B.Sc. (Engg.) (Hans.) ME.,
Dr. - lng (Berlin), F.I.E. (India)
Life Member - ISTE
(Formerly Principal O.U. College of Engineering &
Dean, Faculty of Engineering, O.U. Hyderabad)
2008
421 Pages
ISBN: 978-81-7800-181-0
Contents
1 Introduction
2 Load Flow Analysis
2.1 Bus Classification ............................................................................................... 9
2.2 Modelling for Load Flow Studies ...................................................................... 10
2.3 Gauses - Seidel Iterative Method ...................................................................... 13
2.4 Newton - Raphson Method .............................................................................. 16
2.4.1 Rectangular Coordinates Method ..................................................... 17
2.4.2 The Polar Coordinates Method ........................................................ 19
2.5 Sparsity of Network Admittance Matrices ........................................................ 22
2.6 Triangular Decompostion .................................................................................. 23
2.7 Optimal Ordering ............................................................................................... 25
2.8 Decoupled Methods ........................................................................................... 27
(xiI) Contents
2.9 Fast Decoupled Methods ............................................................................•...... 27
2.10 Load Flow Solution Using Z Bus ...................................................................... 29
2.10.1 Bus Impedance Formation ............................ ~ .................................. 29
2.10.2 Addition of a Line to the Reference Bus .......................................... 29
2.10.3 Addition ofaRadial Line and New Bus ........................................... 30
2.10.4 Addition of a Loop Closing Two Existing Buses in the System ...... 30
2.10.5 Gauss - Seidel Method Using Z-bus for Load Flow Solution ......... 31
2.11 Load Flow Solution with Static Load Model .................................................... 32
2.12 Comparision of Various Methods for Power Flow Solution ............................. 33
Questions ............................................................. ................ .......... .......... ........ 71
Problems ......................... ................... .... ..... ................................... ................. 72
3 Economic Operation of Power Systems
3.1 Characteristics of Steam Plants ........................................................................ 86
3.2 Input Output Curves ......................................................................................... 87
3.3 The Incremental Heat Rate Characteristic ........................................................ 88
3.4 The Incremental Fuel Cost Characteristic ........................................................ 88
3.5 Heat Rate Characteristic .................................................................................... 89
3.6 Incremental Production Cost Characteristics ................................................... 89
3.7 Characteristics of Hydro Plants ........................................................................ 90
3.8 Incremental Water Rate Characteristics ............................................................ 91
3.9 Incremental Production Cost Characteristic ..................................................... 92
3.10 Generating Costs at Thermal Plants .................................................................. 93
3.11 Analytical Form for Input-Output Characteristics of Thermal Units ................ 93
3.12 Constraints in Operation .................................................................................... 94
3.13 Plant Scheduling Methods ................................................................................. 96
3.14 Merit Order Method .......................................................................................... 97
3.15 Equal Incremental Cost Method: Transmission Losses Neglected .................. 97
3.16 Transmission Loss Formula - B. Coefficients .................................................. 99
3.17 Active Power Scheduling ................................................................................. 103
3.18 Penalty Factor .................................................................................................. 106
3.19 Evaluation ofl for Computation ....................................................................... 107
(xfu) Contents
3.20 Hydro Electric Plant Models ............................................................................ 119
3.21 Pumped Storage Plant ...................................................................................... 120
3.22 Hydro Thermal Scheduling .............................................................................. 120
3.23 Energy Scheduling Method .............................................................................. 121
3.24 Short Term Hydro Thermal Scheduling ........................................................... 125
3.24.1 Method of Lagrange Multipliers (losses neglected) ........................ 125
3.24.2 Lagrange Multipliers Method Transmission Losses Considered .... 126
3.24.3 Short Term Hydro Thermal Scheduling using
B-Coefficients for Transmission losses .......................................... 127
Questions ........................................................................................................ 151
Problems ........................................................................................................ 152
4 Optimal Load Flow
4.1 Reactive Power Control for Loss Minimization ............................................... 155
4.2 Gradient Method for Optimal Load Flow ......................................................... 156
4.3 Non - Linear Programming .............................................................................. 157
4.4 Lagrange Function for Optimal Load Flow ..................................................... 158
4.5 Computational Procedures ................................................................ _ ............. 159
4.6 Conditions for Optimal Load Flow ................................................................... 159
4.7 Implementation of optimal conditions .............................................................. 161
Questions ........................................................................................................ 168
Problems ........................................................................................................ 169
5 Unit Commitment
5.1 Cost Function Formulation .............................................................................. 171
5.2 Constraints for Plant Commitment Schedules ................................................. 173
5.3 Priority - List Method ...................................................................................... ·174
5.4 Dynamic Programming .................................................................................... t:z5
