Contents ...................................................... vii
Preface ........................................................ xi
1 Central Operation and Control of Power Systems .............. 1
1.1 General ..................................................... 1
1.2 Control Center of a Power System ............................ 2
1.3 Digital Computer Configuration .............................. 5
1.4 Automatic Generation Control for a Power System ............. 7
1.4.1 Area Control Error .................................... 9
1.4.1.1 CPS1, 1 Minute Average .......................... 12
1.4.1.2 CPS2, 10 Minute Average ......................... 12
1.4.1.3 Disturbance Conditions .......................... 14
1.5 Operation without Central Computers or AGC ................. 14
1.6 Parallel Operation of Generators ........................... 19
1.7 Network Power Flows ........................................ 24
1.7.1 Oversimplified Power Flow (dc Power Flow) ............ 25
1.8 Area Lumped Dynamic Model .................................. 30
Problems ....................................................... 34
References ..................................................... 38
2 Elements of Transmission Networks .......................... 39
2.1 Phasor Notation ............................................ 40
2.2 Symmetrical Component Transformation ....................... 44
2.2.1 Floating Voltage Base Per-Unit Systems ............... 52
2.3 Overhead Transmission Line Representation .................. 56
2.3.1 Inductance of Long Parallel Conductors ............... 59
2.3.2 Balanced Three-Phase Lines ........................... 65
2.3.3 Unbalanced Lines ..................................... 74
2.3.4 Capacitance of Transmission Lines .................... 76
2.3.5 General Method to Determine Aerial Transmission
Line Parameters ...................................... 87
2.4 Transformer Representation ................................. 97
2.4.1 Wye-Delta and Phase-Shift Transformers .............. 100
2.4.2 Multiple-Winding Transformers ....................... 105
2.5 Synchronous Machine Representation ........................ 108
2.5.1 Steady-State Synchronous Machine Equivalent ......... 114
2.5.1.1 Short-Circuit Characteristics ............... 120
2.5.2 Transient Time-Frame Synchronous Machine
Equivalent .......................................... 120
2.5.3 Subtransient Time-Frame Synchronous Machine
Equivalent .......................................... 122
Problems ...................................................... 131
References .................................................... 139
3 Bus Reference Frame ....................................... 141
3.1 Linear Network Injections and Loads ....................... 142
3.2 Bus Impedance Matrix for Elements without Mutual
Coupling .................................................. 151
3.2.1 Adding a Tree Branch to Bus p ....................... 153
3.2.2 Adding a Tree Branch to the Reference ............... 155
3.2.3 Adding a Cotree Link between Buses p and q .......... 156
3.2.4 Adding a Cotree Link from Bus p to Reference ........ 158
3.3 The Bus Admittance Matrix ................................. 160
3.3.1 Bus Impedance Matrix for Elements with Mutual
Coupling ............................................ 165
3.4 Inversion of the YBUS Matrix for Large Systems ............. 169
3.4.1 Tinney's Optimally Ordered Triangular
Factorization [3] ................................... 169
3.4.1.1 Tinney's Schemes for Near-Optimal
Ordering ............................................ 176
3.4.2 Several Iterative Methods for Linear Matrices ....... 180
3.4.2.1 Gaussian Iteration .......................... 181
3.4.2.2 Gauss-Seidel Iteration ...................... 182
Problems ...................................................... 185
References .................................................... 191
4 Network Fault and Contingency Calculations ................ 193
4.1 Fault Calculations Using ZBUS .............................. 193
4.1.1 Approximations Common to Short-Circuit Studies ...... 204
4.2 Fault Calculations Using the YBUS Table of Factors ......... 209
4.3 Contingency Analysis for Power Systems .................... 212
4.3.1 Contingency Analysis for Power Systems .............. 213
4.3.2 Contingencies Using ZBUS in a Superposition Method ... 213
4.3.3 ZBUS Line Contingency Method ......................... 214
4.4 Using the YBUS Table of Factors for Contingencies .......... 215
4.4.1 Double Contingencies Using YBUS Table of Factors
(Balanced Case) ..................................... 219
Problems ...................................................... 223
References .................................................... 229
5 Power Flow on Transmission Networks ....................... 231
5.1 Slack Bus ................................................. 233
5.2 ZBUS Formulation for Load-Flow Equations ................... 234
5.3 Gauss or Gauss-Seidel Iteration Using YBUS ................. 240
5.4 Newton-Raphson Iterative Scheme Using YBUS ................. 243
5.4.1 Approximations to the Jacobian in
the Newton-Raphson Method ........................... 257
5.5 Adjustment of Network Operating Conditions ................ 262
5.6 Operational Power Flow Programs ........................... 275
Problems ...................................................... 278
References .................................................... 284
6 Generator Base Power Setting .............................. 285
6.1 Economic Dispatch of Generation without Transmission
Line Losses ............................................... 286
6.2 Economic Dispatch of Generation with Line Losses .......... 290
6.3 On-Line Execution of the Economic Dispatch ................ 295
6.4 Day-Ahead Economic Dispatch with a Variable Number of
Units On-Line ............................................. 299
6.5 Power Transmission Line Losses for Economic Dispatch ...... 307
6.6 Utilizing the Load-Flow Jacobian for Economic Dispatch .... 314
6.7 Economic Exchange of Power between Areas .................. 320
6.7.1 Economy A Program ................................... 322
Problems ...................................................... 326
References .................................................... 333
7 State Estimation from Real-Time Measurements .............. 335
7.1 The Line Power Flow State Estimator ....................... 336
7.2 State Estimation and Noisy Measurements ................... 344
7.3 Monitoring the Power System ............................... 354
7.4 Determination of Variance ∑2 to Normalize Measurements .... 357
Problems ...................................................... 364
References .................................................... 367
Appendix A: Conductor Resistance and Rating ................... 369
Index ......................................................... 377
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