Optimization principles: practical applications to the operation and markets of the electric power industry
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Piscataway, N.J.
IEEE Press
2003
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| Series: | IEEE Press series on power engineering
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 339 S. graph. Darst. |
| ISBN: | 0471451304 |
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| 264 | 1 | |a Piscataway, N.J. |b IEEE Press |c 2003 | |
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Record in the Search Index
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OPTIMIZATION PRINCIPLES CONTENTS PREFACE XV 1 INTRODUCTION 1 1.1
DEREGULATED ELECTRICITY MARKETS*TERMINOLOGY AND ACRONYMS / 2 1.2 STUDY
PLAN / 3 1.3 ORGANIZATION AND CONVENTIONS / 5 PART I MATHEMATICAL
BACKGROUND 2 FUNDAMENTALS OF MATRIX ALGEBRA 9 2.1 SCALARS, VECTORS, AND
MATRICES / 9 2.2 OPERATIONS ON MATRICES / 11 2.2.1 PRODUCT OF MATRICES /
11 2.2.2 SPECIAL MATRICES / 12 2.2.3 DIVISION OF MATRICES / 13 2.2.4
ORTHOGONALITY / 13 2.3 LINEAR DEPENDENCE AND INDEPENDENCE / 14 2.4
VECTOR SPACES / 15 2.4.1 DISCUSSION OF VECTOR SPACE / 16 VII VIM
CONTENTS 2.5 LINEAR TRANSFORMATIONS / 17 2.5.1 PROPERTIES OF
TRANSFORMATIONS / 17 2.5.2 INVERSE OF A MATRIX / 18 2.6 EIGENVALUES AND
EIGENVECTORS / 18 2.6.1 DEFINITENESS / 22 2.7 LINEAR EQUATIONS / 22
2.7.1 SOLUTION OF LINEAR ALGEBRAIC EQUATIONS / 23 2.8, VECTOR AND MATRIX
NORMS / 24 2.9 CONDITION NUMBER / 26 2.10 SOLVED PROBLEMS / 27 ( ,
2.10.1 INVERSE OF A COMPLEX MATRIX / 27 2.10.2 COMPUTATION OF EIGENVALUE
/ 28 2.10.3 CONFIRMATION OF EIGENVECTOR / 30 2.10.4 EIGENVECTOR
COMPUTATION / 31 2.11 CONCLUSIONS / 32 2.12 EXERCISE PROBLEMS / 32 PART
II LINEAR OPTIMIZATION 3 SOLUTION OF EQUATIONS, INEQUALITIES, AND LINEAR
PROGRAMS 37 3.1 EXTREME VALUES, RELATIVE MAXIMUM AND MINIMUM / 37 3.1.1
NECESSARY AND SUFFICIENT CONDITIONS / 37 3.2 CONCAVE AND CONVEX
FUNCTIONS / 42 3.2.1 CONVEXITY AND CONCAVITY OF MULTIVARIATE FUNCTIONS /
45 3.2.2 CONVEX SETS / 47 3.3 SOLUTION OF LINEAR EQUATION SYSTEMS / 51
3.3.1 EXISTENCE OF SOLUTION FOR SYSTEMS / 51 3.3.2 SOLUTION OF FULLY
SPECIFIED SYSTEM USING CANONICAL FORM / 52 3.3.3 OVERSPECIFIED OR
UNDERSPECIFIED SYSTEMS / 53 3.4 LINEAR OPTIMIZATION PROBLEMS / 59 3.4.1
GRAPHICAL SOLUTION OF A SIMPLE LINEAR PROGRAMMING PROBLEM / 59 3.5
LINEAR PROGRAMS AND CONVEX SETS*RELATION / 62 3.6 LINEAR PROGRAMS / 65
3.6.1 DEFINITIONS PERTAINING TO LINEAR OPTIMIZATION / 67 3.7
ILLUSTRATION OF THE SIMPLEX METHOD / 68 3.7.1 SENSITIVITY OF OPTIMAL
SOLUTION / 73 CONTENTS JX 3.8 SOLUTION OF LINEAR PROGRAMS USING EXCEL
SOLVER / 73 3.8.1 SETUP OF SPREADSHEET TO USE SOLVER / 73 3.8.2
SENSITIVITY REPORT / 75 3.9 TRANSPORTATION PROBLEMS / 76 3.10 DUALITY IN
