Power system state estimation : theory and implementation

Title:

Personal Author:

Abur, Ali, 1957-

Series:

Power engineering

Publication Information:

New York : Marcel Dekker, 2004

ISBN:

9780824755706

Subject Term:

Electric power systems -- State estimation

Added Author:

Exposito, Antonio G.

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010082563	TK1005 A28 2004	Open Access Book	Book	Searching... Unknown
Searching... SPACE Kulim Library	30000010077422	TK1005 A28 2004	Open Access Book	Book	Searching... Unknown

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.

Author Notes

Antonio Gomez Exposito is Chairman, Department of Electrical Engineering, University of Seville, Spain.

Fernando L. Alvarado

Foreword	p. v
Preface	p. vii
1 Introduction	p. 1
1.1 Operating States of a Power System	p. 1
1.2 Power System Security Analysis	p. 2
1.3 State Estimation	p. 5
1.4 Summary	p. 6
2 Weighted Least Squares State Estimation	p. 9
2.1 Introduction	p. 9
2.2 Component Modeling and Assumptions	p. 10
2.2.1 Transmission Lines	p. 10
2.2.2 Shunt Capacitors or Reactors	p. 10
2.2.3 Tap Changing and Phase Shifting Transformers	p. 10
2.2.4 Loads and Generators	p. 12
2.3 Building the Network Model	p. 12
2.4 Maximum Likelihood Estimation	p. 15
2.4.1 Gaussian (Normal) Probability Density Function	p. 15
2.4.2 The Likelihood Function	p. 17
2.5 Measurement Model and Assumptions	p. 18
2.6 WLS State Estimation Algorithm	p. 20
2.6.1 The Measurement Function, h(x[superscript k])	p. 21
2.6.2 The Measurement Jacobian, H	p. 23
2.6.3 The Gain Matrix, G	p. 25
2.6.4 Cholesky Decomposition of G	p. 27
2.6.5 Performing the Forward/Back Substitutions	p. 27
2.7 Decoupled Formulation of the WLS State Estimation	p. 29
2.8 DC State Estimation Model	p. 33
2.9 Problems	p. 33
References	p. 36
3 Alternative Formulations of the WLS State Estimation	p. 37
3.1 Weaknesses of the Normal Equations Formulation	p. 37
3.2 Orthogonal Factorization	p. 42
3.3 Hybrid Method	p. 43
3.4 Method of Peters and Wilkinson	p. 45
3.5 Equality-Constrained WLS State Estimation	p. 46
3.6 Augmented Matrix Approach	p. 48
3.7 Blocked Formulation	p. 50
3.8 Comparison of Techniques	p. 54
3.9 Problems	p. 56
References	p. 57
4 Network Observability Analysis	p. 59
4.1 Networks and Graphs	p. 60
4.1.1 Graphs	p. 60
4.1.2 Networks	p. 61
4.2 Network Matrices	p. 61
4.2.1 Branch to Bus Incidence Matrix	p. 62
4.2.2 Fundamental Loop to Branch Incidence Matrix	p. 63
4.3 Loop Equations	p. 65
4.4 Methods of Observability Analysis	p. 66
4.5 Numerical Method Based on the Branch Variable Formulation	p. 67
4.5.1 New Branch Variables	p. 67
4.5.2 Measurement Equations	p. 68
4.5.3 Linearized Measurement Model	p. 70
4.5.4 Observability Analysis	p. 72
4.6 Numerical Method Based on the Nodal Variable Formulation	p. 76
4.6.1 Determining the Unobservable Branches	p. 79
4.6.2 Identification of Observable Islands	p. 81
4.6.3 Measurement Placement to Restore Observability	p. 84
4.7 Topological Observability Analysis Method	p. 89
4.7.1 Topological Observability Algorithm	p. 89
4.7.2 Identifying the Observable Islands	p. 90
4.8 Determination of Critical Measurements	p. 90
4.9 Measurement Design	p. 93
4.10 Summary	p. 93
4.11 Problems	p. 93
References	p. 97
5 Bad Data Detection and Identification	p. 99
5.1 Properties of Measurement Residuals	p. 101
5.2 Classification of Measurements	p. 104
5.3 Bad Data Detection and Identifiability	p. 104
5.4 Bad Data Detection	p. 105
5.4.1 Chi-squares x[superscript 2] Distribution	p. 105
5.4.2 Use of x[superscript 2] Distribution for Bad Data Detection	p. 106
5.4.3 x[superscript 2]-Test for Detecting Bad Data in WLS State Estimation	p. 108
5.4.4 Use of Normalized Residuals for Bad Data Detection	p. 110
5.5 Properties of Normalized Residuals	p. 111
5.6 Bad Data Identification	p. 111
5.7 Largest Normalized Residual (r[superscript N subscript max]) Test	p. 111
5.7.1 Computational Issues	p. 113
5.7.2 Strengths and Limitations of the r[superscript N subscript max] Test	p. 115
5.8 Hypothesis Testing Identification (HTI)	p. 116
5.8.1 Statistical Properties of e[subscript s]	p. 118
5.8.2 Hypothesis Testing	p. 119
5.8.3 Decision Rules	p. 120
5.8.4 HTI Strategy Under Fixed [beta]	p. 122
5.9 Summary	p. 122
5.10 Problems	p. 123
References	p. 125
6 Robust State Estimation	p. 127
6.1 Introduction	p. 127
