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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Page xi
... Examples IX . Conclusion X. Problem Set 170 182 183 190 190 195 References 6. Interior Point Methods I. Introduction II . Karmarkar's Algorithm III . The Projection Scaling Method IV . The Dual Affine Algorithm 197 197 199 201 202 V ...
... Examples IX . Conclusion X. Problem Set 170 182 183 190 190 195 References 6. Interior Point Methods I. Introduction II . Karmarkar's Algorithm III . The Projection Scaling Method IV . The Dual Affine Algorithm 197 197 199 201 202 V ...
Page xii
... Examples 282 XII . Conclusions 287 XIII . Problem Set 288 References 291 9. Lagrangian Relaxation I. Introduction II ... Example of the Decomposition 326 328 Technique 329 V. Conclusions 336 VI . Problem Set References 11. Optimal Power ...
... Examples 282 XII . Conclusions 287 XIII . Problem Set 288 References 291 9. Lagrangian Relaxation I. Introduction II ... Example of the Decomposition 326 328 Technique 329 V. Conclusions 336 VI . Problem Set References 11. Optimal Power ...
Page xiii
... Examples 373 387 IX . Conclusions 394 X. Problem Set 395 References 12. Unit Commitment 397 401 I. Introduction 401 II . Formulation of Unit Commitment 403 III . Optimization Methods 406 IV . Illustrative Example 410 V. Updating A , ( t ) ...
... Examples 373 387 IX . Conclusions 394 X. Problem Set 395 References 12. Unit Commitment 397 401 I. Introduction 401 II . Formulation of Unit Commitment 403 III . Optimization Methods 406 IV . Illustrative Example 410 V. Updating A , ( t ) ...
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 | 123 |
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
active additional algorithm angle application approach assume basic bound bus voltages buses calculated called Consider constant constraints continuous cost decision defined depends determine dual dynamic programming electric elements equal equation example existing expressed feasible solution Figure formulation frequency genetic given hour incremental initial integer involves iteration Lagrangian limits linear programming load loss magnitude matrix Maximize maximum Minimize multipliers node nonlinear objective function obtained operating optimal optimal solution optimum phase planning population positive power flow power system presented problem procedure quadratic reactive power referred relaxation represent reserve respectively result satisfy schedule selected shown simplex method slack solution solve specified stage Step studies Subject subproblems TABLE techniques tion transformer transmission unit unit commitment usually variables vector voltage x₁