LINEAR PROGRAMMING / 78 3.10.1 PRIMAL DUAL RELATIONS / 78 3.10.2 DUALITY
THEOREMS / 81 3.10.3 GENERAL RELATIONS BETWEEN PRIMAL AND DUAL PROGRAMS
/ 82 3.11 EXERCISE PROBLEMS / 83 4 SOLVED LINEAR PROGRAM PROBLEMS 85 4.1
PROBLEMS INVOLVING OPTIMAL MIXING / 85 4.2 SIMPLE DISPATCH PROBLEM / 87
4.3 SIMPLE AUCTION / 89 4.4 DISPATCH PROBLEM WITH DEMAND BIDS / 91 4.4.1
SENSITIVITY ANALYSIS / 93 4.5 DISPATCH PROBLEM WITH DEMAND BIDS AND
TRANSMISSION NETWORK / 95 4.6 TRADEOFF BETWEEN COST OF EMISSIONS AND
COST OF DISPATCH / 97 4.7 OPTIMAL POWER FLOW (OPF) BASED ON DC LOAD FLOW
/ 99 4.7.1 EFFECT OF TRANSMISSION LIMITATIONS ON SOLUTION / 102 4.8
INTER-REGIONAL DISPATCH / 106 4.8.1 SENSITIVITY REPORT / 110 4.9
EXAMPLES OF TRANSPORTATION PROBLEMS / 110 4.9.1 WAREHOUSE DISTRIBUTION
PROBLEM / 110 4.9.2 INTEGRATING NATURAL GAS TRANSPORTATION AND
ELECTRICITY GENERATION / 113 4.10 SOLUTION OF PRIMAL-DUAL PROBLEMS / 115
4.11 RESERVOIR MANAGEMENT / 119 4.12 SUMMARY / 120 4.13 EXERCISE
PROBLEMS / 121 PART III NONLINEAR OPTIMIZATION 5 MATHEMATICAL BACKGROUND
TO NONLINEAR PROGRAMS 125 5.1 FORM OF NONLINEAR OPTIMIZATION PROBLEM /
125 5.2 PRELIMINARIES / 126 X CONTENTS -^ 5.2.1 THE GRADIENT / 126 5.2.2
DIFFERENTIAL OF A FUNCTION / 128 5.2.3 THE JACOBIAN MATRIX / 131 V 5.2.4
THE HESSIAN MATRIX / 132 5.2.5 DIRECTIONAL SECOND DERIVATIVE / 132 5.3
TAYLOR SERIES EXPANSION OF FUNCTIONS / 133 . 5.3.1 COMPACT FORM OF
TAYLOR'S EXPANSION / 134 5.3.2 SOLUTION OF NONLINEAR EQUATIONS USING THE
JACOBIAN MATRIX / 137 5.4 EXTREME POINTS OF MULTIVARIATE FUNCTIONS / 138
5.4.1 SADDLE POINT / 140 5.5 QUADRATIC FUNCTIONS / 143 5.6 EXERCISE
PROBLEMS / 146 6 UNCONSTRAINED NONLINEAR OPTIMIZATION 149 6.1
CLASSIFICATION OF MINIMIZATION METHODS / 149 6.2 RANDOM SEARCH METHODS /
150 6.3 UNIVARIATE METHOD / 151 6.4 ADVANCED METHODS INVOLVING PATTERN
DIRECTIONS / 154 6.5 CONJUGATE DIRECTIONS / 155 6.6 PATTERN SEARCH
METHOD*POWELL'S METHOD / 158 6.7 DESCENT METHODS / 160 6.7.1 STEEPEST
DESCENT METHOD / 160 6.7.2 MINIMIZING ALONG A DIRECTION / 163 6.8
NEWTON'S METHOD / 165 6.8.1 EFFECT OF STARTING POINT / 169 6.9 SOLUTION
OF NONLINEAR EQUATIONS / 170 6.10 EXERCISE PROBLEMS / 173 7 CONSTRAINED
NONLINEAR OPTIMIZATION 177 7.1 EFFECT OF CONSTRAINTS ON THE SOLUTION
SPACE OF NONLINEAR PROGRAMS / 177 7.2 METHODS FOR SOLVING NONLINEAR
PROGRAMS / 182 7.3 DIRECT SUBSTITUTION METHOD / 182 7.4 METHOD OF
CONSTRAINED VARIATIONS / 184 7.5 LAGRANGE MULTIPLIERS: KUHN-TUCKER
CONDITIONS / 185 7.5.1 KUHN-TUCKER CONDITIONS / 188 7.6 INTERPRETATION
OF LAGRANGE MULTIPLIERS / 190 CONTENTS XI 7.7 CONSTRAINT QUALIFICATION /
192 7.8 TESTING KUHN-TUCKER CONDITIONS / 193 7.9 NATURE OF SOLUTION OF
NONLINEAR PROGRAMS / 195 7.9.1 EXAMPLES / 197 7.10 QUADRATIC PROGRAMS /
