### Theory and Implementation

### Theory and Implementation

#### Get Citation

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.

Preface

INTRODUCTION

Operating States of a Power System

Power System Security Analysis

State Estimation

Summary

WEIGHTED LEAST SQUARES STATE ESTIMATION

Introduction

Component Modeling and Assumptions

Building the Network Model

Maximum Likelihood Estimation

Measurement Model and Assumptions

WLS State Estimation Algorithm

Decoupled Formulation of the WLS State Estimation

DC State Estimation Model

Problems

References

ALTERNATIVE FORMULATIONS OF THE WLS STATE ESTIMATION

Weaknesses of the Normal Equations Formulation

Orthogonal Factorization

Hybrid Method

Method of Peters and Wilkinson

Equality-Constrained WLS State Estimation

Augmented Matrix Approach

Blocked Formulation

Comparison of Techniques

Problems

References

NETWORK OBSERVABILITY ANALYSIS

Networks and Graphs

NetworkMatrices

LoopEquations

Methods of Observability Analysis

Numerical Method Based on the Branch Variable Formulation

Numerical Method Based on the Nodal Variable Formulation

Topological Observability Analysis Method

Determination of Critical Measurements

Measurement Design

Summary

Problems

References

BAD DATA DETECTION AND IDENTIFICATION

Properties of Measurement Residuals

Classification of Measurements

Bad Data Detection and IdentiRability

Bad Data Detection

Properties of Normalized Residuals

Bad Data Identification

Largest Normalized Residual Test

Hypothesis Testing Identification (HTI)

Summary

Problems

References

ROBUST STATE ESTIMATION

Introduction

Robustness and Breakdown Points

Outliers and Leverage Points

M-Estimators

Least Absolute Value (LAV) Estimation

Discussion

Problems

References

NETWORK PARAMETER ESTIMATION

Introduction

Influence of Parameter Errors on State Estimation Results

Identification of Suspicious Parameters

Classification of Parameter Estimation Methods

Parameter Estimation Based on Residua! Sensitivity Analysis

Parameter Estimation Based on State Vector Augmentation

Parameter Estimation Based on Historical Series of Data

Transformer Tap Estimation

Observability of Network Parameters

Discussion

Problems

References

TOPOLOGY ERROR PROCESSING

Introduction

Types of Topology Errors

Detection of Topology Errors

Classification of Methods for Topology Error Analysis

Preliminary Topology Validation

Branch Status Errors

Substation Configuration Errors

Substation Graph and Reduced Model

Implicit Substation Model: State and Status Estimation

Observability Analysis Revisited

Problems

References

STATE ESTIMATION USING AMPERE MEASUREMENTS

Introduction

Modeling of Ampere Measurements

Difficulties in Using Ampere Measurements

Inequality-Constrained State Estimation

Heuristic Determination of F-# Solution Uniqueness

Algorithmic Determination of Solution Uniqueness

Identification of Nonuniquely Observable Branches

Measurement Classification and Bad Data Identification

Problems

References

Appendix A Review of Basic Statistics

Appendix B Review of Sparse Linear Equation Solution

References

Index

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.

Preface

INTRODUCTION

Operating States of a Power System

Power System Security Analysis

State Estimation

Summary

WEIGHTED LEAST SQUARES STATE ESTIMATION

Introduction

Component Modeling and Assumptions

Building the Network Model

Maximum Likelihood Estimation

Measurement Model and Assumptions

WLS State Estimation Algorithm

Decoupled Formulation of the WLS State Estimation

DC State Estimation Model

Problems

References

ALTERNATIVE FORMULATIONS OF THE WLS STATE ESTIMATION

Weaknesses of the Normal Equations Formulation

Orthogonal Factorization

Hybrid Method

Method of Peters and Wilkinson

Equality-Constrained WLS State Estimation

Augmented Matrix Approach

Blocked Formulation

Comparison of Techniques

Problems

References

NETWORK OBSERVABILITY ANALYSIS

Networks and Graphs

NetworkMatrices

LoopEquations

Methods of Observability Analysis

Numerical Method Based on the Branch Variable Formulation

Numerical Method Based on the Nodal Variable Formulation

Topological Observability Analysis Method

Determination of Critical Measurements

Measurement Design

Summary

Problems

References

BAD DATA DETECTION AND IDENTIFICATION

Properties of Measurement Residuals

Classification of Measurements

Bad Data Detection and IdentiRability

Bad Data Detection

Properties of Normalized Residuals

Bad Data Identification

Largest Normalized Residual Test

Hypothesis Testing Identification (HTI)