5.5 Unit Commitment by Dynamic Programming ................................................. 177
Questions ........................................................................................................ 180
Problems ........................................................................................................ 180
Contents
6 Load Frequency Control
6.1 Speed Governing Mechanism .......................................................................... 183
6.2 Speed Governor ................................................................................................ 183
6.3 Steady State Speed Regulation ......................................................................... 185
6.4 Adjustment of Governor Characteristics ......................................................... 185
6.5 Transfer Function of Speed Control Mechanism ............................................ 186
6.6 Transfer Function of a Power System ............................................................ 188
6.7 Transfer Function of the Speed Governor ....................................................... 190
6.8 Governing of Hydro Units ................................................................................ 191
6.9 Penstock Turbine Model .................................................................................. 193
6.10 Modal for a Steam Vessel ................................................................................ 196
6.11 Steam Turbine Model ...................................................................................... 197
6.12 Reheat Type Steam Turbine Model .................................................................. 198
6.13 Single Control Area ........................................................................................... 199
6.14 The basics of Load Frequency Control ........................................................... 200
6.15 Flat Frequency Control .................................................................................... 201
6.16 Real Power Balance for Load Changes ............................................................ 202
6.17 Transfer Function of a Single Area System ..................................................... 203
6.18 Analysis of Single Area System ........................................................................ 205
6.19 Dynamic Response of Load Frequency Control Loop .................................... 208
6.20 Control Strategy ............................................................................................... 209
6.21 PID Controllers ................................................................................................ 212
6.22 The optimal Control Problem ........................................................................... 222
6.23 The Linear Regulator Problem ......................................................................... 222
6.24 Matrix Riccati Equation .................................................................................... 224
6.25 Application of Modern Control Theory ............................................................ 224
6.26 Optimal Load Frequency Control - Single Area System .................................. 225
Contents
6.27 Optimal Control for Tandem Compound Single Reheat Turbine -
Generator System ............................................................................................. 229
6.28 Optimal Control of Hydro Speed Governing System ....................................... 232
6.29 A Review of Optimal Control ........................................................................... 235
6.30 Load Frequency Control with Restrictions on the Rate of
Power Generation '" .................... : ..................................................................... 236
6.31 Load Frequency Control using Output Feedback ............................................ 237
6.32 Load frequency Control and Economic Dispatch ............................................ 238
Questions ....................................................................................................... "39
Problems ........................................................................................................ 240
7 Control of Interconnected Systems
7. 1 Interconnected Operation ................................................................................. 241
7.2 Flat Frequency Control of Interconnected Stations ......................................... 241
7.3 Flat Tie-Line and Flat Frequency Control ........................................................ 244
7.4 Tie-Line Bias Control ........................................................................................ 247
7.5 Complete Tie-Line Bias Control ....................................................................... 250
7.6 Two Area System - Tie-Line Power Model ..................................................... 253
7.7 Block Diagram for Two Area System .............................................................. 254
7.8 Analysis of Two Area System .......................................................................... 255
7.9 Dynamic Response ........................................................................................... 257
7.10 Tie-Line Bias Control- Implementation ........................................................... 266
7.11 The Effect of Bias Factor on System Regulation ............................................ 267
7.12 Scope for Supplementary Control .................................................................... 269
7.13 State Variable Model for a Three Area System ................................................. 269
7.14 State Variable Model for a Two Area System ................................................... 274
7.15 State Variable Model for a Single Area System ................................................ 275
7.16 Model Reduction and Decentralised Control .................................................. ,284
Questions ........................................................................................................ 287
Problems ........................................................................................................ 288
(XVl) Contents
8 Voltage and Reactive Power Control
8.1 Impedance and Reactive Power ....................................................................... 289
8.2 System Voltage and Reactive Power ................................................................ 293
8.3 Reactive Power Generation by Synchronous Machines .................................. 294
8.4 Effect of Excitation Control ............................................................................. 295
8.5 Voltage Regulation and Power Transfer ........................................................... 296
8.6 Exciter and Voltage Regulator .......................................................................... 297
8.7 Block Schematic of Excitation Control ............................................................ 299
8.8 Static Excitation System .................................................................................. 300