203 7.10.1 EXAMPLE OF QUADRATIC PROGRAM / 203 7.10.2 SOLUTION OF
QUADRATIC PROGRAMS VIA LINEAR PROGRAMS / 207 7.11 FEASIBLE DIRECTIONS /
211 7.11.1 EXAMPLE / 213 7.11.2 DIRECTION FINDING PROBLEM / 215 7.12
GRADIENT PROJECTION METHODS*GENERALIZED REDUCED GRADIENT METHOD / 217
7.12.1 PROCEDURE OF GRG METHOD / 217 7.13 SEQUENTIAL LINEAR PROGRAMMING
METHOD / 228 7.14 SEQUENTIAL QUADRATIC PROGRAMMING (SQP) / 233 7.15
SYNTHESIS OF LAGRANGE MULTIPLIERS FROM SOLUTION / 239 7.16 RATE OF
CONVERGENCE / 240 7.17 SUMMARY / 241 7.18 EXERCISE PROBLEMS / 241 8
SOLVED NONLINEAR OPTIMIZATION PROBLEMS 245 8.1 INTRODUCTORY REMARKS /
245 8.1.1 CHOICE OF SOLVER OPTIONS / 246 8.2 EXAMPLES OF UNCONSTRAINED
NONLINEAR OPTIMIZATION / 247 8.2.1 TRANSMISSION VOLTAGE OPTIMIZATION /
248 8.3 EXAMPLES OF CONSTRAINED NONLINEAR OPTIMIZATION / 249 8.3.1 COAL
MINING STRATEGY / 249 8.3.2 OPTIMIZING APARTMENT DEVELOPMENT / 251 8.3.3
POWER SYSTEM DISPATCH / 253 * 8.3.4 SOLUTION USING KUHN-TUCKER
CONDITIONS / 254 8.3.5 SOLUTION USING EXCEL SOLVER / 260 8.4 OPTIMAL
POWER FLOW*FORMULATION AND INTERPRETATION / 265 8.4.1 PROBLEM
FORMULATION FOR SOLVER / 267 8.4.2 RESULTS AND SENSITIVITY SHEETS / 267
8.4.3 LOCATIONAL MARGINAL PRICES / 273 8.4.4 FINITE BRANCH FLOW LIMITS
AND OTHER CONSTRAINTS / 274 8.5 OPTIMAL POWER FLOW*PHASE ANGLE
REGULATORS / 275 XII CONTENTS 8.6 OPTIMAL POWER FLOW*ACTIVE AND REACTIVE
POWER OPTIMIZATION / 276 8.6.1 ADVANTAGES OF REACTIVE POWER OPTIMIZATION
/ 278 ^Y 8.6.2 LOCATIONAL PRICES OF ACTIVE AND REACTIVE POWER / 279
8.6.3 COST ASSOCIATED WITH TRANSMISSION CONGESTION / 280 8.7 DISPATCH OF
AN AC NETWORK IN THE PRESENCE OF DEMAND-SIDE BIDS / 281 8.7.1 PROBLEM
FORMULATION / 282 8.7.2 SOLUTION / 282 8.8 LOSS ALLOCATION / 283 8.9
ELEMENTS OF STATE ESTIMATION / 288 8.9.1 BACKGROUND / 288 8.9.2 SIMPLE
EXAMPLE OF ESTIMATION / 289 8.10 SUMMARY / 292 8.11 EXERCISE PROBLEMS /
293 APPENDICES A BASIC PRINCIPLES OF ELECTRICITY 297 A.I SCOPE / 297 A.2
CHARGE, ELECTRIC, AND MAGNETIC FIELDS / 297 A.3 VOLTAGE, CURRENT, AND
POWER / 299 A.4 VOLTAGE CURRENT AND POWER IN AC CIRCUITS / 300 A.4.1
ACTIVE AND REACTIVE POWER / 303 A.5 APPLICATION TO NETWORKS / 304 B
NETWORK EQUATIONS 307 B.I FLOW IN BRANCHES / 307 B.2 THE DC LOAD ROW /
311 B.3 SOLVED PROBLEMS / 313 B.3.1 THE DC LOAD FLOW / 313 B.3.2 THE AC
LOAD FLOW / 315 C RELATION BETWEEN PSEUDO-INVERSE AND LEAST-SQUARE ERROR
FIT 319 C.I MINIMUM SUM-OF-SQUARES ERROR FIT / 319 C.2 PSEUDO-INVERSE /
322 CONTENTS XIM C.3 MAXIMUM LIKELIHOOD ESTIMATORS / 323 C.4 SOLVED
PROBLEMS / 326 C.4.1 COMPUTATION OF PSEUDO-INVERSE ITERATIVELY / 326
C.4.2 LEAST-SQUARE ERROR POLYNOMIAL FIT / 327 C.5 EXERCISE PROBLEMS /
328 BIBLIOGRAPHY 329 INDEX 333 ABOUT THE AUTHOR 339 |
