terminal voltage, as well as the current fed into the bus. The characteristic is similar to Figure 138, but with more detail of the entire event as seen by the load.

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Figure 139. Results of dropping source, Plot 2.

3.9 DS Quick Advantage Methods The following methods are immediately available to a user who has the EasyPower DS tool, without any or with minimal addition of DS specific data (motor, generator, exciter, governor data, etc.). Thus, having the DS tool will supply a host of features for improving your system model, and gaining insight into your system model’s behavior without spending significant time on data addition.

3.9.1 Steady State Run Checks All Device Pickups, Proper CT Selection In one actual instance, an EasyPower user decided to enter the DS Focus simply to see how a large case performed. That case was really meant only for an Arc Flash study. After entering and running a simple 5 second steady run (which is supposed to do nothing but plot a flat line), a host of protective devices tripped off, filling the message log. Further investigation showed that each device that tripped had an improperly specified CT. Thus, DS can be one additional validation check on your system model, without any DS specific data entered.

3.9.2 Symmetrical Fault Simulation Check on Protective Device Selectivity You can use DS to do a quick check on simulated device selectivity. First, enter DS with your case. Next, go to DS Options and set the Double Click action for bus faults to keep the fault on © EasyPower LLC 2016

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past the time of the simulation. If the simulation end time is 6 seconds, set the fault time to 7 seconds. Finally, fault the applicable bus. DS will simulate the fault and all protective device action to clear the fault. The Message Log will contain a detailed list of devices that operated and the times at which they operated.

3.9.3 Balanced Switching Fault Voltage Depression Check You can use DS to do a quick voltage depression check on your system. First, enter DS with your case. Next, go to DS Options and set the Double Click action for bus faults to keep the fault on past the time of the simulation. If the simulation end time is 6 seconds, set the fault time to 7 seconds. Finally, fault the applicable bus. After the simulation is complete, pan about on the oneline to see the voltage conditions in your system. Note that the voltages shown are those that would exist on your system immediately after the fault was applied before any machines (motors or generators) respond to the fault.

3.9.4 Balanced Switching Fault Contactor Action Check With a minimal amount of data additions, you can get a quick check on motor contactor action. First, go to one contactor in your system, the stability tab, and enable the contactor with some default settings. You can use the ones already there, or set the dropout voltage and time as you think best represents your plant devices. Click on OK and exit the dialog. Now copy this contactor to all of the contactors you want to check, making all of them use the same default setting (use copy, and select all other contactors, and then paste). You may want to avoid saving this case if you had other specific information in each of the contactors. Next, enter DS, and go to DS Options. Set the Double Click action for bus faults to keep the fault on past the time of the simulation. If the simulation end time is 6 seconds, set the fault time to 7 seconds. Finally, fault the applicable bus. Your protective devices should clear that fault, and, if the clearing is delayed or too long, you should see contactors trip on motors that satisfied both the voltage and time setting of the contactor.

3.9.5 Fuse I2T Percentage to Blow to Predict Fuse Fatiguing A feature unique to EasyPower’s DS tool is I2T percentage of blow in a fuse. To use this feature, have a system with a fuse or fuses properly specified in part of your system where other downstream devices should clear the fault first. Next, go to DS Options and set the Double Click action for bus faults to keep the fault on past the time of the simulation. If the simulation end time is 6 seconds, set the fault time to 7 seconds. Finally, fault a bus on the load side of all the protective devices that will be seeing the fault current. After the simulation is complete, review the Message Log and find the message for the fuse in question. You will see a percentage of I2T that the fuse was exposed to during the fault. If the value is above 90%, you may have a condition where the fuse may fatigue from exposure to the fault current. This may cause false operation of the fuse later when exposed to later short circuit currents.

3.9.6 Check Relay Travel to Predict Device Racing A feature unique to EasyPower’s DS tool is percentage of travel in a relay. To use this feature, have a system with a relay or relays properly specified in part of your system where other downstream device should clear the fault first. Next, go to DS Options and set the Double Click action

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for bus faults to keep the fault on past the time of the simulation. If the simulation end time is 6 seconds, set the fault time to 7 seconds. Finally, fault a bus on the load side of all the protective devices that will be seeing the fault current. After the simulation is complete, review the Message Log and find the message for the relay in question. You will see a percentage of disk travel that the relay was exposed to during the fault. If the value is above 90%, you may have a condition where devices are racing and competing to clear the fault. A system designed with conditions like this may make root cause determination more difficult, as the system may not have been truly selective.

3.9.7 Real-Time Simulated Arc Flash to Symmetrical Currents A feature unique to EasyPower’s DS tool is simulation of real-time arc flash behavior. This has most of its real application after dynamics data has been supplied for motors and generators, but still supplies you with useful insight with no dynamics data at all. To use this feature, have a system with protective devices already specified, just as you would do for an Arc Flash study. Next, go to DS Options and set the Double Click action for bus faults to keep the fault on past the time of the simulation. If the simulation end time is 6 seconds, set the fault time to 7 seconds. Also, go to the Arc Flash tab, and check the box that says “Use Arc Flash Simulation for Faults”. Finally, fault a bus at the location you desire to check. After the simulation is complete, review the Message Log and find the list of messages at the end of the simulation that supply detail on the arc flash results. These results will include arc flash energies and PPE for a simulation that included real-time tripping behavior of any number of devices in your system. The Message Log also shows you which devices tripped, and the times they tripped.

3.9.8 Balanced Switching Analysis for Switching of Any Device If you desire to see the voltage and flow conditions in your system that occur immediately after a switching even, you can by following this method. First, enter DS. Next, double click on the breaker or switch that will create the change in the system. After the simulation is complete, review the oneline to see how voltage and flows have changed in the system. These conditions are also called To+ conditions, as they represent the system network condition immediately (+) after the switching event at time To (time T-zero) before any dynamic behavior of machines have manifested.

3.9.9 Run Power Flow with Motors Showing Correct PQ Loading When a motor is partially loaded in real life, the kw loading drops while the var loading can remain fairly constant. Thus, there is a reduction in power factor as mechanical loading decreases. The Power Flow focus however does not do this, and simply scales watts and vars down by the Power Flow scaling factor. To see how the actual motor responds to reduced mechanical load, first add some generic data to your motor in the DS tab in the motor data dialog. As best as you are able, try to match the data in the library with your actual motor HP etc. Next, scale down the motor in the Power Flow tab. This is done using the Power Flow Tab Scaling Factor. This will in essence only scale the mechanical loading of the motor down as the pre-event power flow is solved upon entering DS Focus. Next, enter DS and simply look at the results on the one line.

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3.10 Changing From Droop to Isochronous Mode When an industrial has cogeneration as a significant energy source where it can be used in an islanded mode, we find a number of automatic systems put in place to handle the transition. This typically includes automatic and/or under and over-frequency load shedding as well as changing a governor from droop to isochronous control model. When in droop mode, a generating unit is set up to share loading on the grid for a significant change in speed. When there is a large loss of generation on the grid for example, the speed of all connected units will drop, and will trigger them to each contribute energy to make up for the loss. Upon settling out after a disturbance, the speed of all units would have dropped (or “drooped”) to a new condition depending upon the net generation loss and the droop setting (controlling how each unit shares) on each gen. The grid wide automatic generation control system would then send signals out to generators to increase their output to bring the grid speed back up to nominal conditions. When in isochronous mode, a generating unit is set up to control frequency, and keep it at the nominal condition. This is not a sharing mode of control. Thus if more than one generator is connected on an islanded system, only one will be put in isochronous mode. The rest will be put in droop mode. Backup generators that are a single source of power are always specified to be in isochronous control mode. Cogeneration that is used in islanding conditions needs to be able to accommodate both modes of operation. When connected to the grid, the unit needs to operate in droop mode so that it can share under severe grid events, and when in an island condition needs to operate in isochronous mode to hold frequency. Automatic controls perform this control mode change, and thus there is a need to do the same in a dynamic simulation. The feature in the scripting tool that allows us to make changes to model data at runtime gives us the ability to change a governor’s control mode if it has this feature; i.e. the ability to simulate both droop and isochronous modes of control. The two examples that follow illustrate this method.

3.10.1 Diesel Generator Example In this example, we have a simple one bus system with a diesel generator, and the governor system is specified to be the Woodward Diesel. The test system is show in Figure 140. The test system also includes a base load of 500 kW as well as a load to add (and thus step load the unit) of 200 kW. We will use the scripting feature to both step load the generator as well as to make the governor change its control mode from droop to isochronous. Thus, the unit is pre-set to operate in droop mode initially, which is a common control mode setting when online with the grid prior to an islanding event. For this example however, this unit is already isolated, and we have elected to put it in droop mode to simple prove out correct behavior. Such an isolated test also makes interpretation of results easier. Our script to run this test will be as shown here:

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Command

Equipment

Value 1

Value 2

Run to Time

Time 1.0

Close Switch

S-2

Run for Time

10.0

Set Governor Parameter

GEN-1

1

0.0

Set Governor Parameter

GEN-1

12

-1.0

Set Governor Speed Setpoint

GEN-1

0.0

Run for Time

10.0

This can be interpreted to mean: 

Run the Simulation at Steady-State to 1.0 Second



Close Switch S-2 at 1.0 Second which Closes in the 200 kW Load



Run the Simulation for 10.0 Seconds



Set the Governor Parameter on Generator GEN-1 in Row 1 to 0.0



Set the Governor Parameter on Generator GEN-1 in Row 12 -1.0



Set the Governor Speed Setpoint on Generator GEN-1 to 0.0



Run the Simulation for Another 10.0 Seconds

0. 48

kV

GEN-1 1 MVA 12% 12% 12%

BUS-1 OPEN

L-1 0.5 MW 0 MVAR

L-2 0.2 MW 0 MVAR

Figure 140. Example system for diesel gen.

After entering DS Focus and running the script, we find that the message log has the output as shown in Figure 141. The message log shows the response of the system model to the script actions applied. Notice also how each parameter change is echoed with a Runtime response from the actual model. Thus, we can get validation of whether or not our parameter change was successful. © EasyPower LLC 2016

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Figure 141. Message Log for example diesel system.

The plotted results of the simulation are shown in Figure 142.

Figure 142. Plot output for example diesel system.

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At 1.0 second, the fourth purple curve (kW) shows the 200 kW step-load to the unit. The third green curve (Speed) shows the units quick response to the step load, and shows the unit settling out at a speed below nominal; i.e. below its initial operating speed. This is due to droop. At 11.0 seconds we initiate commands to put the governor in isochronous control mode, and the plot of speed shows a step response and final settling out at nominal speed. Note that more than just a simple setting to change control modes is required. To properly transfer into isochronous control mode (and this is also the case for actual generating units in the field), we not only change a control mode setting, but we also set the Speed Reference Setpoint to 0.0 pu, and we change the droop setting from 0.05 to 0.0. Without these additional changes, the unit will not respond correctly and pull the speed back up to nominal conditions. The second red curve is the mechanical power output of the diesel engine. It shows the mechanical power pickup needed after the load step at 1.0 second, and then shows the additional pulse of power needed to get the unit up to nominal speed after switching to isochronous mode. The first blue curve is the terminal voltage of the unit, and it shows the AVR responding by always bringing the unit back to nominal voltage.

3.10.2 Gas Turbine Generator Example In this example, we have used the same simple one bus system shown in Figure 140, but have replaced the diesel governor with the Pratt & Whitney FT8 gas turbine model. As before, we will use the scripting feature to both step load the generator as well as to make the governor change its control mode from droop to isochronous. Our script to run this test will be as shown here: Command

Equipment

Value 1

Value 2

Run to Time Close Switch

Time 1.0

S-2

Run for Time

10.0

Set Governor Parameter

GEN-1

1

0.0

Set Governor Parameter

GEN-1

2

14.0

Set Governor Parameter

GEN-1

3

1.0

Set Governor Speed Setpoint

GEN-1

1.0

Run for Time

10.0

This can be interpreted to mean: 

Run the Simulation at Steady-State to 1.0 Second



Close Switch S-2 at 1.0 Second which Closes in the 200 kW Load



Run the Simulation for 10.0 Seconds

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

Set the Governor Parameter on Generator GEN-1 in Row 1 to 0.0



Set the Governor Parameter on Generator GEN-1 in Row 2 to 14.0



Set the Governor Parameter on Generator GEN-1 in Row 3 to 1.0



Set the Governor Speed Setpoint on Generator GEN-1 to 1.0



Run the Simulation for Another 10.0 Seconds

After entering DS Focus and running the script, we find that the message log has the output as shown in Figure 143. As with the diesel generator example, the message log shows the response of the system model to the script actions applied. Again, notice also how each parameter change is echoed with a Runtime response from the actual model. Thus, we can get validation of whether or not our parameter change was successful.

Figure 143. Message Log for example gas turbine system.

The plotted results of the simulation are shown in Figure 144.

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Figure 144. Plot output for example gas turbine system.

At 1.0 second, the fourth purple curve (kW) shows the 200 kW step-load to the unit. The third green curve (Speed) shows the units quick response to the step load, and shows unit settling out at a speed below nominal; i.e. below its initial operating speed. Again, this is due to the droop setting in the governor model. At 11.0 seconds we initiate commands to put the governor in isochronous control mode, and the plot of speed shows a step response and final settling out at nominal speed. As before, note that more than just a simple setting to change control modes is required. To properly transfer into isochronous control mode for this governor (and this is also the case for actual generating units in the field), we set the Speed Reference Setpoint to 1.0 pu, change the droop setting from 0.04 to 0.0, and change two other settings (Kpt and Tpt) which alter the tuning of the governor. Without these additional changes, the unit will not respond correctly and pull the speed back up to nominal conditions. The second red curve is the mechanical power output of the gas turbine. It shows the mechanical power pickup needed after the load step at 1.0 second, and then shows the additional pulse of power needed to get the unit up to nominal speed. The first blue curve is the terminal voltage of the unit, and it shows the AVR responding by always bringing the unit back to nominal voltage.

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4.0 Models As noted in the first section of this document, dynamic models operate in a modular behavior, where they respond to input and output. In EasyPower, all DS models are built into the DS Engine, and then interact via terminal conditions (generators, motors, excitation systems) and network conditions (protective devices). As noted earlier, models available in the EasyPower DS Engine are: Generator Models    

Round Rotor Flux Synchronous Salient Pole Flux Synchronous PV1G - Photovoltaic Array and Inverter WT4G - Wind Turbine Generator and Inverter

Excitations System Models                           

Basler AVC1 IEEE Type 1 IEEE Type 2 IEEE Type AC1A IEEE Type AC2 IEEE Type AC2A IEEE Type AC3A IEEE Type AC4A IEEE Type AC5A IEEE Type AC6A IEEE Type AC7B IEEE Type AC8B IEEE Type DC1A IEEE Type DC2A IEEE Type DC3A IEEE Type DC4B IEEE Type ST1A IEEE Type ST2 IEEE Type ST2A IEEE Type ST3A IEEE Type ST4B IEEE Type ST5B IEEE Type ST6B IEEE Type ST7B IEEE Type AC8B Inverter Q Control (for WT4G and PV1G models only) Simple Excitation System

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

STAMFORD 1

Governor System Models                

Caterpillar Diesel 1 Cummins Diesel 1 Cummins Gas Engine 1 Gas Turbine Gas Turbine 2 Gas Turbine WD (Woodward) Hydro IEEE Hydro 2 IEEE Hydro 3 IEEE Steam PWFT8 (Pratt & Whitney) Split Shaft Gas Turbine Steam Turbine WECC Gas Turbine Woodward Diesel Woodward Steam PID 1

Power System Stabilizer Models    

IEEE Type PSS1A IEEE Type PSS2B IEEE Type PSS3B IEEE Type PSS4B

Motor Models  

Double Cage Flux Induction Salient Pole Flux Synchronous

Protective Device Models       

Contactors - Automatic Drop Out Action ATS’ - Automatic Transfer Action All Protective Devices in EasyPower Power Protector – Relays, LV Breakers, Fuses Over-Voltage Relays Under-Voltage Relays Under-Frequency Relays Source Inverter Solid State Blocking for Faults

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In this section, each model is documented in detail, so that users are aware of a model’s behavior, best application and simulation response.

4.1 Generator Models The synchronous generator you are going to simulate in EasyPower is either of a round rotor or a salient pole design. The EasyPower DS Engine includes both models. To choose which model to use, you need to ascertain if its rotor is solid iron (round rotor), or a water-wheel low speed design (salient pole). Figure 145 shows a round rotor without windings, and Figure 146 shows a salient pole rotor. The two following sections supply details on both the salient pole and round rotor generator models.

Figure 145. Round rotor with no windings showing solid iron construction (from “Design of Electrical Apparatus, 3rd Edition, John H. Kuhlmann”).

Figure 146. Salient pole rotor showing water wheel type construction (from “Design of Electrical Apparatus, 3rd Edition, John H. Kuhlmann”).

Two additional models, the PV1G and WT4G are simulated as a generator in EasyPower as of Version 9.5. Thus, to include inverter dynamic behavior, a generator model must be used, and the PV1G or WT4G model specified in the stability tab. These models are also only supplied in a “Grid Connected” form. This means that they are not intended for use in a stand-alone mode.

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4.1.1 Round Rotor Synchronous Generator Introduction The Round Rotor Synchronous Generator model in the DS Engine has been developed with the help of Mr. F. Paul deMello, a noted machines and dynamic stability expert. Material written on the subject of classic sub-transient machine models can be found in many textbooks and papers. For EasyPower, this model was developed using classic materials written by Mr. deMello, as well as detailed development and critical review time with him. Suffice it to say, the models developed here fall in line with methods that are not new, and which have been in use for decades to simulate the detailed action of a synchronous machine. The Circuit Model The classic block diagram of the round rotor generator is shown in Figure 147. From Figure 147, we see that the model includes transient and sub-transient effects, d and q axis modeling, saturation on both axes, and excitation field effects as an input from an external excitation system. The model produces as its output air-gap flux, which then can be used to produce a Thevenin driving voltage behind an internal machine impedance for connection with the network. The EasyPower model also produces (as will be seen later) machine speed from a separate inertia model. In Figure 147, we also see that the model has an input from the terminal current of the machine (Id and Iq). These values, of course, must be converted from terminal form to d and q-axis form, for input into the model. In Table 5, all of the parameters necessary for the model are tabulated, and given brief descriptions. These correspond to parameters seen in the Figure 147 blocks, as well as the machine rating (for proper scaling in the DS Engine), and the inertia component. In “ALL” cases in the DS Engine (generators and motors), inertia is a combined value of inertia. For generators, it represents the total inertia of the generator rotor and prime mover (turbine or engine). For a motor, it represents the total inertia of the motor rotor and load (pump, fan, etc.). Another important note about Figure 147, is that the circuit shown is, in reality, only for the rotor of the generator. We can thus conclude that the majority of the time constant effects, etc. take place in the rotor. Now, there are effects that take place in the stator, but given that DS simulations are typically not used to simulate any transient effects in the stator (DC offset, transient Ldi/dt effects, etc.), and the network is solved as a simple set of network equations (i.e. not including transient Ldi/dt and C(dv/dt) effects), the rotor is where the predominant effects are located. Thus, the generator model presented here does not include any transient stator effects. Why a D-Q Axis Model As can be seen in Figure 147, all modeling of the rotor is performed using a form broken into a d-axis section and q-axis section. The d and q-axis formulation is simply a mathematical technique used to simplify modeling so that equations can readily be formed on the rotor independent of rotor position (angle), and so that parameters can be created that are easy to

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determine. A quick look at the simple 2-pole rotor shown in Figure 147 shows why a d and qaxis formulation is appropriate and why it is an excellent method to simplify modeling.

X X Eq' E fd







1



'



Tdo s

 ' d

' d





 kd

Tdo'' s

X X X ad I fd

X X

1

 X d  X d' 

 X d'' 

 Xl 

2

X

' d

'' d

 Xl 

' d

 Xl 

' d

 X d'' 

' d

 Xl 



 d''



 Xl 



Id





 d''  '' Saturation

 ''    ''  2

 '' 

d

2

q

 q''  X q  X l 

 ''  X d  X l   X aq I kd





X

q



 X q' 

X X

' q

' q



1



'

Tqo s

Iq



 X q'' 

 Xl 

X

' q

 Xl 

2

1 ''

Ed'





Tqo s

 kq

X X X X

' q

 X q'' 

' q

 Xl 

'' q

 Xl 

' q



 q'' 

 Xl 

Figure 147. Round Rotor Generator model block diagram.

In Figure 148, we see that for definition purposes, the d-axis (direct axis) is defined along the center of the rotor, and the q-axis (quadrature axis) is defined 90 degrees away in an orthogonal relationship. Thus, effects on the d-axis do not affect the q-axis, and vice versa, lending to a

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mathematical simplification. Each axis can be analyzed independently. Now, in reality, any relationships between the rotor and the stator are linked across the air-gap. Thus, if we were to write coupling equations, we would need to write them in a distributed manner all along the circumference of the air-gap. This would necessitate a very complex and detailed set of equations, based on construction and the physical relationships between the rotor and stator

Power Angle d-Axis Center Line of Phase A

Center Line of Phase B q-axis Air Gap q-axis

d-axis Air Gap Center Line of Phase C

Figure 148. Synchronous generator rotor positional definitions.

To simplify this work, engineers (notably R. H. Park in 1929) determined that the reaction of the rotor could be broken into two orthogonal terms, denoted as the d and q-axis. The construction of the rotor worked well with this simplification, where the physical differences in the rotor from top to bottom are accumulated into two quadrature effects. Notice in Figure 148 how, due to the need for adding windings on the rotor, the rotor mechanically breaks somewhat into two pieces. The air-gap on the d-axis is somewhat consistent all along the top of the pole piece, and the qaxis air-gap has a deeper air-gap (due to windings). The quadrature d and q-axis formulation method is the method used in the EasyPower round rotor generator model. That model uses a separate d and q-axis set of equations, and relates them to the stator through the angle of the rotor relative to the centerline of Phase A, which we denote as top dead center of the machine. Thus, as the rotor rotates relative to the stator, the flux linkages across the air-gap are constantly changing based on the angle of the rotor. In essence, we have a transformer with an air-gap in its core, where the one winding is constantly rotating relative to the other. As the winding rotates, the air-gap changes due to the physical construction of the rotor. It is unfortunate that we only have time and space in this manual for a brief overview of the reasons and methods involved in creating formulations for the synchronous machine model.

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There are many texts that can help you in this area, if you choose to do further study. There is also much technical content and history that one would be wise to at least perform a casual read to gain insight into the behavior of the synchronous machine. As an overall method, the self and mutual inductances of the rotor and stator are built into a set of equations. Those equations are then formulated into a block diagram as shown in Figure 147, for simulation in a time step oriented integration method. Machine reactances represent the mutual and self-inductances of the machine, and the time constants include the effect of resistance. Table 6. Round Rotor Generator Model Parameters.

Parameter

Units

Rated MVA Rated Efficiency Rated Speed Rated Voltage Rated Current Rated PF

MVA Percent RPM Volts LL Amps

Ra Xl

pu pu

Stator winding resistance (armature resistance) Stator winding leakage reactance

Xd Xq X’d X’q X’’d = X’’q

pu pu pu pu pu

d-axis unsaturated synchronous reactance q-axis unsaturated synchronous reactance d-axis unsaturated transient reactance q-axis unsaturated transient reactance d & q-axis unsaturated sub-transient reactance

T’do T’qo T’’do T’’qo

Seconds Seconds Seconds Seconds

d-axis transient OC time constant q-axis transient OC time constant d-axis sub-transient OC time constant q-axis sub-transient OC time constant

E1 E2 S( E1 ) S( E2 )

pu pu pu pu

First voltage to define saturation Second voltage to define saturation Saturation at E1 Saturation at E2

H D Windage

kW-Sec / kVA pu pu

Combined machine and prime mover inertia Machine damping, normally = 0 Machine friction and windage

Note:

Description

OC means Open Circuit

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Finally (and to illustrate the importance of further study into synchronous machine modeling), we supply some discussions of interest in regards to the round rotor generator and machines in general. Transient. The transient terms on the d-axis correspond to the field winding. Transient is used, since the field winding supplies a changing reaction as the field voltage is changed. In fact, the transient open circuit time constant T’do, can be measured by switching a DC source on the field of the generator. The current in the field will gradually grow according to an exponential time constant, over 2 to 10 seconds. The plot in Figure 149 shows an actual test, where 12 V DC was applied to the field of a generator. The time constant is the time it takes the current to grow to 63% of its final value. Sub-Transient. Note that the sub-transient nature of the model on the d-axis is due solely to amortisseur effects in the rotor. In the round rotor generator, these are due to the solid nature of the rotor. Currents flow in a distributed fashion in the rotor iron, when there is slip between the stator rotating mmf (created by the stator currents) and the rotor’s rotating mmf (the field). Under a dynamic response, currents can be generated in the rotor iron (a reluctance effect), and thus can impact the response of the generator. In a salient pole machine, amortisseur windings or bars are added in and through the pole face of the rotor (parallel to the shaft), to supply needed damping (induction motor reluctance effect). Thus, the sub-transient nature of the model has been created to specifically model physical amortisseur components of the generator. The name sub-transient is also a bit misleading, as we have come to re-write its definition in terms of short circuit current magnitude and the “smallest machine impedance” in mind. In reality, the sub-transient term on the d-axis is the amortisseur term of the machine, and due to construction simply has the shortest time constant and lowest machine reactance. As noted in Concordia’s text, “The name sub-transient is used in order to distinguish these reactances from the transient reactances, which are defined in the same way except that the presence of the amortisseur windings is ignored. Historically, the machine without amortisseur was analyzed first and the name transient appropriated for that case.” Q-Axis. The q-axis circuit in the round rotor generator looks like a symmetrical version of the d-axis. This is due to actually simulating two equivalent amortisseur windings for the q-axis. Since the q-axis does not involve the field, there is actually no transient effect on the q-axis. However, due to solid rotor effects of the round rotor generator, an equivalent transient effect still occurs, but is due solely to amortisseur effects. As is noted for the salient pole generator in the next section, that machine does not have any transient q-axis effect, as there are no solid rotor effects, and no field linkage on the q-axis. X’’d = X’’q. Refer to “Synchronous Motor Modeling” for more detail on synchronous machine data, and for specific reasons why X’’d and X’’q are

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specified equal. This is a requirement for the all generator models used in the EasyPower.

(Applied DC Voltage VR and Measured Current Ife) Figure 149. Test measurement of field time constant.

Some Linking Relationships The model displayed in Figure 147 shows field voltage Efd, Id and Iq as inputs, and air-gap flux (ψ’’d and ψ’’q) as outputs. These seem all well and good, but a few defining relationships will help in understanding the interconnected nature of the model. Field voltage, Efd, is an input from an excitation system model, and thus is generated externally. This represents an actual separate piece of equipment that is producing a field voltage to supply current to the windings of the field. Without the input field voltage, the generator cannot be excited, and thus it will not produce any voltage. The EasyPower round rotor model assumes that if Efd is zero, that no terminal voltage will be created in an open circuit condition. This is the theoretical response. In reality, some residual magnetism will exist in the field, which will then create a small terminal voltage on the machine when rotating with no field applied. In the next section we will discuss the unit’s inertia model, which necessitates an input of electrical air-gap torque from the generator model. The air-gap torque is calculated using the airgap flux and current in the stator windings of the generator. This calculation can be performed as a d and q-axis calculation on rotor convention, or after conversion of the air-gap flux onto the stator reference. Due to the fact that we already have stator currents on a d and q-axis reference (needed as input into the model), we will calculate air-gap torque using d and q-axis components. This calculation is: TAirgap  I q d"  I d q"

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This equation may not seem logical, as there is an intermixing of d and q-axis components; however, it is correct when the detail of the formulations are included. This equation is supplied in per unit (all EasyPower machine modeling is internally performed in per unit). Finally, as noted in the first sections in this manual, the Thevenin equivalent voltage is needed for the network model. As noted earlier, the network includes a Thevenin equivalent voltage source, where the source impedance is defned as RA + jX’’d. This source then needs a voltage to drive the network. This voltage is the airgap flux times the speed of the machine: Ed"   "q 1  p  Eq"   "d 1  p 

For these equations, the per unit speed (1+ p) corresponds to 1.0 at rated speed of the generator (see definition of p below). Again, the mixture of d and q-axis components is seen, which is the correct implementation. To complete the calculation, a conversion from the d and q-axis domain back to the stator refererence is needed as well, which as seen from Figure 148, simply involves knowing the position of the rotor, relative to the stator. As with most DS machine models that are simulating dynamics without transient effects (network and stator Ldi/dt etc. effects), rotor position at rated speed (which is the defined condition at initialization of the model) is assumed to be stationary and equal to the power angle, determined by machine loading. This is due to the fact that the network and rotor speed are the same, and makes modeling easier to formulate. Internally, all EasyPower machine models assume that initialization occurs at rated speed (and thus frequency), and that the system is operating at rated frequency. This simplification generates a fixed angle (i.e. power angle is not changing) assuming there are no imbalances in delivered and generated power. Inertia Model The inertia modeling used in the round rotor generator is formulated according to classical inertia modeling in machines, and is shown in Figure 150. In Figure 150, we see the speed of the machine (p) being controlled by torque difference across the machine’s shaft, and being integrated (1/s) via the machine inertia (H). All values in Figure 150 are in per unit. We also see that we have elected to include friction and windage losses, modeled as a constant torque. Without modeling friction and windage, if the unit is tripped, it will not be able to have a speed recovery. Simply put, when the valve on the governor system is fully shut (PMech = 0.0), the only way to slow the unit down is via friction and windage. This is typically compensated for in other stability packages by allowing the governor to output a slight negative power. This is the case if you ever notice a governor having a small negative limit specified instead of zero power. Figure 151 is supplied to illustrate this. That figure shows generator frequency for an actual unit trip (Meas) overlaid with a simulated response (Sim). This test is typically called a partial load rejection, as the unit was loaded to a small fraction of its rated output before tripping the unit. After the steam valve goes fully closed, the frequency of the unit turns around (starts to drop).