8.9 Brushless Excitation Scheme ........................................................................... 301
8.10 Automatic Voltage Regulators for Alternators .................................................. 302
8.11 Analysis of Generator Voltage Control ............................................................. 303
8.12 Steady State Performance Evaluation .............................................................. 306
8.13 Dynamic Response of Voltage Regulation Control ........................................... 306
8.14 Stability Compensation for Voltage Control ..................................................... 307
8.15 Stabilizing Transformer .................................................................................... 307
8.16 Voltage Regulators ............................................................................................ 309
8.17 ieee Type 1 Excitation System ......................................................................... 310
8.18 Power System Stabilizer .................................................................................. 313
8.19 Reactive Power Generation by Turbo Generator ............................................. 314
8.20 Synchronous Compensators ............................................................................ 314
8.21 Reactors 315
8.22 Capacitors315
8.23 Tap---Changing Transformers ........................................................................... 316
8.24 Tap-Staggering Method ................................................................................... 317
8.25 Voltage Regulation and Short Circuit Capacity ................................................. 318
8.26 Loading Capability of a Line ............................................................................. 320
8.27 Compensation in Power Systems ..................................................................... 320
(xviI) Contents
8.28 Load Compensation .......................................................................................... 321
8.29 Static Compensators ........................................................................................ 328
8.30 Steady State Perfonnance of Static var compensators ................................... 331
8.31 Overvoltages on Sudden Loss of Load ............................................................ 334
8.32 Voltage Dips ...................................................................................................... 335
8.33 Subsynchronous Resonance ............................................................................ 337
Questions ........................................................................................................ 343
Problems ........................................................................................................ 344
9 Introduction to Advanced Topics
9.1 Facts Controllers .............................................................................................. 346
9.1.1 Series Controllers ............................................................................ 346
9.1.2 Shunt Controller .............................................................................. 347
9.1.3 Series - Series Controllers .............................................................. 347
9.1.4 Series - Shunt Controllers .............................................................. 348
9.1.5 Power Flow Control ...................................................................... 348
9.1.6 Static Var Compensator(SVC) ........................................................ 349
9.1.7 Unified Power Flow Controller ....................................................... 349
9.1.8 Advantages due to FACTS devices ................................................. 349
9.2 Voltage Stability ................................................................................................ 350
9.3 Power Quality ................................................................................................... 352
9.3.1 Power Quality Index ....................................................................... 353
9.3.2 Voltage Sags .................................................................................... 353
9.3.3 Rectifier Loads ................................................................................ 355
9.3.4 Flicker ............................................................................................. 355
9.3.5 Power Acceptability or Voltage Tolerance ....................................... 356
9.3.6 Solutions to Power Quality.problem ............................................... 356
9.4 Data Base for Control ....................................................................................... 357
9.5 State Estimation ................................................................................................ 358
9.6 Power System Security .................................................................................... 360
(xviii) Contents
9.7 Steady State Security Assessment ................................................................... 361
9.8 Application to Outage Studies .......................................................................... 362
9.9 Pattern Recognition Methods ........................................................................... 363
9.10 Power System Control Centres ........................................................................ 365
9.11 Level Decomposition in Power Systems ......................................................... 367
9.12 NetworkAutomation ........................................................................................ 368
9.13 LoadPrediction ................................................................................................. 369
9.14 Load Prediction using Matereological Data ...................................................... 371
9.15 Spetral Expansion Method ................................................................................ 376
9.16 Prediction by Scaling a Standard Load .......................................................... 377
9.17 Short - Term Load Forecasting Using Exponential Smoothing ....................... 378
9.18 Peak Power Demand Prediction ....................................................................... 378
9.19 State Estimation in Load Forecasting ............................................................... 379
9.20 Generating Capacity Reliability and Outage Probabilities ................................. 380
Questions ........................................................................................................ 386
Objective Questions .......................................................................... 387
Answers to Objective Questions ...................................................... 400
References ......................................................................................... 401
Index ................................................................................................. 407
Link
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