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Power System State Estimation : Theory and Implementation - Ali Abur

Power System State Estimation

Theory and Implementation

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Offering an up-to-date account of the strategies utilized in state estimation of electric power systems, this text provides a broad overview of power system operation and the role of state estimation in overall energy management. It uses an abundance of examples, models, tables, and guidelines to clearly examine new aspects of state estimation, the testing of network observability, and methods to assure computational efficiency.

Includes numerous tutorial examples that fully analyze problems posed by the inclusion of current measurements in existing state estimators and illustrate practical solutions to these challenges.

Written by two expert researchers in the field, Power System State Estimation extensively details topics never before covered in depth in any other text, including novel robust state estimation methods, estimation of parameter and topology errors, and the use of ampere measurements for state estimation. It introduces various methods and computational issues involved in the formulation and implementation of the weighted least squares (WLS) approach, presents statistical tests for the detection and identification of bad data in system measurements, and reveals alternative topological and numerical formulations for the network observability problem.

Industry Reviews

"...brings a fresh perspective to the problem of state estimation...offers a blend of theory and mathematical rigor that is unique and very exciting." - Fernando L. Alvarado, The University of Wisconsin, Madison, U.S.A."

Forewordp. v
Prefacep. vii
Introductionp. 1
Operating States of a Power Systemp. 1
Power System Security Analysisp. 2
State Estimationp. 5
Summaryp. 6
Weighted Least Squares State Estimationp. 9
Introductionp. 9
Component Modeling and Assumptionsp. 10
Transmission Linesp. 10
Shunt Capacitors or Reactorsp. 10
Tap Changing and Phase Shifting Transformersp. 10
Loads and Generatorsp. 12
Building the Network Modelp. 12
Maximum Likelihood Estimationp. 15
Gaussian (Normal) Probability Density Functionp. 15
The Likelihood Functionp. 17
Measurement Model and Assumptionsp. 18
WLS State Estimation Algorithmp. 20
The Measurement Function, h(x[superscript k])p. 21
The Measurement Jacobian, Hp. 23
The Gain Matrix, Gp. 25
Cholesky Decomposition of Gp. 27
Performing the Forward/Back Substitutionsp. 27
Decoupled Formulation of the WLS State Estimationp. 29
DC State Estimation Modelp. 33
Problemsp. 33
Referencesp. 36
Alternative Formulations of the WLS State Estimationp. 37
Weaknesses of the Normal Equations Formulationp. 37
Orthogonal Factorizationp. 42
Hybrid Methodp. 43
Method of Peters and Wilkinsonp. 45
Equality-Constrained WLS State Estimationp. 46
Augmented Matrix Approachp. 48
Blocked Formulationp. 50
Comparison of Techniquesp. 54
Problemsp. 56
Referencesp. 57
Network Observability Analysisp. 59
Networks and Graphsp. 60
Graphsp. 60
Networksp. 61
Network Matricesp. 61
Branch to Bus Incidence Matrixp. 62
Fundamental Loop to Branch Incidence Matrixp. 63
Loop Equationsp. 65
Methods of Observability Analysisp. 66
Numerical Method Based on the Branch Variable Formulationp. 67
New Branch Variablesp. 67
Measurement Equationsp. 68
Linearized Measurement Modelp. 70
Observability Analysisp. 72
Numerical Method Based on the Nodal Variable Formulationp. 76
Determining the Unobservable Branchesp. 79
Identification of Observable Islandsp. 81
Measurement Placement to Restore Observabilityp. 84
Topological Observability Analysis Methodp. 89
Topological Observability Algorithmp. 89
Identifying the Observable Islandsp. 90
Determination of Critical Measurementsp. 90
Measurement Designp. 93
Summaryp. 93
Problemsp. 93
Referencesp. 97
Bad Data Detection and Identificationp. 99
Properties of Measurement Residualsp. 101
Classification of Measurementsp. 104
Bad Data Detection and Identifiabilityp. 104
Bad Data Detectionp. 105
Chi-squares x[superscript 2] Distributionp. 105
Use of x[superscript 2] Distribution for Bad Data Detectionp. 106
x[superscript 2]-Test for Detecting Bad Data in WLS State Estimationp. 108
Use of Normalized Residuals for Bad Data Detectionp. 110
Properties of Normalized Residualsp. 111
Bad Data Identificationp. 111