© EasyPower LLC 2016

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The flat line slope during the speed reduction is the slowing down of the unit from friction and windage losses, where the slope of the response can be used to calculate the percent friction and windage losses of the machine. The simulated response in Figure 151 was created using the Steam Turbine Governor model in EasyPower, with a matching generator with properly set inertia (H), and friction and windage torque. Finally, load damping (D) is included, if desired, as a feedback from speed if there is no damping from system load. In most simulations, this value is left equal to zero, the default value in EasyPower. TFric Wind

TAirgap





Generator Air Gap Torque

TMech PMech From Prime Mover







1 2H

1 1  p

1 s

p

D

Figure 150. Inertia vs. Speed Integral Model.

By definition, p is the per unit difference in speed from rated synchronous speed. For example, if the rated speed of the machine were 3600 RPM, and the actual speed were 3600 RPM, then p would be: p 

3600  1.0  0.0 3600

If the actual speed were 3590 RPM, then p would be: p 

3590  1.0  0.00277 3600

If the actual speed were 3630 RPM, then p would be: p 

3630  1.0  0.00833 3600

You can also see that PMech from the governor system (prime mover and governor combination) is divided by speed to convert its output to torque.

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1.025 Freq - Meas Freq - Sim

1.020

Speed (pu)

1.015

1.010

1.005

1.000

0.995 0.0

5.0

10.0

15.0

20.0

25.0

Time (Seconds)

Figure 151. Partial load rejection of actual machine measurement with simulated response.

Inertia Constant The inertia constant H, is defined in kW-sec/kVA. With this per unit form of definition, we can directly simulate speed change according to the inertia equations just discussed. This value, however, is rarely supplied; instead, other forms (units) of inertia are supplied. The most typical English units value is WK2 or WR2, both in lb-ft2. The constant H can easily be calculated from lb-ft2 using the following equation:

H

0.231 wk 2  RPM 2 1x10 6 Base kVA

Again, as noted earlier, the value of inertia calculated here must include the inertia of the generator rotor, rotor (or engine) of the prime mover, and all connecting shafts and equipment. Though machine speed is calculated within the generator model, it represents the speed of the combined generator and prime mover. For those accustomed to having inertia specified in metric units, the following equation can be used: H

© EasyPower LLC 2016

5.482  kg  m 2  RPM 2 1x10 6 Base kVA

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Calculation of Inertia Constant from Test To calculate the inertia constant from test, one must monitor machine speed or output frequency while subjecting the unit to a partial load rejection. Between 10 and 20% of rated load is typical. If the test shown above in Figure 151 is looked at much closer from 2 to 5 seconds, one will discern a clear initial slope as shown in Figure 152. This initial slope is the units change in frequency vs. time with no governor operation, or with the input shaft power remaining constant. Using this slope (df/dt), the Rated MVA of machine, the initial power Po before the rejection test and an equation that relates these, we can determine the machine inertia constant. For this example test, the real and reactive power before tripping was 10.681 MW and –5.53 MVar. The frequency was 60 Hz before the trip and the final frequency oscillated between 60.18 and 60.23 Hz after the trip. From the figures, we derive the machine inertia from the initial slope of the speed response to be:

df pu dt

 61.88 - 61.09    60.0  = 0.026318 pu =  3.4912 - 2.9909 sec

Po 10.681 kw - sec Rated MVA 66.916 Machine Inertia H = = = 3.03 df 2  0.026318  kVA 2 pu dt

Figure 152. Zoom in of partial load rejection to discern slope.

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Initialization Initialization for generator models should only be performed in an online condition. No provision is made in the EasyPower DS Engine to start a generator from an offline condition. The reason for this is simple; to actually start up a generator, there are a host of automatic controls and operator actions that spin the unit up and synchronize it with the grid. These are not being simulated. The process is not like a simple, “close the breaker and go” motor start simulation. If the generator is offline it will initialize with all states, Efd, and PMech set to zero. Closing the generator breaker will start the unit like an induction motor; however, no field will ever be applied, and thus doing such a simulation is basically unusable. We suggest only closing into a generator that is already online to simulate closing actions. When the round rotor generator model is initialized, steps are taken to set all of the generator’s internal States (see Dynamics 101 tutorial for a clear definition of a State), so that the generated Thevenin voltage (discussed above) combined with the terminal voltage conditions and the source impedance of the generator (RA + jX’’d) will create the same power conditions from the initial power flow case. This is accomplished by assuming all DStates (see Dynamics 101 tutorial for a clear definition of a DState) are zero (no changes, we are at steady-state), and then progressing back through the block diagram in Figure 147. All States and the required field voltage (Efd) are easily determined this way - that is, if we neglect saturation. This nonlinear effect unfortunately puts a damper on our direct initialization of the generator. Thus an iterative process is used (called a slew run), where all of the States are set as the machine slews into matching the terminal conditions. After the slew run is complete: 

Generator terminal P (watts) will equal that required of the power flow.



Generator terminal Q (vars) will equal that required of the power flow.



The angle of the generator rotor will be set.



Field voltage (Efd) will be set.



All internal States will be set.

The slew run performs the updates shown in Figure 153 while running the generator through a slightly modified time simulation. As seen in Figure 153, DStates are prepared, the model is integrated, and conditions are updated. However, we have two additional corrections being made on each iteration. First, the field voltage is being updated using feedback error based on the terminal var conditions. Second, the machine angle (rotor angle), is being update using a feedback error based on the terminal watt conditions. Saturation is automatically included in the “Calc Variables” update. All updates in the generator are feed forward (move forward in time), where the feedback errors help to align the generators internal conditions including saturation and the required terminal conditions.

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Start

Calc DStates

Integrate

Calc Variables

Update Terminal Conditions

PError  PLF  PTerm QError  QLF  QTerm

E fd  E fd   QError   AccFactorQ  Angle  Angle   PError  AccFactorP 

No DStates < Threshold

Yes Finished

Figure 153. Generator slew run.

Note: 

PLF and QLF are generator terminal conditions specified by the initial power flow case.



AccFactorP and AccFactorQ are deceleration factors to keep the feedback stable.



Threshold is a value pre-set that is a small value to force the generator very close to absolute steady-state (all DStates very close to zero).

Saturation Defining the saturation model completes the equations needed for a complete generator model. First, two new constants A and B will be defined that are used in the saturation equation used at runtime. The constants are calculated as:

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S  E1  E1 S  E2  E2

E1  E2 A 1

B

S  E1  E1 S  E2  E2

S  E1  E1

 E1  A 

2

where E1, E2, S(E1) and S(E2) are defined from the generator’s saturation curve. See Section 3.6 on “How Do I Determine Machine Saturation” for a method to generate E1, E2, S(E1), and S(E2) values from a machine saturation curve. Once the values of A and B are determined, saturation is calculated in real time from the magnitude of ψ’’ using:



pu Sat  B  ''  A pu Sat  0



2

for

 ''  A

for

 ''  A

The data supplied as input, E1, E2, S(E1), S(E2), thus helps us define a new equation that outputs an amount of saturation. Once the constants A and B are determined for the saturation function, we then can produce a saturation correction for the machine in real-time. For typical data of: E1 E2 S(E1) S(E2)

= 1.0 = 1.2 = 0.12 = 0.30

we get A and B constants of: A B

= 0.7268 = 1.6077

If these are put into our saturation function, we get a plot like that seen in the next figure. We can see that this function is doing a fine job of representing our original input data. At |ψ’’| = 1.0, Sat( 1.0 ) is clearly very near 0.12. At |ψ’’| = 1.2, Sat( 1.2 ) is roughly 0.36. So a slight error (greater saturation) is introduced at higher values of |ψ’’|.

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0.40 0.35

Sat( |ψ''| ) pu

0.30 0.25 0.20 0.15 0.10 0.05 0.00 0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

|ψ''| (pu)

Figure 154. Plot of Sat( |ψ’’| ) vs. |ψ’’|.

One final note: It is interesting to notice for the machine model, that |ψ’’| is used as the input to the saturation function, instead of the machine’s terminal voltage. This is by design, as the machines saturation on the rotor is driven by the airgap flux (represented by |ψ’’|). However, with a little more research, we see that a machines saturation curve is defined using the terminal voltage of the machine. The reason for what appears to be a lack of consistency is that when the machine’s saturation curve is determined, the generator is open circuit. Thus no current is flowing in the stator windings. From the open circuit condition, at rated speed, we can state that |ψ’’| = |ETerm| and can see that the saturation curve is, by open circuit definition, the conditions at the airgap.

4.1.2 Salient Pole Synchronous Generator As with the round rotor generator model, the salient pole generator model was developed with the help of Mr. F. Paul deMello. This model is actually a simplification of the round rotor generator model, due to eliminating parts of the q-axis in the circuit model. Figure 155 shows the circuit model, where we see the following differences: 

Saturation is only involved in the d-axis.



The q-axis model is simplified to include only the sub-transient amortisseur effect.



The q-axis model has no transient component, since no second amortisseur effect is needed. The rotor is composed of laminated poles at the end of a water wheel type structure, and thus has no solid rotor effects.



Since saturation is on the d-axis only, initialization is direct, and no slew run is needed.

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X X Eq' E fd



1



 

'



Tdo s

1 Tdo'' s



 kd

X X

'' d

 Xl 

' d

 Xl 

' d

 X d'' 

' d

 Xl 



 d''



Saturation

X X

' d

' d

X ad I fd



 

 X d  X d' 

 X d'' 

 Xl 

X

2

' d

 Xl 



Id



X  

 X q'' 

Iq

''

 q''

q

1 Tqo s

Figure 155. Salient pole generator model block diagram.

Everything else about the salient pole generator falls in line with discussions of the round rotor generator model in the previous section. Parameters for the model are listed in Table 6, where brief descriptions of each are provided. Parameters there correspond to the items seen in the Figure 155 blocks, as well as the machine rating (for proper scaling in the DS Engine) and the inertia component.

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Table 7. Salient pole generator model parameters.

Parameter

Units

Rated MVA Rated Eff Rated Speed Rated Voltage Rated Current Rated PF

MVA Percent RPM Volts LL Amps

Ra Xl

pu pu

Stator winding resistance (armature resistance) Stator leakage reactance

Xd Xq X’d X’’d = X’’q

pu pu pu pu

d-axis unsaturated synchronous reactance q-axis unsaturated synchronous reactance d-axis unsaturated transient reactance d & q-axis unsaturated sub-transient reactance

T’do T’’do T’’qo

Seconds Seconds Seconds

d-axis transient OC time constant d-axis sub-transient OC time constant q-axis sub-transient OC time constant

E1 E2 S( E1 ) S( E2 )

pu pu pu pu

First voltage to define saturation Second voltage to define saturation Saturation at E1 Saturation at E2

H D Windage

kW-Sec / kVA Combined machine and prime mover inertia pu Machine damping, normally = 0 pu Machine friction and windage

Notes:

© EasyPower LLC 2016

Description

OC - Open Circuit

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4.1.3 PV1G - Photovoltaic Inverter Converter Current Limit I

IQcmd

2 MaxTD

-I

2 Qcmd

Min

IQmxv

1.6



I MaxTD

-I

I MaxTD = 1.7

1 1+ 0.02s

IQcmd  E FD  Zerox Brkpt

Vterm

dvtrp4

dttrp4

dttrp3

dttrp2

dttrp1

PQ = 0: Q Priority Flag PQ = 1: P Priority Flag

LVPL 1.22

dvtrp3

-1.0 pu

Min

VTerm

VTerm

dvtrp2

IQmx  IFD 

1

I

Time  sec 

0.0 pu

dvtrp1

Vterm IQhl

2 Pcmd

dttrp5

dvtrp5

0

2 MaxTD

dttrp6

dvtrp6

PQFlag

Min

Min

Qmax 1.0

POrd

1

Min

IQmxv

I Pmx I Pcmd

Zero Voltage Ride Through

0

dV

I Phl

VTerm

I Pmx

1 1+ 0.02s

IQ

High Voltage Reactive Current Management

LVPL

IP 1 1+ 0.02s Rate Limit R Rpwr

Low Voltage Active Current Management

P I Source L L

Figure 156. Photovoltaic Inverter model block diagram.

Parameter Brkpt Iphl Iqhl ImaxTD RRpwr Qmax Zerox dvtrp1 dvtrp2 dvtrp3 dvtrp4 dvtrp5 dvtrp6 dttrp1 dttrp2 dttrp3 dttrp4 dttrp5 dttrp6

© EasyPower LLC 2016

Units pu pu pu pu pu pu pu pu pu pu pu pu pu Seconds Seconds Seconds Seconds Seconds Seconds

Description LVPL characteristic breakpoint voltage Hard active current limit Hard reactive current limit Max temperature dependent converter current Active current ramp rate limit Reactive power max LVPL characteristic zero crossing voltage Terminal voltage at 75% ∆VTerm = -0.25 pu Terminal voltage at 50% ∆VTerm = -0.50 pu Terminal voltage at 30% ∆VTerm = -0.70 pu Terminal voltage at 15% ∆VTerm = -0.85 pu Terminal voltage at 110% ∆VTerm = +0.10 pu Terminal voltage at 115% ∆VTerm = +0.15 pu The time to trip for: 0.50 pu < VTerm < 0.75 pu The time to trip for: 0.30 pu < VTerm < 0.50 pu The time to trip for: 0.15 pu < VTerm < 0.30 pu The time to trip for: 0.00 pu < VTerm < 0.15 pu The time to trip for: 1.10 pu < VTerm < 1.15 pu The time to trip for: 1.15 pu < VTerm

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Description Use this model to simulate: 

Photovoltaic arrays using an inverter interface with the grid.

In this model: 

RRpwr is a rate limit applied to the block it is displayed with.



The LVPL limit is a non-windup limit.



The IPmx limit is a windup limit.



IQcmd is supplied by the Inverter Q Control model via the EFD variable.

Notes: 

The high voltage reactive current management reduces reactive current to limit terminal voltage to 1.2 pu.



The low voltage active current management emulates a phase locked loop, which reduces active current at low voltage conditions.



The LVPL (low voltage power logic) block caps active current. Together with the ramp rate limit RRpwr, this affects the voltage recovery behavior.

References: 1. Western Electricity Coordinating Council Renewable Energy Modeling Task Force Progress Report to MVWG on PV System Modeling July 8, 2010. 2. Western Electricity Coordinating Council Modeling and Validation Work Group, WECC Wind Power Plant Dynamic Modeling Guide (DRAFT) Prepared by WECC Renewable Energy Modeling Task Force, August 2010 3. K. Clark, N. Miller, R. Walling, “Modeling of GE Solar Photovoltaic Plants for Grid Studies”, April 2010. Copyright©2009 GE Energy. All rights reserved. 4. K. Clark, N. Miller, R. Walling, “Modeling of GE Wind Turbine-Generator for Grid Studies”, April 2010. 5. FINAL PROJECT REPORT WECC WIND GENERATOR DEVELOPMENT Prepared for CIEE By: National Renewable Energy Laboratory. March, 2010

© EasyPower LLC 2016

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4.1.4 WT4G - Wind Turbine with Inverter Converter Current Limit 2 I 2MaxTD - IQcmd

IQcmd

Min

IQmxv

1.6

PElec

1 1 + sTpw

   

dPmx

PRef

K ip

 P Ord  

K pp +

s



dvtrp2

IQmx  IFD 

1

I MaxTD = 1.7

VTerm

1 1+ 0.02s

1 1+ 0.02s

IQcmd  E FD 

1.22

Zerox Brkpt

dvtrp4

dttrp4

dttrp3

dttrp2

dttrp1

PQ = 0: Q Priority Flag PQ = 1: P Priority Flag

LVPL

sK f 1 + sTf

dvtrp3

-1.0 pu

Min

VTerm dPmn

Time  sec 

0.0 pu

dvtrp1

Vterm IQhl

2 I 2MaxTD - I Pcmd

dttrp5

dvtrp5

PQFlag

Min 0

1.0

dttrp6

dvtrp6

I MaxTD Min

Qmax

I Pmx I Pcmd

1

Min

IQmxv

PRef

Zero Voltage Ride Through dV

I Phl

VTerm

I Pmx 0

IQ

High Voltage Reactive Current Management

LVPL

Vterm

IP 1 1+ 0.02s Rate Limit R Rpwr

I Pcmd

Low Voltage Active Current Management

P I Source L L

Figure 157. Wind Turbine Inverter model block diagram.

Parameter Tpw Tf Brkpt Iphl Iqhl ImaxTD Kf Kip Kpp RRpwr Qmax Zerox dPmx dPmn dvtrp1 dvtrp2 dvtrp3 dvtrp4 dvtrp5 dvtrp6 dttrp1 dttrp2 dttrp3 dttrp4 dttrp5 dttrp6

© EasyPower LLC 2016

Units Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu Seconds Seconds Seconds Seconds Seconds Seconds

Description Real power transducer time constant Real power control rate feedback time constant LVPL characteristic breakpoint voltage Hard active current limit Hard reactive current limit Max temperature dependent converter current Real power control rate feedback gain Real power control integral gain Real power control proportional gain Active current ramp rate limit Reactive power max LVPL characteristic zero crossing voltage Real power control limit max Real power control limit min Terminal voltage at 75% ∆VTerm = -0.25 pu Terminal voltage at 50% ∆VTerm = -0.50 pu Terminal voltage at 30% ∆VTerm = -0.70 pu Terminal voltage at 15% ∆VTerm = -0.85 pu Terminal voltage at 110% ∆VTerm = +0.10 pu Terminal voltage at 115% ∆VTerm = +0.15 pu The time to trip for: 0.50 pu < VTerm < 0.75 pu The time to trip for: 0.30 pu < VTerm < 0.50 pu The time to trip for: 0.15 pu < VTerm < 0.30 pu The time to trip for: 0.00 pu < VTerm < 0.15 pu The time to trip for: 1.10 pu < VTerm < 1.15 pu The time to trip for: 1.15 pu < VTerm

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Description Use this model to simulate: 

Wind turbines with an inverter interface with the grid.

In this model: 

RRpwr is a rate limit applied to the block it is displayed with.



The LVPL limit is a non-windup limit.



The dPmx and dPmn limit is a non-windup limit.



The IPmx limit is a windup limit.



IQcmd is supplied by the Inverter Q Control model via the EFD variable.

Notes: 

The high voltage reactive current management reduces reactive current to limit terminal voltage to 1.2 pu.



The low voltage active current management emulates a phase locked loop, which reduces active current at low voltage conditions.



The LVPL (low voltage power logic) block caps active current. Together with the ramp rate limit RRpwr, this affects the voltage recovery behavior.

References: 1. Western Electricity Coordinating Council Renewable Energy Modeling Task Force Progress Report to MVWG on PV System Modeling July 8, 2010. 2. Western Electricity Coordinating Council Modeling and Validation Work Group, WECC Wind Power Plant Dynamic Modeling Guide (DRAFT) Prepared by WECC Renewable Energy Modeling Task Force, August 2010 3. K. Clark, N. Miller, R. Walling, “Modeling of GE Solar Photovoltaic Plants for Grid Studies”, April 2010. Copyright©2009 GE Energy. All rights reserved. 4. K. Clark, N. Miller, R. Walling, “Modeling of GE Wind Turbine-Generator for Grid Studies”, April 2010. 5. FINAL PROJECT REPORT WECC WIND GENERATOR DEVELOPMENT Prepared for CIEE By: National Renewable Energy Laboratory. March, 2010

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4.2 Excitation System Models In the previous section on generators, it was noted that the field voltage (Efd) was an input to both the generator models. Also, during initialization, Efd was determined after properly initializing the model. The value of Efd is controlled and supplied from the excitation system. EasyPower DS includes 26 excitation system models.                            

Basler AVC1 IEEE Type 1 IEEE Type 2 IEEE Type AC1A IEEE Type AC2 IEEE Type AC2A IEEE Type AC3A IEEE Type AC4A IEEE Type AC5A IEEE Type AC6A IEEE Type AC7B IEEE Type AC8B IEEE Type DC1A IEEE Type DC2A IEEE Type DC3A IEEE Type DC4B IEEE Type ST1A IEEE Type ST2 IEEE Type ST2A IEEE Type ST3A IEEE Type ST4B IEEE Type ST5B IEEE Type ST6B IEEE Type ST7B IEEE Type AC8B Inverter Q Control Simple Excitation System STAMFORD 1

The majority of these models are specified by the IEEE. The most recent version of the IEEE Standard on excitation systems is IEEE Standard 421.5 – 2005, and it is entitled, “IEEE Recommended Practice for Excitation System Models”. We highly recommend obtaining a copy and referencing that standard for details on modeling excitation systems. It is an excellent reference.

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In addition, the reference includes details on how each of the component blocks are modeled. This is especially useful when trying to understand windup and non-windup limits. Refer to Annex E in the standard for an excellent discussion on the application of limits. All of the IEEE type models listed above are presently defined in the 421.5 Standard with exception only to the IEEE Type 1 and Type 2 models, which are historical IEEE models. Each model is functionally specified to model a particular form of excitation system, of which there are many. Each sub-section in this section that documents a particular excitation system will note the intended excitation system to be simulated, and we have supplied a table below that correlates manufacturer excitation systems and AVRs to the model names above. As noted, the excitation system’s purpose is to supply and control the field of the generator so that the terminal voltage of the generator is controlled. The excitation system includes several components depending upon type (AC, DC, bus fed, separately excited, etc.), and we will purpose to note each component included in each model. These components could be but are not limited to: 

The AVR (automatic voltage regulator). This is the main control section where control blocks are implemented on purpose to obtain satisfactory generator terminal voltage response.



The Amplifier. This is typically blended in with the AVR, but is the section that takes the low level control voltages and boosts them to levels either for the field of the exciter, or for the field of the generator. Often a simple limit simulating the min and max range of the amplifier system is all that is included, and the gain of the amplifier washes into the main gain of the excitation system.



The Exciter. The exciter is a rotating machine or static amplifier used to amplify a low level signal up to the voltage and current needed to drive the field of the generator. The time constant TE has historically been reserved for the time constant simulating the exciter. If a unit is brushless, then the exciter is typically an alternator with a rectifier on its output, all on the shaft of the generator. Hence the term, “rotating rectifier”.

As seen in every excitation system model documented in this section, terminal voltage is fed back into the automatic voltage regulator (AVR) portion of the excitation system. Thus, the excitation system is simply a means to an end. It holds and forces conditions that satisfy the AVR set-point (referred to as VRef or “Vee Ref” or the voltage reference) requirement, thus maintaining generator terminal voltage. In Table 8, we have supplied an exciter mapping from Manufacturer to EasyPower exciter model. This is not exhaustive, and we would encourage feedback from our users with additional mappings that we can include in this table.

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Table 8. Exciter Mapping - Manufacturer to Exciter Model. Manufacturer

Exciter Type

Model

ABB

UNITROL UNITROL D UNITROL P UNITROL F UNITROL 5000 Stabilizer Option Stabilizer Option MB-PSS (Multi-band)

ST1A ST5B ST5B ST5B ST5B PSS2B PSS3B PSS4B

ABB-Westinghouse

Mag-A-Stat Rototrol Silverstat TRA AB KC (with some approximations)

DC1A DC1A DC1A DC1A DC1A DC1A

Allis Chalmers

Regulex

DC1A

Alstom

Static Excitation Systems Eurorec Micrrec K4.1 ALSPA P320

ST1A ST7B ST7B ST7B

Asea

Static Excitation Systems

ST1A

Brown Boveri

Static Excitation Systems

ST1A

Basler

DECS applied to DC Commutator Exciter Some generic Basler AC exciters DECS applied to AC rotating rectifier DECS SSE DECS applied to static excitation Stabilizer Option PSS-100 AVC63-12 AVC125-10

DC4B AC5A AC7B AC8B ST1A ST4B PSS2B PSS2B Basler AVC1 Basler AVC1

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Table 8 Continued. Manufacturer

Exciter Type

Model Type

Brush

PRISMIC A50-B PRISMIC A30 PRISMIC A10 PRISMIC A50-S PRISMIC A50-A DCP PRISMIC T20

AC7B AC8B AC8B ST4B ST4B ST5B PSS2B

Canadian GE

Silcomatic Silcomatic 5

ST1A ST4B

C. A. Parsons

Stationary Diode System

AC6A

Cutler Hammer

Westinghouse Type WDR Retrofit

AC1A

Eaton

ECS2100 applied to AC Rotating Rectifier ECS2100 static excitation system ECS2100 static excitation system

AC7B ST4B ST6B

Eaton Cutler Hammer

Westinghouse Type WDR Retrofit ECS2100 applied to DC Commutator Stabilizer Option

DC2A DC4B PSS2B

Electric Machinery

Some generic EM AC exciters

AC5A

GE

Amplidyne GDA SVR GFA 4 ALTERREX ALTHYREX with rotating thyrsitor ALTERREX regulator replacement EX2000/2100 Potential Source Static Excitation System SCT-PPT SCT-SCPT GENERREX with Compound Power Source GENERREX with Potential Power Source EX2000/2100 Bus-Fed Potential Source EX2000/2100 Bus-Fed Static Source GENERREX-PPS GENERREX-CPS Stabilizer Option STATIC EX2000BR

DC1A DC1A DC2A DC3A AC3A AC4A AC7B AC7B ST1A ST2A ST2A ST3A ST3A ST4B ST4B ST4B ST4B PSS2B ST2

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Table 8 Continued. Manufacturer

Exciter Type

Model Type

GEC-Elliot

Static Excitation System

ST1A

Hitachi

Static Excitation System

ST1A

Mitsubishi

Static Excitation System

ST1A

Rayrolle-Parsons

Static Excitation System

ST1A

Siemens

RG3 THYRISIEM AG THYRIPOL AG THYRIPOL Stabilizer Option

AC7B AC7B ST1A ST6B PSS3B

Toshiba

Static Excitation Systems

ST1A

Westinghouse

PRX-400 BJ30 Brushless Excitation System High Initial Response Brushless System Type PS with Type WTA Voltage Regulator Type PS with Type WTA-300 Voltage Regulator Type PS with Type WHS Voltage Regulator WDR MGR

DC2A DC3A AC1A AC2A ST1A ST1A ST1A ST1A ST1A

Westinghouse Canada

Solid State Thyristor Excitation System

ST1A

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4.2.1 Basler AVC1 VPMG K VS  1

K VS  0

VRef

VT

IT

1 1+sTR

VC1  VT   RC  jX C  IT

1+sTR2 1+sTR1

 

K VP

VR Max



 KA s

 

1+sTC 1+sTB



VR 



VFE

VR Min

VPSS

1 sT E





E FD

0



KE

 VF

sK F 1+sTF1 1+sTF2 

VX

VX = E FD SE  E FD 

Figure 158. Basler AVC1 Exciter model block diagram.

Parameter RC XC TB TC TE TF1 TF2 TR TR1 TR2 KA KE KF KVP KVS VR Min VR Max VPMG E1 E2 S(E1) S(E2)

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Units pu pu Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu

Description Load compensation resistance Load compensation reactance AVR second Lead/Lag block lag time constant AVR second Lead/Lag block lead time constant Exciter time constant AVR feedback time constant AVR feedback time constant Signal transducer time constant AVR first Lead/Lag block lag time constant AVR first Lead/Lag block lead time constant AVR gain Exciter gain AVR feedback gain Voltage source gain If 0, Use Term Voltage; If 1, Use PMG Voltage AVR min limit AVR max limit Voltage of PMG output EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate a Basler excitation system as noted in Basler documentation: * This model is for the Basler AVC63-12 and AVC125-10 excitation system used with a brushless rotating exciter. It is assumed that the exciter rectifier power is either supplied from a PMG (permanent magnet generator) or taken from generator terminals. In this model: 

The AVR is simulated from the TR block up to the output voltage VR.



