Power Systems Signal Processing for Smart Grids
By Ribeiro, Paulo F.; Cerqueira, Augusto Santiago; Ribeiro, Moises Vidal; Silveira, Paulo Márcio da; Duque, Carlos Augusto
Power Systems Signal Processing for Smart Grids
By Ribeiro, Paulo F.; Cerqueira, Augusto Santiago; Ribeiro, Moises Vidal; Silveira, Paulo Márcio da; Duque, Carlos Augusto
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With special relation to smart grids, this book provides clear and comprehensive explanation of how Digital Signal Processing (DSP) and Computational Intelligence (CI) techniques can be applied to solve problems in the power system.
Its unique coverage bridges the gap between DSP, electrical power and energy engineering systems, showing many different techniques applied to typical and expected system conditions with practical power system examples.
Surveying all recent advances on DSP for power systems, this book enables engineers and researchers to understand the current state of the…mehr
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Its unique coverage bridges the gap between DSP, electrical power and energy engineering systems, showing many different techniques applied to typical and expected system conditions with practical power system examples.
Surveying all recent advances on DSP for power systems, this book enables engineers and researchers to understand the current state of the art and to develop new tools. It presents:
an overview on the power system and electric signals, with description of the basic concepts of DSP commonly found in power system problems
the application of several signal processing tools to problems, looking at power signal estimation and decomposition, pattern recognition techniques, detection of the power system signal variations
description of DSP in relation to measurements, power quality, monitoring, protection and control, and wide area monitoring
a companion website with real signal data, several Matlab codes with examples, DSP scripts and samples of signals for further processing, understanding and analysis
Practicing power systems engineers and utility engineers will find this book invaluable, as will researchers of electrical power and energy systems, postgraduate electrical engineering students, and staff at utility companies.
- Produktdetails
- Wiley - IEEE .
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 448
- Erscheinungstermin: Dezember 2013
- Englisch
- Abmessung: 250mm x 175mm x 28mm
- Gewicht: 939g
- ISBN-13: 9781119991502
- ISBN-10: 1119991501
- Artikelnr.: 37305172
- Wiley - IEEE .
- Verlag: Wiley & Sons
- 1. Auflage
- Seitenzahl: 448
- Erscheinungstermin: Dezember 2013
- Englisch
- Abmessung: 250mm x 175mm x 28mm
- Gewicht: 939g
- ISBN-13: 9781119991502
- ISBN-10: 1119991501
- Artikelnr.: 37305172
xxiii 1 Introduction 1 1.1 Introduction 1 1.2 The Future Grid 2 1.3
Motivation and Objectives 3 1.4 Signal Processing Framework 4 1.5
Conclusions 8 References 10 2 Power Systems and Signal Processing 11 2.1
Introduction 11 2.2 Dynamic Overvoltage 12 2.2.1 Sustained Overvoltage 12
2.2.2 Lightning Surge 13 2.2.3 Switching Surges 15 2.2.4 Switching of