Largest Normalized Residual (r[superscript N subscript max]) Testp. 111
Computational Issuesp. 113
Strengths and Limitations of the r[superscript N subscript max] Testp. 115
Hypothesis Testing Identification (HTI)p. 116
Statistical Properties of e[subscript s]p. 118
Hypothesis Testingp. 119
Decision Rulesp. 120
HTI Strategy Under Fixed [beta]p. 122
Summaryp. 122
Problemsp. 123
Referencesp. 125
Robust State Estimationp. 127
Introductionp. 127
Robustness and Breakdown Pointsp. 128
Outliers and Leverage Pointsp. 129
Concept of Leverage Pointsp. 130
Identification of Leverage Measurementsp. 131
M-Estimatorsp. 135
Estimation by Newton's Methodp. 137
Iteratively Re-weighted Least Squares Estimationp. 139
Least Absolute Value (LAV) Estimationp. 140
Linear Regressionp. 141
LAV Estimation as an LP Problemp. 141
Simplex Based Algorithmp. 145
Interior Point Algorithmp. 150
Discussionp. 153
Problemsp. 153
Referencesp. 154
Network Parameter Estimationp. 157
Introductionp. 157
Influence of Parameter Errors on State Estimation Resultsp. 158
Identification of Suspicious Parametersp. 163
Classification of Parameter Estimation Methodsp. 164
Parameter Estimation Based on Residual Sensitivity Analysisp. 165
Parameter Estimation Based on State Vector Augmentationp. 167
Solution Using Conventional Normal Equationsp. 170
Solution Based on Kalman Filter Theoryp. 172
Parameter Estimation Based on Historical Series of Datap. 173
Transformer Tap Estimationp. 179
Observability of Network Parametersp. 187
Discussionp. 188
Problemsp. 189
Referencesp. 190
Topology Error Processingp. 195
Introductionp. 195
Types of Topology Errorsp. 197
Detection of Topology Errorsp. 197
Classification of Methods for Topology Error Analysisp. 201
Preliminary Topology Validationp. 203
Branch Status Errorsp. 204
Residual Analysisp. 205
State Vector Augmentationp. 209
Substation Configuration Errorsp. 213
Inclusion of Circuit Breakers in the Network Modelp. 214
WLAV Estimatorp. 218
WLS Estimatorp. 221
Substation Graph and Reduced Modelp. 225
Implicit Substation Model: State and Status Estimationp. 228
Observability Analysis Revisitedp. 237
Problemsp. 240
Referencesp. 242
State Estimation Using Ampere Measurementsp. 245
Introductionp. 245
Modeling of Ampere Measurementsp. 247
Difficulties in Using Ampere Measurementsp. 252
Inequality-Constrained State Estimationp. 255
Heuristic Determination of P-[theta] Solution Uniquenessp. 261
Algorithmic Determination of Solution Uniquenessp. 264
Procedure Based on the Residual Covariance Matrixp. 265
Procedure Based on the Jacobian Matrixp. 268
Identification of Nonuniquely Observable Branchesp. 270
Measurement Classification and Bad Data Identificationp. 274
LS Estimationp. 275
LAV Estimationp. 277
Problemsp. 279
Referencesp. 280
Review of Basic Statisticsp. 283
Random Variablesp. 283
The Distribution Function (d.f.), F(x)p. 283
The Probability Density Function (p.d.f), f(x)p. 284
Continuous Joint Distributionsp. 284
Independent Random Variablesp. 285
Conditional Distributionsp. 285
Expected Valuep. 285
Variancep. 286
Medianp. 286
Mean Squared Errorp. 286
Mean Absolute Errorp. 287
Covariancep. 287
Normal Distributionp. 288
Standard Normal Distributionp. 289
Properties of Normally Distributed Random Variablesp. 291
Distribution of Sample Meanp. 292
Likelihood Function and Maximum Likelihood Estimatorp. 293
Properties of MLE'sp. 293
Central Limit Theorem for the Sample Meanp. 294
Review of Sparse Linear Equation Solutionp. 295
Solution by Direct Methodsp. 297
Elementary Matricesp. 298
LU Factorization Using Elementary Matricesp. 299
Crout's Algorithmp. 299
Doolittle's Algorithmp. 301
Factorization of Sparse Symmetric Matricesp. 302
Ordering Sparse Symmetric Matricesp. 303
Factorization Path Graphp. 304
Sparse Forward/Back Substitutionsp. 305
Solution of Modified Equationsp. 307
Partial Refactorizationp. 309
Compensationp. 311
Sparse Inversep. 313
Orthogonal Factorizationp. 315
Storage and Retrieval of Sparse Matrix Elementsp. 318
Inserting and/or Deleting Elements in a Linked Listp. 320
Adding a Nonzero Elementp. 320
Deleting a Nonzero Elementp. 321
Referencesp. 322
Indexp. 325
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9780824755706
ISBN-10: 0824755707
Series: Power Engineering
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 327
Published: 1st March 2004
Country of Publication: US
Dimensions (cm): 22.86 x 15.24  x 1.91
Weight (kg): 0.52
Edition Number: 1