The block before the TR block simulates load compensation, a form of line drop compensation.



The brushless exciter is simulated to the right of VR, and is a simplified model that excludes field current feedback. See the IEEE AC1A model for more information regarding a more detailed simulation of the rotating rectifier.



The switch KVS allows the amplifier (which feeds the field of the exciter) to have its power supplied from either the terminals of the generator or from a separate permanent magnet generator.



The AVR limits on block KA are non-windup.



The feedback loop incorporates rate feedback.

* From Basler supplied documentation entitled, “Mathematical Per-Unit Model of the AVC6312 and AVC125-10 Regulator”, June 11, 2002.

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4.2.2 IEEE Type 1 Excitation System

SE

 π

VRef

VT

1 1+sTR 





 

VR Max 

KA 1+sTA 

 







1 K E + sTE

E FD

VR Min

VPSS

sK F

1+sTF  Figure 159. IEEE Type 1 model block diagram.

Parameter TA TE TF TR KA KE KF VR Max VR Min E1 E2 S(E1) S(E2)

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu

AVR time constant Exciter time constant Field voltage feedback time constant Transducer time constant AVR gain Exciter KE Field voltage feedback gain AVR limit max AVR limit min EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

DC exciters.

In this model: 

The first block models the transducer time constant.



The second block models the AVR.



The third block simulates a rotating exciter.



The saturation block simulates saturation in the rotating exciter.



The limit on the second block is non-windup.



The feedback block employs rate feedback.

Notes: 

The IEEE Type 1 excitation system model corresponds to IEEE recommendations of 1969.



This model is included for those with historic model data for an IEEE Type 1 system.



This model matches the updated IEEE DC1A model very closely, and can be used for a DC1A. Refer to the discussion below for more information on how to apply the DC1A, which is adequate for application of the IEEE Type 1 as well.



The EasyPower implementation of the IEEE Type 1 model does not include any automatic calculation of exciter limits VRMax and VRMin, or the value KE, as noted below in the IEEE 421.5 Standard. All parameters shown in Table 8 above are fixed. This autocalculation feature will be added in a later version.

From IEEE Standard 421.5, Section 5.1, discussing the DC1A model: * This model, described by the block diagram of Figure 5-1, is used to represent fieldcontrolled dc commutator exciters with continuously acting voltage regulators (especially the direct-acting rheostatic, rotating amplifier, and magnetic amplifier types).5 Because this model has been widely implemented by the industry, it is sometimes used to represent other types of systems when detailed data for them are not available or when a simplified model is required.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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* The principal input to this model is the output, VC, from the terminal voltage transducer and load compensator model previously described. At the summing junction, terminal voltage transducer output, VC, is subtracted from the set point reference, VREF. The stabilizing feedback, VF, is subtracted and the power system stabilizing signal, VS, is added to produce an error voltage. In the steady state, these last two signals are zero, leaving only the terminal voltage error signal. The resulting signal is amplified in the regulator. The major time constant, TA, and gain, KA, associated with the voltage regulator are shown incorporating non-windup limits typical of saturation or amplifier power supply limitations. A discussion of windup and non-windup limits is provided in Annex E. These voltage regulators utilize power sources that are essentially unaffected by brief transients on the synchronous machine or auxiliary buses. The time constants, TB and TC, may be used to model equivalent time constants inherent in the voltage regulator, but these time constants are frequently small enough to be neglected and provision should be made for zero input data.

* The voltage regulator output, VR, is used to control the exciter, which may be either separately excited or self-excited as discussed in the IEEE Committee Report [B20]. When a self-excited shunt field is used, the value of KE reflects the setting of the shunt field rheostat. In some instances, the resulting value of KE can be negative and allowance should be made for this. * Most of these exciters utilize self-excited shunt fields with the voltage regulator operating in a mode commonly termed buck-boost. The majority of station operators manually track the voltage regulator by periodically trimming the rheostat set point so as to zero the voltage regulator output. This may be simulated by selecting the value of KE so that initial conditions are satisfied with VR = 0, as described in the IEEE Committee Report [B20]. In some programs, if KE is entered as zero, it is automatically calculated by the program for self-excitation. * From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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* If a nonzero value for KE is provided, the program should not recalculate KE, as a fixed rheostat setting is implied. For such systems, the rheostat is frequently fixed at a value that would produce self-excitation near rated conditions. Systems with fixed field rheostat settings are in widespread use on units that are remotely controlled. A value for KE = 1 is used to represent a separately excited exciter. * The term SE[EFD] is a nonlinear function with values defined at two or more chosen values of EFD, as described in Annex C. The output of this saturation block, VX, is the product of the input, EFD, and the value of the nonlinear function SE[EFD] at this exciter voltage. * A signal derived from field voltage is normally used to provide excitation system stabilization, VF, via the rate feedback with gain, KF, and time constant, TF.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.3 IEEE Type 2 Excitation System SE

 π

VRef

VT

1 1+sTR 





 

VR Max 



KA 1+sTA 

 





1 K E + sTE

E FD

VR Min

VPSS

sK F

1+sTF2 1+sTF1  Figure 160. IEEE Type 2 model block diagram.

Parameter TA TE TF1 TF2 TR KA KE KF VR Max VR Min E1 E2 S(E1) S(E2)

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu

AVR time constant Exciter time constant Field voltage feedback time constant 1 Field voltage feedback time constant 2 Transducer time constant AVR gain Exciter KE Field voltage feedback gain AVR limit max AVR limit min EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

Brushless, AC Exciters.

In this model: 

The first block models the transducer time constant.



The second block models the AVR.



The third block simulates an AC exciter and rotating rectifier.



The saturation block simulates saturation in the exciter.



The limit on the second block is non-windup.



The feedback block employs rate feedback.

Notes: 

The IEEE Type 2 excitation system model corresponds to IEEE recommendations of 1969.



Updated models (IEEE AC1A, AC6A, AC8B) for brushless systems will include more detail in modeling field current feedback effects.



The new IEEE AC5A comes closest to matching this model. The IEEE Type 2 includes an additional transducer time constant block, and the AC5A includes an additional lead term in the AVR rate feedback loop. Refer to the discussion below for more detail on the AC5A, which is adequate discussion for the IEEE Type 2 as well.



This model is included for those with historic model data for an IEEE Type 2 system.

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From IEEE Standard 421.5, Section 6.5, discussing the AC5A model: * The model shown in Figure 6-5, designated as Type AC5A, is a simplified model for brushless excitation systems. The regulator is supplied from a source, such as a permanent magnet generator, which is not affected by system disturbances. Unlike other ac models, this model uses loaded rather than open circuit exciter saturation data in the same way as it is used for the dc models (Annex C). Because the model has been widely implemented by the industry, it is sometimes used to represent other types of systems when either detailed data for them are not available or simplified models are required.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.4 IEEE Type AC1A Excitation System VRef

VA Max

VT

1 1+sTR 

 



 

VR Max

1+sTC  1+sTB 

KA 1+sTA 

LV Gate

HV Gate

VR Min

VA Min

VPSS

  VR 

1 sTE

VE SE  VE 

sK F 1+sTF 

I N < 0.433

FEX = 1- 0.577I N

0.433< I N < 0.750

FEX =

2 N

0.750< I N < 1.000

FEX = 1.732 1- I N 

I N > 1.000

0.75- I

π

E FD

0

VOEL

VUEL

VE

FEX = f  I N 



VFE

 



KE

IN =

K C I FD VE

KD

I FD

FEX = 0

Figure 161. IEEE Type AC1A model block diagram.

Parameter TR TA TB TC TE TF KA KC KD KE KF VAMax VAMin VRMax VRMin E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Sensor time constant Main AVR time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Exciter time constant Feedback lag time constant First block main AVR gain Exciter KC – Field current feedback Exciter KD – Field current feedback Exciter KE Feedback gain AVR control max AVR control min Regulator max - Amplifier Regulator min - Amplifier EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

Brushless, AC Exciters.

In this model: 

The first block models the transducer time constant.



The second and third blocks model the AVR.



The fourth block (TE) simulates a rotating exciter.



The saturation block simulates saturation in the rotating exciter.



The limit on the third block is non-windup.



The feedback block employs rate feedback.

Notes: 

The IEEE Type AC1A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.



This model includes field current feedback effects, as IFD is fed back into the model from the generator.

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From IEEE Standard 421.5, Section 6.1: * The model shown in Figure 6-1 represents the field-controlled alternator-rectifier excitation systems designated Type AC1A. These excitation systems consist of an alternator main exciter with non-controlled rectifiers. The exciter does not employ selfexcitation, and the voltage regulator power is taken from a source that is not affected by external transients. The diode characteristic in the exciter output imposes a lower limit of zero on the exciter output voltage, as shown in Figure 6-1. * For large power system stability studies, the exciter alternator synchronous machine can be represented by the simplified model shown in Figure 6-1. The demagnetizing effect of load current, IFD, on the exciter alternator output voltage, VE, is accounted for in the feedback path that includes the constant, KD. This constant is a function of the exciter alternator synchronous and transient reactances, see Ferguson, Herbst, and Miller [B12] and Gayek [B13]. * Exciter output voltage drop due to rectifier regulation is simulated by inclusion of the constant KC (which is a function of commutating reactance) and the rectifier regulation curve, FEX, as described in Annex D. Brushless Modeling Detail The AC1A excitation system is brushless and thus has an alternator with rotating rectifier on the shaft of the unit. To properly include the dynamic behavior of the alternator (which is a machine with reactances and time constants), it should be modeled with a detailed alternator model, much as is the main generator. It is known, however, that no model presently available in the IEEE model library fully models the effects of the alternator, and its impact on the field of the generator. The IEEE AC1A model only includes moderate detail, with parameters and functions (KD, KC, KE, TE, etc), via equations instead of an additional machine model. A paper published by deMello, et al., “Dynamic Aspects of Excitation Systems and Power System Stabilizers”, published in 1987, and presented at a Brazilian conference of Specialists in Planning and Operations, notes that an accurate model of the alternator behavior should be modeled with a separate machine model. However, since few will have the required additional data (machine impedances and time constants) to include detailed modeling of such a nature, we have elected to use the “moderate” detail included in the AC1A, AC6A and AC8B excitation system models defined by IEEE.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.5 IEEE Type AC2 Excitation System VRef VA Max

VT

 

VPSS



 

1+sTC  1+sTB 

VR Max KA 1+sTA 

 VA

LV Gate





VH

VF FEX = 1- 0.577I N 0.75- I 2N

0.433< I N < 0.750

FEX =

0.750< I N < 1.000

FEX = 1.732 1- I N 

I N > 1.000

VR

KL





1 sTE

 

VR Min VL

VA Min

I N < 0.433



KB



VE

π

E FD

FEX

0

FEX = f  I N 

VLR KH

sK F

1+sTF 

VFE





K E  SE  VE 

IN =

 KD

K C I FD VE

I FD

FEX = 0

Figure 162. IEEE Type AC2 model block diagram.

Parameter TA TB TC TE TF KA KB KC KD KE KF KH KL VAMax VAMin VLR VRMax VRMin E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Main AVR time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Exciter time constant Feedback time constant First block main AVR gain Third block AVR gain Exciter KC – Field current feedback Exciter KD – Field current feedback Exciter KE Feedback gain Feedback gain Feedback gain AVR control max AVR control min Field current feedback limit setting Regulator max - Amplifier Regulator min - Amplifier EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

Dynamic Stability Reference Manual

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Description Use this model to simulate excitation systems with: 

Brushless, AC Exciters or as a general purpose excitation system.

In this model: 

The first block models the AVR lead / lag.



The second through fifth blocks model the rest of the AVR.



The sixth block (TE) is meant to simulate a simplistic rotating exciter.



The saturation block is meant to simulate saturation in the rotating exciter.



The first and third limits are non-windup.



The second limit is windup.



The feedback block employs rate feedback and is a part of the AVR.

Notes: 

The IEEE Type AC2 excitation system model corresponds to IEEE recommendations of 1981. It has been superseded by the AC2A model of 2005. Refer to the AC2A model for more notes describing components of this model from IEEE Standard 421.5 - 2005.



This model includes field current feedback effects, as IFD is fed back into the model from the generator.



See “Brushless Modeling Detail” for the AC1A model for discussion on all model components after VR.

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4.2.6 IEEE Type AC2A Excitation System VRef

VFE Max - K D I FD

VA Max

VT

 

VPSS



 

K E +SE (VE )

VR Max

1+sTC  1+sTB 

KA

1+sTA 

  VA 

VA Min

KB

LV Gate

HV Gate

VR Min VUEL

VH

  VR 

1 sTE

I N < 0.433

FEX = 1- 0.577I N

0.433< I N < 0.750

FEX = 0.75- I 2N

0.750< I N < 1.000

FEX = 1.732 1- I N 

I N > 1.000

π

E FD

0

VOEL

VE SE  VE 

KH

VF

VE

sK F 1+sTF 

FEX = f  I N 



VFE

 



KE

IN =

KD

K C I FD VE

I FD

FEX = 0

Figure 163. IEEE Type AC2A model block diagram.

Parameter TA TB TC TE TF KA KB KC KD KE KF KH VAMax VAMin VRMax VRMin VFEMax E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Main AVR time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Exciter time constant Feedback time constant First block main AVR gain Third block AVR gain Exciter KC – Field current feedback Exciter KD – Field current feedback Exciter KE Feedback gain Feedback gain AVR control max AVR control min Regulator max - Amplifier Regulator min - Amplifier Exciter max characteristic EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

Dynamic Stability Reference Manual

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Description Use this model to simulate excitation systems with: 

Brushless, AC Exciters.

In this model: 

The first block models the AVR lead / lag.



The second through fifth blocks model the rest of the AVR.



The sixth block (TE) is meant to simulate a simplistic rotating exciter.



The saturation block is meant to simulate saturation in the rotating exciter.



The first and third limits are non-windup.



The second limit is windup.



The feedback block employs rate feedback and is a part of the AVR.

Notes: 

The IEEE Type AC2A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.



This model includes field current feedback effects, as IFD is fed back into the model from the generator.



See “Brushless Modeling Detail” for the AC1A model for discussion on all model components after VR.

From IEEE Standard 421.5, Section 6.2: * The model shown in Figure 6-2, designated as Type AC2A, represents a high initial response field-controlled alternator-rectifier excitation system. The alternator main exciter is used with non-controlled rectifiers. The Type AC2A model is similar to that of Type AC1A except for the inclusion of exciter time constant compensation and exciter field current limiting elements. The exciter time constant compensation consists essentially of a direct negative feedback, VH, around the exciter field time constant, reducing its effective value and thereby increasing the small signal response bandwidth of the excitation system.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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* The time constant is reduced by a factor proportional to the product of gains, KB and KH, of the compensation loop and is normally more than an order of magnitude lower than the time constant without compensation. To obtain high initial response with this system, a very high forcing voltage, VRMAX, is applied to the exciter field. A limiter sensing exciter field current serves to allow high forcing but limit the current. By limiting the exciter field current, exciter output voltage, VE, is limited to a selected value, which is usually determined by the specified excitation system nominal response. Although this limit is realized physically by a feedback loop as described in Annex F, the time constants associated with the loop can be extremely small and can cause computational problems. For this reason, the limiter is shown in the model as a positive limit on exciter voltage back of commutating reactance, which is in turn a function of generator field current. For small limiter loop time constants, this has the same effect, but it circumvents the computational problem associated with the high gain, low time constant loop. The limits on VE are used to represent the effects of feedback limiter operation, as described in Annex F.

* Figure 6-2—Type AC2A—High initial response alternator-rectifier excitation system with non-controlled rectifiers and feedback from exciter field current

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.7 IEEE Type AC3A Excitation System KR

VRef

VFE Max - K D I FD VA Max

VT







 

1+sTC  1+sTB 

VPSS



HV Gate

KA



1+sTA 



VA

K E +SE (VE ) π

  VR 

1 sTE

VE SE  VE  I N < 0.433

FEX = 1- 0.577I N

0.433< I N < 0.750

2 N

0.750< I N < 1.000 I N > 1.000

FEX =

0.75- I

π

E FD

VE Min

VA Min

VUEL

VE

VF

VFE





FEX = 1.732 1- I N 

FEX = f  I N 





KE

IN =

K C I FD VE

FEX = 0 VN

KD

KN

VN

s 1+sTF 

I FD

KF

E FD

E FDN

Figure 164. IEEE Type AC3A model block diagram.

Parameter TA TB TC TE TF KA KC KD KE KF KN KR VAMax VAMin VEMin VFEMax EFDN E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Main AVR time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Exciter time constant Feedback time constant Main AVR gain Exciter KC – Field current feedback Exciter KD – Field current feedback Exciter KE Feedback gain – From EFD = 0 to EFDN Feedback gain – From EFDN up Self excitation feedback gain AVR control max AVR control min Exciter min output limit Exciter max characteristic Feedback gain breakpoint EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

Self-Excited Brushless, AC Exciters.

In this model: 

The first block models the AVR lead / lag.



KR is a feedback multiplier to simulate self-excitation.



The TE block simulates the rotating exciter.



The saturation block is meant to simulate saturation in the rotating exciter.



All limits are non-windup.



The feedback block employs rate feedback and a non-linear saturation effect.

Notes: 

The IEEE Type AC3A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.



This model includes field current feedback effects, as IFD is fed back into the model from the generator.



See “Brushless Modeling Detail” for the AC1A model for discussion on all model components after VR.

From IEEE Standard 421.5, Section 6.3: * The model shown in Figure 6-3, represents the field-controlled alternator-rectifier excitation systems designated Type AC3A. These excitation systems include an alternator main exciter with non-controlled rectifiers. The exciter employs self-excitation, and the voltage regulator power is derived from the exciter output voltage. Therefore, this system has an additional nonlinearity, simulated by the use of a multiplier whose inputs are the voltage regulator command signal, VA, and the exciter output voltage, EFD, times KR. This model is applicable to excitation systems employing static voltage regulators. For large power system stability studies, the exciter alternator synchronous machine model is simplified. The demagnetizing effect of load current (IFD) on the dynamics of the exciter alternator output voltage, VE, is accounted for. The feedback path includes the constant KD, which is a function of the exciter alternator synchronous and transient reactances.

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Figure 6-3—Type AC3A—Alternator-rectifier exciter with alternator field current limiter

* Exciter output voltage drop due to rectifier regulation is simulated by inclusion of the constant, KC (which is a function of commutating reactance), and the regulation curve, FEX, as described in Annex D. The excitation system stabilizer in this model has a nonlinear characteristic. The gain is KF with exciter output voltage less than EFDN. When exciter output exceeds EFDN, the value of this gain becomes KN. The limits on VE are used to represent the effects of feedback limiter operation, as described in Annex F.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.8 IEEE Type AC4A Excitation System VRef

VT

1 1+sTR 



VR Max - K C I FD

VI Max



1+sTC  1+sTB 

  VPSS VI Min

HV Gate

VUEL

VR

KA 1+sTA 

E FD

VR Min

Figure 165. IEEE Type AC4A model block diagram.

Parameter TA TB TC TR KA KC VI Max VI Min VR Max VR Min

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Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu

AVR time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Transducer time constant AVR gain Loading effect gain for exciter limit AVR input limit max AVR input limit min AVR / Exciter limit max AVR / Exciter limit min

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Description Use this model to simulate excitation systems with: 

AC Exciters with controlled rectifier exciter.

In this model: 

The first block models the transducer time constant.



The second block models the AVR lead / lag.



The third block simulates the overall gain and time constant.



The first limit is an input limit, and is a wind-up limit.



The second limit is an non-windup limit.



No AVR feedback circuit is employed.

Notes: 

The IEEE Type AC4A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.

From IEEE Standard 421.5, Section 6.4: * The Type AC4A alternator-supplied controlled-rectifier excitation system illustrated in Figure 6-4 is quite different from the other type ac systems. This high initial response excitation system utilizes a full Thyristor bridge in the exciter output circuit.

Figure 6-4—Type AC4A alternator-supplied controlled-rectifier exciter

* The voltage regulator controls the firing of the thyristor bridges. The exciter alternator uses an independent voltage regulator to control its output voltage to a constant value. These effects are not modeled; however, transient loading effects on the exciter alternator are included. * From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved. © EasyPower LLC 2016

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* Exciter loading is confined to the region described as mode 1 in Annex D, and loading effects can be accounted for by using the exciter load current and commutating reactance to modify excitation limits. The excitation system stabilization is frequently accomplished in thyristor systems by a series lag-lead network rather than through rate feedback. The time constants, TB and TC, allow simulation of this control function. The overall equivalent gain and the time constant associated with the regulator and/or firing of the thyristors are simulated by KA and TA, respectively.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.9 IEEE Type AC5A Excitation System VRef

VR Max

VT







VR

KA 1+sTA 

 

1 sTE



-



VFE

VR Min

VPSS





E FD

0



KE

 VF

sK F 1+sTF3  1+sTF1 1+sTF2 

VX

VX = E FD SE  E FD 

Figure 166. IEEE Type AC5A model block diagram.

Parameter TA TE TF1 TF2 TF3 KA KE KF VR Max VR Min E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu

AVR time constant Exciter time constant AVR feedback block first lag time constant AVR feedback block second lag time constant AVR feedback block lead time constant AVR gain Exciter KE AVR feedback gain AVR limit max AVR limit min EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

Brushless AC Exciters.

In this model: 

The first and feedback blocks model the AVR.



The only limit is a non-windup limit.



Everything to the right of VR models the exciter.

Notes: 

The IEEE Type AC4A excitation system model corresponds to IEEE recommendations of 2005.

From IEEE Standard 421.5, Section 6.5: * The model shown in Figure 6-5, designated as Type AC5A, is a simplified model for brushless excitation systems. The regulator is supplied from a source, such as a permanent magnet generator, which is not affected by system disturbances.

Figure 6-5—Type AC5A—Simplified rotating rectifier excitation system representation

* Unlike other ac models, this model uses loaded rather than open circuit exciter saturation data in the same way as it is used for the dc models (Annex C). Because the model has been widely implemented by the industry, it is sometimes used to represent other types of systems when either detailed data for them are not available or simplified models are required.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved. © EasyPower LLC 2016

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4.2.10 IEEE Type AC6A Excitation System VRef

VUEL

VA Max

VT

1 1+sTR 



 

 

1+sTK  KA 1+sTA 

VT VR Max 



 

1 sTE

 

VT VR Min

VA Min

VPSS

I N < 0.433

FEX = 1- 0.577I N

0.433< I N < 0.750

FEX = 0.75- I

2 N

0.750< I N < 1.000

FEX = 1.732 1- I N 

I N > 1.000

1+sTC  1+sTB 

VE

π

E FD

0

VE SE  VE 

VH Max

1+sTJ  1+sTH 

FEX = 0



KH



 0

VFE LIM

FEX =f  I N 



 



KE

IN =

K C I FD VE

KD

I FD

Figure 167. IEEE Type AC6A model block diagram.

Parameter TR TK TA TB TC TE TJ TH KA KC KD KE KH VFELim VHMax VAMax VAMin VRMax VRMin E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Sensor time constant First Lead/Lag block lead time constant First Lead/Lag block lag time constant Second Lead/Lag block lag time constant Second Lead/Lag block lead time constant Exciter time constant Feedback block lead time constant Feedback block lag time constant First block gain Exciter KC – Field current feedback Exciter KD – Field current feedback Exciter KE Feedback gain VFE limit value Feedback max AVR control max AVR control min Regulator max - Amplifier Regulator min - Amplifier Saturation voltage point 1 Saturation voltage point 2 Saturation at E1 Saturation at E2

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Description Use this model to simulate excitation systems with: 

Brushless, AC Exciters.

In this model: 

The first block models the transducer time constant.



The second and third blocks model the AVR.



The fourth block (TE) models the exciter time constant.



The VTVRMax limit block models an AVR amplifier output powered by the terminals of the generator. This limiter is a windup limiter.



The saturation component simulates saturation in the AC exciter.



The limit on the third block is non-windup.



The feedback block employs a lead-lag element.



The zero limit on the 1/sTe block is non-windup.



The VHMax limit is a windup limiter.

Notes: 

The IEEE Type AC6A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.



This model includes field current feedback effects, as IFD is fed back into the model from the generator.



See “Brushless Modeling Detail” for the AC1A model for discussion on all model components after VR.

From IEEE Standard 421.5, Section 6.6: * The model shown in Figure 6-6 is used to represent field-controlled alternatorrectifier excitation systems with system-supplied electronic voltage regulators. The maximum output of the regulator, VR, is a function of terminal voltage, VT. The field current limiter included in the original model AC6A remains in the 2005 update of this document, although over-excitation and under-excitation limiters are now described more fully in Clause 9 and Clause 10 respectively. * From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.11 IEEE Type AC7B Excitation System VR Max VRef VOEL

 VT    

VPSS

 K IR

K DR

1 s

  

VR 



K PA 



K IA s

VA

VA Min

s

1+sTDR 

 



VFE Max - K D I FD

K P VT

VA Max

K PR

π

K E + SE (VE ) 

1 sTE

 

VE

π

E FD

VE Min

-K L VFE K F2

SE  VE 

FEX = f  I N 

VR Min

VFE

sK F 1+sTF  I N < 0.433

FEX = 1 - 0.577I N

0.433 < I N < 0.750

FEX = 0.75 - I 2N

0.750 < I N < 1.000

FEX = 1.732 1 - I N 

I N > 1.000



  

KE

IN =

K C I FD VE

KD

I FD

K F1

FEX = 0

Figure 168. IEEE Type AC7B model block diagram.

Parameter TDR TE TF KC KD KE KF KF1 KF2 KL KP KPA KIA KPR KIR KDR VFE Max VE Min VA Max VA Min VR Max VR Min E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description AVR Differential control time constant Exciter time constant AVR feedback time constant Field current feedback gain Field current feedback gain Exciter KE AVR feedback gain Exciter feedback gain 1 Exciter feedback gain 2 Amplifier min limit Amplifier gain on terminal voltage Amplifier proportional gain Amplifier integral gain AVR proportional control gain AVR integral control gain AVR differential control gain Exciter max Exciter min Amplifier max Amplifier min AVR max AVR min Saturation voltage point 1 Saturation voltage point 2 Saturation at E1 Saturation at E2

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Description Use this model to simulate excitation systems with: 

Brushless, AC Exciters with PID control.

In this model: 

The AVR is modeled by the large PID block and the rate feedback block with KF.



The block with KPA models the amplifier.



Everything to the right of VFE models the rotating alternator/rectifier.



The block with TE models the alternator time constant.



The saturation component simulates saturation in the alternator.



All limits on block are non-windup limits.



The min limit with KL is a windup limit.

Notes: 

The IEEE Type AC7A excitation system model corresponds to IEEE recommendations of 2005.



The OEL (over excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.



This model includes field current feedback effects, as IFD is fed back into the model from the generator.



See “Brushless Modeling Detail” for the AC1A model for discussion on all model components after VR.

From IEEE Standard 421.5, Section 6.7: * These excitation systems consist of an AC alternator with either stationary or rotating rectifiers to produce the dc field requirements. Upgrades to earlier ac excitation systems, which replace only the controls but retain the ac alternator and diode rectifier bridge, have resulted in this new model, as shown in Figure 6-7. Some of the features of this excitation system include a high bandwidth inner loop regulating generator field voltage or exciter current (KF2, KF1), a fast exciter current limit, VFEMAX, to protect the field of the ac alternator, and the PID generator voltage regulator (AVR). An alternative rate feedback loop (KF, TF) is provided for stabilization if the AVR does not include a derivative term. If a PSS control is supplied, the Type PSS2B or PSS3B models are appropriate. * From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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Figure 6-7—Type AC7B—Alternator-rectifier excitation system

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.12 IEEE Type AC8B Excitation System

K PR

VRef

VE Max - K D I FD

VR Max

VT

1 1+sTR 





 

K IR

1 s

K DR

s 1+sTDR 



KA

  

1+sTA 

K E + SE (VE ) 

1 sTE

 

VR Min

VPSS

I N  0.433

SE  VE 

FEX  0.75  I

0.750  I N  1.000

FEX  1.732 1  I N 

2 N

E FD

FEX = f  I N 



FEX  1  0.577 I N

FEX  0



VE Min

VFE

0.433  I N  0.750 I N  1.000

VE

  

KE

IN =

K C I FD VE

KD

I FD

Figure 169. IEEE Type AC8B model block diagram.