Capacitor Banks 17 2.3 Fault Current and DC Component 21 2.4 Voltage Sags
and Voltage Swells 25 2.5 Voltage Fluctuations 27 2.6 Voltage and Current
Imbalance 29 2.7 Harmonics and Interharmonics 29 2.8 Inrush Current in
Power Transformers 42 2.9 Over-Excitation of Transformers 45 2.10
Transients in Instrument Transformers 47 2.10.1 Current Transformer (CT)
Saturation (Protection Services) 47 2.10.2 Capacitive Voltage Transformer
(CVT) Transients 54 2.11 Ferroresonance 55 2.12 Frequency Variation 56 2.13
Other Kinds of Phenomena and their Signals 56 2.14 Conclusions 57
References 58 3 Transducers and Acquisition Systems 59 3.1 Introduction 59
3.2 Voltage Transformers (VTs) 60 3.3 Capacitor Voltage Transformers 64 3.4
Current Transformers 67 3.5 Non-Conventional Transducers 71 3.5.1 Resistive
Voltage Divider 71 3.5.2 Optical Voltage Transducer 72 3.5.3 Rogowski Coil
73 3.5.4 Optical Current Transducer 74 3.6 Analog-to-Digital Conversion
Processing 75 3.6.1 Supervision and Control 78 3.6.2 Protection 79 3.6.3
Power Quality 79 3.7 Mathematical Model for Noise 80 3.8 Sampling and the
Anti-Aliasing Filtering 81 3.9 Sampling Rate for Power System Application
84 3.10 Smart-Grid Context and Conclusions 84 References 85 4 Discrete
Transforms 87 4.1 Introduction 87 4.2 Representation of Periodic Signals
using Fourier Series 87 4.2.1 Computation of Series Coefficients 90 4.2.2
The Exponential Fourier Series 92 4.2.3 Relationship between the
Exponential and Trigonometric oefficients 93 4.2.4 Harmonics in Power
Systems 95 4.2.5 Proprieties of a Fourier Series 97 4.3 A Fourier Transform
98 4.3.1 Introduction and Examples 98 4.3.2 Fourier Transform Properties
103 4.4 The Sampling Theorem 104 4.5 The Discrete-Time Fourier Transform
108 4.5.1 DTFT Pairs 109 4.5.2 Properties of DTFT 110 4.6 The Discrete
Fourier Transform (DFT) 110 4.6.1 Sampling the Fourier Transform 116 4.6.2
Discrete Fourier Transform Theorems 116 4.7 Recursive DFT 117 4.8 Filtering
Interpretation of DFT 120 4.8.1 Frequency Response of DFT Filter 123 4.8.2
Asynchronous Sampling 124 4.9 The z-Transform 126 4.9.1 Rational
z-Transforms 128 4.9.2 Stability of Rational Transfer Function 131 4.9.3
Some Common z-Transform Pairs 131 4.9.4 z-Transform Properties 133 4.10
Conclusions 133 References 133 5 Basic Power Systems Signal Processing 135
5.1 Introduction 135 5.2 Linear and Time-Invariant Systems 135 5.2.1
Frequency Response of LTI System 138 5.2.2 Linear Phase FIR Filter 140 5.3
Basic Digital System and Power System Applications 142 5.3.1 Moving Average
Systems: Application 142 5.3.2 RMS Estimation 144 5.3.3 Trapezoidal
Integration and Bilinear Transform 146 5.3.4 Differentiators Filters:
Application 148 5.3.5 Simple Differentiator 151 5.4 Parametric Filters in
Power System Applications 153 5.4.1 Filter Specification 154 5.4.2
First-Order Low-Pass Filter 155 5.4.3 First-Order High-Pass Filter 155
5.4.4 Bandstop IIR Digital Filter (The Notch Filter) 156 5.4.5 Total
Harmonic Distortion in Time Domain (THD) 159 5.4.6 Signal Decomposition
using a Notch Filter 161 5.5 Parametric Notch FIR Filters 161 5.6 Filter
Design using MATLAB1 (FIR and IIR) 163 5.7 Sine and Cosine FIR Filters 163
