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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 | |