Parameter TR TA TE TDR KPR KIR KDR KA KC KD KE VR Max VR Min VE Max VE Min E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Transducer time constant Main AVR time constant Exciter time constant Differential time constant for PID control Proportional gain for PID control Integral gain for PID control Differential gain for PID control Main AVR time constant Exciter KC – Field current feedback Exciter KD – Field current feedback Exciter KE Regulator max - Amplifier Regulator min - Amplifier Exciter max Exciter min Saturation voltage point 1 Saturation voltage point 2 Saturation at E1 Saturation at E2

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Description Use this model to simulate excitation systems with: 

Brushless, AC Exciters and PID AVR control.

In this model: 

The first block models the transducer time constant.



The second group of blocks (PID group) and the third block (with KA) models the AVR.



The fourth block (TE) models the exciter time constant.



The limit on the fourth block models the exciter limit and includes field current feedback effects. This limiter is a non-windup limiter.



The saturation component simulates saturation in the AC exciter.



The limit on the third block is non-windup.

Notes: 

The IEEE Type AC8B excitation system model corresponds to IEEE recommendations of 2005.



This model includes field current feedback effects, as IFD is fed back into the model from the generator.



See “Brushless Modeling Detail” for the AC1A model for discussion on all model components after VR.

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From IEEE Standard 421.5, Section 6.8: * The block diagram of the AC8B model is shown in Figure 6-8. The AVR in this model consists of PID control, with separate constants for the proportional (KPR), integral (KIR), and derivative (KDR) gains. The values for the constants are chosen for best performance for each particular generator excitation system. The representation of the brushless exciter (TE, KE, SE, KC, KD) is similar to the model Type AC2A. Sample data for this model is shown in Annex H. The Type AC8B model can be used to represent static voltage regulators applied to brushless excitation systems. Digitally based voltage regulators feeding dc rotating main exciters can be represented with the AC Type AC8B model with the parameters KC and KD set to 0. For thyristor power stages fed from the generator terminals, the limits VRMAX and VRMIN should be a function of terminal voltage: VT × VRMAX and VT × VRMIN. This may be accommodated in simulation programs using an additional logic state to identify bus or PMG fed systems from terminal fed systems. The limits on VE are used to represent the effects of feedback limiter operation, as described in Annex F.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.13 IEEE Type DC1A Excitation System VUEL1

VUEL 0

VRef

Alternate

VR Max

UEL

VT



 

VPSS



 

1+sTC  1+sTB 

KA 1+sTA 

HV Gate

VR Min

VF

VR 

1 sTE



-



VFE



E FD

0



KE

 VX

VX = E FD SE  E FD 

sK F

1+sTF  Figure 170. IEEE Type DC1A model block diagram.

Parameter TA TB TC TE TF KA KE KF VR Max VR Min E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu

Description AVR time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Exciter time constant AVR feedback time constant AVR and Exciter gain Exciter KE AVR feedback gain AVR limit max AVR limit min EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

DC Exciters.

In this model: 

The blocks up to VR and the feedback block model the AVR.



All limits are non-windup.



Everything to the right of VR models the exciter.

Notes: 

The IEEE Type DC1A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.

From IEEE Standard 421.5, Section 5.1: * This model, described by the block diagram of Figure 5-1, is used to represent fieldcontrolled dc commutator exciters with continuously acting voltage regulators (especially the direct-acting rheostatic, rotating amplifier, and magnetic amplifier types).5 Because this model has been widely implemented by the industry, it is sometimes used to represent other types of systems when detailed data for them are not available or when a simplified model is required. * The principal input to this model is the output, VC, from the terminal voltage transducer and load compensator model previously described. At the summing junction, terminal voltage transducer output, VC, is subtracted from the set point reference, VREF. The stabilizing feedback, VF, is subtracted and the power system stabilizing signal, VS, is added to produce an error voltage. In the steady state, these last two signals are zero, leaving only the terminal voltage error signal. The resulting signal is amplified in the regulator. The major time constant, TA, and gain, KA, associated with the voltage regulator are shown incorporating nonwindup limits typical of saturation or amplifier power supply limitations. A discussion of windup and non-windup limits is provided in Annex E. These voltage regulators utilize power sources that are essentially unaffected by brief transients on the synchronous machine or auxiliary buses. The time constants, TB and TC, may be used to model equivalent time constants inherent in the voltage regulator, but these time constants are frequently small enough to be neglected and provision should be made for zero input data. * From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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* The voltage regulator output, VR, is used to control the exciter, which may be either separately excited or self-excited as discussed in the IEEE Committee Report [B20]. When a self-excited shunt field is used, the value of KE reflects the setting of the shunt field rheostat. In some instances, the resulting value of KE can be negative and allowance should be made for this. Most of these exciters utilize self-excited shunt fields with the voltage regulator operating in a mode commonly termed buck-boost. The majority of station operators manually track the voltage regulator by periodically trimming the rheostat set point so as to zero the voltage regulator output. This may be simulated by selecting the value of KE so that initial conditions are satisfied with VR = 0, as described in the IEEE Committee Report [B20]. In some programs, if KE is entered as zero, it is automatically calculated by the program for self-excitation. * If a nonzero value for KE is provided, the program should not recalculate KE, as a fixed rheostat setting is implied. For such systems, the rheostat is frequently fixed at a value that would produce self-excitation near rated conditions. Systems with fixed field rheostat settings are in widespread use on units that are remotely controlled. A value for KE = 1 is used to represent a separately excited exciter. * The term SE[EFD] is a nonlinear function with values defined at two or more chosen values of EFD, as described in Annex C. The output of this saturation block, VX, is the product of the input, EFD, and the value of the nonlinear function SE[EFD] at this exciter voltage. A signal derived from field voltage is normally used to provide excitation system stabilization, VF, via the rate feedback with gain, KF, and time constant, TF.

Figure 5-1—Type DC1A—DC commutator exciter

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.14 IEEE Type DC2A Excitation System VUEL1

VUEL 0

VRef

Alternate

VT VR Max

UEL

VT



 

VPSS



 

1+sTC  1+sTB 

KA 1+sTA 

HV Gate VT VR Min

VF

VR 

1 sTE



-



VFE



E FD

0



KE

 VX

VX = E FD SE  E FD 

sK F

1+sTF  Figure 171. IEEE Type DC2A model block diagram.

Parameter TA TB TC TE TF KA KE KF VR Max VR Min E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu

Description AVR time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Exciter time constant AVR feedback time constant AVR and Exciter gain Exciter KE AVR feedback gain AVR limit max AVR limit min EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

DC Exciters.

In this model: 

The blocks up to VR and the feedback block model the AVR.



All limits are non-windup.



Everything to the right of VR models the exciter.



The output limits of the AVR amplifier have an additional terminal voltage effect.

Notes: 

The IEEE Type DC2A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.

From IEEE Standard 421.5, Section 5.2: * The model shown in Figure 5-2 is used to represent field-controlled dc commutator exciters with continuously acting voltage regulators having supplies obtained from the generator or auxiliary bus. It differs from the Type DC1A model only in the voltage regulator output limits, which are now proportional to terminal voltage VT. It is representative of solid-state replacements for various forms of older mechanical and rotating amplifier regulating equipment connected to dc commutator exciters.

Figure 5-2Type DC2A—DC commutator exciter with bus-fed regulator

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.15 IEEE Type DC3A Excitation System

VRef  VT





VR Max

KV VErr

-

-K V

VRMax - VRMin s K V TRH

VRH

VR Min

if  VErr > K V



then VR = VRMax

if  VErr < K V



then VR = VRH

if  VErr < -K V



then VR = VRMin

VR 

1 sT E

 

VFE

E FD

0





KE

 VX

VX = E FD SE  E FD 

Figure 172. IEEE Type DC3A model block diagram.

Parameter TE TRH KE KV VR Max VR Min E1 E2 S(E1) S(E2)

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Units Seconds Seconds pu pu pu pu pu pu pu pu

Description Exciter time constant AVR time constant Exciter KE Input limit AVR limit max AVR limit min EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

Older DC Exciters.

In this model: 

The KV input limit is a windup limit.



The limit on the first block is a non-windup limit.



Everything to the right of VR models the exciter.

Notes: 

The IEEE Type DC3A excitation system model corresponds to IEEE recommendations of 2005.

From IEEE Standard 421.5, Section 5.3: * The systems discussed in the previous sub-clauses are representative of the first generation of high gain, fast-acting excitation sources. The Type DC3A model is used to represent older systems, in particular those dc commutator exciters with non-continuously acting regulators that were commonly used before the development of the continuously acting varieties. * These systems respond at basically two different rates, depending upon the magnitude of voltage error. For small errors, adjustment is made periodically with a signal to a motoroperated rheostat. Larger errors cause resistors to be quickly shorted or inserted and a strong forcing signal applied to the exciter. Continuous motion of the motor-operated rheostat occurs for these larger error signals, even though it is bypassed by contactor action. Figure 53 illustrates this control action. The exciter representation is similar to that of systems described previously. Note that no excitation system stabilizer is represented. * Depending upon the magnitude of voltage error, VREF – VC, different regulator modes come into play. If the voltage error is larger than the fast raise/lower contact setting, KV (typically 5%), VRMAX or VRMIN is applied to the exciter, depending upon the sign of the voltage error. For an absolute value of voltage error less than KV, the exciter input equals the rheostat setting VRH. The rheostat setting is notched up or down, depending upon the sign of the error. The travel time representing continuous motion of the rheostat drive motor is TRH. A nonwindup limit (see Annex E) is shown around this block, to represent the fact that when the rheostat reaches either limit, it is ready to come off the limit immediately when the input signal reverses. * From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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* Additional refinements, such as dead band for small errors, have been considered, but were not deemed justified for the relatively few older machines using these voltage regulators.

Figure 5-3—Type DC3A—DC commutator exciter with non-continuously acting regulators

* The model assumes that the quick raise/lower limits are the same as the rheostat limits. It does not account for time constant changes in the exciter field as a result of changes in field resistance (as a result of rheostat movement and operation of quick action contacts).

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.16 IEEE Type DC4B Excitation System Alternate OEL Inputs

VOEL 0 VUEL 0

VOEL1

Alternate UEL Inputs

VUEL1

VRMax KA

VT







VPSS

VT VR Max

VT

VRef 



KP



KI s





HV Gate

LV Gate



VA

KA

1+sTA  VT VR Min

VR 



VFE

sK D 1+sTD

VF

1 sT E





E FD

0



KE

 VX

VRMin KA

VX = E FD SE  E FD 

sK F

1+sTF  Figure 173. IEEE Type DC4B model block diagram.

Parameter TA TE TD TF KA KD KE KP KI VR Max VR Min E1 E2 S(E1) S(E2)

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Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu

Description Main system time constant Exciter time constant AVR PID differential time constant AVR rate feedback time constant Main system gain AVR PID differential gain Exciter KE AVR PID proportional gain AVR PID integral gain AVR limit max AVR limit min EFD voltage 1 for saturation EFD voltage 2 for saturation Exciter saturation at E1 Exciter saturation at E2

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Description Use this model to simulate excitation systems with: 

Older DC Exciters.

In this model: 

The KV input limit is a windup limit.



The limit on the first block is a non-windup limit.



Everything to the right of VR models the exciter.

Notes: 

The IEEE Type DC4B excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.

From IEEE Standard 421.5, Section 5.4: * These excitation systems utilize a field-controlled dc commutator exciter with a continuously acting voltage regulator having supplies obtained from the generator or auxiliary bus. The replacement of the controls only as an upgrade (retaining the dc commutator exciter) has resulted in a new model. The block diagram of this model is shown in Figure 5-4. This excitation system typically includes a proportional, integral, and differential (PID) generator voltage regulator (AVR). An alternative rate feedback loop (KF, TF) for stabilization is also shown in the model if the AVR does not include a derivative term. If a PSS control is supplied, the appropriate model is the Type PSS2B model.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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Figure 5-4—Type DC4B—DC commutator exciter with PID style regulator

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.17 IEEE Type ST1A Excitation System Alternative PSS Inputs

VPSS 0

Alternative UEL Inputs

VUEL 0

VT

VUEL 2

VOEL

VUEL1

VRef

1 1+sTR 

VPSS1













VI

VT VR Max - K C I FD

VA Max

VI Max HV Gate

1+sTC  1+sTC1  1+sTB  1+sTB1 

VI Min

KA 1+sTA 

VA 



LV Gate

HV Gate

 

VT VR Min

I LR

VA Min K LR

 

E FD



I FD

0

VF

sK F 1+sTF 

Figure 174. IEEE Type ST1A model block diagram.

Parameter TA TB TB1 TC TC1 TF TR KA KC KF KLR ILR VA Max VA Min VR Max VR Min VI Max VI Min

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Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu

Description AVR main time constant AVR Lead/Lag block lag time constant 1 AVR Lead/Lag block lag time constant 2 AVR Lead/Lag block lead time constant 1 AVR Lead/Lag block lead time constant 2 AVR rate feedback time constant Input transducer time constant AVR main gain Field loading gain AVR rate feedback gain Field current feedback gain Field current feedback limit start setting AVR limit max AVR limit min Exciter limit max Exciter limit min AVR input limit max AVR input limit min

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Description Use this model to simulate excitation systems with: 

Static Exciters.

In this model: 

The AVR (KA block) limit is a non-windup limit.



All other limits are windup limits.

Notes: 

The IEEE Type ST1A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.

From IEEE Standard 421.5, Section 7.1: * The computer model of the Type ST1A potential-source controlled-rectifier excitation system shown in Figure 7-1 is intended to represent systems in which excitation power is supplied through a transformer from the generator terminals (or the unit’s auxiliary bus) and is regulated by a controlled rectifier. The maximum exciter voltage available from such systems is directly related to the generator terminal voltage (except as noted, as follows). * In this type of system, the inherent exciter time constants are very small, and exciter stabilization may not be required. On the other hand, it may be desirable to reduce the transient gain of these systems for other reasons. The model shown is sufficiently versatile to represent transient gain reduction implemented either in the forward path via time constants, TB and TC (in which case KF would normally be set to zero), or in the feedback path by suitable choice of rate feedback parameters, KF and TF. Voltage regulator gain and any inherent excitation system time constant are represented by KA and TA, respectively. The time constants, TC1 and TB1, allow for the possibility of representing transient gain increase, in which case TC1 would be greater than TB1.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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Figure 7-1—Type ST1A—Potential-source, controlled-rectifier exciter

* The way in which the firing angle for the bridge rectifiers is derived affects the inputoutput relationship, which is assumed to be linear in the model by choice of a simple gain, KA. For many systems a truly linear relationship applies. In a few systems, the bridge relationship is not linearized, leaving this nominally linear gain a sinusoidal function, the amplitude of which may be dependent on the supply voltage. As the gain is normally set very high, a linearization of this characteristic is normally satisfactory for modeling purposes. The representation of the ceiling is the same whether the characteristic is linear or sinusoidal. * In many cases, the internal limits on VI can be neglected. The field voltage limits that are functions of both terminal voltage and synchronous machine field current should be modeled. The representation of the field voltage positive limit as a linear function of synchronous machine field current is possible because operation of the rectifier bridge in such systems is confined to the mode 1 region as described in Annex D. The negative limit would have a similar current-dependent characteristic, but the sign of the term could be either positive or negative depending upon whether a constant firing angle or constant extinction angle is chosen for the limit. As field current is normally low under this condition, the term is not included in the model. As a result of the very high forcing capability of these systems, a field current limiter is sometimes employed to protect the generator rotor and exciter. The limit start setting is defined by ILR and the gain is represented by KLR. To permit this limit to be ignored, provision should be made to allow KLR to be set to zero. This limiter is described here to maintain consistency with the original ST1A model. However, this document describes over-excitation and under-excitation limiters more fully in Clause 9 and Clause 10, respectively. * While for the majority of these excitation systems, a fully controlled bridge is employed, the model is also applicable to systems in which only half of the bridge is controlled, in which case the negative field voltage limit is set to zero (VRMIN = 0).

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.18 IEEE Type ST2 Excitation System sK F

1+sTF  KE

VRef

VT

1 1+sTR 







VF



VUEL



IT

E FD Max 

VE = K P V T + jK I I T



 VB



VE

π 

I FD

K I I N = C FD VE

IN

FEX = f  I N 



1 sT E





VR Min

VPSS VT

KA 1+sTA 

HV Gate





VR Max

E FD

0

I N < 0.433

FEX = 1- 0.577I N

0.433< I N < 0.750

FEX = 0.75- I 2N

0.750< I N < 1.000

FEX = 1.732 1- I N 

I N > 1.000

FEX = 0

Figure 175. IEEE Type ST2 model block diagram.

Parameter TA TE TF TR KA KC KE KF KI KP VR Max VR Min EFD Max

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Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu

Description AVR main time constant Exciter time constant AVR rate feedback time constant Input transducer time constant AVR main gain Exciter KC – Field current feedback Exciter KE AVR rate feedback gain Load compensation gain for terminal current Load compensation gain for terminal voltage AVR limit max AVR limit min Exciter output limit max

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Description Use this model to simulate excitation systems with: 

Static Exciters with a compound source.

In this model: 

All limits are non-windup limit.

Notes: 

This model has been superseded by the IEEE ST2A, and has been kept in the model library for backwards compatibility. The only difference between the two models is the circle just to the right of VR. The ST2 utilizes a Summing Function while the ST2A utilizes a Multiplication Function.



See the IEEE ST2A model documentation for more information regarding the application of this excitation system.



The UEL (under excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.

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4.2.19 IEEE Type ST2A Excitation System Alternate UEL Inputs VUEL 0

VUEL1 sK F

1+sTF  KE

VRef

VT

1 1+sTR 







VF



VR Max





IT



VE = K P V T + jK I I T



π VB



VE

π 

I FD

K I I N = C FD VE

IN

FEX = f  I N 



1 sT E





VR Min

VPSS VT

KA 1+sTA 

HV Gate



E FD Max E FD

0

I N < 0.433

FEX = 1- 0.577I N

0.433< I N < 0.750

FEX = 0.75- I 2N

0.750< I N < 1.000

FEX = 1.732 1- I N 

I N > 1.000

FEX = 0

Figure 176. IEEE Type ST2A model block diagram.

Parameter TA TE TF TR KA KC KE KF KI KP VR Max VR Min EFD Max

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Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu

Description AVR main time constant Exciter time constant AVR rate feedback time constant Input transducer time constant AVR main gain Exciter KC – Field current feedback Exciter KE AVR rate feedback gain Load compensation gain for terminal current Load compensation gain for terminal voltage AVR limit max AVR limit min Exciter output limit max

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Description Use this model to simulate excitation systems with: 

Static Exciters with a compound source.

In this model: 

All limits are non-windup limit.

Notes: 

The IEEE Type ST2A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.

From IEEE Standard 421.5, Section 7.2: * Some static systems utilize both current and voltage sources (generator terminal quantities) to comprise the power source. These compound-source rectifier excitation systems are designated Type ST2A and are modeled as shown in Figure 7-2. It is necessary to form a model of the exciter power source utilizing a phasor combination of terminal voltage, VT, and terminal current, IT. Rectifier loading and commutation effects are accounted for as described in Annex D. EFDMAX represents the limit on the exciter voltage due to saturation of the magnetic components. The regulator controls the exciter output through controlled saturation of the power transformer components. TE is a time constant associated with the inductance of the control windings.

Figure 7-2—Type ST2A—Compound-source rectifier exciter

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.20 IEEE Type ST3A Excitation System VG Max KG VRef

VT

1 1+sTR 

VUEL

VI Max





VI



HV Gate



VPSS

VI Min

IT

FEX = 1- 0.577I N

0.433< I N < 0.750

FEX = 0.75- I

2 N

0.750< I N < 1.000

FEX = 1.732 1- I N 

VE = K P V T + j  K I + K P X L  IT



E FD Max



KM 1 + sTM



VR Min

I N < 0.433

I N > 1.000 VT

KA 1+sTA 

1+sTC 1+sTB

VM Max

VG

VR Max

VM

π

E FD

VM Min

FEX = 0

VB Max 

VE

VB

π 

K P = K P e jθP

I FD

K I I N = C FD VE

IN

FEX = f  I N 

Figure 177. IEEE Type ST3A model block diagram.

Parameter TA TB TC TM TR KA KC KG KI KM KP XL VB Max VG Max VM Max VM Min VI Max VI Min VR Max VR Min EFD Max

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description AVR main time constant AVR Lead/Lag block lag time constant AVR Lead/Lag block lead time constant Field voltage regulator time constant Input transducer time constant AVR main gain Exciter KC – Field current feedback Field voltage regulator feedback gain Load compensation gain for terminal current Field voltage regulator gain Load compensation gain for terminal voltage Load compensation reactance for terminal current Field current feedback and compensation limit max Field voltage regulator feedback limit max Field voltage regulator limit max Field voltage regulator limit min AVR input limit max AVR input limit min AVR limit max AVR limit min Exciter output limit max

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Description Use this model to simulate excitation systems with: 

Static Exciters.

In this model: 

The KA and KM block limits are non-windup limit.



All other limits are windup limits.

Notes: 

The IEEE Type ST3A excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) input is disabled. In a future revision, this will be connected to modeled limiters.

From IEEE Standard 421.5, Section 7.3: * Some static systems utilize a field voltage control loop to linearize the exciter control characteristic as shown in Figure 7-3. This also makes the output independent of supply source variations until supply limitations are reached. * These systems utilize a variety of controlled-rectifier designs: full thyristor complements or hybrid bridges in either series or shunt configurations. The power source may consist of only a potential source, either fed from the machine terminals or from internal windings. Some designs may have compound power sources utilizing both machine potential and current. These power sources are represented as phasor combinations of machine terminal current and voltage and are accommodated by suitable parameters in the model shown. The excitation system stabilizer for these systems is provided by a series lag-lead element in the voltage regulator, represented by the time constants TB and TC. The inner loop field voltage regulator is comprised of the gains KM and KG and the time constant TM. This loop has a wide bandwidth compared with the upper limit of 3 Hz for the models described in this recommended practice. The time constant TM may be increased for study purposes, eliminating the need for excessively short computing increments while still retaining the required accuracy at 3 Hz. Rectifier loading and commutation effects are accounted for as discussed in Annex D. The limit, VBMAX, is determined by the saturation level of power components.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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Figure 7-3—Type ST3A—Potential- or compound-source controlled-rectifier exciter with field voltage control loop

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.21 IEEE Type ST4B Excitation System KG VUEL

VRef

VT

1 1+sTR 



VM Max VOEL

VR Max

 



K PR +-



VPSS

K IR s

VR

IT





VR Min



K PM +-

K IM s

VM

LV Gate

π

E FD

VM Min

I N < 0.433

FEX = 1- 0.577I N

0.433< I N < 0.750

FEX = 0.75- I 2N

0.750< I N < 1.000

FEX = 1.732 1- I N 

I N > 1.000 VT



1 1+sT  A



FEX = 0

VB Max

VE

VE = K P V T +j K I +K P X L I T K P =K P e jθP

π

IN = I FD

K C I FD VE

IN

-

VB

FEX = f  I N 

Figure 178. IEEE Type ST4B model block diagram.

Parameter TA TR KC KG KI KIM KIR KP KPM KPR XL VB Max VM Max VM Min VR Max VR Min

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Units Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description AVR main time constant Input transducer time constant Exciter KC – Field current feedback Field voltage regulator feedback gain Load compensation gain for terminal current Field voltage regulator integral control gain AVR integral control gain Load compensation gain for terminal voltage Field voltage regulator proportional control gain AVR proportional control gain Load compensation reactance for terminal current Field current feedback and compensation limit max Field voltage regulator limit max Field voltage regulator limit min AVR limit max AVR limit min

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Description Use this model to simulate excitation systems with: 

Static Exciters.

In this model: 

The KPR and KPM block limits are non-windup limits.



VB Max limit is a windup limit.

Notes: 

The IEEE Type ST4B excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.

From IEEE Standard 421.5, Section 7.4: * This model is a variation of the Type ST3A model, with a proportional plus integral (PI) regulator block replacing the lag-lead regulator characteristic that was in the ST3A model. Both potential- and compound-source rectifier excitation systems are modeled as shown in Figure 7-4. The PI regulator blocks have non-windup limits that are represented as described in Annex A. The voltage regulator of this model is typically implemented digitally, so the model is identified with the suffix “B.” * The other features of the regulator are a low value gate for the OEL limit function, and the UEL and V/Hz control are summed into the input to the regulator. This means that on a unit with PSS control, the PSS will be active if the unit goes into UEL limit control, unlike some previous designs that had take-over type limiters. The description of rectifier regulation, FEX, may be found in Annex D. There is flexibility in the power component model to represent bus-fed exciters (KI and XL both equal to zero), compound static systems (XL = 0), and potential- and compound- source systems where XL is not zero. The appropriate PSS model to use with the ST4B excitation model is Type PSS2B.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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Figure 7-4—Type ST4B—Potential- or compound-source controlled-rectifier exciter

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.22 IEEE Type ST5B Excitation System  

 

X>0



X>0 VR Max



KR VOEL VUEL VT





HV Gate

LV Gate





VT VR Max VR Max

1+sTC1  1+sTC2  1+sTB1  1+sTB2 

 

VPSS

VRef

VR Min

VR Max

KR

KR

1+sTUC1  1+sTUC2  1+sTUB1  1+sTUB2  VR Min

VR Max

KR

KR

1+sTOC1  1+sTOC2  1+sTOB1  1+sTOB2 

KR VR Min

  VR 

1 1 + sT1

E FD

VT VR Min

KC

I FD

UEL Section

OEL Section

VR Min KR

Figure 179. IEEE Type ST5B model block diagram.

Parameter T1 TB1 TB2 TC1 TC2 TOB1 TOB2 TOC1 TOC2 TUB1 TUB2 TUC1 TUC2 KC KR VR Max VR Min

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Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu

Description Field voltage regulator time constant AVR Lead/Lag block lag time constant 1 AVR Lead/Lag block lag time constant 2 AVR Lead/Lag block lead time constant 1 AVR Lead/Lag block lead time constant 2 AVR OEL Lead/Lag block lag time constant 1 AVR OEL Lead/Lag block lag time constant 2 AVR OEL Lead/Lag block lead time constant 1 AVR OEL Lead/Lag block lead time constant 2 AVR UEL Lead/Lag block lag time constant 1 AVR UEL Lead/Lag block lag time constant 2 AVR UEL Lead/Lag block lead time constant 1 AVR UEL Lead/Lag block lead time constant 2 Field feedback gain Field voltage regulator gain Exciter limit max Exciter limit min

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Description Use this model to simulate excitation systems with: 

Static Exciters with automated UEL, OEL circuit block changing.

In this model: 

All limits are non-windup limits.

Notes: 

The IEEE Type ST5B excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.

From IEEE Standard 421.5, Section 7.5: * The Type ST5B excitation system shown in Figure 7-5 is a variation of the Type ST1A model, with alternative over-excitation and under-excitation inputs and additional limits. The corresponding stabilizer models that can be used with these models are the Type PSS2B, PSS3B, or PSS4B. Sample data for the model is provided in Annex H.

Figure 7-5—Type ST5B—Static potential-source excitation system

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.2.23 IEEE Type ST6B Excitation System I FD Alternate OEL Inputs

VOEL

I LR

VOEL



K CI





K LR

VT

1 1+sTR 





VA Max HV Gate

 



K FF







VPSS

K K PA + IA s

 VA



KM







if ( VB  0 )

if ( VB = 0 )

VR Min

VUEL

VB

VT

VR Max LV Gate



VR

π

E FD

VR Min

VA Min

VRef VG

KG

1+sTG 

Figure 180. IEEE Type ST6B model block diagram.

Parameter TG TR ILR KCI KFF KG KIA KLR KM KPA VA Max VA Min VR Max VR Min VB

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Units Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Field voltage regulator feedback time constant Input transducer time constant Exciter field current feedback constant Exciter field current feedback gain Field voltage regulator feed-forward gain Field voltage regulator feedback gain AVR integral control gain Exciter field current feedback gain Field voltage regulator gain AVR proportional control gain AVR limit max AVR limit min Field voltage regulator limit max Field voltage regulator limit min Field voltage regulator output scaling and switch

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Description Use this model to simulate excitation systems with: 

Static Exciters.

In this model: 

The KPA and KIA block limits are non-windup limits.



The VRMax and VRMin limits are windup limits.



If VB is zero, then the terminal voltage is used to scale the output.



If VB is non-zero, then the value of VB is used to scale the output.

Notes: 

The IEEE Type ST6B excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.