Summary

Problems

References

ROBUST STATE ESTIMATION

Introduction

Robustness and Breakdown Points

Outliers and Leverage Points

M-Estimators

Least Absolute Value (LAV) Estimation

Discussion

Problems

References

NETWORK PARAMETER ESTIMATION

Introduction

Influence of Parameter Errors on State Estimation Results

Identification of Suspicious Parameters

Classification of Parameter Estimation Methods

Parameter Estimation Based on Residua! Sensitivity Analysis

Parameter Estimation Based on State Vector Augmentation

Parameter Estimation Based on Historical Series of Data

Transformer Tap Estimation

Observability of Network Parameters

Discussion

Problems

References

TOPOLOGY ERROR PROCESSING

Introduction

Types of Topology Errors

Detection of Topology Errors

Classification of Methods for Topology Error Analysis

Preliminary Topology Validation

Branch Status Errors

Substation Configuration Errors

Substation Graph and Reduced Model

Implicit Substation Model: State and Status Estimation

Observability Analysis Revisited

Problems

References

STATE ESTIMATION USING AMPERE MEASUREMENTS

Introduction

Modeling of Ampere Measurements

Difficulties in Using Ampere Measurements

Inequality-Constrained State Estimation

Heuristic Determination of F-# Solution Uniqueness

Algorithmic Determination of Solution Uniqueness

Identification of Nonuniquely Observable Branches

Measurement Classification and Bad Data Identification

Problems

References

Appendix A Review of Basic Statistics

Appendix B Review of Sparse Linear Equation Solution

References

Index

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.

Preface

INTRODUCTION

Operating States of a Power System

Power System Security Analysis

State Estimation

Summary

WEIGHTED LEAST SQUARES STATE ESTIMATION

Introduction

Component Modeling and Assumptions

Building the Network Model

Maximum Likelihood Estimation

Measurement Model and Assumptions

WLS State Estimation Algorithm

Decoupled Formulation of the WLS State Estimation

DC State Estimation Model

Problems

References

ALTERNATIVE FORMULATIONS OF THE WLS STATE ESTIMATION

Weaknesses of the Normal Equations Formulation

Orthogonal Factorization

Hybrid Method

Method of Peters and Wilkinson

Equality-Constrained WLS State Estimation

Augmented Matrix Approach

Blocked Formulation

Comparison of Techniques

Problems

References

NETWORK OBSERVABILITY ANALYSIS

Networks and Graphs

NetworkMatrices

LoopEquations

Methods of Observability Analysis

Numerical Method Based on the Branch Variable Formulation

Numerical Method Based on the Nodal Variable Formulation

Topological Observability Analysis Method

Determination of Critical Measurements

Measurement Design

Summary

Problems

References

BAD DATA DETECTION AND IDENTIFICATION

Properties of Measurement Residuals

Classification of Measurements

Bad Data Detection and IdentiRability

Bad Data Detection

Properties of Normalized Residuals

Bad Data Identification

Largest Normalized Residual Test

Hypothesis Testing Identification (HTI)