6.2 Robustness and Breakdown Points	p. 128
6.3 Outliers and Leverage Points	p. 129
6.3.1 Concept of Leverage Points	p. 130
6.3.2 Identification of Leverage Measurements	p. 131
6.4 M-Estimators	p. 135
6.4.1 Estimation by Newton's Method	p. 137
6.4.2 Iteratively Re-weighted Least Squares Estimation	p. 139
6.5 Least Absolute Value (LAV) Estimation	p. 140
6.5.1 Linear Regression	p. 141
6.5.2 LAV Estimation as an LP Problem	p. 141
6.5.3 Simplex Based Algorithm	p. 145
6.5.4 Interior Point Algorithm	p. 150
6.6 Discussion	p. 153
6.7 Problems	p. 153
References	p. 154
7 Network Parameter Estimation	p. 157
7.1 Introduction	p. 157
7.2 Influence of Parameter Errors on State Estimation Results	p. 158
7.3 Identification of Suspicious Parameters	p. 163
7.4 Classification of Parameter Estimation Methods	p. 164
7.5 Parameter Estimation Based on Residual Sensitivity Analysis	p. 165
7.6 Parameter Estimation Based on State Vector Augmentation	p. 167
7.6.1 Solution Using Conventional Normal Equations	p. 170
7.6.2 Solution Based on Kalman Filter Theory	p. 172
7.7 Parameter Estimation Based on Historical Series of Data	p. 173
7.8 Transformer Tap Estimation	p. 179
7.9 Observability of Network Parameters	p. 187
7.10 Discussion	p. 188
7.11 Problems	p. 189
References	p. 190
8 Topology Error Processing	p. 195
8.1 Introduction	p. 195
8.2 Types of Topology Errors	p. 197
8.3 Detection of Topology Errors	p. 197
8.4 Classification of Methods for Topology Error Analysis	p. 201
8.5 Preliminary Topology Validation	p. 203
8.6 Branch Status Errors	p. 204
8.6.1 Residual Analysis	p. 205
8.6.2 State Vector Augmentation	p. 209
8.7 Substation Configuration Errors	p. 213
8.7.1 Inclusion of Circuit Breakers in the Network Model	p. 214
8.7.2 WLAV Estimator	p. 218
8.7.3 WLS Estimator	p. 221
8.8 Substation Graph and Reduced Model	p. 225
8.9 Implicit Substation Model: State and Status Estimation	p. 228
8.10 Observability Analysis Revisited	p. 237
8.11 Problems	p. 240
References	p. 242
9 State Estimation Using Ampere Measurements	p. 245
9.1 Introduction	p. 245
9.2 Modeling of Ampere Measurements	p. 247
9.3 Difficulties in Using Ampere Measurements	p. 252
9.4 Inequality-Constrained State Estimation	p. 255
9.5 Heuristic Determination of P-[theta] Solution Uniqueness	p. 261
9.6 Algorithmic Determination of Solution Uniqueness	p. 264
9.6.1 Procedure Based on the Residual Covariance Matrix	p. 265
9.6.2 Procedure Based on the Jacobian Matrix	p. 268
9.7 Identification of Nonuniquely Observable Branches	p. 270
9.8 Measurement Classification and Bad Data Identification	p. 274
9.8.1 LS Estimation	p. 275
9.8.2 LAV Estimation	p. 277
9.9 Problems	p. 279
References	p. 280
Appendix A Review of Basic Statistics	p. 283
A.1 Random Variables	p. 283
A.2 The Distribution Function (d.f.), F(x)	p. 283
A.3 The Probability Density Function (p.d.f), f(x)	p. 284
A.4 Continuous Joint Distributions	p. 284
A.5 Independent Random Variables	p. 285
A.6 Conditional Distributions	p. 285
A.7 Expected Value	p. 285
A.8 Variance	p. 286
A.9 Median	p. 286
A.10 Mean Squared Error	p. 286
A.11 Mean Absolute Error	p. 287
A.12 Covariance	p. 287
A.13 Normal Distribution	p. 288
A.14 Standard Normal Distribution	p. 289
A.15 Properties of Normally Distributed Random Variables	p. 291
A.16 Distribution of Sample Mean	p. 292
A.17 Likelihood Function and Maximum Likelihood Estimator	p. 293
A.17.1 Properties of MLE's	p. 293
A.18 Central Limit Theorem for the Sample Mean	p. 294
Appendix B Review of Sparse Linear Equation Solution	p. 295
B.1 Solution by Direct Methods	p. 297
B.2 Elementary Matrices	p. 298
B.3 LU Factorization Using Elementary Matrices	p. 299
B.3.1 Crout's Algorithm	p. 299
B.3.2 Doolittle's Algorithm	p. 301
B.3.3. Factorization of Sparse Symmetric Matrices	p. 302
B.3.4 Ordering Sparse Symmetric Matrices	p. 303
B.4 Factorization Path Graph	p. 304
B.5 Sparse Forward/Back Substitutions	p. 305
B.6 Solution of Modified Equations	p. 307
B.6.1 Partial Refactorization	p. 309
B.6.2 Compensation	p. 311
B.7 Sparse Inverse	p. 313
B.8 Orthogonal Factorization	p. 315
B.9 Storage and Retrieval of Sparse Matrix Elements	p. 318
B.10 Inserting and/or Deleting Elements in a Linked List	p. 320
B.10.1 Adding a Nonzero Element	p. 320
B.10.2 Deleting a Nonzero Element	p. 321
References	p. 322
Index	p. 325

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Table of Contents