From IEEE Standard 421.5, Section 7.6: * The AVR shown in Figure 7-6 consists of a PI voltage regulator with an inner loop field voltage regulator and pre-control. The field voltage regulator implements a proportional control. The pre-control and the delay in the feedback circuit increase the dynamic response. If the field voltage regulator is not implemented, the corresponding parameters KFF and KG are set to 0. VR represents the limits of the power rectifier. The ceiling current IFD limitation is included in this model. The power for the rectifier, VB, may be supplied from the generator terminals or from an independent source. Inputs are provided for external models of the overexcitation limiter (VOEL), under-excitation limiter (VUEL), and PSS (VS). Sample data for the model is provided in Annex H.

Figure 7-6—Type ST6B—Static potential-source excitation system with field current limiter

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved. © EasyPower LLC 2016

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4.2.24 IEEE Type ST7B Excitation System VOEL 0

1+sTG 1+sTF

VT

Alternate OEL Inputs

Alternate OEL Input

VOEL1 VMax

VSCL

 

VRef



VDroop

 

LV Gate



HV Gate





VR Max VT   VRef FB

 HV Gate

K PA VH



VMin

Alternate UEL Inputs

VUEL 0

Alternate UEL Input VUEL 2

VOEL 2

VPSS

VR Min VT

VUEL1

 

1 + sTC 1 + sTB

LV Gate



LV Gate

VL



 

VR

HV Gate

E FD

VR Min VT



VR Max VT KL

K IA

1+sTIA 

KH

Figure 181. IEEE Type ST7B model block diagram.

Parameter TB TC TF TG TIA KIA KL KH KPA VMax VMin VR Max VR Min

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu

Description AVR lag time constant AVR lead time constant Terminal voltage input lag time constant Terminal voltage input lead time constant Field voltage feedback time constant Field voltage feedback gain Field voltage feedback gain Field voltage feedback gain AVR main control gain Auxiliary signal input limit max Auxiliary signal input limit min Regulator limit max Regulator limit min

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Description Use this model to simulate excitation systems with: 

Static Exciters.

In this model: 

All limits are windup limits.



The VRMax and VRMin limits are windup limits.

Notes: 

The IEEE Type ST6B excitation system model corresponds to IEEE recommendations of 2005.



The UEL (under excitation limiter) and OEL (over excitation limiter) inputs are disabled. In a future revision, these will be connected to modeled limiters.



The VSC and VDroop signal input are disabled.

From IEEE Standard 421.5, Section 7.7: * The model ST7B in Figure 7-7 is representative of static potential-source excitation systems. In this system, the AVR consists of a PI voltage regulator. A phase lead-lag filter in series allows introduction of a derivative function, typically used with brushless excitation systems. In that case, the regulator is of the PID type. In addition, the terminal voltage channel includes a phase lead-lag filter. The AVR includes the appropriate inputs on its reference for over-excitation limiter (OEL1), under-excitation limiter (UEL), stator current limiter (SCL), and current compensator (DROOP). All these limitations, when they work at voltage reference level, keep the PSS (VS signal from Type PSS1A, PSS2A, or PSS2B) in operation. However, the UEL limitation can also be transferred to the high value (HV) gate acting on the output signal. In addition, the output signal passes through a low value (LV) gate for a ceiling over-excitation limiter (OEL2). All control loops in the diagram, including limitation functions, are built to obtain a non-windup behavior of any integrator (see Annex E). Sample data for the model are provided in Annex H.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

© EasyPower LLC 2016

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Figure 7-7—Type ST7B—Static potential-source excitation system

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

© EasyPower LLC 2016

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4.2.25 Inverter Q Control - For WT4G and PV1G Models Only 1

Q Elec

1+sT 

Kqd

Ipqd

VErmx

VReg

1  1+sTr   VRef VErmn

Q Max

K iv s





1 fN

 

K pv

1+sTv 

Q wv

IQmx  I FD 

1 1+sTC 

Varflg

  QCmd

1

If  VReg < VFrz  Lock States

0

PFA Ref

 K Q1 s

Q Ref

tan

Q Min

IQmx

VMax

Q Max QGen

Q Min

VMin







K V1 s

IQcmd

 E FD 

Vterm -IQmx

0

1

PElec

1+sTP 



1

IQmx  I FD 

Pfaflg

Figure 182. Inverter Q Control model block diagram.

Parameter TC TIpqd Tp Tr Tv fN Kiv Kpv Kqd KQI KVI VErmx VErmn VMax VMin VFrz QMax QMin Varflg Pfaflg

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu 1/0 1/0

Description Communication delay and filtering in control Reactive power droop controller time constant Power measurement lag time constant Voltage measurement lag time constant Proportional voltage controller time constant Wind park unit commitment Voltage regulator integral controller gain Voltage regulator proportional controller gain Reactive power droop controller gain Reactive power integral controller gain Voltage integral controller gain Voltage error limit max Voltage error limit min Voltage output limit max Voltage output limit min Voltage regulator freezing voltage Reactive power limit max Reactive power limit min Var control mode Power factor control mode

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Description Use this model to simulate: 

The inverter control for models PV1G and WT4G.

In this model: 

Varflg and Pfaflg are used to set the control mode of the Q Control model. This table shows settings for the three main control modes: Control Mode Voltage Control (normal operation) Constant Q Control Power Factor Control

Varflg 1 0 0

Pfaflg 0 0 1



fN is used to present wind farms with a reduced number of wind generators on line. For PV systems, fN is set to 1.



IQmx is fed back from the WT4G and PV1G models via the field current variable IFD.



IQcmd is sent to the WT4G and PV1G models via the field voltage variable EFD.

Notes: From [2] Section 2.2,2: The steady-state and dynamic characteristics of Type 3 and Type 4 WTGs are dominated by the power converter. From [3] Section 2.1: The fundamental frequency electrical dynamic performance of a solar plant is completely dominated by the converter. The control of active and reactive power is handled by fast, high bandwidth regulators within the convertor controls. From [5] Section 2.0: For the Type 4 WTG, the power converter acts as a buffer between the grid and the electric generator, thus, any transients occurring in the grid are not translated to the electric generator. Under normal or fault transients, the power converter can be fully controlled. References: 1. Western Electricity Coordinating Council Renewable Energy Modeling Task Force Progress Report to MVWG on PV System Modeling July 8, 2010. 2. Western Electricity Coordinating Council Modeling and Validation Work Group, WECC Wind Power Plant Dynamic Modeling Guide (DRAFT) Prepared by WECC Renewable Energy Modeling Task Force, August 2010.

© EasyPower LLC 2016

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3. K. Clark, N. Miller, R. Walling, “Modeling of GE Solar Photovoltaic Plants for Grid Studies”, April 2010. Copyright©2009 GE Energy. All rights reserved. 4. K. Clark, N. Miller, R. Walling, “Modeling of GE Wind Turbine-Generator for Grid Studies”, April 2010. 5. FINAL PROJECT REPORT WECC WIND GENERATOR DEVELOPMENT Prepared for CIEE By: National Renewable Energy Laboratory. March, 2010.

© EasyPower LLC 2016

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4.2.26 Simple Excitation System

VRef

VT





 

EMax

1+ sTA  1+ sTB 

K 1+sTE 



E FD

EMin

VPSS

Figure 183. Simple Exciter model block diagram.

Parameter TA TB TE K EMin EMax

© EasyPower LLC 2016

Units Seconds Seconds Seconds pu pu pu

Description AVR Lead Time Constant AVR Lag Time Constant Exciter Time Constant Exciter Gain Exciter Min Limit Exciter Max Limit

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Description Use this model to simulate excitation systems that need: 

A generic excitation system response.

In this model: 

The lead-lag block is meant to simulate the AVR.



The second block is meant to simulate a simplistic rotating or simple static exciter.



The limit on the second block is non-windup.

© EasyPower LLC 2016

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4.2.27 STAMFORD 1 Excitation System VRef

AVR Output Windup Limit

Transducer Time Constant

VT

AVR Gain and Time Constant

 1   1+sTR   

E A1 1 sT E

 

VFE

E A2 Stabilizing (Damping) Section

VF

E C1 VR 

KA

1+sTA 

VPSS

Exciter Output Windup Limit

KF 1+sTF2 

sTF1 1+sTF1 

Automatic Voltage Regulator (AVR)



0



E FD

E C2 KE

 VX

VX = E FD SE  E FD 

Exciter with Saturation

Figure 184. STAMFORD 1 AVR, and exciter model block diagram.

Parameter KA KF TR TA TF1 TF2 EA1 EA2 KE TE EC1 EC2 E1 E2 SE1 SE2

© EasyPower LLC 2016

Units pu pu Seconds Seconds Seconds Seconds pu pu pu Seconds pu pu pu pu pu pu

Description AVR Forward Gain AVR Feedback Gain Transducer Time Constant AVR Time Constant Stabilizing Section 1st Time Constant Stabilizing Section 2nd Time Constant AVR output Windup Max Limit AVR output Windup Min Limit Exciter Gain Exciter Time Constant Exciter output Windup Max Limit Exciter output Windup Min Limit Exciter Voltage for SE1 Exciter Voltage for SE2 Exciter Saturation at E1 Exciter Saturation at E2

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Description Use this model to simulate excitation systems with: 

Stamford supplied excitation system.

In this model: 

Both limits are windup limits.



The saturation block is meant to simulate saturation in a rotating exciter.

© EasyPower LLC 2016

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4.3 Governor Models In the previous section on generators, it was noted that mechanical power (PMech) was an input to both the round rotor and salient pole models. Also, during initialization, PMech was determined after properly initializing the model. The value of PMech is controlled and supplied from the governor system. EasyPower DS includes 15 governor system models.                

Caterpillar Diesel 1 Cummins Diesel 1 Cummins Gas Engine 1 Gas Turbine Gas Turbine 2 Gas Turbine WD (Woodward) Hydro IEEE Hydro 2 IEEE Hydro 3 IEEE Steam PWFT8 (Pratt & Whitney) Split Shaft Gas Turbine Steam Turbine WECC Gas Turbine Woodward Diesel Woodward Steam PID 1

Similar to the excitation system, the governor system is actually composed of several components. These components are typically made to model but not limited to: 

The prime mover. This is the turbine, engine, etc., that rotates the shaft of the generator.



The governor controls. These are created specifically with control blocks to supply a tunable control system for controlling the speed of the generator.



Valve control time constants. In cases where time is needed to open or close a valve (motor or hydraulic operation, etc.), this must be modeled.



Firing delay. In a diesel engine, the firing delay is modeled as a pure e-st delay function. This translates into a time step oriented delay line.



Load limits. In gas turbines, input air temperature affects the maximum power output of the unit.

© EasyPower LLC 2016

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4.3.1 Caterpillar Diesel 1 Governor System  





NE PI Control

1.0

VMax

Δω (pu)



Rated RPM

KI s

   TL Min

VMin

Speed Error Limit TL Max =

TMax  Rated Torque  Rated RPM  K A K C K G 1000

TL Min =

Rated Torque 1+ 

Actuator (Injector)

TL Max





Torque Limit

KP

K G 1000 NE

KA 1 + sTA

Duration vs. Fuel Conversion

TMin  Rated Torque  Rated RPM  K A K C K G 1000



K C e-sT Engine

Rated Torque =



PMech

Torque in N-m

1000  Rated MVA  60000 Nm 2π  Rated RPM 

Figure 185. Caterpillar Diesel 1 governor model block diagram.

Parameter T TA KA KC KG KI KP VMax VMin TMax TMin Rated RPM Rated MVA

© EasyPower LLC 2016

Units Seconds Seconds pu pu pu NM per RPM NM per RPM pu pu NM NM RPM MVA

Description Engine delay or dead time Actuator time constant Actuator gain Engine gain Fuel conversion gain Integral gain Proportional gain Speed error limit max Speed error limit min Torque control max Torque control min Rated RPM of engine Rated MVA

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Description Use this model to simulate governor systems for: 

Caterpillar diesel engine prime mover systems.

In this model: 

The droop is modeled via the varied gain settings.



Between the first π operators and the ÷ operator, units are physical.



All limits are wind-up limits.



TLMax and TLMin are calculated as shown in the model figure.



Rated Torque is calculated as shown in the model figure.



Delay block has unlimited memory.

Notes: 

* The delay or dead time of the diesel engine is composed of three delays: the time elapsed until the actuator output actually injects the fuel into the cylinder, the fuel burning time to produce torque, and the time until all cylinders produce torque at the engine shaft.



In lieu of detailed information supplied by the manufacturer, the engine delay or dead time can be estimated assuming one quarter of a shaft revolution to physically inject fuel, plus one shaft revolution divided by the number of pistons to produce torque. Using engine speed or RPM, that equation can be written as:

T=

 0.25   60   RPM 

+

 60 

 RPM    Number Pistons 

* “Synchronous Generators – Volume 1”, Ion Boldea.

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4.3.2 Cummins Diesel 1 Governor System

PID Control

KP

Speed Ref

VMax

 



KI s



1+  Fuel System Engine Dynamics Combustion

TMax

   

KC

e-sT 1 + as

e-sTC



PMech

Engine Gain

TMin

VMin

Speed Error Limit

K Ds 1+sTD 

Torque Limit

Figure 186. Cummins Diesel 1 governor model block diagram.

Parameter a T TC TD KC KD KI KP TMax TMin VMax VMin

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu

Description Fuel system time constant Fuel system delay or dead time Engine combustion delay or dead time Differential control time constant Engine gain Differential control gain Integral control gain Proportional control gain Torque control max Torque control min Speed error limit max Speed error limit min

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Description Use this model to simulate governor systems for: 

Cummins diesel engine prime mover systems.

In this model: 

The droop is modeled via the varied gain settings.



All limits are wind-up limits.



All delay blocks have unlimited memory.

Notes: 

* The delay or dead time of the diesel engine is composed of three delays: the time elapsed until the actuator output actually injects the fuel into the cylinder, the fuel burning time to produce torque, and the time until all cylinders produce torque at the engine shaft.



In lieu of detailed information supplied by the manufacturer, the engine delay or dead time can be estimated assuming one quarter of a shaft revolution to physically inject fuel, plus one shaft revolution divided by the number of pistons to produce torque. Using engine speed in RPM, that equation can be written as:

T=

 0.25   60   RPM 

+

 60 

 RPM    Number Pistons 

* “Synchronous Generators – Volume 1”, Ion Boldea.

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4.3.3 Gas Turbine Governor System AT







KT







1

1+ sT3 

Speed Ref

VMax 

Per Unit Change In Speed 1 R







1 1+  sT1 

Low Value

1 1+  sT2 





PMech 

VMin

DT Turbine Damping

Figure 187. Gas Turbine Governor model block diagram.

Parameter T1 T2 T3 AT KT R VMax VMin DT

© EasyPower LLC 2016

Units Seconds Seconds Seconds pu pu pu pu pu pu

Description Governor control time constant Combustion chamber time constant Exhaust temp measurement time constant Ambient temperature load limit Load limit gain Droop Governor control max Governor control min Turbine Damping

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Description Use this model to simulate governor systems for: 

Gas turbine prime movers.

In this model: 

The first block models the droop.



The second block (T1) models the governor time constant.



The third block models the combustion chamber time constant.



Dr models turbine speed damping.



The limit on the second block is non-windup.

Notes: 

Set AT to 1.0 when operating at design ambient temperature.



Set AT less than 1.0 when ambient temperature is higher than rated.



Set AT greater than 1.0 when ambient temperature is lower than rated.



Load limiting is a protective function, and thus setting K T and AT is based on the design of the turbine.



VMax limits the power output of the turbine from the fuel path, and thus can serve as an operational limit.



The low value gate causes normal behavior (no temperature limiting) until the load limiting feedback loop value falls below the value on its left side input.

© EasyPower LLC 2016

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4.3.4 Gas Turbine 2 Governor System Temperature Control 1 + sT5 sTT



W

 



1

K4 +

1+ sT4 

Turbine Exhaust Delay

K5 1 + sT3

f1

w f1

e-sETD

Turbine

TC Temperature Control Setpoint

Speed Ref

Per Unit Change In Speed 

Radiation Shield

Thermocouple

G Max

1 + sX   Z + sY 

FL Max Low Value



K6 K3

Speed Governor

1.0



Fuel Control Delay

FL Min

G Min

e-sT







Valve Positioner

1 1+ sTF 

a  c+ bs  FMin





Fuel FMax System

Gas Turbine Dynamics

Turbine 1 f2 w f 1+ sTCD  w f2 Combustor Delay 

KF





e-sECR



TScale



PMech

1.0

f1 = TR - a f1 1.0 - w f1  - b f1ω

f 2 = a f2 + bf2 w f2 - cf2 ω

Figure 188. Gas Turbine 2 Governor model block diagram.

Parameter b ECR ETD T T3 T4 T5 TCD TF TT X Y K3 K4 K5 KF a c aF1 bF1 TR aF2 bF2

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu

Description Valve Positioner time constant Combustor delay time Combustor delay time Turbine Exhaust delay time Radiation Shield time constant Thermocouple time constant Temperature Control time constant Gas Turbine Dynamics time constant Fuel System time constant Temperature Control time constant Speed Governor time constant Speed Governor time constant Fuel Control gain Radiation Shield simulation constant Radiation Shield simulation constant Fuel System feedback gain Valve Positioner gain Valve Positioner constant Turbine temperature simulation constant Turbine temperature simulation constant Turbine temperature simulation constant Turbine torque simulation constant Turbine torque simulation constant

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Parameter cF2 K6 TC TScale W Z FMax FMin GMax GMin FLMax FLMin

© EasyPower LLC 2016

Units pu pu pu pu pu pu pu pu pu pu pu pu

Description Turbine torque simulation constant Fuel bias Temperature Control setpoint Power output scaling factor+ Speed Governor gain Speed Governor constant Fuel System limit max Fuel System limit min Speed Governor limit max Speed Governor limit min Fuel System limit max for earlier models Fuel System limit min for earlier models

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Description Use this model to simulate governor systems for: 

Gas turbine prime movers.

In this model: 

All limits except the FLMax and FLMin are non-windup limits.



All delay blocks have unlimited memory.

Notes: 

For the Gas Turbine 2 model, the value of TC is set equal to TR at initialization. This is done since the value of TC needs to be determined for rated condition of the turbine. If we assume the rated condition is 1.0 pu, or wf1 = approximately 1.0, then via equation f1, we see that TC = TR. Note that at initial conditions the speed (or ∆ω, actually change in speed) is equal to zero and also falls out of the equation.



Consider that if we assume that TR = 750 degree F, then a typical value of af1 can be estimated from a typical range of exhaust temperatures at non full-load conditions. From Figure 189 shown below, we see that exhaust temperatures for a typical combustion turbine vary along the length of the combustion area. At the exhaust, the temperatures are the hottest. From the figure, we also see an approximate 25% reduction in temperature from full load to no load, and thus a 12.5% reduction from full load to half load. Thus, if we use: TR = 750 degree F wf1 = 0.5 pu ∆ω = 0 f1 = 650 (approximate 12.5% temperature reduction from 750) bf1 = 0 (ignore speed cooling effects) then, f1 = TR - a f1 1 - w f1  - bf1Δω 650 = 750 - a f1 1 - 0.5 - 0  0

af1 = 200 

Note that values of K4 and K5 should be selected so that the output of the Radiation Shield block is equal to the input at steady-state. Thus, for our typical numbers above, the result of function f1 is equal to 650 (i.e. the exhaust temperature at half load condition).

© EasyPower LLC 2016

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

When initialization is complete, there will be an immediate difference between TC and the output of the Thermocouple block. However, since the temperature control block is initialized to its Max value, the difference will not cause any difference in the output of the Temperature Control block. This is a correct initialization and operating condition, as the output of the Thermocouple block (which is a representation of the actual exhaust temperature), must always be below the set point value TC or else the model will go into temperature limiting. The only time the model will temperature limit is when the output of the Thermocouple block exceeds TC so that a negative value is delivered to the Temperature Control block. When this happens, the Temperature Control block will start to deliver a value less than the Max value. If this output value is less than the output of the Speed Governor block, it will be used to control the governor via the Low Value select block. Thus, the unit would go into temperature limiting.

Figure 189. Gas Turbine typical temperature profile.

© EasyPower LLC 2016

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References: 1. Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies, “Dynamic Models for Combined Cycle plant in Power System Studies”, IEEE Trans. on Power Systems, Vol. 9, No 3, August 1994, pp1698-1708. 2. L. N. Hannett, Afzal Khan “Combustion Turbine Dynamic Model Validation from Test”, IEEE Trans. on Power Systems, Vol. 8, No 1, February 1993, pp152-158.

© EasyPower LLC 2016

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4.3.5 Gas Turbine WD Governor System - Woodward

K Droop

1+ sTD  Per Unit Change In Speed 

 





PTerm

1

Temperature Control

TScale

1 + sT5 sTT

Speed Ref

G Max

 



1

K4 +

1+ sT4 



Low Value



K6

K3

e-sT



Fuel Control Delay

sK D

G Min Speed Governor

1.0





Turbine Exhaust Delay

K5 1 + sT3

f1

w f1

e-sETD

Turbine

TC Temperature Control Setpoint

KP

KI s

Radiation Shield

Thermocouple







Valve Positioner

FMax Fuel System

1 1+ sTF 

a  c+ bs  FMin

Gas Turbine Dynamics

e-sECR

Turbine 1 f2 w f 1+ sTCD  w f2

Combustor Delay 

KF







TScale



PMech

1.0

f1 = TR - a f1 1.0 - w f1  - bf1ω f 2 = a f2 + b f2 w f2 - cf2 ω

Figure 190. Gas Turbine WD governor model block diagram.

Parameter b ECR ETD T T3 T4 T5 TCD TF TD TT K3 K4 K5 KF KD KI KP KDroop

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu

Description Valve Positioner time constant Combustor delay time Combustor delay time Turbine Exhaust delay time Radiation Shield time constant Thermocouple time constant Temperature Control time constant Gas Turbine Dynamics time constant Fuel System time constant Power feedback time constant Temperature Control time constant Fuel Control gain Radiation Shield simulation constant Radiation Shield simulation constant Fuel System feedback gain Speed Governor differential gain Speed Governor integral gain Speed Governor proportional gain Power feedback droop

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Parameter a c aF1 bF1 TR aF2 bF2 cF2 K6 TC TScale FMax FMin GMax GMin

© EasyPower LLC 2016

Units pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Valve Positioner gain Valve Positioner constant Turbine temperature simulation constant Turbine temperature simulation constant Turbine temperature simulation constant Turbine torque simulation constant Turbine torque simulation constant Turbine torque simulation constant Fuel bias Temperature Control setpoint Power output scaling factor Fuel System limit max Fuel System limit min Speed Governor limit max Speed Governor limit min

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Description Use this model to simulate governor systems for: 

Gas turbine prime movers.

In this model: 

All limits are non-windup limits.



All delay blocks have unlimited memory.

Notes: 

Refer to the Gas Turbine 2 model for additional application notes.

References: 1. L. N. Hannett, Afzal Khan “Combustion Turbine Dynamic Model Validation from Test”, IEEE Trans. on Power Systems, Vol. 8, No 1, February 1993, pp152-158.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

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4.3.6 Hydro Governor System DTurb

Per Unit Change In Speed 

Speed Limit Speed Ref UO Pilot Valve and Servomotor  1 Q   1+ sTP  UC









Gate Limit G Max 1 s

G Min

1 1+ sTG

Gate

Gate Servomotor





  

1 TW s

1.0





 

AT







PMech

Q NL

Turbine Dynamics

RP

Permanent Droop

R T sTR 1+ sTR Transient Droop

Figure 191. Hydro governor model block diagram.

Parameter TG TP TR TW AT DTurb Q QNL RP RT Uo Uc GMax GMin

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu

Description Gate Servomotor time constant Pilot Valve and Servomotor time constant Transient Droop washout time constant Turbine Dynamics time constant Water to mechanical power gain Turbine load damping Gain Water at no-load Permanent Droop Transient Droop Speed limit max Speed limit min Gate limit max Gate limit min

Dynamic Stability Reference Manual

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Description Use this model to simulate governor systems for: 

Hydro turbine prime movers.

In this model: 

All limits are non-windup limits.



DTurb models turbine speed damping.

References: 1. Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies, “Hydraulic Turbine and Turbine Control Models for System Dynamic Studies”, IEEE Trans. on Power Systems, Vol. 7, No 1, February 1992, pp167178. 2. IEEE Committee Report “Dynamic Models for Steam and Hydro Turbines in Power System Studies”, IEEE Trans. On Power Apparatus and System Vol. 92, No. 6, November/December 1973, pp1904-1915. 3. L. N. Hannett, B. Fardanesh “Field Tests to Validate Hydro Turbine-Governor Model Structure and Parameters”, IEEE Trans. on Power Systems, Vol. 9, No 4, November 1994, pp1744-1750.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

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4.3.7 IEEE Hydro 2 Governor System Speed Ref PMax

Per Unit Change In Speed 

K 1 + sT2  1 + sT1 1 + sT3 







1 - sTW 1 + 0.5sTW

PMech

PMin Figure 192. IEEE Hydro 2 governor model block diagram.

Parameter T1 T2 T3 TW K PMax PMin

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds pu pu pu

Description Governor lag time constant Governor lead time constant Governor lag time constant Turbine Dynamics time constant Gain Governor limit max Governor limit min

Dynamic Stability Reference Manual

Page 261

Description Use this model to simulate governor systems for: 

Hydro turbine prime movers.

In this model: 

All limits are windup limits.

© EasyPower LLC 2016

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4.3.8 IEEE Hydro 3 Governor System Speed Ref UO 

Per Unit Change In Speed 







1 TG 1+sTP 

UC







PMax 1 s

PMin

 a 23 1 + 

  a13a 21   a11  sTW  a 23    1 + a11sTW

PMech

Water Turbine

Droop

Permanent Droop

D RT sTR 1+ sTR Transient Droop

Figure 193. IEEE Hydro 3 governor model block diagram.

Parameter TP TR TW a11 a13 a21 a23 TG Droop DRT Uo Uc PMax PMin

© EasyPower LLC 2016

Units Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu

Description Governor time constant Governor transient droop time constant Water Turbine dynamics time constant Water Turbine dynamics constant Water Turbine dynamics constant Water Turbine dynamics constant Water Turbine dynamics constant Governor inverse of gain Governor permanent droop Governor transient droop Speed limit max Speed limit min Water power limit max Water power limit min

Dynamic Stability Reference Manual

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Description Use this model to simulate governor systems for: 

Hydro turbine prime movers.

In this model: 

All limits are non-windup limits.

© EasyPower LLC 2016

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4.3.9 IEEE Steam 1 Governor System 

 

 

K3

K5

 



PMech HP 

Speed Ref K1

PMax

Per Unit Change K 1+ sT2  In Speed 1+ sT1  





K7

PR Up

 

1 T3

1 s

1 1+ sT4 

1 1+ sT5 

1 1+ sT6 



1 1+ sT7 





PMech

PR Dn PMin

K2

K6

K4









 

Governor

K8 

 

PMech LP

Low and High Pressure Turbines

Figure 194. IEEE Steam 1 governor model block diagram.

Parameter T1 T2 T3 T4 T5 T6 T7 K K1 K2 K3 K4 K5 K6 K7 K8 PMax PMin PRUp PRDn

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Governor lag time constant Governor lead time constant Governor time constant Low / High Pressure Turbine time constant Low / High Pressure Turbine time constant Low / High Pressure Turbine time constant Low / High Pressure Turbine time constant Governor gain Low / High Pressure Turbine gain Low / High Pressure Turbine gain Low / High Pressure Turbine gain Low / High Pressure Turbine gain Low / High Pressure Turbine gain Low / High Pressure Turbine gain Low / High Pressure Turbine gain Low / High Pressure Turbine gain Steam power limit max Steam power limit min Rate limit max Rate limit min

Dynamic Stability Reference Manual

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Description Use this model to simulate governor systems for: 

Steam turbine prime movers.

In this model: 

The PMax and PMin limits are non-windup limits.



The PRUp and PRDn limits are windup limits

References: 1. Working Group on Prime Mover and Energy Supply Models for System Dynamic Performance Studies, “Dynamic Models for Fossil Fueled Steam Units in Power System Studies”, IEEE Trans. on Power Systems, Vol. 6, No. 2, May 1991, pp753-761. 2. IEEE Committee Report “Dynamic Models for Steam and Hydro Turbines in Power System Studies”, IEEE Trans. On Power Apparatus and System Vol. 92, No. 6, November / December 1973, pp1904-1915.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

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4.3.10 Pratt & Whitney PWFT8 Governor System Temperature Control Setpoint Tc Thermocouple  1 K temp   1+ sT4 

PTerm 1 TScale

e



-sTpwr











f1

w f1

e-sETD

wf



1+ sT  

 K pt





Low Val Min

K6

P1u 3 

pt

P2 u 2  u

P3 u + P4

N

1.0

Turbine

K5 1 + sT3

1 1+ sT5 

Max 

K4 +

Turbine Exhaust Delay

1

K Droop

1+ sTd  Speed Ref

Radiation Shield

K3

e-sT



Fuel Control Delay







Valve Positioner

Fuel System

a  c+ bs 

1 1+ sTauF 

Gas Turbine Dynamics

e-sECR

Turbine 1 f 1+ sTcd  w f2 2

TScale

Combustor Delay

f1 = TR - a f1 1.0 - w f1  - b f1ω



KF

f 2 = a f2 + bf2 w f2 - cf2 ω

 Per Unit Change in Speed

Figure 195. PWFT8 governor model block diagram.