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| spelling | Rau, Narayan S. Verfasser aut Optimization principles practical applications to the operation and markets of the electric power industry Narayan S. Rau Piscataway, N.J. IEEE Press 2003 XVII, 339 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier IEEE Press series on power engineering Optimisation mathématique Tableurs Électricité, Services publics d' - Gestion - Modèles mathématiques Mathematisches Modell Electric utilities Management Mathematical models Electronic spreadsheets Mathematical optimization Optimierung (DE-588)4043664-0 gnd rswk-swf Optimierung (DE-588)4043664-0 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012802368&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rau, Narayan S. Optimization principles practical applications to the operation and markets of the electric power industry Optimisation mathématique Tableurs Électricité, Services publics d' - Gestion - Modèles mathématiques Mathematisches Modell Electric utilities Management Mathematical models Electronic spreadsheets Mathematical optimization Optimierung (DE-588)4043664-0 gnd |
| subject_GND | (DE-588)4043664-0 |
| title | Optimization principles practical applications to the operation and markets of the electric power industry |
| title_auth | Optimization principles practical applications to the operation and markets of the electric power industry |
| title_exact_search | Optimization principles practical applications to the operation and markets of the electric power industry |
| title_full | Optimization principles practical applications to the operation and markets of the electric power industry Narayan S. Rau |
| title_fullStr | Optimization principles practical applications to the operation and markets of the electric power industry Narayan S. Rau |
| title_full_unstemmed | Optimization principles practical applications to the operation and markets of the electric power industry Narayan S. Rau |
| title_short | Optimization principles |
| title_sort | optimization principles practical applications to the operation and markets of the electric power industry |
| title_sub | practical applications to the operation and markets of the electric power industry |
| topic | Optimisation mathématique Tableurs Électricité, Services publics d' - Gestion - Modèles mathématiques Mathematisches Modell Electric utilities Management Mathematical models Electronic spreadsheets Mathematical optimization Optimierung (DE-588)4043664-0 gnd |
| topic_facet | Optimisation mathématique Tableurs Électricité, Services publics d' - Gestion - Modèles mathématiques Mathematisches Modell Electric utilities Management Mathematical models Electronic spreadsheets Mathematical optimization Optimierung |
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