Electric Power System Applications of OptimizationA study of electric power system applications of optimization. It highlights essential trends in optimizational and genetic algorithms; linear programming; interior point methods of linear, quadratic, and non-linear systems; decomposition and Lagrange relaxation methods; unit commitment; optimal power flow; Var planning; and hands-on applications. |
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Page vi
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Page vii
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Contents
Introduction | 1 |
Electric Power System Models | 19 |
Reactive Capability Limits | 32 |
20 | 57 |
PowerFlow Computations | 65 |
30 | 77 |
Constrained Optimization and Applications | 80 |
65 | 89 |
Decomposition Method | 325 |
Formulation of the Decomposition Problem | 326 |
Algorithm of Decomposition Technique | 328 |
Illustrative Example of the Decomposition Technique | 329 |
Conclusions | 336 |
References | 338 |
Optimal Power Flow | 339 |
OPFFuel Cost Minimization | 340 |
66 | 95 |
Power Systems Application Examples | 124 |
VII | 133 |
VIII | 139 |
Interior Point Methods | 197 |
Nonlinear Programming | 229 |
Dynamic Programming | 257 |
Characteristics of Dynamic Programming | 260 |
Concept of Suboptimization and the Principle of Optimality | 261 |
Formulation of Dynamic Programming | 263 |
Backward and Forward Recursion | 268 |
Computational Procedure in Dynamic Programming | 278 |
Computational Economy in DP | 279 |
Conversion of a Final Value Problem into an Initial Value Problem | 282 |
Conclusions | 287 |
Problem Set | 288 |
References | 291 |
Lagrangian Relaxation | 293 |
Concepts | 294 |
The Subgradient Method for Setting the Dual Variables | 295 |
Setting T | 302 |
Comparison with Linear ProgrammingBased Bounds | 307 |
An Improved Relaxation | 309 |
Summary of Concepts | 310 |
Past Applications | 311 |
Summary | 313 |
Illustrative Examples | 320 |
Conclusions | 321 |
Problem Set | 322 |
References | 323 |
OPFActive Power Loss Minimization | 344 |
OPFVAr Planning | 349 |
OPFAdding Environmental Constraints | 358 |
Commonly Used Optimization Technique LP | 360 |
Commonly Used Optimization Technique NLP | 373 |
Illustrative Examples | 387 |
Conclusions | 394 |
Problem Set | 395 |
References | 397 |
Unit Commitment | 401 |
Formulation of Unit Commitment | 403 |
Optimization Methods | 406 |
Illustrative Example | 410 |
Updating At in the Unit Commitment Problem | 422 |
Unit Commitment of Thermal Units Using Dynamic Programming | 425 |
Illustrative Problems | 434 |
Problem Set | 436 |
441 | |
Genetic Algorithms | 443 |
Definition and Concepts Used in Genetic Computation | 444 |
Genetic Algorithm Approach | 446 |
Theory of Genetic Algorithms | 449 |
The Schemata Theorem | 452 |
General Algorithm of Genetic Algorithms | 454 |
Application of Genetic Algorithms | 455 |
Application to Power Systems | 457 |
Illustrative Examples | 469 |
Epilog | 473 |
Common terms and phrases
application assume b₁ basic variable bus voltages buses calculated chromosome coefficients Consider control variables crossover decision variables decomposition defined dual dynamic programming economic dispatch electric power system elements equation feasible solution formulation frequency fuel cost genetic algorithms given Illustrative Example incremental initial interior point method iteration Lagrange multipliers Lagrangian relaxation limits linear programming linear programming problem loss minimization mathematical matrix Maximize Maximize z maximum minimum multipliers node nonlinear programming objective function obtained operating OPF problem Optimal Power Flow optimal solution optimization problem optimum output P₁ P₂ parameters phase angle phase-shifter primal quadratic programming reactive power recursive schedule shown in Figure simplex method slack bus slack variables solve specified stage start-up subgradient method Subject subproblems Theorem tion transmission U₁ unit commitment Update upper bound V₁ V₂ vector voltage magnitude x₁ zero