Power System State Estimation, Ali Abur,

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Power System State Estimation

Theory and Implementation

2004

Ali Abur

MARCEL DEKKER

فهرست کامل مطالب

Introduction
1.1 Operating States of a Power System
1.2 Power System Security Analysis
1.3 State Estimation
1.4 Summary
2 Weighted Least Squares State Estimation
2.1 Introductio
2.2 Component Modeling and Assumptions
2.2.1 Transmission Lines
2.2.2 Shunt Capacitors or Reactors
2.2.3 Tap Changing and Phase Shifting Transformers
2.2.4 Loads and Generators
2.3 Building the Network Model
2.4 Maximum Likelihood Estimation
2.4.1 Gaussian (Normal) Probability Density Function
2.4.2 The Likelihood Function
2.5 Measurement Model and Assumptions
2.6 WLS State Estimation Algorithm
2.6.1 The Measurement Function, A(a^)
2.6.2 The Measurement Jacobian, R
2.6.3 The Gain Matrix, G
2.6.4 Cholesky Decomposition of (7
2.6.5 Performing the Forward/Back Substitutions
2.7 Decoupled Formulation of the
WLS State Estimation
2.8 DC State Estimation Model
2.9 Problems
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
3 Alternative Formulations of the WLS State Estimation
3.1 Weaknesses of the Normal Equations Formulation
3.2 Orthogonal Factorization
3.3 Hybrid Method
3.4 Method of Peters and Wilkinson
3.5 Equality-Constrained WLS State Estimation
3.6 Augmented Matrix Approach
3.7 Blocked Formulation
3.8 Comparison of Techniques
3.9 Problems
References
4 Network Observability Analysis
4.1 Networks and Graphs
4.1.1 Graphs
4.1.2 Networks
4.2 NetworkMatrices
4.2.1 Branch to Bus Incidence Matrix
4.2.2 Fundamental Loop to Branch Incidence Matrix
4.3 LoopEquations
4.4 Methods of Observability Analysis
4.5 Numerical Method Based on the Branch Variable Formulation
4.5.1 New Branch Variables
4.5.2 Measurement Equations
4.5.3 Linearized Measurement Model
4.5.4 Observability Analysis
4.6 Numerical Method Based on the Nodal Variable Formulation
4.6.1 Determining the Unobservable Branches
4.6.2 Identification of Observable Islands
4.6.3 Measurement Placement to Restore
Observability
4.7 Topological Observability Analysis
Method
4.7.1 Topological Observability Algorithm
4.7.2 Identifying the Observable Islands
4.8 Determination of Critical Measurements
4.9 Measurement Design
4.10 Summary
4.11 Problems
References
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
5 Bad Data Detection and Identification
5.1 Properties of Measurement Residuals
5.2 Classification of Measurements
5.3 Bad Data Detection and IdentiRability
5.4 Bad Data Detection
5.4.1 Chi-squares x^ Distribution
5.4.2 Use of x^ Distribution for Bad Data Detection
5.4.3 x^-Test for Detecting Bad Data in WLS State Estimation
5.4.4 Use of Normalized Residuals for Bad Data
Detection
5.5 Properties of Normalized Residuals
5.6 Bad Data Identification
5.7 Largest Normalized Residual (r^aa) Test
5.7.1 Computational Issues
5.7.2 Strengths and Limitations of the r^ag Test
5.8 Hypothesis Testing Identification (HTI)
5.8.1 Statistical Properties of eg
5.8.2 Hypothesis Testing
5.8.3 Decision Rules
5.8.4 HTI Strategy Under Fixed /3
5.9 Summary
5.10 Problems
Reference
6 Robust State Estimation
6.1 Introductio
6.2 Robustness and Breakdown Points
6.3 Outliers and Leverage Points
6.3.1 Concept of Leverage Points
6.3.2 Identification of Leverage Measurements
6.4 M-Estimators
6.4.1 Estimation by Newton's Method
6.4.2 Iteratively Re-weighted Least Squares
Estimation