5.8 Smart-Grid Context and Conclusions 165 References 166 6 Multirate
Systems and Sampling Alterations 167 6.1 Introduction 167 6.2 Basic Blocks
for Sampling Rate Alteration 167 6.2.1 Frequency Domain Interpretation 168
6.2.2 Up-Sampling in Frequency Domain 169 6.2.3 Down-Sampling in Frequency
Domain 169 6.3 The Interpolator 170 6.3.1 The Input-Output Relation for the
Interpolator 172 6.3.2 Multirate System as a Time-Varying System and Nobles
Identities 172 6.4 The Decimator 174 6.4.1 Introduction 174 6.4.2 The
Input-Output Relation for the Decimator 174 6.5 Fractional Sampling Rate
Alteration 175 6.5.1 Resampling Using MATLAB1 175 6.6 Real-Time Sampling
Rate Alteration 176 6.6.1 Spline Interpolation 177 6.6.2 Cubic B-Spline
Interpolation 180 6.7 Conclusions 184 References 184 7 Estimation of
Electrical Parameters 185 7.1 Introduction 185 7.2 Estimation Theory 185
7.3 Least-Squares Estimator 187 7.3.1 Linear Least-Squares 188 7.4
Frequency Estimation 191 7.4.1 Frequency Estimation Based on Zero Crossing
(IEC61000-4-30) 192 7.4.2 Short-Term Frequency Estimator Based on Zero
Crossing 195 7.4.3 Frequency Estimation Based on Phasor Rotation 198 7.4.4
Varying the DFT Window Size 200 7.4.5 Frequency Estimation Based on LSE 201
7.4.6 IIR Notch Filter 203 7.4.7 Small Coefficient and/or Small Arithmetic
Errors 203 7.5 Phasor Estimation 205 7.5.1 Introduction 205 7.5.2 The PLL
Structure 207 7.5.3 Kalman Filter Estimation 209 7.5.4 Example of Phasor
Estimation using Kalman Filter 211 7.6 Phasor Estimation in Presence of DC
Component 212 7.6.1 Mathematical Model for the Signal in Presence of DC
Decaying 213 7.6.2 Mimic Method 214 7.6.3 Least-Squares Estimator (LSE) 215
7.6.4 Improved DTFT Estimation Method 216 7.7 Conclusions 224 References
224 8 Spectral Estimation 227 8.1 Introduction 227 8.2 Spectrum Estimation
227 8.2.1 Understanding Spectral Leakage 229 8.2.2 Interpolation in
Frequency Domain: Single-Tone Signal 232 8.3 Windows 236 8.3.1
Frequency-Domain Windowing 236 8.4 Interpolation in Frequency Domain:
Multitone Signal 240 8.5 Interharmonics 243 8.5.1 Typical Interhamonic
Sources 246 8.5.2 The IEC Standard 61000-4-7 247 8.6 Interharmonic
Detection and Estimation Based on IEC Standard 250 8.7 Parametric Methods
for Spectral Estimation 254 8.7.1 Prony Method 254 8.7.2 Signal and Noise
Subspace Techniques 262 8.8 Conclusions 269 References 270 9 Time-Frequency
Signal Decomposition 271 9.1 Introduction 271 9.2 Short-Time Fourier
Transform 274 9.2.1 Filter Banks Interpretation 274 9.2.2 Choosing the
Window: Uncertainty Principle 276 9.2.3 The Time-Frequency Grid 279 9.3
Sliding Window DFT 280 9.3.1 Sliding Window DFT: Modified Structure 282
9.3.2 Power System Application 282 9.4 Filter Banks 284 9.4.1 Two-Channel
Quadrature-Mirror Filter Bank 288 9.4.2 An Alias-Free Realization 290 9.4.3
A PR Condition 290 9.4.4 Finding the Filters from P(z) 292 9.4.5 General
Filter Banks 294 9.4.6 Harmonic Decomposition Using PR Filter Banks 295
9.4.7 The Sampling Frequency 298 9.4.8 Extracting Even Harmonics 298 9.4.9
The Synthesis Filter Banks 300 9.5 Wavelet 300 9.5.1 Continuous Wavelet
Transform 301 9.5.2 The Inverse Continuous Wavelet Transform 305 9.5.3