Parameter b ECR ETD T T3 T4 T5 TauF TCD TD TPT TPWR a c K3 K4 K5 K6 KDroop KF KPT KTemp

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu

Description Valve Positioner time constant Combustor delay time Combustor delay time Fuel Control delay time Radiation Shield time constant Thermocouple time constant Temperature Control time constant Fuel System time constant Gas Turbine Dynamics time constant Power feedback time constant Speed Control time constant Power Feedback delay time Valve Positioner gain Valve Positioner constant Fuel Control gain Radiation Shield simulation constant Radiation Shield simulation constant Fuel bias Power feedback droop Fuel System feedback gain Speed Control gain Temperature Control gain

Dynamic Stability Reference Manual

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PMech

Parameter aF1 bF1 TR aF2 bF2 cF2 P1 P2 P3 P4 Max Min TC TScale

© EasyPower LLC 2016

Units pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Turbine temperature simulation constant Turbine temperature simulation constant Turbine temperature simulation constant Turbine torque simulation constant Turbine torque simulation constant Turbine torque simulation constant Speed Governor control constant - cubic Speed Governor control constant - square Speed Governor control constant - linear Speed Governor control constant - constant Speed Governor limit max Speed Governor limit min Temperature Control set point Power output scaling factor

Dynamic Stability Reference Manual

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Description Use this model to simulate governor systems for: 

Gas turbine prime movers.

In this model: 

All limits are windup limits.



All delay blocks have unlimited memory.

Notes: 

Refer to the Gas Turbine 2 model for additional application notes.

© EasyPower LLC 2016

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4.3.11 Split Shaft Gas Turbine 1 Governor System Speed Ref

FMax

Per Unit Change In Speed 



1 Droop



Turbine

Fuel Control

K 1+sT1  1+ sT2 1+sT3 

1 1+ sTF 



FMin

Method for Fuel Rate Limit Old State = State Integrate()

PFollow

RA

if  PMech >  PFollow + F Rate Pkup  

y = mx + b

. rate = State - Old State . if  rate > R A  . .

PMech

State = Old State + R A

b =  F Rate NL  t m=

. end if end if

1

1+ sTR 

  F Rate FL  -  F Rate NL   Δt

y = Fuel Rate Limit = R A

Figure 196. Split Shaft Gas Turbine 1 governor model block diagram.

Parameter T1 T2 T3 TF TR Droop FMax FMin F Rate FL F Rate NL F Rate Pkup K

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu

Description Turbine model lead time constant Turbine model lag time constant Turbine model lag time constant Fuel control time constant Power follow time constant Governor droop Fuel limit max Fuel limit min Fuel rate at full load Fuel rate at no load Fuel rate pickup Turbine model gain

Dynamic Stability Reference Manual

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Description Use this model to simulate governor systems for: 

Split shaft gas turbine prime movers.

In this model: 

All limits are non-windup limits.

Notes: 

Refer to “Impact Loading of Isolated Generators”, by Conrad St. Pierre, IEEE Transactions on Industry Applications, VOL. IA-17, No. 6, November/December 1981 for more details on split shaft turbine governor models and their response.

© EasyPower LLC 2016

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4.3.12 Steam Turbine Governor System Speed Ref

VMax 

Per Unit Change In Speed 





1

1 R

1+ sT1 

1+ sT2  1+ sT3 





PMech 

VMin

DT

Turbine Damping

Figure 197. Steam Turbine governor model block diagram.

Parameter T1 T2 T3 R DT VMax VMin

© EasyPower LLC 2016

Units Seconds Seconds Seconds pu pu pu pu

Description Governor control time constant Steam Turbine re-heater lead time constant Steam Turbine re-heater lag time constant Droop Turbine Damping Governor max limit Governor min limit

Dynamic Stability Reference Manual

Page 272

Description Use this model to simulate governor systems for: 

Steam turbines with governor action and a re-heater time constant.

In this model: 

The first block models the droop.



The second block models the governor time constant.



The third lead-lag block models the turbine.



DT models turbine speed damping.



The limit on the second block is non-windup.

Notes: 

T2/T3 is a fraction that represents the portion of turbine power developed from the highpressure turbine.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

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4.3.13 WECC Gas Turbine Governor System 1

1+ sTLTR 

Rate Limit

if ( DV > L INC ) R LIM = LTRATE else

DV





R LIM = R MAX



VMax

RLim Speed Ref



Droop

  1 R

1+ sT4  KA 1+ sT5 

Speed Deadband

EPS

Low Value



Gov Lead- Lag Control

FIdle

Turbine



1 sT1



VMin

Gov Time Constant

Ambient Temperature Load Limit    KT    

 



Power vs. Output Valve Position Deadband

1+ sAT2  1+ sBT2 

PGov



DB2

V

DB1



PMech 

FIdle Zero Power Fuel Flow 1

1+ sT3  Turbine Exhaust Temp Time Constant

L MAX

 Per Unit Change In Speed

DT

Turbine Damping

Figure 198. WECC Gas Turbine governor model block diagram.

Parameter T1 T2 T3 T4 T5 TLTR A B FIdle R DT KA EPS KT LTRate LInc RMax VMax VMin © EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Governor time constant Turbine model time constant Turbine exhaust model time constant Governor Control lead time constant Governor Control lag time constant Rate limit time constant Turbine model lead multiplier Turbine model lag multiplier Zero Power Fuel Flow Droop Turbine Damping Governor Control gain Speed Deadband Ambient Temperature Load Limit Maximum long term fuel valve opening rate Valve position change allowed at fast rate Maximum fuel valve opening rate Governor max limit Governor min limit

Dynamic Stability Reference Manual

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Parameter DB1 DB2 PGov1 PGov2 PGov3 PGov4 PGov5 PGov6 V1 V2 V3 V4 V5 V6

© EasyPower LLC 2016

Units pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description Output dead band 1 Output dead band 2 Power output point 1 Power output point 2 Power output point 3 Power output point 4 Power output point 5 Power output point 6 Valve position 1 Valve position 2 Valve position 3 Valve position 4 Valve position 5 Valve position 6

Dynamic Stability Reference Manual

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Description Use this model to simulate governor systems for: 

Gas turbine prime movers.

In this model: 

The governor time constant block limit is non-windup.



The governor rate limit is a windup limit.



All six valve positions and power outputs must be supplied.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

Page 276

4.3.14 Woodward Diesel Governor System

TMax

Electronic Control Box



Per Unit Change In Speed 





Per Unit Speed 1+ 

Actuator

Speed Ref



1+ sT3 



K 1+ sT4 

1+ sT + s T T 

s 1+ sT5 1+ sT6 

2



1

1 2

Engine



e-sTD

PMech

TMin

R Throttle Feedback

Figure 199. Woodward Diesel Governor model block diagram.

Parameter T1 T2 T3 T4 T5 T6 TD K R TMax TMin Droop / Isoch

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu

Description Control box time constant Control box time constant Control box time constant Actuator time constant Actuator time constant Actuator time constant Engine firing delay time Actuator gain Throttle feedback gain (affects droop) Max actuator torque Min actuator torque Switch (droop mode or isochronous mode)

Dynamic Stability Reference Manual

Page 277

Description Use this model to simulate governor systems for: 

Diesel engine prime mover.

In this model: 

The first block models the electronic control box.



The second block models the actuator.



The third block models the engine firing delay.



The limit on the second block is non-windup.

Notes: 

In isochronous mode, the Speed Ref value is forced to zero.



This model is based upon a Woodward governor with electronic speed sensing and a hydraulic actuator.



Only use Isochronous mode when the generator is operating in an isolated mode.



Use droop mode when connected with other generators.

Multiplication by Speed Due to diesel engine design, the engine would typically limit the fuel input on a per cycle basis. Since the energy developed per cycle is proportional to the fuel input per cycle, multiplying energy developed per cycle by speed then produces the mechanical power delivered to the shaft of the generator. From this, we note that the limits on the actuator are actually torque limits.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

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4.3.15 Woodward Steam PID1 Governor System Speed Ref

PMax 

Per Unit Change In Speed 



 

 T  K 1+ sTA  1+ E  s   1+ sTB 

Governor WW MicroNet

1 1+  sTC 

1 1+ sTD 

Actuator

Turbine Casing

PMech

PMin

Dr Droop

Figure 200. Woodward Steam PID 1 Governor model block diagram.

Parameter TA TB TE TC TD K PMax PMin Dr

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu

Description Governor control time constant Governor control time constant Governor control time constant Actuator time constant Turbine time constant Governor control gain Max power output Min power output Droop

Dynamic Stability Reference Manual

Page 279

Description Use this model to simulate governor systems for: 

Steam turbine prime mover with PID governor.

In this model: 

The first block models the governor control.



The second block models the actuator.



The third block models the turbine time constant.



The limit on the second block is non-windup.

Notes: 

This model is based upon a Woodward WW Micronet Governor.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

Page 280

4.3.16 Cummins Gas Engine 1 Governor System

PID Control Speed Ref

KP

Dynamics B

(RPM)

Moving Average

pu Change

Filter

in Speed



FMax

 

x



  

 KI  s  

1.0 Rated K cal (Max 100 Pnts) RPM

1+st D 

Datalink Actuator Dynamics A Delay Delay

e

FMin K Ds

Speed Diff (RPM)

Datalink

-sTms

e

-sTst

% Fuel Flow

K im2tot

1 1 + st ta

1 1 + st im Dynamics C

1- K im2tot

  

Engine % Flow to Combustion pu Torque Gain Delay

e

-sTcmb

1

1+ st trb 

2

K FT

pu Torque

x

PMech pu

% Fuel Flow

Control Limit Note: KFT is typically set to 0.01 to convert from percent to pu.



 

 1.0

Figure 201. Cummins Gas Engine 1 governor model block diagram.

Parameter RatedRPM Kp Ki Kd Td

FMax FMin Tms Tst Tta Kim2tot Tim Ttrb Tcmb KFT Kcal

© EasyPower LLC 2016

Units RPM %Flow/RPM %Flow/RPM/Sec %Flow-Sec/RPM Seconds %Flow %Flow Seconds Seconds Seconds pu Seconds Seconds Seconds puTorque/%Flow pu

Description Machine Rated RPM Governor Proportional Gain Governor Integral Gain Governor Deviation Gain Governor Derivative Time Constant Fuel Flow Max Limit Fuel Flow Min Limit Datalink Associated Nominal Time Delay Actuator Datalink Associated Nominal Time Delay Dynamics A Time Constant Dynamics B Fraction Dynamics B Time Constant Dynamics C Time Constant Combustion Time Delay Percent Flow to Per Unit Torque Gain Number of Engine Speed Samples to Average

Dynamic Stability Reference Manual

Page 281

Description Use this model to simulate governor systems for: 

Cummins gas engine prime mover systems.

In this model: 

The droop is modeled via the varied gain settings.



All limits are wind-up limits.



All delay blocks have unlimited memory.



The speed moving average calculation has a 100 point maximum.



KFT is typically set to 0.01 to convert % to pu.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

Page 282

4.4 PSS Models As seen in each Excitation System model figure, there is an input labeled VPSS. This is the signal from a power system stabilizer (PSS) that supplies additional damping of power oscillations. These devices must be carefully tuned for a particular generator and excitation system vs. the stiffness and response of the grid at their location. When tuning, we typically consider the local mode of oscillation as well as a system mode that needs damping. The Power System Stabilizer Models included in EasyPower DS are:    

IEEE Type PSS1A IEEE Type PSS2B IEEE Type PSS3B IEEE Type PSS4B

© EasyPower LLC 2016

Dynamic Stability Reference Manual

Page 283

4.4.1 IEEE PSS1A Power System Stabilizer VST Max 0: Power 1: Δω

1 1+ sT6 

Ks

1 1 + A1s + A 2s2 

sT5 1+ sT5 

1+ sT1  1+ sT2 

1+ sT3  1+ sT4 

VPSS

VST Min

Figure 202. IEEE PSS1A model block diagram.

Parameter T1 T2 T3 T4 T5 T6 KS VST Max VST Min A1 A2 Input

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu 1/0

Description 1st lead time constant 1st lag time constant 2nd lead time constant 2nd lag time constant Washout time constant First block time constant The stabilizer gain PSS output max PSS output min Lag quadratic funtion constant 1 Lag quadratic funtion constant 2 Input selection

Dynamic Stability Reference Manual

Page 284

Description Use this model to simulate: 

Speed or Power input power system stabilizers with an IEEE PSS1A form.

In this model: 

The first block is most likely a transducer time constant.



The second block models the net stabilizer gain and a washout.



The third block models a quadratic lag function.



The fourth and fifth blocks model the lead/lag section.



The output limit is a wind-up limit.

Notes: 

This model is based upon an IEEE PSS2B PSS model.

From IEEE Standard 421.5, Section 8.1: * Figure 8-1 shows the generalized form of a PSS with a single input. Some common stabilizer input signals, VSI, are speed, frequency, and power. T6 may be used to represent a transducer time constant. Stabilizer gain is set by the term KS and signal washout is set by the time constant T5. In the next block, A1 and A2 allow some of the low-frequency effects of high-frequency torsional filters (used in some stabilizers) to be accounted for. When not used for this purpose, the block can be used to assist in shaping the gain and phase characteristics of the stabilizer, if required. The next two blocks allow two stages of lead-lag compensation, as set by constants T1 to T4. Stabilizer output can be limited in various ways, not all of which are shown in Figure 22. This model shows only simple stabilizer output limits, VSTMAX and VSTMIN. For some systems, the stabilizer output is removed if the generator terminal voltage deviates outside a chosen band, as shown in the supplementary discontinuous excitation control model Type DEC3A of Figure 11-3. In other systems, the stabilizer output is limited as a function of generator terminal voltage as included in the Type DEC1A model of Figure 11-1. The stabilizer output, VST, is an input to the supplementary discontinuous control models. Where the discontinuous control models are not used, VS = VST.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

© EasyPower LLC 2016

Dynamic Stability Reference Manual

Page 285

4.4.2 IEEE PSS2B Power System Stabilizer VMax f

sTW1 1+ sTW1 

sTW2 1+ sTW2 

1 1+ sT9 



 

 1+ sT 7   1+ sT M 8 

   

N





K1



1+ sT1  1+ sT2 

1+ sT3  1+ sT4 

1+ sT5  1+ sT6 

VPSS VMin

K3

P

sTW3

1+ sTW3 

sTW4

K2

1+ sTW4 

1+ sT10 

Figure 203. IEEE Type PSS2B model block diagram.

Parameter T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 TW1 TW2 TW3 TW4 K1 K2 K3 VMax VMin M N

© EasyPower LLC 2016

Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds

Description 1st lead time constant 1st lag time constant 2nd lead time constant 2nd lag time constant 3rd lead time constant 3rd lag time constant Filter lead time constant Filter lag time constant Freq branch time constant Power branch time constant 1st freq branch washout time constant 2nd freq branch washout time constant 1st power branch washout time constant 2nd power branch washout time constant Main PSS gain 1st power branch gain 2nd power branch gain PSS output max PSS output min M N

Dynamic Stability Reference Manual

Page 286

Description Use this model to simulate: 

Power system stabilizers with an IEEE PSS2B form.

In this model: 

The first blocks model the first washout for two inputs.



The second blocks model the second washout for two inputs.



The top third block models a single time constant.



The bottom third block models a single time constant with gain.



The middle block is a gain block for the bottom input signal.



The fourth block (with M and N) models the ramp tracking filter.



The fifth block models the PSS gain.



The sixth block models the first lead-lag block.



The seventh block models the second lead-lag block.



The eighth block models the third lead-lag block.

Notes: 

This model is based upon an IEEE PSS2B PSS model.



All limits are wind-up limiters.

From IEEE Standard 421.5, Section 8.2: * This stabilizer model, shown in Figure 8-2, is designed to represent a variety of dualinput stabilizers, which normally use combinations of power and speed or frequency to derive the stabilizing signal. * In particular, this model can be used to represent two distinct types of dual-input stabilizer implementations as described as follows: a) Stabilizers that, in the frequency range of system oscillations, act as electrical power input stabilizers. These use the speed or frequency input for the generation of an equivalent mechanical power signal, to make the total signal insensitive to mechanical power change. * From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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b) Stabilizers that use a combination of speed (or frequency) and electrical power. These systems usually use the speed directly (i.e., without phase-lead compensation) and add a signal proportional to electrical power to achieve the desired stabilizing signal shaping. * While the same model is used for the two types of dual-input stabilizers described in the preceding items a) and b), the parameters used in the model for equivalent stabilizing action will be very different. For each input, two washouts can be represented (TW1 to TW4) along with a transducer or integrator time constants (T6, T7). For the first type of dual-input stabilizer, KS3 would normally be 1 and KS2 would be equal to T7/2H, where H is the inertia constant of the synchronous machine. VSI1 would normally represent speed or frequency and VSI2 would be a power signal. The indices M and N allow a “ramptracking” or simpler filter characteristic to be represented. To model all existing field uses of the ramp-tracking filter, the indices M and N should allow integers up to 5 and 4, respectively. Typical values of M = 5, N = 1 or M = 2, N = 4 are in use by several utilities. Phase compensation is provided by the two lead-lag or lag-lead blocks (T1 to T4). Output limiting options are similar to those described for the PSS1A model. * For many types of studies, the simpler single-input PSS1A model, with appropriate parameters, may be used in place of the two-input PSS2B model. * The PSS2B model shown in Figure 8-2 is a slight variation of the PSS2A model from the 1992 recommended practice. An additional block with lag time constant T11 and lead time constant T10 can be used to model stabilizers which incorporate a third lead-lag function.”

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.4.3 IEEE PSS3B Power System Stabilizer

P

1

1+ sT1 

K S1

sTW1

1+ sTW1 

VST Max  

Δω

1 1+ sT2 

K S2



sTW3 1+  sTW3 

2

1 + A1s + A 2s 1 + A 3s + A 4s 2

2

1 + A 5s + A 6 s 1 + A 7 s + A 8s 2

VPSS VST Min

sTW2 1+ sTW2 

Figure 204. IEEE Type PSS3B model block diagram.

Parameter T1 T2 TW1 TW2 TW3 A1 A2 A3 A4 A5 A6 A7 A8 KS1 KS2 VST Max VST Min

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Units Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu

Description Power input transducer time constant Speed input transducer time constant Power input washout time constant Speed input washout time constant Stabilizer washout time constant First block lead quadratic funtion constant 1 First block lead quadratic funtion constant 2 First block lag quadratic funtion constant 1 First block lag quadratic funtion constant 2 Second block lead quadratic funtion constant 1 Second block lead quadratic funtion constant 2 Second block lag quadratic funtion constant 1 Second block lag quadratic funtion constant 2 Power input gain Speed input gain PSS output max PSS output min

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Description Use this model to simulate: 

Power system stabilizers with an IEEE PSS3B form.

In this model: 

The first block set model transducer time constants.



The second block set model the washouts for each input.



The third block models the stabilizer washout.



The fourth and fifth blocks model the lead/lag section.



The output limit is a windup limit.

Notes: 

This model is based upon an IEEE PSS3B PSS model.

From IEEE Standard 421.5, Section 8.3: * The PSS model PSS3B shown in Figure 8-3 has dual inputs of electrical power (VSI1 = PE) and rotor angular frequency deviation (VSI2 = ∆ω). The signals are used to derive an equivalent mechanical power signal. By combining this signal with electrical power, a signal proportional to accelerating power is produced. The time constants T1 and T2 represent the transducer time constants, and the time constants TW1 to TW3 represent the washout time constants for electric power, rotor angular speed, and derived mechanical power, respectively. In this model, the stabilizing signal VST results from the vector summation of processed signals for electrical power and angular frequency deviation. * The desired amplitude and phase for the stabilizing signal is obtained by matching the polarity and magnitude of the gain constants KS1 and KS2. Phase compensation is provided by the two subsequent filters A1 to A8. The maximum allowed influence of the stabilizing signal on the AVR may be adjusted with the limit values VSTMAX and VSTMIN.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.4.4 IEEE PSS4B Power System Stabilizer VL Max

K L1 Digital Transducer Model

Optional Notch Filters

K L2 Δω

-1.759x10-3s + 1 s 2 + f12 s 2 + f 22 -4 2 -2 2 2 2 1.2739x10 s + 1.7823x10 s + 1 s + b1s + f1 s + b 2s + f 22

Digital Transducer Model 2

P

80s + 1 s3 + 82s 2 + 161s + 80

1 1+ 2HS

K L11 + sTL1 1+ sTL2

1+ sTL3  1+ sTL4 

K L17 + sTL7 1+ sTL8

1+sTL9  1+ sTL11  1+sTL10  1+ sTL12 

2 3

2

2 4

KL 

VL Min VST Max

VI Max

K I1

K I11 + sTI1 1+ sTI2

1+ sTI3  1+ sTI5  1+ sTI4  1+ sTI6 

K I2

K I17 + sTI7 1+ sTI8

1+ sTI9  1+ sTI11  1+ sTI10  1+ sTI12 







KI 

VPSS

VST Min

VI Min VH Max

Optional Notch Filters 2

1+ sTL5    1+ sTL6 

K H1

K H11 + sTH1 1+ sTH2

1+ sTH3  1+ sTH5  1+ sTH4  1+ sTH6 

K H2

K H17 + sTH7 1+ sTH8

1+ sTH9  1+ sTH11  1+ sTH10  1+ sTH12 

s +f s +f s 2 + b3s + f 32 s 2 + b 4s + f 42





KH 

VH Min

Figure 205. IEEE Type PSS4B model block diagram.

Parameter TL1 TL2 TL3 TL4 TL5 TL6 TL7 TL8 TL9 TL10 TL11 TL12 TI1 TI2 TI3 TI4 TI5 TI6 TI7 TI8 TI9 TI10 TI11 TI12

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Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds

Description Low band time constant 1 Low band time constant 2 Low band time constant 3 Low band time constant 4 Low band time constant 5 Low band time constant 6 Low band time constant 7 Low band time constant 8 Low band time constant 9 Low band time constant 10 Low band time constant 11 Low band time constant 12 Intermediate band time constant 1 Intermediate band time constant 2 Intermediate band time constant 3 Intermediate band time constant 4 Intermediate band time constant 5 Intermediate band time constant 6 Intermediate band time constant 7 Intermediate band time constant 8 Intermediate band time constant 9 Intermediate band time constant 10 Intermediate band time constant 11 Intermediate band time constant 12

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Parameter TH1 TH2 TH3 TH4 TH5 TH6 TH7 TH8 TH9 TH10 TH11 TH12 b1 b2 b3 b4 f1 f2 f3 f4 Hs KL1 KL2 KI1 KI2 KH1 KH2 KL KI KH VL Max VL Min VL Max VL Min VL Max VL Min VST Max VST Min

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Units Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds Seconds pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu pu

Description High band time constant 1 High band time constant 2 High band time constant 3 High band time constant 4 High band time constant 5 High band time constant 6 High band time constant 7 High band time constant 8 High band time constant 9 High band time constant 10 High band time constant 11 High band time constant 12 Speed input notch filter constant Speed input notch filter constant Power input notch filter constant Power input notch filter constant Speed input notch filter constant Speed input notch filter constant Power input notch filter constant Power input notch filter constant Machine inertia Low band gain 1 Low band gain 2 Intermediate band gain 1 Intermediate band gain 2 High band gain 1 High band gain 2 Low band output gain Intermediate band output gain High band output gain Low band output max Low band output min Intermediate band output max Intermediate band output min High band output max High band output min PSS output max PSS output min

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Description Use this model to simulate: 

Power system stabilizers with an IEEE PSS4B form.

In this model: 

All limits are windup limits.

Notes: 

This model is based upon an IEEE PSS4B PSS model.

From IEEE Standard 421.5, Section 8.4: * The PSS4B model represents a structure based on multiple working frequency bands as shown in Figure 8-4a. Three separate bands, respectively dedicated to the low-, intermediateand high-frequency modes of oscillations, are used in this delta-omega (speed input) PSS. * The low band is typically associated with the power system global mode, the intermediate with the inter-area modes, and the high with the local modes. Each of the three bands is composed of a differential filter, a gain, and a limiter. Their outputs are summed and passed through a final limiter VSTMIN/VSTMAX resulting in PSS output VST. * The PSS4B measures the rotor speed deviation in two different ways. ∆ωL-I feeds the low and intermediate bands, while ∆ωH is dedicated to the high-frequency band. The equivalent model of these two speed transducers is shown in Figure 8-4b. Tunable notch filters Ni(s), optionally used for turbo-generators torsional modes, are defined as shown in Equation (4). Ni  s  

s 2  ni2 s 2  Bwi s  ni2

(4)

* with ωni the filter frequency, and Bwi its 3 dB bandwidth. Sample data sets are shown in H.21, which also contains a brief description of the tuning philosophy used in the PSS4B model.

* From IEEE Standard 421.5 – 2005. Copyright 2006, by IEEE. All rights reserved.

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4.5 Motor Models As noted in the first chapter of this manual, motors are modeled using two main model components: the machine and the load. And so, we have defined a “motor system” to be a combination of an actual motor and the rotating load fed by the motor’s shaft. This corresponds with Figure 2 and Figure 3 for induction and synchronous motors respectively. The motor and load are integrated together in the machine speed equations. Decelerating torque is supplied by the load model, accelerating torque is supplied by the motor and speed is supplied by the machine model back to the load. The load model simply updates its torque based on the machine’s present speed condition, either by equations or a digitized torque speed relationship. An internal Thevenin voltage is generated by the motor model, and supplied to the network. Terminal current is fed back into the motor model. Following is a detailed description of the EasyPower Double Cage Induction and Synchronous motor models.

4.5.1 Double Cage Flux Induction Motor The double cage induction motor model in the DS Engine is a fully detailed flux level model including double cage rotor dynamics and saturation (see model block diagram in Figure 206 below). As with the generator models, this model was created with the help of F. P. deMello, a noted machine modeling expert, and conforms to a symmetrical model with its reference axes rotating at synchronous speed. It uses real and imaginary axes instead of d and q, which eliminates the need for conversion of values (machine terminal current and E’’ driving voltage) into and out of the model. This reduces computations, removing the need for calls to sine and cosine functions. The effect of saturation is included on both axes. The model block diagram supplied below defines the rotor dynamics. In an additional section below, the machine speed dynamics are discussed. Definitions A few definitions of variables used in the model will help in its description. Those definitions are: p  Speed in

radians Sec

E ''  ER''  jEI''  Thevenin Voltage Behind ZThev I  I R  jI I  Terminal Current

ZThev  RA  jX ''

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I

E ''  ETerm ZThev

Note that the model in Figure 206 is defined with a generator sign convention. That means that I, and electrical power are defined positive for current, watts and vars flowing out of the motor. Also, note that EKR, EKI, E’R, and E’I are used at other locations in the model where drawing a connecting line in the diagram would have made the model block diagram a bit cluttered. Inertia Equation The relationship between motor speed, load torque and motor electrical torque is defined in a separate set of equations from the rotor and stator dynamics. p (the main link between motor speed and electrical torque, and pronounced as pee - theta) is defined as change in speed (from zero, where zero is sync speed) in radians per second. p thus has the same sign as p (the per unit speed deviation, and pronounced as pee - delta) as defined for synchronous machines and is the opposite sign from slip. In fact, p is simply the negative of the machine slip. Thus, when the motor is at synchronous speed, p is equal to zero. When the motor is at a given slip (slower than synchronous frequency), p is negative. For example, an 1800 RPM motor with 150 RPM of slip will have a p equal to:  150  p  p  2 f      2 f  1800 

p   0.08333 pu  2 60   31.416

Radians Sec

and, since the motor is spinning slower than synchronous speed, slip equals:  150  slip   p     0.08333 pu  1800 

To calculate p during the simulation, we need the inertia-speed integral relationship modeled. This is performed as seen in Figure 207 below, with all quantities now placed in a load convention, where TLoad is the mechanical load torque. TLoad is always positive and represents the load torque as speed increases, and is typically modeled with a speed squared, speed cubed or digitized torque vs. speed characteristic.