Summary

Problems

References

ROBUST STATE ESTIMATION

Introduction

Robustness and Breakdown Points

Outliers and Leverage Points

M-Estimators

Least Absolute Value (LAV) Estimation

Discussion

Problems

References

NETWORK PARAMETER ESTIMATION

Introduction

Influence of Parameter Errors on State Estimation Results

Identification of Suspicious Parameters

Classification of Parameter Estimation Methods

Parameter Estimation Based on Residua! Sensitivity Analysis

Parameter Estimation Based on State Vector Augmentation

Parameter Estimation Based on Historical Series of Data

Transformer Tap Estimation

Observability of Network Parameters

Discussion

Problems

References

TOPOLOGY ERROR PROCESSING

Introduction

Types of Topology Errors

Detection of Topology Errors

Classification of Methods for Topology Error Analysis

Preliminary Topology Validation

Branch Status Errors

Substation Configuration Errors

Substation Graph and Reduced Model

Implicit Substation Model: State and Status Estimation

Observability Analysis Revisited

Problems

References

STATE ESTIMATION USING AMPERE MEASUREMENTS

Introduction

Modeling of Ampere Measurements

Difficulties in Using Ampere Measurements

Inequality-Constrained State Estimation

Heuristic Determination of F-# Solution Uniqueness

Algorithmic Determination of Solution Uniqueness

Identification of Nonuniquely Observable Branches

Measurement Classification and Bad Data Identification

Problems

References

Appendix A Review of Basic Statistics

Appendix B Review of Sparse Linear Equation Solution

References

Index

Preface

INTRODUCTION

Operating States of a Power System

Power System Security Analysis

State Estimation

Summary

WEIGHTED LEAST SQUARES STATE ESTIMATION

Introduction

Component Modeling and Assumptions

Building the Network Model

Maximum Likelihood Estimation

Measurement Model and Assumptions

WLS State Estimation Algorithm

Decoupled Formulation of the WLS State Estimation

DC State Estimation Model

Problems

References

ALTERNATIVE FORMULATIONS OF THE WLS STATE ESTIMATION

Weaknesses of the Normal Equations Formulation

Orthogonal Factorization

Hybrid Method

Method of Peters and Wilkinson

Equality-Constrained WLS State Estimation

Augmented Matrix Approach

Blocked Formulation

Comparison of Techniques

Problems

References

NETWORK OBSERVABILITY ANALYSIS

Networks and Graphs

NetworkMatrices

LoopEquations

Methods of Observability Analysis

Numerical Method Based on the Branch Variable Formulation

Numerical Method Based on the Nodal Variable Formulation

Topological Observability Analysis Method

Determination of Critical Measurements

Measurement Design

Summary

Problems

References

BAD DATA DETECTION AND IDENTIFICATION

Properties of Measurement Residuals

Classification of Measurements

Bad Data Detection and IdentiRability

Bad Data Detection

Properties of Normalized Residuals

Bad Data Identification

Largest Normalized Residual Test

Hypothesis Testing Identification (HTI)

Summary

Problems

References

ROBUST STATE ESTIMATION

Introduction

Robustness and Breakdown Points

Outliers and Leverage Points

M-Estimators

Least Absolute Value (LAV) Estimation

Discussion

Problems

References

NETWORK PARAMETER ESTIMATION

Introduction

Influence of Parameter Errors on State Estimation Results

Identification of Suspicious Parameters

Classification of Parameter Estimation Methods

Parameter Estimation Based on Residua! Sensitivity Analysis

Parameter Estimation Based on State Vector Augmentation

Parameter Estimation Based on Historical Series of Data

Transformer Tap Estimation

Observability of Network Parameters

Discussion

Problems

References

TOPOLOGY ERROR PROCESSING

Introduction

Types of Topology Errors

Detection of Topology Errors

Classification of Methods for Topology Error Analysis

Preliminary Topology Validation

Branch Status Errors

Substation Configuration Errors

Substation Graph and Reduced Model

Implicit Substation Model: State and Status Estimation

Observability Analysis Revisited

Problems

References

STATE ESTIMATION USING AMPERE MEASUREMENTS

Introduction

Modeling of Ampere Measurements

Difficulties in Using Ampere Measurements

Inequality-Constrained State Estimation

Heuristic Determination of F-# Solution Uniqueness

Algorithmic Determination of Solution Uniqueness

Identification of Nonuniquely Observable Branches

Measurement Classification and Bad Data Identification

Problems

References

Appendix A Review of Basic Statistics

Appendix B Review of Sparse Linear Equation Solution

References

Index

Preface

INTRODUCTION

Operating States of a Power System

Power System Security Analysis

State Estimation

Summary

WEIGHTED LEAST SQUARES STATE ESTIMATION

Introduction

Component Modeling and Assumptions

Building the Network Model

Maximum Likelihood Estimation

Measurement Model and Assumptions

WLS State Estimation Algorithm

Decoupled Formulation of the WLS State Estimation

DC State Estimation Model

Problems

References

ALTERNATIVE FORMULATIONS OF THE WLS STATE ESTIMATION

Weaknesses of the Normal Equations Formulation

Orthogonal Factorization

Hybrid Method

Method of Peters and Wilkinson

Equality-Constrained WLS State Estimation

Augmented Matrix Approach

Blocked Formulation

Comparison of Techniques

Problems

References

NETWORK OBSERVABILITY ANALYSIS

Networks and Graphs

NetworkMatrices

LoopEquations

Methods of Observability Analysis

Numerical Method Based on the Branch Variable Formulation

Numerical Method Based on the Nodal Variable Formulation

Topological Observability Analysis Method

Determination of Critical Measurements

Measurement Design

Summary

Problems

References

BAD DATA DETECTION AND IDENTIFICATION

Properties of Measurement Residuals

Classification of Measurements

Bad Data Detection and IdentiRability

Bad Data Detection

Properties of Normalized Residuals

Bad Data Identification

Largest Normalized Residual Test

Hypothesis Testing Identification (HTI)