Discrete Wavelet Transform (DWT) 305 9.5.4 The Inverse Discrete Wavelet
Transform 308 9.5.5 Discrete-Time Wavelet Transform 308 9.5.6 Design Issues
in Wavelet Transform 313 9.5.7 Power System Application of Wavelet
Transform 316 9.5.8 Real-Time Wavelet Implementation 318 9.6 Conclusions
319 References 319 10 Pattern Recognition 321 10.1 Introduction 321 10.2
The Basics of Pattern Recognition 322 10.2.1 Datasets 323 10.2.2 Supervised
and Unsupervised Learning 323 10.3 Bayes Decision Theory 323 10.4 Feature
Extraction on the Power Signal 324 10.4.1 Effective Value (RMS) 324 10.4.2
Discrete Fourier Transform 325 10.4.3 Wavelet Transform 325 10.4.4
Cumulants of Higher-Order Statistics 325 10.4.5 Principal Component
Analysis 326 10.4.6 Normalization 327 10.4.7 Feature Selection 328 10.5
Classifiers 329 10.5.1 Minimum Distance Classifiers 329 10.5.2 Nearest
Neighbor Classifier 329 10.5.3 The Perceptron 330 10.5.4 Least-Squares
Methods 334 10.5.5 Multilayer Perceptron 337 10.5.6 Support Vector Machines
342 10.6 System Evaluation 348 10.6.1 Estimation of the Classification
Error Probability 349 10.6.2 Limited-Size Dataset 350 10.7 Pattern
Recognition Examples in Power Systems 350 10.7.1 Power Quality Disturbance
Classification 350 10.7.2 Load Forecasting in Electric Power Systems 351
10.7.3 Power System Security Assessment 353 10.8 Conclusions 353 References
353 11 Detection 355 11.1 Introduction 355 11.2 Why Signal Detection for
Electric Power Systems? 355 11.3 Detection Theory Basics 356 11.3.1
Detection on the Bayesian Framework 356 11.3.2 Newman-Pearson Criterion 357
11.3.3 Receiving Operating Characteristics 358 11.3.4 Deterministic Signal
Detection in White Gaussian Noise 358 11.3.5 Deterministic Signals with
Unknown Parameters 363 11.4 Detection of Disturbances in Power Systems 368
11.4.1 The Power System Signal 368 11.4.2 Optimal Detection 369 11.4.3
Feature Extraction 370 11.4.4 Commonly Used Detection Algorithms 370 11.5
Examples 371 11.5.1 Transmission Lines Protection 371 11.5.2 Detection
Algorithms Based on Estimation 373 11.5.3 Saturation Detection in Current
Transformers 377 11.6 Smart-Grid Context and Conclusions 380 References 381
12 Wavelets Applied to Power Fluctuations 383 12.1 Introduction 383 12.2
Basic Theory 384 12.3 Application of Wavelets for Time-Varying Generation
and Load Profiles 385 12.3.1 Fluctuation Analyses with FFT 385 12.3.2
Methodology 386 12.3.3 Load Fluctuations 387 12.3.4 Wind Farm Generation
Fluctuations 389 12.3.5 Smart Microgrid 390 12.4 Conclusions 392 References
392 13 Time-Varying Harmonic and Asymmetry Unbalances 395 13.1 Introduction
395 13.2 Sequence Component Computation 396 13.3 Time-Varying Unbalance and
Harmonic Frequencies 397 13.4 Computation of Time-Varying Unbalances and
Asymmetries at Harmonic Frequencies 398 13.5 Examples 401 13.5.1 Inrush
Current 401 13.5.2 Voltage Sag 404 13.5.3 Unbalance in Converters 407 13.6
Conclusions 410 References 411 Index 413
xxiii 1 Introduction 1 1.1 Introduction 1 1.2 The Future Grid 2 1.3
Motivation and Objectives 3 1.4 Signal Processing Framework 4 1.5
Conclusions 8 References 10 2 Power Systems and Signal Processing 11 2.1