6.5 Least Absolute Value (LAV) Estimation
6.5.1 Linear Regression
6.5.2 LAV Estimation as an LP Problem
6.5.3 Simplex Based Algorithm
6.5.4 Interior Point Algorithm
6.6 Discussion
6.7 Problems
References
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
7 Network Parameter Estimation
7.1 Introduction
7.2 Influence of Parameter Errors on State
Estimation Results
7.3 Identification of Suspicious Parameters
7.4 Classification of Parameter Estimation
Methods
7.5 Parameter Estimation Based on Residua! Sensitivity Analysis
7.6 Parameter Estimation Based on State
Vector Augmentation
7.6.1 Solution Using Conventional Normal Equation
7.6.2 Solution Based on Kalman Filter Theory
7.7 Parameter Estimation Based on Historical Series of Data
7.8 Transformer Tap Estimation
7.9 Observability of Network Parameters
7.10 Discussion
7.11 Problems
References
8 Topology Error Processing
8.1 Introduction
8.2 Types of Topology Errors
8.3 Detection of Topology Errors
8.4 Classification of Methods for Topology Error Analysis
8.5 Preliminary Topology Validation
8.6 Branch Status Errors
8.6.1 Residual Analysis
8.6.2 State Vector Augmentation
8.7 Substation Configuration Errors
8.7.1 Inclusion of Circuit Breakers in the Network Model
8.7.2 WLAV Estimator
8.7.3 WLS Estimator
8.8 Substation Graph and Reduced Model
8.9 Implicit Substation Model: State and
Status Estimation
8.10 Observability Analysis Revisited
8.11 Problems
References
9 State Estimation Using Ampere Measurements
9.1 Introduction
9.2 Modeling of Ampere Measurements
9.3 Difficulties in Using Ampere
Measurements
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
9.4 Inequality-Constrained State Estimation
9.5 Heuristic Determination of F-# Solution Uniqueness
9.6 Algorithmic Determination of Solution
Uniqueness
9.6.1 Procedure Based on the Residual Covariance Matrix
9.6.2 Procedure Based on the Jacobian Matrix
9.7 Identification of Nonuniquely Observable Branches
9.8 Measurement Classification and Bad Data Identific
9.8.1 LS Estimation
9.8.2 LAV Estimation
9.9 Problems
References
Appendix A Review of Basic Statistics
A.I Random Variables
A.2 The Distribution Function (d.f.), F(x)
A.3 The Probability Density Function (p.d.f), f(x)
A.4 Continuous Joint Distributions
A.5 Independent Random Variables
A.6 Conditional Distributions
A.7 Expected Value
A.8 Variance
A.9 Median
A.10 Mean Squared Error
A.11 Mean Absolute Error
A.12 Covariance
A.13 Normal Distribution
A.14 Standard Normal Distribution
A.15 Properties of Normally Distributed Random Variables
A.16 Distribution of Sample Mean
A.17 Likelihood Function and Maximum
Likelihood Estimator
A.17.1 Properties of MLE's
A.18 Central Limit Theorem for the Sample Mean
Appendix B Review of Sparse Linear Equation Solution
B.I Solution by Direct Methods
B.2 Elementary Matrices
B.3 LU Factorization Using Elementary Matrices
B.3.1 Grout's Algorithm
B.3.2 Dooh'ttle's Algorithm
B.3.3 Factorization of Sparse Symmetric Matrice
B.3.4 Ordering Sparse Symmetric Matrices
B.4 Factorization Path Graph
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
B.5 Sparse Forward/Back Substitutions
B.6 Solution of Modified Equations
B.6.1 Partial Refactorization
B.6.2 Compensation
B.7 Sparse Inverse
B.8 Orthogonal Factorization
B.9 Storage and Retrieval of Sparse Matrix Elements
B.10 Inserting and/or Deleting Elements in a Linked List
B.10.1 Adding a Nonzero Element
B.10.2 Deleting a Nonzero Element
References