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| Foreword | |
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| Preface | |
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| Introduction | |
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| Operating States of a Power System | |
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| Power System Security Analysis | |
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| State Estimation | |
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| Summary | |
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| Weighted Least Squares State Estimation | |
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| Introduction | |
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| Component Modeling and Assumptions | |
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| Transmission Lines | |
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| Shunt Capacitors or Reactors | |
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| Tap Changing and Phase Shifting Transformers | |
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| Loads and Generators | |
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| Building the Network Model | |
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| Maximum Likelihood Estimation | |
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| Gaussian (Normal) Probability Density Function | |
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| The Likelihood Function | |
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| Measurement Model and Assumptions | |
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| WLS State Estimation Algorithm | |
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| The Measurement Function, h(x[superscript k]) | |
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| The Measurement Jacobian, H | |
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| The Gain Matrix, G | |
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| Cholesky Decomposition of G | |
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| Performing the Forward/Back Substitutions | |
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| Decoupled Formulation of the WLS State Estimation | |
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| DC State Estimation Model | |
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| Problems | |
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| References | |
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| Alternative Formulations of the WLS State Estimation | |
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| Weaknesses of the Normal Equations Formulation | |
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| Orthogonal Factorization | |
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| Hybrid Method | |
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| Method of Peters and Wilkinson | |
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| Equality-Constrained WLS State Estimation | |
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| Augmented Matrix Approach | |
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| Blocked Formulation | |
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| Comparison of Techniques | |
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| Problems | |
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| References | |
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| Network Observability Analysis | |
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| Networks and Graphs | |
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| Graphs | |
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| Networks | |
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| Network Matrices | |
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| Branch to Bus Incidence Matrix | |
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| Fundamental Loop to Branch Incidence Matrix | |
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| Loop Equations | |
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| Methods of Observability Analysis | |
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| Numerical Method Based on the Branch Variable Formulation | |
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| New Branch Variables | |
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| Measurement Equations | |
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| Linearized Measurement Model | |
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| Observability Analysis | |
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| Numerical Method Based on the Nodal Variable Formulation | |
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| Determining the Unobservable Branches | |
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| Identification of Observable Islands | |
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| Measurement Placement to Restore Observability | |
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| Topological Observability Analysis Method | |
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| Topological Observability Algorithm | |
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| Identifying the Observable Islands | |
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| Determination of Critical Measurements | |
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| Measurement Design | |
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| Summary | |
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| Problems | |
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| References | |
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| Bad Data Detection and Identification | |
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| Properties of Measurement Residuals | |
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| Classification of Measurements | |
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| Bad Data Detection and Identifiability | |
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| Bad Data Detection | |
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| Chi-squares x[superscript 2] Distribution | |
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| Use of x[superscript 2] Distribution for Bad Data Detection | |
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| x[superscript 2]-Test for Detecting Bad Data in WLS State Estimation | |
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| Use of Normalized Residuals for Bad Data Detection | |
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| Properties of Normalized Residuals | |
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| Bad Data Identification | |
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| Largest Normalized Residual (r[superscript N subscript max]) Test | |
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| Computational Issues | |
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| Strengths and Limitations of the r[superscript N subscript max] Test | |
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| Hypothesis Testing Identification (HTI) | |
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| Statistical Properties of e[subscript s] | |
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| Hypothesis Testing | |
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| Decision Rules | |
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| HTI Strategy Under Fixed [beta] | |
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| Summary | |
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| Problems | |
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| References | |
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| Robust State Estimation | |
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| Introduction | |
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| Robustness and Breakdown Points | |
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| Outliers and Leverage Points | |
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| Concept of Leverage Points | |
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| Identification of Leverage Measurements | |
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| M-Estimators | |
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| Estimation by Newton's Method | |
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| Iteratively Re-weighted Least Squares Estimation | |
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| Least Absolute Value (LAV) Estimation | |
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| Linear Regression | |
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| LAV Estimation as an LP Problem | |
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| Simplex Based Algorithm | |
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| Interior Point Algorithm | |
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| Discussion | |
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| Problems | |
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| References | |
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| Network Parameter Estimation | |
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| Introduction | |
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| Influence of Parameter Errors on State Estimation Results | |
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| Identification of Suspicious Parameters | |
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| Classification of Parameter Estimation Methods | |
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| Parameter Estimation Based on Residual Sensitivity Analysis | |
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| Parameter Estimation Based on State Vector Augmentation | |
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| Solution Using Conventional Normal Equations | |
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| Solution Based on Kalman Filter Theory | |
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| Parameter Estimation Based on Historical Series of Data | |
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| Transformer Tap Estimation | |
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| Observability of Network Parameters | |
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| Discussion | |
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| Problems | |
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| References | |
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| Topology Error Processing | |
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| Introduction | |
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| Types of Topology Errors | |
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| Detection of Topology Errors | |
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| Classification of Methods for Topology Error Analysis | |
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| Preliminary Topology Validation | |
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| Branch Status Errors | |
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| Residual Analysis | |
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| State Vector Augmentation | |
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| Substation Configuration Errors | |
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| Inclusion of Circuit Breakers in the Network Model | |
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| WLAV Estimator | |
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| WLS Estimator | |
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| Substation Graph and Reduced Model | |
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| Implicit Substation Model: State and Status Estimation | |
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| Observability Analysis Revisited | |
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| Problems | |
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| References | |
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| State Estimation Using Ampere Measurements | |
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| Introduction | |
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| Modeling of Ampere Measurements | |
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| Difficulties in Using Ampere Measurements | |
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| Inequality-Constrained State Estimation | |
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| Heuristic Determination of P-[theta] Solution Uniqueness | |
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| Algorithmic Determination of Solution Uniqueness | |
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| Procedure Based on the Residual Covariance Matrix | |
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| Procedure Based on the Jacobian Matrix | |
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| Identification of Nonuniquely Observable Branches | |
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| Measurement Classification and Bad Data Identification | |
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| LS Estimation | |
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| LAV Estimation | |
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| Problems | |
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| References | |
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| Review of Basic Statistics | |
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| Random Variables | |
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| The Distribution Function (d.f.), F(x) | |
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| The Probability Density Function (p.d.f), f(x) | |
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| Continuous Joint Distributions | |
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| Independent Random Variables | |
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| Conditional Distributions | |
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| Expected Value | |
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| Variance | |
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| Median | |
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| Mean Squared Error | |
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| Mean Absolute Error | |
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| Covariance | |
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| Normal Distribution | |
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| Standard Normal Distribution | |
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| Properties of Normally Distributed Random Variables | |
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| Distribution of Sample Mean | |
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| Likelihood Function and Maximum Likelihood Estimator | |
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| Properties of MLE's | |
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| Central Limit Theorem for the Sample Mean | |
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| Review of Sparse Linear Equation Solution | |
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| Solution by Direct Methods | |
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| Elementary Matrices | |
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| LU Factorization Using Elementary Matrices | |
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| Crout's Algorithm | |
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| Doolittle's Algorithm | |
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| Factorization of Sparse Symmetric Matrices | |
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| Ordering Sparse Symmetric Matrices | |
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| Factorization Path Graph | |
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| Sparse Forward/Back Substitutions | |
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| Solution of Modified Equations | |
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| Partial Refactorization | |
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| Compensation | |
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| Sparse Inverse | |
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| Orthogonal Factorization | |
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| Storage and Retrieval of Sparse Matrix Elements | |
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| Inserting and/or Deleting Elements in a Linked List | |
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| Adding a Nonzero Element | |
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| Deleting a Nonzero Element | |
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| References | |
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| Index | |