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EKR 

''

To p

 X ''  X  X'  X  l

l

1



EI' 

'

To s

 



 X '  X ''  X'  X  

'

ER



X  X '



''

EKI

To s

 X '  X ''  X'  X  l



EI''



X'  X 

2

l

l



1

 IR



EI''



E '' Saturation

'

To p

EI'

E '' 

 E ''    E ''  2

R

2

I

ER''



E '' 

 

X  X '





II



 X '  X ''  X'  X 

X'  X  l

2

l



1 '

To s

'

ER





1 



EKR

''

To s

 X '  X ''  X'  X  l



ER'' 

 X ''  X  X'  X  l

l

''

To p



EKI

Figure 206. Double Cage Induction Motor flux model.

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Table 9. Induction motor model parameters.

Parameter

Units

Description

Rated HP Rated Eff Rated Speed Rated Voltage Rated Current Rated PF

HP Percent RPM Volts LL Amps

Rated Slip Start Trq Start Crt Start PF Pull-Out Trq

pu pu pu pu

Rated slip Starting torque Starting current Starting power factor Rated pull-out torque

Ra Xl X X’ X’’ T’o T’’o

pu pu pu pu pu Seconds Seconds

Stator winding resistance (armature resistance) Stator leakage reactance Unsaturated synchronous reactance Unsaturated transient reactance Unsaturated sub-transient reactance Transient OC time constant Sub-transient OC time constant

E1 E2 S( E1 ) S( E2 )

pu pu pu pu

First voltage to define saturation Second voltage to define saturation Saturation at E1 Saturation at E2

H

kW-Sec / kVA Combined machine and load inertia

Ld Tran Str Ld Tran Rmp

Seconds Seconds

Time at which load transfers – starting to running Time it takes to transfer load – starting to running

SoftSt V1 SoftSt V2 SoftSt V3 SoftSt T12 SoftSt T23 SoftSt I Limit SoftSt KI SoftSt TI SoftSt Trigger SoftSt UTS StPt

% % % Seconds Seconds Times FLA pu Seconds

First soft-start voltage Second soft-start voltage Third soft-start voltage Time between first and second soft-start voltage Time between second and third soft-start voltage Soft-start current limit specified in times FLA Soft-start current limit gain Soft-start current limit time constant When set to 1 at runtime, forces soft-start action “Up To Speed” set point where current limit stops

%

Notes: OC means Open Circuit

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TLoad



1 2Hs



slip

2 f

 p

TE Figure 207. Inertia vs. Speed integral model.

For this to be complete, we must provide the calculation of electrical torque or TE as determined by parameters within the flux model in Figure 206. TE (now provided in a load convention), is calculated as:



TE   ER'' I R  EI'' I I



Load Modeling Several load models are supplied for the motor. The two most common (speed squared and speed cubed) utilize the following equations to define load torque at any speed: Speed Squared Load

Speed Cubed Load

2

TLoad

 1.0  p   THeld    1.0  p Held 

3

TLoad

 1.0  p   THeld    1.0  p Held 

where THELD and pHELD are the torque and speed of the motor at initial online conditions. One additional load model utilizes a lookup table for supplying any TLOAD for a given motor speed. That table is user entered for modeling any torque vs. speed relationship that can be digitized. Refer to “Induction Motor Modeling - Part 3” for more detail on how each load model works for both this double cage induction as well as the synchronous motor model. Saturation Saturation is modeled the same as described in the section on the round rotor synchronous generator. Initialization – Off Line at Zero Speed When the motor is offline, it will be initialized to a zero speed, unity (1.0) slip condition. p is thus equal to -1.0. All States and DStates are initialized to zero. The machine is ready for starting at any time. It will automatically start as voltage is applied to its terminals.

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To properly start a motor, there must be a properly defined load model, so that load is being applied continuously at all of the motor’s speed conditions. Also, due to the motor model equation formulation, an in-depth study will reveal that the electrical airgap torque is not 1.0 pu when the motor is at a rated running condition. And thus, to properly scale motor load (which is based on the premise that 100% or 1.0 pu torque exists at rated running conditions), we must first determine what the electrical air gap torque is at rated conditions. And so, the motor model is always initialized twice (both for Off Line and On Line (next section) conditions). The first initialization assumes a rated terminal voltage and loading condition. From this first initialization, we can determine the appropriate values of held torque and held speed (see Load Modeling above) to generate a fully defined torque speed relationship for the speed squared and speed cubed load curves. For digitized curves, no “held” value is needed. However, there is still the need for properly scaling airgap torque to match the load torque speed curve that is created based on the assumption that 1.0 pu is 100% load, representing rated running conditions. After the online rated-load initialization, the motor is then reset and initialized as defined in the paragraph above. Initialization – On Line and Running After performing the first rated load initialization as just discussed (to properly scale load models), the motor must be initialized according to the power flow terminal voltage, P and Q conditions. This second initialization calculates the complex terminal current (real and imaginary), and then works back through the model diagram in Figure 206 to initialize all of the machine states, with the exception of slip. All DStates are set to zero. Now, the only initialization left is slip. Due to the non-linear nature of this model (with saturation and separately modeled load torque), the actual slip of the machine cannot be determined directly. To get the model to a stable initial condition, two additional initialization techniques are applied. First, an estimate of slip (S) is generated using the equivalent Type 1 circuit model shown in Figure 208. The Type 1 parameters are back calculated using the following equations:

Ra  Ra Xa  Xl X M  X  Xl X1 

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 X  Xl  X '  Xl 

X  X  '

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X2 

X

R1 

R2

'

 X l  X ''  X l 

X

'

 X '' 

 X  X  X 

 X 

l

1

T

' o do

'

 Xl   X2



oTdo''

Slip is then initialized to the rated per unit terminal power times slip, or: slip   rated slip  PDesired

This initial value just gets us in the ball park, and uses the natural ratio effect of per unit power, as multiplied into the rated slip. Rated slip and rated P are not necessarily linear, but this gives us an estimate to begin searching for a better estimate. RA

jXA

jX1

jX2

R1/S

R2/S

jXM

Figure 208. Double cage induction motor impedance model – Type 1 form.

Next, an iterative loop with error feedback is used to improve our slip estimate. In that loop, statements are processed as shown in Figure 209. During this iterative estimate of slip, additional code is included to monitor the operating location of the motor on the torque speed curve. If the motor is found to go past the pull-out torque towards locked rotor (as slip increases, attempting to meet the desired power), then an error message is triggered which notes that the motor cannot meet the power desired in the power flow. Such error checking is critical, since power flows often include scaled lumped motors for loading conditions at unit substations, causing an actual individual motor to then be overloaded. This checking supplies additional information to help the user create a valid and consistent power flow case.

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Finally, due to machine non-linearities (discussed next), a slew run is performed to get the machine model to a final and settled on-line running condition, where all model States are set to produce the desired power flow terminal power conditions.

Start

Calc PTerm Using Type 1 Circuit

Let PDesired be the Power Flow Terminal Power

PError  PDesired  PTerm

slip  slip   PError  AccFactor 

Past Pull-Out

Yes No

No PError < 0.0001

Yes Finished

Error – Unable to Satisfy Load

Figure 209. Slip estimate for induction motor.

Given that the actual running slip is a function of the model, we need to perform a slew run (mini dynamic simulation of the motor with some feedback to equate terminal P) to get the motor initialized properly. The machine model includes a non-linear load, and models saturation, which also has a non-linear effect. After the slew run is complete: 

Motor terminal P will equal that required of the power flow.



Motor terminal Q will be a new value (consistent with the flux model equations and not necessarily what the user may have specified for the motor - see “Induction Motor Modeling - Part 4” for more detail).

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

Slip should be what is needed for the desired power. If the motor is initialized with a rated (1.0 pu) terminal voltage and with rated load specified, then we would expect the slip to match rated slip of the motor.

The slew run performs the follow updates while running the motor through its normal time simulation function: Start

Calc DStates

Integrate

Calc Variables

Calc PTerm

PLF is the Power from the Power Flow PError  PLF  PTerm

slip  slip   PError  AccFactor 

No Max DState < 0.001

Yes Finished

Figure 210. Slew run for induction motor.

Once the maximum DState falls below an acceptable level, all motor conditions are stored as being the initialized conditions of the motor. Comments on Pull-Out Torque Pull-Out Torque is the maximum torque seen on the torque-speed curve, and is typically a guaranteed value supplied by the manufacturer, and not the actual capability of the machine.

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Because of this, when performing parameter derivation, make sure that pull-out torque is either equal to or slightly higher than the value supplied by the manufacturer. Tripping a Motor When a motor is tripped offline via a network switching action, the motor will spin down as any motor would in practice. Thus, a trip and fast re-closing action will actually simulate a reenergization of the motor, generating transient torques on the shaft of the motor. No special actions are needed to re-start a motor that has been tripped off. A simple network action will reapply voltage to the motor, and it will react according to the present condition it is in. Thus, motors that are tripped off, do not stop simulating. They simply spin down and continue simulating throughout the run. In fact plotting of a motors terminal voltage will show that a back voltage from the motor exists as the motor spins down. Motor Voltage Rating In EasyPower, the induction motor model data may have a different base voltage than the base voltage for the bus the motor is connected to. EasyPower performs all conversions to integrate the motor model and the network so that the motor is applied correctly, given the rated voltage of the motor vs. the applied voltage from the network. Soft-Start Capability In EasyPower, the induction motor model includes soft-start capability. The default data and range for the parameters are: Parameter Name Default Value SoftSt V1 (%) 100.0 SoftSt V2 (%) 100.0 SoftSt V3 (%) 100.0 SoftSt T12 (sec) 0.0 SoftSt T23 (sec) 0.0 SoftSt I Limit (X FLA) 0.0 SoftSt KI (pu) 10.0 SoftSt TI (sec) 0.2 SoftSt Trigger 0.0 SoftSt UTS StPt 100.0

Max 100.0 100.0 100.0 1000.0 1000.0 1000.0 1000.0 1000.0 1.0 100.0

Min 1.0 1.0 1.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0

The parameters control the applied voltage to the motor, simulating a voltage reduction soft-start with zero through impedance. The application of the first voltage V1 occurs at the moment a nonzero voltage is applied to a motor that has never been online or started previously in the same simulation. The way the voltage profile (V1, V2, V3 over time T12 and T23) is applied is as shown in Figure 211 below.

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Applied Voltage Scaling

Notice that the times T12 and T23 are relative to the starting point of the motor. Also, the motor start is typically initiated through the closing of a breaker or switch on the motor, or upstream from the motor if it is initialized with a zero voltage condition prior to starting the simulation.

100% V3

Final Motor Scaling Always 100%

V2 V1

T12

Point of Motor Start

T23 Time

Figure 211. Soft-start voltage application.

At any time during the soft-start, and if I Limit is a non-zero value, the current will be limited at the input to the soft-start. The control block diagram that illustrates the soft-start current limiting action is shown in Figure 212 below. Current Feedback (pu)

1.0

ILimit

  

KI

Close Switch if ILimit > 0

Soft Start Voltage (pu)

Motor Bus

VLimit

1 + sTI 0.1

Low Value

1 1 + s  0.01

Soft Start

Applied Voltage Scaling

1 100% V3

Final Motor Scaling Always 100%

100 Motor

V2

Slow down soft-start to produce smoother transitions

V1

Point of Motor Start

T12

T23 Time

Figure 212. Soft-start current limit control.

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Note that the current limit will be active as long as the motor’s speed is below SoftSt UTS StPt, the soft-start’s Up To Speed (UTS) set point. The soft start will end its action when V3 is reached, and then transition to an across the line condition, unless the motor’s speed is still below SoftSt UTS StPt and the current limit is active. When the Soft St Trigger parameter is set to 1 at runtime during a simulation, the soft-start action as defined will be forced on. This can occur at any time during a simulation, and is executed by using the Set Motor Parameter command in a script. Note that the most common use of this method is at the same moment a motor breaker/contactor is being closed back in again after having tripped of previously. This would thus create a motor re-start action with the soft-start in play. If a motor re-start action is forced by reclosing an opened breaker without this added step, note that the motor will start across the line, even if the soft-start was active during motor starting. Two key settings disable the actions of the soft-start. If V1 is set exactly to 100.0, the ramp function of the soft-start is disabled. And, if I Limit is set exactly to 0.0 (zero), the current limit action of the soft-start is disabled. Thus, to completely disable all soft-start action, both of these must be set to disable their action. The ramp action can be used without the current limit, and the current limit can be used without the ramp action. A typical set of values for applying a motor soft-start action would be as follows: Parameter Name SoftSt V1 (%) SoftSt V2 (%) SoftSt V3 (%) SoftSt T12 (sec) SoftSt T23 (sec) SoftSt I Limit (X FLA) SoftSt KI (pu) SoftSt TI (sec) SoftSt Trigger SoftSt UTS StPt (%)

Value 30.0 100.0 100.0 7.0 0.0 2.5 10.0 0.2 0.0 100.0

Comment Starts at 30% voltage

Takes 7 seconds to complete voltage ramp Keeps I below 2.5 times motor FLA

Keeps current limit on as needed

Another use of the Soft St Trigger parameter is performing a motor voltage ramp down. To do this, set the soft start parameters as follows, and then set Soft St Trigger to 1 in a script at the time you desire the ramp down to occur. Parameter Name SoftSt V1 (%) SoftSt V2 (%) SoftSt V3 (%) SoftSt T12 (sec) SoftSt T23 (sec)

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Value 99.9 1.0 1.0 3.0 0.0

Comment Activates soft start with little voltage change Ramp down to 1% voltage Ramp down quickly in 3 seconds

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SoftSt I Limit (X FLA) SoftSt KI (pu) SoftSt TI (sec) SoftSt Trigger SoftSt UTS StPt (%)

1.0 10.0 0.2 0.0 100.0

Keeps I at or below rated current

Keeps current limit on as needed

To get a clean motor-off transition, we suggest opening the motor’s breaker just before V3 is reached. If the motor’s breaker is not opened before reaching V3, the soft-start will transition to an across the line condition and thus force a motor restart. If the motor’s breaker is opened at the exact same time that V3 is reached this will produce a single time step sudden spike in terminal voltage on the motor. The artifact should not affect the simulation, but it does not present the best simulation plot results. This is why we recommend opening the motor’s breaker just before reaching V3. Motor Starting and Running Combinations Motor starting, running, tripping and re-starting can be simulated by using scripts. Thus, we have a host of simulation combinations that can be created. In this section, we illustrate several ways that motor can be started and restarted. Each time a motor starts from an offline condition, it is in a special mode which only occurs once during a single dynamic simulation. This special mode includes using the motor starting load defined, performing a starting to running load transition if desired (defined by Ld Tran Str and Ld Tran Rmp), and application of the soft-start if desired. To create a motor across-the-line re-start, simply reclose a motor’s upstream breaker/contactor. To include the soft start action, set SoftSt Trigger to 1 at run time. Now consider several simulation combinations that can be created using scripts, motor parameter settings and contactor behavior: Online Motor Re-start with No Contactor  Motor initializes online  Motor runs during simulation  Motor is tripped off by upstream loss of voltage  Motor does not have a contactor with drop out simulated  Voltage is restored to the motor by restoring upstream voltage  Motor will re-start across the line and use its running load Online Motor Re-Start with Contactor  Motor initializes online  Motor runs during simulation  Motor is tripped off by upstream loss of voltage  Motor has a contactor with drop out simulated  Motor’s contactor drops out  Voltage is restored to the motor by restoring upstream voltage and closing its contactor  Motor will re-start across the line and use its running load

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Online Motor Re-Start with Contactor and Soft Start  Motor initializes online  Motor runs during simulation  Motor is tripped off by upstream loss of voltage  Motor has a contactor with drop out simulated  Motor’s contactor drops out  Motor has valid and active soft-start parameters  Soft St Trigger is set to 1 at same time voltage is restored  Voltage is restored to the motor by restoring upstream voltage and closing its contactor  Motor will re-start using its soft-start and use its running load Offline Motor Across-the-Line Start  Motor initializes offline  Motor does not have a contactor with drop out simulated  Motor is started by closing upstream device or its own breaker  Motor has Ld Tran Str set to never transfer to running load  Motor starts using starting load  Motor runs using starting load Offline Motor Across-the-Line Start with Load Transition  Motor initializes offline  Motor does not have a contactor with drop out simulated  Motor is started by closing upstream device or its own breaker  Motor has Ld Tran Str set to transfer starting load to running load during simulation  Motor starts using starting load  Motor runs using starting load until transfer time  Motor transfers to running load  Motor runs with running load Offline Motor Soft-Start  Motor initializes offline  Motor may or may not have contactor with drop out simulated  Motor is started by closing upstream device or its own breaker/contactor  Motor may or may not have Motor Ld Tran Str set to transfer to running load  Motor has valid and active soft-start parameters  Motor starts using starting load  Motor starts with soft-start active  Motor runs using starting load and transfers to running load if set And, many more combinations of starting and re-start action could be created using the parameters made available to you in the motor model. We suggest performing several simulations on small test systems to get a more complicated and involved motor start/re-start simulation running. Then transfer settings and re-enter scripts into your larger model to apply it to your system.

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4.5.2 Synchronous Motor The synchronous motor model uses the exact model representing the salient pole generator model. The model block diagram is repeated in Figure 213 below. The differences are: 

Inclusion of load modeling in place of the prime mover; thus there is no governor model. All load modeling is identical to that documented for the EasyPower double cage induction motor model.



A fixed field excitation system; thus there is no excitation system model (excitation system models for synchronous motors may be added in a future revision).



The inertia constant H now represents the total inertia of the motor rotor and the load inertia.



During starting, the field voltage is set to zero, simulating a shorted field. The field is then applied at a given speed. Both field voltage and application speed are user specified.



An additional reverse power detector is automatically included with the model so that the field is removed if a reverse power condition is detected (when the motor is tripped off with a group of other induction motors). The delay time for this action can be user specified.

Machine Dynamics Modeling Given the synchronous motor uses the same model as the salient pole generator, no additional detail is supplied here on the machine dynamics. Refer to the section on salient pole synchronous generators for more information and modeling details. There is an additional white paper entitled “Synchronous Motor Modeling – Assessing Performance Data” that details a host of additional information regarding synchronous motor modeling and data. It draws out the definitions of all of the machine impedances and time constants from a double cage circuit model, which is also the foundation for both the round rotor and salient pole synchronous generator models. Load Modeling Also, since the loading model is the same as that used for the double cage induction motor model, no additional detail will be supplied here on load modeling. Refer to the double cage induction motor modeling section form more information and modeling details.

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X X Eq' E fd



1



 

'

Tdo s



1 Tdo'' s



 kd

X X

'' d

 Xl 

' d

 Xl 

' d

 X d'' 

' d

 Xl 



 d''



Saturation

X X

' d

' d

X ad I fd





X



d

 X d' 

 X d'' 

 Xl 

X

2

' d

 Xl 



Id



X  

 X q'' 

Iq

''

 q''

q

1 Tqo s

Figure 213. Synchronous motor model block diagram.

Table 10. Synchronous motor model parameters.

Parameter

Units

Rated HP Rated Eff Rated Speed Rated Voltage Rated Current Rated PF

HP Percent RPM Volts LL Amps

Ra Xl

pu pu

Stator winding resistance (armature resistance) Stator leakage reactance

Xd Xq X’d X’’d = X’’q

pu pu pu pu

d-axis unsaturated synchronous reactance q-axis unsaturated synchronous reactance d-axis unsaturated transient reactance d & q-axis unsaturated sub-transient reactance

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Description

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T’do T’’do T’’qo

Seconds Seconds Seconds

d-axis transient OC time constant d-axis sub-transient OC time constant q-axis sub-transient OC time constant

E1 E2 S( E1 ) S( E2 )

pu pu pu pu

First voltage to define saturation Second voltage to define saturation Saturation at E1 Saturation at E2

H

kW-Sec / kVA Combined machine and load inertia

Ld Tran Str Ld Tran Rmp

Seconds Seconds

Time at which load transfers – starting to running Time it takes to transfer load – starting to running

EFD App Speed % EFD App Value %

See Note 2 below Value of field voltage to apply during starting

Rev Pwr Del

Seconds

Time it takes to trip the reverse power detection

SoftSt V1 SoftSt V2 SoftSt V3 SoftSt T12 SoftSt T23 SoftSt I Limit SoftSt KI SoftSt TI SoftSt Trigger SoftSt UTS StPt

% % % Seconds Seconds Times FLA pu Seconds

First soft-start voltage Second soft-start voltage Third soft-start voltage Time between first and second soft-start voltage Time between second and third soft-start voltage Soft-start current limit specified in times FLA Soft-start current limit gain Soft-start current limit time constant When set to 1 at runtime, forces soft-start action “Up To Speed” set point where current limit stops

%

Notes: 1. OC means Open Circuit. 2. EFD App Speed actually serves a dual purpose for field application: EFD App Speed >= 50

The % speed at which the field will be applied to the starting motor.

EFD App Speed < 50

The absolute simulation time in seconds when the field will be applied to starting the motor.

Applied Field Voltage at Starting For starting motors, “EFD App Value” will need to be set to match the starting conditions of the motor. If this value is set to 100%, then after the start is complete, one should find the terminal conditions of the motor near the rated current and power factor specified for the motor. However, in most cases, the applied field voltage at starting is much greater (from 200 to 400%) to achieve faster and more assured synchronization. Thus, “EFD App Value” should be set to

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match such a value. Note that “EFD App Value” is in percent of the rated field voltage for the motor at rated conditions. For example, if the field voltage of a motor is equal to 125 volts when operated at rated terminal voltage, terminal current and power factor, and the field voltage applied at starting is 425 volts, then “EFD App Value” should be equal to 425 / 125 * 100% = 340%. In addition, when a high value of “EFD App Value” is used when applying the field, note that it should be dropped back down to a value around 100% to keep the motor from an over-current condition as it exports vars with the high field voltage after synchronism is reached. To do this, one will need to make use of a script to start the motor (a simple double click on a breaker will not suffice). After the motor has started, a “Set Motor Parameter” script command will need to be used to drop the field voltage back down to the desired value. Consider this example script: Script Command

Equipment

Value 1

Value 2

Run to Time

Time 1.0

Close Switch

M-1-Starter

Run to Time

5.0

Set Motor Parameter

M-1

25

100.0

Run to Time

10.0

The resulting message log could look like this: 0.0000 1.0008 1.0008 1.0008 5.0008 5.0008 5.0008 10.0008

Script Script Runtime Script Script Runtime Script Script

OK OK OK OK OK OK OK OK

Simulation Run To 1.0000 Seconds. M-1-STARTER Device Closed. M-1 Sync Motor Starting Simulation Run To 5.0000 Seconds. M-1 Set Motor Parameter in Row 25 to 100.00000. M-1 Changing Synchronous Motor parameter FlashValue from 340.000 to 100.000. Simulation Run To 10.0000 Seconds. Simulation Complete.

Soft-Start Capability The soft-start capability for synchronous motors is identical to that for the induction motor just described in the previous section. Please refer to that documentation.

4.6 Motor Load Models Refer to “Induction Motor Modeling - Part 3” for a full description of the three motor load models and how they are applied.

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4.7 Protective Device Modeling As noted earlier, all protective devices modeled in Power Protector are simulated in the DS Engine if appropriate data is supplied and the Power Protector feature is enabled (has been purchased). For users without Power Protector, no protective devices are transferred into the DS Focus. Modeling of protective devices includes:         

Fuses LV Breakers Relays Under-Frequency Relay Action Contactor Drop Out Action ATS Auto-Transfer Action Over-Voltage Relay Action Under-Voltage Relay Action Source Inverter Solid State Blocking Action for Faults

In all cases, for devices that include a minimum and maximum curve for device operation (for example, an uncertainty band or fuse min melt and max clear curve) the more severe max clear curve is used to determine when a device will be tripped. This will thus keep a fault condition on longer, and corresponds to a consistent tripping action that matches the EasyPower Arc Flash tool. More specifically, we note the following for each protective device: Fuses

Fuses are simulated using an accumulated I2T action. When current through a fuse causes the trip time to drop below 1000 seconds, I2T energy begins to accumulate. The I2T trip value is updated on each time step corresponding to the present current flowing through the fuse. When the accumulated I2T meets or exceeds the I2T trip value, the fuse is tripped (actually the EasyPower switch on the oneline is opened to simulate this). Note that the energy accumulated in the fuse is not reset during a given simulation. This memory action is performed since a typical dynamic simulation runs for 10 to 50 seconds, and we believe this is not long enough to allow any significant dissipation of heat from the fuse. From this memory action, multiple faults through a fuse can contribute to a faster fuse blowing action, which in reality would exist in the field.

LV Breakers Low Voltage Breakers are simulated using a time accumulation method. When current through a LV Breaker causes the trip time to drop below 1000 seconds, then a timer is used (accumulating time) to trip the device as long as the current remains above the devices pickup setting. When the accumulated time exceeds the trip time at the current point on the devices TCC (specified and

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updated by the present current flowing through the device), the device will trip. The device instantaneously resets if the current drops below the pickup setting. Relays

Relays are simulated using time accumulation as a simulated induction disc turns. This assumes that digital relays are performing a similar action. Thus the device is simulating travel time and tripping in accordance to the time dial setting. When current through a Relay causes the trip time to drop below 1000 seconds, the disc simulator starts timing. When the time passing by meets or exceeds the trip time from the relays TCC based on present current through the device, the device will trip. If the current drops below the pickup setting before tripping, the device will simulate travel-back of the induction disc (again assuming digital devices will do the same). This travel-back assumes that the full travel-back of any relay is 60 seconds when on the maximum time dial, with this effect ratio’ed accordingly to other time dial settings. From this travel-back action, we are simulating memory, and thus are including the capability of a relay to trip faster on a second fault application.

UF Relays

Under-Frequency Relays use a single under-frequency setting and timer. When the bus frequency drops below the setting, and has stayed below for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the frequency goes above its setting. Under-Frequency Relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet.

Contactors

Contactors operate like the Under-Frequency Relay, and trip after voltage has dropped below its setting for the time specified. The device resets instantaneously.

ATS

ATS’ only perform automatic operation from left (Normal) to right (Emergency) as seen on the oneline. Their behavior is as follows: Assuming we are originating on the Normal side, if the source is lost (voltage drops below the Trip Voltage setting for a time longer than the Delay on Start setting), the ATS is prepared for transfer. If the voltage on the Emergency side is above the ATS Required Voltage setting, then the transfer will continue. If not, the ATS remains on the Normal side. The ATS model does not presently simulate the Neutral position in its transfer. Therefore, if transferring, it stays on the Normal Source side until the Neutral Delay time and Mechanical Delay time are satisfied. To simulate the Neutral

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position, an additional bus would need to be simulated in the network, and that has not been implemented in the present version. The ATS will not auto-transfer-back if the Emergency Source is lost. The action presently modeled is a one-way transfer. OV Relays

Over-Voltage Relays use a single over-voltage setting and timer. When the bus voltage goes above the setting, and has stayed above for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the voltage goes below its setting. Over-Voltage Relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet.

UV Relays

Under-Voltage Relays use a single under-voltage setting and timer. When the bus voltage goes below the setting, and has stayed below for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the voltage goes above its setting. Under-Voltage Relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet.

Inv Block

Inverters (when no DS data is specified) include a blocking action when the fault current (specified in the inverter data dialog), has stayed above 102% FLA for the time specified. Upon blocking, the inverter current injection is removed from the network model and the inverter does not interact with the grid.

If you have EasyPower Power Protector, the DS Engine will automatically simulate your defined protective devices in any TMS or DS simulation. Also, these protective device simulations need no additional data on your part, and thus the method by which each protective device is simulated needs clarification. Internally, protective devices can have differences in how they behave over time. In the DS Engine, we have elected to simulate these devices using standard approaches that will supply what we believe to be an adequate level of detail in your simulations. In the future, more detail may be added to the particular action of some protective devices. However, we believe that our users need reasonable functionality without excessive data entry. To this end, we have adopted the following simulation methods.

4.7.1 Fuses Fuses use I2T to determine when the device will trip. Thus we are using an accumulation of energy. The method used follows these steps every time the device is checked, which is hard coded in the engine to be every half cycle: 1. Get current through device.