Summary

Problems

References

ROBUST STATE ESTIMATION

Introduction

Robustness and Breakdown Points

Outliers and Leverage Points

M-Estimators

Least Absolute Value (LAV) Estimation

Discussion

Problems

References

NETWORK PARAMETER ESTIMATION

Introduction

Influence of Parameter Errors on State Estimation Results

Identification of Suspicious Parameters

Classification of Parameter Estimation Methods

Parameter Estimation Based on Residua! Sensitivity Analysis

Parameter Estimation Based on State Vector Augmentation

Parameter Estimation Based on Historical Series of Data

Transformer Tap Estimation

Observability of Network Parameters

Discussion

Problems

References

TOPOLOGY ERROR PROCESSING

Introduction

Types of Topology Errors

Detection of Topology Errors

Classification of Methods for Topology Error Analysis

Preliminary Topology Validation

Branch Status Errors

Substation Configuration Errors

Substation Graph and Reduced Model

Implicit Substation Model: State and Status Estimation

Observability Analysis Revisited

Problems

References

STATE ESTIMATION USING AMPERE MEASUREMENTS

Introduction

Modeling of Ampere Measurements

Difficulties in Using Ampere Measurements

Inequality-Constrained State Estimation

Heuristic Determination of F-# Solution Uniqueness

Algorithmic Determination of Solution Uniqueness

Identification of Nonuniquely Observable Branches

Measurement Classification and Bad Data Identification

Problems

References

Appendix A Review of Basic Statistics

Appendix B Review of Sparse Linear Equation Solution

References

Index

Preface

INTRODUCTION

Operating States of a Power System

Power System Security Analysis

State Estimation

Summary

WEIGHTED LEAST SQUARES STATE ESTIMATION

Introduction

Component Modeling and Assumptions

Building the Network Model

Maximum Likelihood Estimation

Measurement Model and Assumptions

WLS State Estimation Algorithm

Decoupled Formulation of the WLS State Estimation

DC State Estimation Model

Problems

References

ALTERNATIVE FORMULATIONS OF THE WLS STATE ESTIMATION

Weaknesses of the Normal Equations Formulation

Orthogonal Factorization

Hybrid Method

Method of Peters and Wilkinson

Equality-Constrained WLS State Estimation

Augmented Matrix Approach

Blocked Formulation

Comparison of Techniques

Problems

References

NETWORK OBSERVABILITY ANALYSIS

Networks and Graphs

NetworkMatrices

LoopEquations

Methods of Observability Analysis

Numerical Method Based on the Branch Variable Formulation

Numerical Method Based on the Nodal Variable Formulation

Topological Observability Analysis Method

Determination of Critical Measurements

Measurement Design

Summary

Problems

References

BAD DATA DETECTION AND IDENTIFICATION

Properties of Measurement Residuals

Classification of Measurements

Bad Data Detection and IdentiRability

Bad Data Detection

Properties of Normalized Residuals

Bad Data Identification

Largest Normalized Residual Test

Hypothesis Testing Identification (HTI)

Summary

Problems

References

ROBUST STATE ESTIMATION

Introduction

Robustness and Breakdown Points

Outliers and Leverage Points

M-Estimators

Least Absolute Value (LAV) Estimation

Discussion

Problems

References

NETWORK PARAMETER ESTIMATION

Introduction

Influence of Parameter Errors on State Estimation Results

Identification of Suspicious Parameters

Classification of Parameter Estimation Methods

Parameter Estimation Based on Residua! Sensitivity Analysis

Parameter Estimation Based on State Vector Augmentation

Parameter Estimation Based on Historical Series of Data

Transformer Tap Estimation

Observability of Network Parameters

Discussion

Problems

References

TOPOLOGY ERROR PROCESSING

Introduction

Types of Topology Errors

Detection of Topology Errors

Classification of Methods for Topology Error Analysis

Preliminary Topology Validation

Branch Status Errors

Substation Configuration Errors

Substation Graph and Reduced Model

Implicit Substation Model: State and Status Estimation

Observability Analysis Revisited

Problems

References

STATE ESTIMATION USING AMPERE MEASUREMENTS

Introduction

Modeling of Ampere Measurements

Difficulties in Using Ampere Measurements

Inequality-Constrained State Estimation

Heuristic Determination of F-# Solution Uniqueness

Algorithmic Determination of Solution Uniqueness

Identification of Nonuniquely Observable Branches

Measurement Classification and Bad Data Identification

Problems

References

Appendix A Review of Basic Statistics

Appendix B Review of Sparse Linear Equation Solution

References

Index