Introduction 11 2.2 Dynamic Overvoltage 12 2.2.1 Sustained Overvoltage 12
2.2.2 Lightning Surge 13 2.2.3 Switching Surges 15 2.2.4 Switching of
Capacitor Banks 17 2.3 Fault Current and DC Component 21 2.4 Voltage Sags
and Voltage Swells 25 2.5 Voltage Fluctuations 27 2.6 Voltage and Current
Imbalance 29 2.7 Harmonics and Interharmonics 29 2.8 Inrush Current in
Power Transformers 42 2.9 Over-Excitation of Transformers 45 2.10
Transients in Instrument Transformers 47 2.10.1 Current Transformer (CT)
Saturation (Protection Services) 47 2.10.2 Capacitive Voltage Transformer
(CVT) Transients 54 2.11 Ferroresonance 55 2.12 Frequency Variation 56 2.13
Other Kinds of Phenomena and their Signals 56 2.14 Conclusions 57
References 58 3 Transducers and Acquisition Systems 59 3.1 Introduction 59
3.2 Voltage Transformers (VTs) 60 3.3 Capacitor Voltage Transformers 64 3.4
Current Transformers 67 3.5 Non-Conventional Transducers 71 3.5.1 Resistive
Voltage Divider 71 3.5.2 Optical Voltage Transducer 72 3.5.3 Rogowski Coil
73 3.5.4 Optical Current Transducer 74 3.6 Analog-to-Digital Conversion
Processing 75 3.6.1 Supervision and Control 78 3.6.2 Protection 79 3.6.3
Power Quality 79 3.7 Mathematical Model for Noise 80 3.8 Sampling and the
Anti-Aliasing Filtering 81 3.9 Sampling Rate for Power System Application
84 3.10 Smart-Grid Context and Conclusions 84 References 85 4 Discrete
Transforms 87 4.1 Introduction 87 4.2 Representation of Periodic Signals
using Fourier Series 87 4.2.1 Computation of Series Coefficients 90 4.2.2
The Exponential Fourier Series 92 4.2.3 Relationship between the
Exponential and Trigonometric oefficients 93 4.2.4 Harmonics in Power
Systems 95 4.2.5 Proprieties of a Fourier Series 97 4.3 A Fourier Transform
98 4.3.1 Introduction and Examples 98 4.3.2 Fourier Transform Properties
103 4.4 The Sampling Theorem 104 4.5 The Discrete-Time Fourier Transform
108 4.5.1 DTFT Pairs 109 4.5.2 Properties of DTFT 110 4.6 The Discrete
Fourier Transform (DFT) 110 4.6.1 Sampling the Fourier Transform 116 4.6.2
Discrete Fourier Transform Theorems 116 4.7 Recursive DFT 117 4.8 Filtering
Interpretation of DFT 120 4.8.1 Frequency Response of DFT Filter 123 4.8.2
Asynchronous Sampling 124 4.9 The z-Transform 126 4.9.1 Rational
z-Transforms 128 4.9.2 Stability of Rational Transfer Function 131 4.9.3
Some Common z-Transform Pairs 131 4.9.4 z-Transform Properties 133 4.10
Conclusions 133 References 133 5 Basic Power Systems Signal Processing 135
5.1 Introduction 135 5.2 Linear and Time-Invariant Systems 135 5.2.1
Frequency Response of LTI System 138 5.2.2 Linear Phase FIR Filter 140 5.3
Basic Digital System and Power System Applications 142 5.3.1 Moving Average
Systems: Application 142 5.3.2 RMS Estimation 144 5.3.3 Trapezoidal
Integration and Bilinear Transform 146 5.3.4 Differentiators Filters:
Application 148 5.3.5 Simple Differentiator 151 5.4 Parametric Filters in
Power System Applications 153 5.4.1 Filter Specification 154 5.4.2
First-Order Low-Pass Filter 155 5.4.3 First-Order High-Pass Filter 155
5.4.4 Bandstop IIR Digital Filter (The Notch Filter) 156 5.4.5 Total