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2. Look up time to trip off the device’s TCC max clear curve. 3. If the time to trip is >= 1000 (i.e. off the manufacturer’s curve) do nothing, and skip past all remaining steps. 4. If the time to trip is < 1000 (above steady-state pickup level), determine the I2T to trip (from the current through the device and the time to trip). 5. Accumulate actual I2T from current through the device and the time between successive checks of the device (hard coded to check every half cycle). 6. If the actual I2T is >= the I2T to trip, trip the device. When the device trips, the switching device in the power flow associated with this protective device will open. If the device is already open, then no action is taken. For fuses, we will assume that if the device does not open, even though it is exposed to high currents, the energy accumulated during the simulation will not dissipate. Thus, if a second fault event occurs and the device is exposed to additional high currents (where the time to trip is < 1000), then we will start accumulating on top of the previous energy accumulation. Since the time constants involved in removing accumulated energy from a fuse are in the order of 120 seconds, and most dynamic simulations last under 30 seconds, there is no reason to reset, or to reduce the accumulated energy.

4.7.2 Low Voltage Breakers Low Voltage Breakers use time accumulation and I2T accumulation to determine when the device will trip. The method used (hard coded in the engine to evaluate conditions every half cycle) follows these steps every time the device is checked: 1. Get current through device. 2. Look up time to trip off the devices TCC max clear curve. 3. If the time to trip is >= 1000 (i.e. off the manufacturers curve), do nothing and skip past all remaining steps. 4. If the time to trip is < 1000 (picked up), use this time to check for tripping. 5. Accumulate time between successive checks of the device (hard coded to check every half cycle) for the definite time sections. 6. If the actual time is >= the trip time (step 2), trip the device. 7. Accumulate I2T energy between successive checks of the device (hard coded to check every half cycle) for the I2T sections.

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8. If the energy accumulated is greater than the I2T curve, trip the device. When the device trips, the switching device in the power flow associated with this protective device will open. If the device is already open, then no action is taken. For low voltage breakers, we have assumed that if the current drops below pickup, the device will perform an instantaneous reset.

4.7.3 Relays Relays use travel time to determine when the device will trip. Thus we are using an accumulation-of-time or simulated disc rotation. The method used (hard coded in the engine to evaluate conditions every half cycle) follows these steps every time the device is checked: 1. Get current through device. 2. Look up time to trip off the device’s TCC max clear curve. 3. If the time to trip is >= 1000 (i.e. off the manufacturers curve), do nothing and skip past all remaining steps. 4. If the time to trip is < 1000 (picked up), accumulate actual time from the time between successive checks of the device (hard coded to check every half cycle). 5. If the actual time is >= the time to trip, trip the device. Now, once the device is tripped, an additional timer is started that includes the breaker delay time and any auxiliary time delay. Once that timer is satisfied, the device which the relay is pointing to is opened. If the device is already open, then no action is taken. If the relay resets due to the fault clearing before its operation, the relay goes into a travel back mode to simulate induction disc travel back. The time to fully reset is based on a typical IAC-53 relay taking approximately 60 seconds to fully travel back when having traveled to near tripping, at a maximum time dial (the maximum distance that is possible for the relay to cover). Also, since the shaded pole magnetic device is still cutting a field across the device, the rate of rotation is of a constant velocity. Consider a relay using a 5 time dial setting, and where the max time dial is 10. If the relay is exposed to current that causes a 1.0 second trip time for that setting, then if the relay resets just before tripping, the relay will need 30 seconds to travel back to rest. If a second fault of the same magnitude as the first is applied after 15 seconds of travel back time (a fault that generates a 1.0 second trip time when the disc is fully reset, based on the TCC), the relay will now trip in only 0.5 seconds, since it has only returned half way. If a relay does not have a breaker defined to trip (see the trip device definition in the Relay data dialog and right most columns), then we will use the same method for locating a protective device as used in Power Protector and Arc Flash. We would recommend not relying upon this, but to edit your relay data to input the actual device that the relay trips.

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4.7.4 Under-Frequency Relay An under-frequency relay has been included with the DS Engine. This relay is entered in the Relay equipment data dialog, and is specified as shown in Figure 214. The one relay that has been entered into the Library is located in the ABB manufacturer selection and Type KF. After importing the ABB Type KF relay, in the System tab, you will notice the Device Function set to 81 and the Device Function Type set to “Other”. Both of these are important for the DS Engine to recognize the device as an under-frequency relay. Finally, specify the breaker to trip, and any aux time involved with additional time delay relays.

Figure 214. Relay data dialog for Under-Frequency – System tab.

To set the relay, go to the Setting tab, and enter values only for the bottom Frequency category, where you will find the Frequency Range, Delay and Frequency Setting values. Make selections as appropriate. If you have an under-frequency relay made by another manufacturer with different ranges and settings, go to the Device Library, find the ABB Type KF relay, and copy it under the manufacturer you desire. Then, modify the three value categories to meet the specification for your relay.

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Figure 215. Relay data dialog for Under-Frequency – Settings tab.

The under-frequency relay model in the DS Engine simulates a standard under-frequency relay action. If the bus frequency drops below the Frequency Setting, and stays below the value for a time greater than or equal to the Delay, then the device will trip. After tripping, both breaker delay and the aux time delay are satisfied before actually tripping the device specified by the relay settings (see Figure 214 above). If the bus frequency rises above the Frequency Setting before the Delay is satisfied, the relay will instantaneously reset. In this version, under-frequency relays (actually all relays for that matter) only connect to CTs. The relay references the bus frequency (for its frequency input) for the bus closest to the CT. When PTs are added to EasyPower, the under-frequency relay will be able to be connected to a PT. Note that bus frequency is synthesized from the bus voltage angle, and may not be exactly equal to bus frequency as measured by an actual relay. The calculation used to determine bus frequency is: Bus Freq 

AngleBusVoltage Now  AngleBusVoltage LastTime 2  t 

where the values of bus voltage angle are in radians, and the time step ∆t is in seconds. After the calculation above, filtering is applied in the form of a simple time constant equation, where the time constant used is 10 times the time step of the simulation. An example of calculated bus frequency without and with filtering vs. machine speed is shown in Figure 216 and Figure 217 below. Notice that even with filtering there is a slight departure from the smooth machine speed

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curve when there are sudden changes in the network (in this case switch opening of a utility source and then a feeder breaker on under-frequency).

0.9900

1.0100

COGEN [Spd PU]

GEN-BUS [Frq PU]

0.9900

1.0100

EasyPower DS

0.0

COGEN [Spd PU] GEN-BUS [Frq PU]

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3.0

Time (Seconds)

Figure 216. Bus frequency (red) vs. machine frequency (blue) – without smoothing.

0.9900

1.0100

COGEN [Spd PU]

GEN-BUS [Frq PU]

0.9900

1.0100

EasyPower DS

0.0

COGEN [Spd PU] GEN-BUS [Frq PU]

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3.0

Time (Seconds)

Figure 217. Bus frequency (red) vs. machine frequency (blue) – with smoothing.

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4.7.5 ATS Model The ATS model in the DS Engine simulates one-way automatic transfer from Normal (left) to Emergency (right) on an ATS equipment item. The settings for this device are found under the Stability tab in the ATS equipment dialog, and are: Parameter

Units

Description

Trip Voltage Del on Start Req Voltage Neutral Del Mech Del

Percent Seconds Percent Seconds Seconds

Normal bus voltage at which ATS picks up Time in under-voltage condition before transfer Voltage required on Emergency bus for transfer Neutral delay time Mechanical delay time.

In addition: 

Once the voltage has dropped below the Trip Voltage for a time of Del on Start, and the Emergency bus voltage is greater than Req Voltage, a transfer is commenced, and is delayed for Neutral Del + Mech Del seconds. After the delay is satisfied, the ATS is transferred to the Emergency bus.



If the voltage on the Emergency bus is not above the Req Voltage, then no transfer is made. If the Emergency bus voltage rises above Req Voltage, and a transfer is in process, then the ATS will transfer. Thus, the Req Voltage is the last check for a transfer. If all conditions are satisfied for a transfer, the ATS will wait for the Emergency bus voltage to rise above Req Voltage, and then instantaneously transfer.



If the Normal bus voltage rises above Trip Voltage before Del on Start is satisfied, the ATS performs an instantaneous reset, and remains on the Normal bus.



When the ATS’ Switch Type is a “Primary Selector Switch”, then all ATS functionality is disabled.



You must own EasyPower Power Protector to have the contactor model feature in the DS Engine.

4.7.6 Contactor Model The contactor model supplied with the DS Engine performs in a simplistic manner with only two data items needed (under-voltage threshold and time to trip). The contactor simply responds to an under-voltage condition, and if subjected to a level below the under-voltage threshold for the time to trip, will cause the switching device it is associated with to switch open in the simulation. Contactors can be found within fused switch and low voltage breaker equipment dialogs, under the Stability tab. They are both enabled and specified in that tab.

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You must own EasyPower Power Protector to have the contactor model feature active in the DS Engine. Here are a few more application notes regarding contactors: 

If the switching device a contactor is associated with is already open, and the contactor says to open, then no action is taken.

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Contactors will auto-trip off at the beginning of a simulation where the contactor is located in an isolated (and thus disconnected) part of your system. The model is responding to its initial voltage being zero, which is below its trip threshold. Since the initial power flow represents steady-state, then by definition these contactors must be off.

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Care must be taken to make sure that a protective upstream device is included in your simulation when using a contactor that is exposed to a fault current condition. If such is not done, then a contactor (sensing an under-voltage condition from a fault on its load side), will interrupt the fault. In the simulation, this will happen cleanly, and without mishap. However in real life, due to contactors not being rated to interrupt SC current, the contactor would most likely explode into a mass of molten metal.

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If the voltage at the contactor goes above the under-voltage threshold before the time to trip is satisfied, the contactor will perform an instantaneous reset.

4.7.7 Under-Voltage Relay An under-voltage relay has been included with the DS Engine. This relay is entered in the Relay equipment data dialog, and is specified similar to the under-frequency relay as shown in Figure 218 and Figure 219. The one relay that has been entered into the Library is located in the ABB manufacturer selection and Type 27. After importing the ABB Type 27 relay, in the System tab, you will notice the Device Function set to 27 and the Device Function Type set to “Other”. Both of these are important for the DS Engine to recognize the device as an under-voltage relay. Finally, specify the breaker to trip, and any aux time involved with additional time delay relays.

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Figure 218. Relay data dialog for Under-Voltage – System tab.

Figure 219. Relay data dialog for Under-Voltage – Settings tab.

Under-voltage relays use a single under-voltage setting and timer. When the bus voltage goes below the setting, and has stayed below for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the voltage goes above its setting. Under-voltage relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet. The CT ratio has no effect on the relay, as the relay senses the voltage of the bus closest to the CT connection.

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4.7.8 Over-Voltage Relay An over-voltage relay has been included with the DS Engine. This relay is entered in the Relay equipment data dialog, and is specified similar to the under-frequency relay as shown in Figure 220 and Figure 221. The one relay that has been entered into the Library is located in the ABB manufacturer selection and Type 59. After importing the ABB Type 59 relay, in the System tab, you will notice the Device Function set to 59 and the Device Function Type set to “Other”. Both of these are important for the DS Engine to recognize the device as an under-voltage relay. Finally, specify the breaker to trip, and any aux time involved with additional time delay relays.

Figure 220. Relay data dialog for Over-Voltage – System tab.

Over-voltage relays use a single over-voltage setting and timer. When the bus voltage goes above the setting, and has stayed above for the time specified, the device will trip its specified breaker. The relay performs an instantaneous reset if the voltage goes below its setting. Over-voltage relays are presently only able to be connected onto a Current Transformer (CT). In a future revision, we anticipate adding Potential Transformers (PT) to the equipment pallet. The CT ratio has no effect on the relay, as the relay senses the voltage of the bus closest to the CT connection.

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Figure 221. Relay data dialog for Over-Voltage – Settings tab.

4.7.9 Inverter Blocking During Fault Inverters include a blocking action when the fault current (specified in the inverter data dialog, see Figure 222) has stayed above 102% FLA for the time specified. Upon blocking, the inverter current injection is removed from the network model and the inverter does not interact with the grid. This action is default when no stability data has been entered for the inverter. Note that the present version of the DS Engine does not allow the P1VG and WT4G models to be specified with the inverter.

Figure 222. Inverter - Settings tab.

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5.0 Messaging The DS Engine Message Log is supplied to inform the user of particular model behavior. There simply is not enough room on the oneline to present the number of messages that can be generated by a large case, and so a message log provides a convenient chronology of the simulation performed as well as particular model behavior in the simulation. In the author’s view, the message log is essential to fully document a simulation. Due to the real-time nature of the simulation, and the complexity of even a few dynamic models running together, there is a need for a clear and concise chronology of events. All messages in the Message Log are meant to supply the user with necessary feedback on the condition of their models during a simulation. We encourage the user to always review the Message Log after each simulation, as a condition may need attention so that your simulation is performed correctly. For example, if the following warning is generated: "Gas Turbine Gov1 on Max Limit." You will need to determine why this generator’s governor is on a limit, then fix the issue and rerun the simulation. The Message Log will need to be checked again to see if the warning has been eliminated. Without a correction, in this example, the system will not be in steady-state before running the simulation. As soon as the simulation is run, the system model will be trying to satisfy system power balance, since this generator was unable to meet its requirement. Messages are broken down into four basic types: 

Script – Notes a Script command action was taken.

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Runtime – Notes a message from the DS Engine or a model at run time.

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Initialization – Notes a message from the DS Engine or a model at initialization time.

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Command – Notes a message from a user button command.

Messages also have a status. The five major status conditions reported are: 

Error !!! – The DS Engine or a model has encountered an error. This must be resolved before your simulation can be run. You will not be allowed to perform a simulation until the error is resolved.

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Warning – The DS Engine or a model has encountered a condition that could compromise the accuracy of your simulation. We suggest resolving all warnings, even though the simulation will be allowed to proceed.

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Pass – At initialization time, if a model initializes properly, this message is displayed.

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

OK – This status accompanies informational messages. For example, this could accompany a message from a protective device noting that it has picked up on an overcurrent condition.

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Pausing – This status appears when the user issues a button command to pause the simulation.

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Stepping – This status appears when using the stepping capability in DS.

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Result – This status appears with information messages that are a result of a simulation. This would include Arc Flash results, relay percent travel, etc.

In the following sections, messages are grouped by type, and are supplied a description of conditions that can lead to the message as well as methods to correct the condition cited (if necessary).

5.1 Exciter Max Limit Messages "Basler AVC1 Exciter on VRMax Limit." "IEEET1 AVR on Max Limit." "IEEET2 AVR on Max Limit." "IEEE AC1A on AVR Max Limit." "IEEE AC1A on Regulator Max Limit." "IEEE AC2 VR on Max Limit." "IEEE AC2 AVR Output VA on Max Limit." "IEEE AC2A VR on Max Limit." "IEEE AC2A AVR Output VA on Max Limit." "IEEE AC2A Exciter Output VE on Max Limit." "IEEE AC3A Exciter Output VE on Max Limit." "IEEE AC3A AVR Output VA on Max Limit." "IEEE AC4A Regulator on Max Limit." "IEEE AC5A Exciter on Max Limit." "IEEE AC6A on AVR Max Limit." "IEEE AC6A on Regulator Max Limit." "IEEE AC6A feedback on VHMax limit." "IEEE AC7B VA on Max Limit." "IEEE AC7B VR on Max Limit." "IEEE AC7B Exciter Output VE on Max Limit." "IEEE AC8B on AVR Max Limit." "IEEE AC8B on Exciter Output Max Limit." "IEEE DC1A Exciter on Max Limit." "IEEE DC2A Exciter on Max Limit." "IEEE DC3A Exciter on Max Limit." "IEEE DC4B Exciter on Max Limit."

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"IEEE DC4B Regulator on Max Limit." "IEEE ST1A AVR on Max Limit." "IEEE ST1A Exciter on Max Limit." "IEEE ST2 Regulator on Max Limit." "IEEE ST2 Exciter on Max Limit." "IEEE ST2A Regulator on Max Limit." "IEEE ST2A Exciter on Max Limit." "IEEE ST3A Regulator on Max Limit." "IEEE ST3A Exciter on Max Limit." "IEEE ST3A Initial Efd is on Max Limit." "IEEE ST4B Regulator on Max Limit." "IEEE ST4B Exciter on Max Limit." "IEEE ST5B Rectifier on Max Limit." "IEEE ST5B Regulator on Max Limit." "IEEE ST6B AVR on VR Max Limit." "IEEE ST6B Regulator on Max Limit." "IEEE ST7B AVR Input on Max Limit." "IEEE ST7B AVR Output on Max Limit." "Simple Exciter on Max Limit." "Stamford1 Exciter EFD on Max Limit of EC1." "Stamford1 Exciter AVR on Max Limit of EA1." Description - At Initialization, these exciter models trigger the messages noted when on a maximum limit either in the AVR or the output of the exciter. This is typically caused by overexciting the generator past the model settings, or by having an unreasonable limit specified in the exciter model. Fix - Try reducing generator var export (in the power flow case, lower control voltage for a PV or Swing generator, or reduce Q for a PQG) or changing the limit (make it larger).

5.2 Exciter Min Limit Messages "Basler AVC1 Exciter on VRMin Limit." "IEEET1 AVR on Min Limit." "IEEET2 AVR on Min Limit." "IEEE AC1A on Neg EFD Output Limit." "IEEE AC1A on AVR Min Limit." "IEEE AC1A on Regulator Min Limit." "IEEE AC2 VR on Min Limit." "IEEE AC2 AVR Output VA on Min Limit." "IEEE AC2 Exciter Output VE is < zero." "IEEE AC2A VR on Min Limit." "IEEE AC2A AVR Output VA on Min Limit." "IEEE AC2A Exciter Output VE is < zero."

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"IEEE AC3A Exciter Output VE on Min Limit." "IEEE AC3A AVR Output VA on Min Limit." "IEEE AC4A Regulator on Min Limit." "IEEE AC5A Exciter on Min Limit." "IEEE AC6A on Neg EFD Output Limit." "IEEE AC6A on AVR Min Limit." "IEEE AC6A on Regulator Min Limit." "IEEE AC6A feedback on zero limit." "IEEE AC7B VA on Min Limit." "IEEE AC7B VR on Min Limit." "IEEE AC7B Exciter Output VE on Min Limit." "IEEE AC7B AVR Output-VA*KP*VT on Min Limit." "IEEE AC8B on AVR Min Limit." "IEEE AC8B on Exciter Output Min Limit." "IEEE DC1A Exciter on Min Limit." "IEEE DC2A Exciter on Min Limit." "IEEE DC3A Exciter on Min Limit." "IEEE DC4B Exciter on Min Limit." "IEEE DC4B Regulator on Min Limit." "IEEE ST1A AVR on Min Limit." "IEEE ST1A Exciter on Min Limit." "IEEE ST2 Regulator on Min Limit." "IEEE ST2 Exciter on Zero Limit." "IEEE ST2A Regulator on Min Limit." "IEEE ST2A Exciter on Zero Limit." "IEEE ST3A Regulator on Min Limit." "IEEE ST3A Exciter on Zero Limit." "IEEE ST4B Regulator on Min Limit." "IEEE ST4B Exciter on Min Limit." "IEEE ST5B Rectifier on Min Limit." "IEEE ST5B Regulator on Min Limit." "IEEE ST6B AVR on VR Min Limit." "IEEE ST6B Regulator on Min Limit." "IEEE ST6B Ifd Feedback on LV Gate Limit." "IEEE ST7B AVR Input on Min Limit." "IEEE ST7B AVR Output on Min Limit." "Simple Exciter on Min Limit." "Stamford1 Exciter EFD on Min Limit of EC2." "Stamford1 Exciter AVR on Max Limit of EA2." Description - At Initialization, these exciter models trigger the messages noted when on a minimum limit, either in the AVR section or the exciter section. This is typically caused by under-exciting the generator past the model settings, or by having an unreasonable limit specified in the exciter model.

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Fix - Try reducing generator var import (in the power flow case, raise control voltage for a PV or Swing generator, or increase Q for a PQG) or changing the limit (make it smaller or more negative).

5.3 Exciter Gate Limit Messages "IEEE AC1A on OEL Low Value Gate Limit." "IEEE AC1A on UEL High Value Gate Limit." "IEEE AC2A AVR on VOEL Limit." "IEEE AC2A AVR on VUEL Limit." "IEEE AC3A AVR on VUEL Limit." Description - At Initialization, these exciter models trigger the messages noted when on a low or high gate limit in the Over and Under Excitation Limiter inputs (OEL, UEL). This is typically caused by an out of range var expectation on the generator, or an incorrect value set for the OEL and UEL. Fix - Try modifying generator var import/export (in the power flow case, change control voltage for a PV or Swing generator, or change Q for a PQG) or changing the limit.

5.4 Governor Max Limit Messages "Caterpillar Diesel 1 PID Output is on TMax Limit." "Cummins Diesel1 Gov on Max Limit." "Cummins Gas Engine1 Gov on Max Limit." "Diesel Gov1 on Max Limit." "Gas Turbine Gov1 on Max Limit." "Gas Turbine2 Gov on Max Limit." "Gas Turbine2 Low Value Output on Max Limit." "Gas Turbine WDGov on Max Limit." "Hydro Turbine Gov on Max Limit." "IEEE Hydro2 Turbine Gov on Max Limit." "IEEE Hydro3 Turbine Gov on Max Limit." "IEEE Steam Turbine Gov on Max Limit." "Pratt & Whitney FT8 Gov U on Max Limit." "Splitshaft1 Gas Turbine Gov on Max Limit." "Steam Turbine Gov1 on Max Limit." "WECC Gast on Max Limit." "Woodward Diesel Gov1 on Max Limit." "Woodward Steam PID1 on Max Limit." Description – Governor models control the mechanical power delivered to the shaft of a generator. If the generator is asking for more power than can be supplied by the prime mover,

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this message will be generated at initialization. Note that whenever a governor reports this condition, a steady-state run will not be steady-state. The power required by the system is not being met, and the governor is on a limit. As soon as your simulation begins, other generating units in the system will have to pick up the extra generation needed to balance out the system. Fix - Reduce the power output of the generator in the power flow or increase the max limit setting in the governor model to remove this warning.

5.5 Governor Min Limit Messages "Caterpillar Diesel 1 PID Output is on TMin Limit." "Cummins Diesel1 Gov on Min Limit." "Cummins Gas Engine1 Gov on Min Limit." "Diesel Gov1 on Min Limit." "Gas Turbine Gov1 on Min Limit." "Gas Turbine2 Gov on Min Limit." "Gas Turbine2 Low Value Output on Min Limit." "Gas Turbine WDGov on Min Limit." "Hydro Turbine Gov on Min Limit." "IEEE Hydro2 Turbine Gov on Min Limit." "IEEE Hydro3 Turbine Gov on Min Limit." "IEEE Steam Turbine Gov on Min Limit." "Pratt & Whitney FT8 Gov U on Min Limit." "Splitshaft1 Gas Turbine Gov on Min Limit." "Steam Turbine Gov1 on Min Limit." "WECC Gast on Min Limit." "Woodward Diesel Gov1 on Min Limit." "Woodward Steam PID1 on Min Limit." Description – Governor models control the mechanical power delivered to the shaft of a generator. If the generator is asking for less power than can be supplied by the prime mover, this message will be generated at initialization. Note that whenever a governor reports this condition, that a steady-state run will not be steady-state. The power required by the system is not being met, and the governor is on a limit. As soon as your simulation begins, other generating units in the system will have to reduce generation to balance out the system. Fix - Increase the power output of the generator in the power flow or decrease the min limit setting in the governor model to remove this warning. Note - Typically for a min limit message to appear, either erroneous data has been entered for the governor model, or the generator in the power flow case is absorbing power. The min limit for most governor / prime mover models is zero. This simply states that the prime mover will not become a load. In actual practice, the min limit is often set to the level of turbine power output that would trip the reverse power relay, or some other form of minimum power protection. These

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messages thus alert the user to an improper initialization, where the unit would have actually tripped offline.

5.6 Governor Runtime Load Limit Messages "Gas Turbine Gov1 Now ON Ambient Temp Load Limit." "Gas Turbine Gov1 Now OFF Ambient Temp Load Limit." "WECC Gast Now ON Ambient Temp Load Limit." "WECC Gast Now OFF Ambient Temp Load Limit." Description - As for Max Limit messages discussed above, this message is supplied (typically during run-time) when a unit is being over-loaded. This can happen during a contingency, where there is a major loss of generation and remaining units must then pick up the load, forcing them into an overload condition. The load limit in this case performs automatic control, causing the generator’s gas turbine not to continue in overload. The messages supplied inform you when the turbine goes into and out of load limit control. Fix – Though this is a message simply noting a control action, if you desire to keep this message from appearing (meaning you desire to keep the turbine from moving into a temperature load limit condition), then create a system contingency that does not have a large imbalance of load requirement vs. available generation. Create a condition where load and generation are balanced, and where generation has some headroom (generator capability greater than load requirement). Alternatively, since the temperature load limit takes time to be reached (time constant simulates how the turbine heats up over time when in an overload condition), only allow overload conditions that have a duration and level that will not cause the unit to reach the temperature load limit.

5.7 Governor Initialization Load Limit Messages "Gas Turbine 1 Exceeding Ambient Temperature Load Limit at Initialization." "WECC Gast Exceeding Ambient Temperature Load Limit at Initialization." Description - As for Max Limit messages discussed above, this message is supplied (during initialization) when a unit is over-loaded. Since the governor is limited, upon running a simulation, the generator will be forced to a lower power level, creating a non steady-state response if run steady-state. Fix - Reduce the power output of the generator in the power flow or increase the max limit setting in the governor model to remove this warning.

5.8 Slew Run Messages "Round Rotor Gen Slew Run Diverged (IMag)." "Round Rotor Gen Slew Run Exceeded Max Iters."

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"Ind2 Motor Slew Run Diverged (IMag)." "Ind2 Motor Slew Run Diverged (Slip)." "Ind2 Motor Slew Run Exceeded Max Iters for PF Conditions." "Ind2 Motor Slew Run Exceeded Max Iters at Full Load." Description - These are initialization errors. The machine model noted incorporates saturation and other non-linear methods, and thus initialization of the model cannot be performed directly. An iterative error driven minimization technique is used (slew run). If the generator terminal conditions are extreme, this iterative technique may diverge. Several message types are seen when these conditions occur, and these are: 

Diverged (IMag) - This notes that the terminal current magnitude triggered the divergence sensor.



Exceeded Max Iters - This notes that the slew run did not converge by the time it reached the maximum number of allowed iterations.



Diverged (Slip) – This notes that induction motor slip triggered the divergence sensor.

Fix - Review the machine’s terminal conditions (P and Q) and determine if the equipment is indeed being asked to perform far beyond its rated capability. Modify the machine in the power flow case to bring it within an acceptable loading. Alternatively, the model data may be corrupt, and may not be representing a reasonable machine characteristic. If you are using your own data, try replacing it with EasyPower-provided model data from the model library. Compare constants to see where your data may be in error. Odd Root Cause – In the process of running simulations with induction motors, we have found an instance where this message is generated, but the causes above are not at the root of the issue. In one instance we discovered that the base frequency had been set to a high value of 400 Hz, due to a system being created after running a 400 Hz simulation of an airport runway grid. The high base frequency caused a motor with data specified for 50 or 60 Hz to diverge during the slew run.

5.9 Slip Estimate Messages "Ind2 Motor Cannot Meet Power Required (Slip Estimate)." "Ind2 Motor Slip Run Diverged (IMag - Slip Estimate)." "Ind2 Motor Slip Run Diverged (Slip - Slip Estimate)." Description – At initialization, in addition to a slew run (see section just above), induction motor models also need to develop an estimate of slip to enter the slew run. Since the torque-slip curve is non-linear, determining this initial estimate again necessitates an iterative technique. These messages appear when the slip estimate cannot be found. Several message types are seen, and these are:

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

Cannot Meet Power Required – This message is generated when the full torque-slip curve has been traversed, and no value of torque can supply the power required of the motor.



Diverged (IMag) – This notes that the iterative estimate method diverged, and that terminal current magnitude triggered the divergence sensor.

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Diverged (Slip) – This notes that the iterative estimate method diverged, and that slip triggered the divergence sensor.

Fix – Review the machine’s terminal conditions (P and Q) and determine if the equipment is indeed being asked to supply power far beyond the unit’s capability. Modify the machine in the power flow case to bring it within an acceptable loading. Alternatively, the model data may be corrupt, and not be representing a reasonable machine characteristic. If you are using your own data, try replacing it with EasyPower-provided model data from the model library. Compare constants to see where your data may be in error. Odd Root Cause – In the process of running simulations with induction motors, we have found an instance where this message is generated, but the causes above are not at the root of the issue. In one instance we discovered that the base frequency had been set to a high value of 400 Hz, due to a system being created after running a 400 Hz simulation of an airport runway power grid. The high base frequency caused a motor with data specified for 50 or 60 Hz to diverge during the slip estimate.

5.10 Data Error Messages 5.10.1 Generator Error Messages "Round Rotor Gen E2 is