Harmonic Distortion in Time Domain (THD) 159 5.4.6 Signal Decomposition
using a Notch Filter 161 5.5 Parametric Notch FIR Filters 161 5.6 Filter
Design using MATLAB1 (FIR and IIR) 163 5.7 Sine and Cosine FIR Filters 163
5.8 Smart-Grid Context and Conclusions 165 References 166 6 Multirate
Systems and Sampling Alterations 167 6.1 Introduction 167 6.2 Basic Blocks
for Sampling Rate Alteration 167 6.2.1 Frequency Domain Interpretation 168
6.2.2 Up-Sampling in Frequency Domain 169 6.2.3 Down-Sampling in Frequency
Domain 169 6.3 The Interpolator 170 6.3.1 The Input-Output Relation for the
Interpolator 172 6.3.2 Multirate System as a Time-Varying System and Nobles
Identities 172 6.4 The Decimator 174 6.4.1 Introduction 174 6.4.2 The
Input-Output Relation for the Decimator 174 6.5 Fractional Sampling Rate
Alteration 175 6.5.1 Resampling Using MATLAB1 175 6.6 Real-Time Sampling
Rate Alteration 176 6.6.1 Spline Interpolation 177 6.6.2 Cubic B-Spline
Interpolation 180 6.7 Conclusions 184 References 184 7 Estimation of
Electrical Parameters 185 7.1 Introduction 185 7.2 Estimation Theory 185
7.3 Least-Squares Estimator 187 7.3.1 Linear Least-Squares 188 7.4
Frequency Estimation 191 7.4.1 Frequency Estimation Based on Zero Crossing
(IEC61000-4-30) 192 7.4.2 Short-Term Frequency Estimator Based on Zero
Crossing 195 7.4.3 Frequency Estimation Based on Phasor Rotation 198 7.4.4
Varying the DFT Window Size 200 7.4.5 Frequency Estimation Based on LSE 201
7.4.6 IIR Notch Filter 203 7.4.7 Small Coefficient and/or Small Arithmetic
Errors 203 7.5 Phasor Estimation 205 7.5.1 Introduction 205 7.5.2 The PLL
Structure 207 7.5.3 Kalman Filter Estimation 209 7.5.4 Example of Phasor
Estimation using Kalman Filter 211 7.6 Phasor Estimation in Presence of DC
Component 212 7.6.1 Mathematical Model for the Signal in Presence of DC
Decaying 213 7.6.2 Mimic Method 214 7.6.3 Least-Squares Estimator (LSE) 215
7.6.4 Improved DTFT Estimation Method 216 7.7 Conclusions 224 References
224 8 Spectral Estimation 227 8.1 Introduction 227 8.2 Spectrum Estimation
227 8.2.1 Understanding Spectral Leakage 229 8.2.2 Interpolation in
Frequency Domain: Single-Tone Signal 232 8.3 Windows 236 8.3.1
Frequency-Domain Windowing 236 8.4 Interpolation in Frequency Domain:
Multitone Signal 240 8.5 Interharmonics 243 8.5.1 Typical Interhamonic
Sources 246 8.5.2 The IEC Standard 61000-4-7 247 8.6 Interharmonic
Detection and Estimation Based on IEC Standard 250 8.7 Parametric Methods
for Spectral Estimation 254 8.7.1 Prony Method 254 8.7.2 Signal and Noise
Subspace Techniques 262 8.8 Conclusions 269 References 270 9 Time-Frequency
Signal Decomposition 271 9.1 Introduction 271 9.2 Short-Time Fourier
Transform 274 9.2.1 Filter Banks Interpretation 274 9.2.2 Choosing the
Window: Uncertainty Principle 276 9.2.3 The Time-Frequency Grid 279 9.3
Sliding Window DFT 280 9.3.1 Sliding Window DFT: Modified Structure 282
9.3.2 Power System Application 282 9.4 Filter Banks 284 9.4.1 Two-Channel
Quadrature-Mirror Filter Bank 288 9.4.2 An Alias-Free Realization 290 9.4.3
A PR Condition 290 9.4.4 Finding the Filters from P(z) 292 9.4.5 General
Filter Banks 294 9.4.6 Harmonic Decomposition Using PR Filter Banks 295
9.4.7 The Sampling Frequency 298 9.4.8 Extracting Even Harmonics 298 9.4.9
The Synthesis Filter Banks 300 9.5 Wavelet 300 9.5.1 Continuous Wavelet
Transform 301 9.5.2 The Inverse Continuous Wavelet Transform 305 9.5.3
Discrete Wavelet Transform (DWT) 305 9.5.4 The Inverse Discrete Wavelet
Transform 308 9.5.5 Discrete-Time Wavelet Transform 308 9.5.6 Design Issues
in Wavelet Transform 313 9.5.7 Power System Application of Wavelet
Transform 316 9.5.8 Real-Time Wavelet Implementation 318 9.6 Conclusions
319 References 319 10 Pattern Recognition 321 10.1 Introduction 321 10.2
The Basics of Pattern Recognition 322 10.2.1 Datasets 323 10.2.2 Supervised
and Unsupervised Learning 323 10.3 Bayes Decision Theory 323 10.4 Feature
Extraction on the Power Signal 324 10.4.1 Effective Value (RMS) 324 10.4.2
Discrete Fourier Transform 325 10.4.3 Wavelet Transform 325 10.4.4
Cumulants of Higher-Order Statistics 325 10.4.5 Principal Component
Analysis 326 10.4.6 Normalization 327 10.4.7 Feature Selection 328 10.5
Classifiers 329 10.5.1 Minimum Distance Classifiers 329 10.5.2 Nearest
Neighbor Classifier 329 10.5.3 The Perceptron 330 10.5.4 Least-Squares
Methods 334 10.5.5 Multilayer Perceptron 337 10.5.6 Support Vector Machines
342 10.6 System Evaluation 348 10.6.1 Estimation of the Classification
Error Probability 349 10.6.2 Limited-Size Dataset 350 10.7 Pattern
Recognition Examples in Power Systems 350 10.7.1 Power Quality Disturbance
Classification 350 10.7.2 Load Forecasting in Electric Power Systems 351
10.7.3 Power System Security Assessment 353 10.8 Conclusions 353 References
353 11 Detection 355 11.1 Introduction 355 11.2 Why Signal Detection for
Electric Power Systems? 355 11.3 Detection Theory Basics 356 11.3.1
Detection on the Bayesian Framework 356 11.3.2 Newman-Pearson Criterion 357
11.3.3 Receiving Operating Characteristics 358 11.3.4 Deterministic Signal
Detection in White Gaussian Noise 358 11.3.5 Deterministic Signals with
Unknown Parameters 363 11.4 Detection of Disturbances in Power Systems 368
11.4.1 The Power System Signal 368 11.4.2 Optimal Detection 369 11.4.3
Feature Extraction 370 11.4.4 Commonly Used Detection Algorithms 370 11.5
Examples 371 11.5.1 Transmission Lines Protection 371 11.5.2 Detection
Algorithms Based on Estimation 373 11.5.3 Saturation Detection in Current
Transformers 377 11.6 Smart-Grid Context and Conclusions 380 References 381
12 Wavelets Applied to Power Fluctuations 383 12.1 Introduction 383 12.2
Basic Theory 384 12.3 Application of Wavelets for Time-Varying Generation
and Load Profiles 385 12.3.1 Fluctuation Analyses with FFT 385 12.3.2
Methodology 386 12.3.3 Load Fluctuations 387 12.3.4 Wind Farm Generation
Fluctuations 389 12.3.5 Smart Microgrid 390 12.4 Conclusions 392 References
392 13 Time-Varying Harmonic and Asymmetry Unbalances 395 13.1 Introduction
395 13.2 Sequence Component Computation 396 13.3 Time-Varying Unbalance and
Harmonic Frequencies 397 13.4 Computation of Time-Varying Unbalances and
Asymmetries at Harmonic Frequencies 398 13.5 Examples 401 13.5.1 Inrush
Current 401 13.5.2 Voltage Sag 404 13.5.3 Unbalance in Converters 407 13.6
Conclusions 410 References 411 Index 413