Power Systems Signal Processing for Smart Grids

Professor Paulo F. Ribeiro, Calvin College, USAProfessor Ribeiro is professor of Engineering at Calvin College, Michigan. He has been involved with the application of advanced signal processing, applied to power quality and power systems in general, for the past fifteen years. For the past six years he has chaired the IEEE Task Force on Probabilistic Aspects of Harmonics. In 1994 he proposed the use of wallets to power quality applications; this has been followed by many people and has generated much research, several Masters and a PhD Thesis. Dr. Ribeiro is active in the IEEE, CIGRE and IEC working groups on power quality, and is a Registered Professional Engineer in the State of Iowa.

• About the Authors xiii Preface xvAccompanyingWebsite xxiAcknowledgments xxiii1 Introduction 11.1 Introduction 11.2 The Future Grid 21.3 Motivation and Objectives 31.4 Signal Processing Framework 41.5 Conclusions 8References 102 Power Systems and Signal Processing 112.1 Introduction 112.2 Dynamic Overvoltage 122.2.1 Sustained Overvoltage 122.2.2 Lightning Surge 132.2.3 Switching Surges 152.2.4 Switching of Capacitor Banks 172.3 Fault Current and DC Component 212.4 Voltage Sags and Voltage Swells 252.5 Voltage Fluctuations 272.6 Voltage and Current Imbalance 292.7 Harmonics and Interharmonics 292.8 Inrush Current in Power Transformers 422.9 Over-Excitation of Transformers 452.10 Transients in Instrument Transformers 472.10.1 Current Transformer (CT) Saturation (Protection Services) 472.10.2 Capacitive Voltage Transformer (CVT) Transients 542.11 Ferroresonance 552.12 Frequency Variation 562.13 Other Kinds of Phenomena and their Signals 562.14 Conclusions 57References 583 Transducers and Acquisition Systems 593.1 Introduction 593.2 Voltage Transformers (VTs) 603.3 Capacitor Voltage Transformers 643.4 Current Transformers 673.5 Non-Conventional Transducers 713.5.1 Resistive Voltage Divider 713.5.2 Optical Voltage Transducer 723.5.3 Rogowski Coil 733.5.4 Optical Current Transducer 743.6 Analog-to-Digital Conversion Processing 753.6.1 Supervision and Control 783.6.2 Protection 793.6.3 Power Quality 793.7 Mathematical Model for Noise 803.8 Sampling and the Anti-Aliasing Filtering 813.9 Sampling Rate for Power System Application 843.10 Smart-Grid Context and Conclusions 84References 854 Discrete Transforms 874.1 Introduction 874.2 Representation of Periodic Signals using Fourier Series 874.2.1 Computation of Series Coefficients 904.2.2 The Exponential Fourier Series 924.2.3 Relationship between the Exponential and Trigonometric oefficients 934.2.4 Harmonics in Power Systems 954.2.5 Proprieties of a Fourier Series 974.3 A Fourier Transform 984.3.1 Introduction and Examples 984.3.2 Fourier Transform Properties 1034.4 The Sampling Theorem 1044.5 The Discrete-Time Fourier Transform 1084.5.1 DTFT Pairs 1094.5.2 Properties of DTFT 1104.6 The Discrete Fourier Transform (DFT) 1104.6.1 Sampling the Fourier Transform 1164.6.2 Discrete Fourier Transform Theorems 1164.7 Recursive DFT 1174.8 Filtering Interpretation of DFT 1204.8.1 Frequency Response of DFT Filter 1234.8.2 Asynchronous Sampling 1244.9 The z-Transform 1264.9.1 Rational z-Transforms 1284.9.2 Stability of Rational Transfer Function 1314.9.3 Some Common z-Transform Pairs 1314.9.4 z-Transform Properties 1334.10 Conclusions 133References 1335 Basic Power Systems Signal Processing 1355.1 Introduction 1355.2 Linear and Time-Invariant Systems 1355.2.1 Frequency Response of LTI System 1385.2.2 Linear Phase FIR Filter 1405.3 Basic Digital System and Power System Applications 1425.3.1 Moving Average Systems: Application 1425.3.2 RMS Estimation 1445.3.3 Trapezoidal Integration and Bilinear Transform 1465.3.4 Differentiators Filters: Application 1485.3.5 Simple Differentiator 1515.4 Parametric Filters in Power System Applications 1535.4.1 Filter Specification 1545.4.2 First-Order Low-Pass Filter 1555.4.3 First-Order High-Pass Filter 1555.4.4 Bandstop IIR Digital Filter (The Notch Filter) 1565.4.5 Total Harmonic Distortion in Time Domain (THD) 1595.4.6 Signal Decomposition using a Notch Filter 1615.5 Parametric Notch FIR Filters 1615.6 Filter Design using MATLAB1 (FIR and IIR) 1635.7 Sine and Cosine FIR Filters 1635.8 Smart-Grid Context and Conclusions 165References 1666 Multirate Systems and Sampling Alterations 1676.1 Introduction 1676.2 Basic Blocks for Sampling Rate Alteration 1676.2.1 Frequency Domain Interpretation 1686.2.2 Up-Sampling in Frequency Domain 1696.2.3 Down-Sampling in Frequency Domain 1696.3 The Interpolator 1706.3.1 The Input–Output Relation for the Interpolator 1726.3.2 Multirate System as a Time-Varying System and Nobles Identities 1726.4 The Decimator 1746.4.1 Introduction 1746.4.2 The Input–Output Relation for the Decimator 1746.5 Fractional Sampling Rate Alteration 1756.5.1 Resampling Using MATLAB1 1756.6 Real-Time Sampling Rate Alteration 1766.6.1 Spline Interpolation 1776.6.2 Cubic B-Spline Interpolation 1806.7 Conclusions 184References 1847 Estimation of Electrical Parameters 1857.1 Introduction 1857.2 Estimation Theory 1857.3 Least-Squares Estimator 1877.3.1 Linear Least-Squares 1887.4 Frequency Estimation 1917.4.1 Frequency Estimation Based on Zero Crossing (IEC61000-4-30) 1927.4.2 Short-Term Frequency Estimator Based on Zero Crossing 1957.4.3 Frequency Estimation Based on Phasor Rotation 1987.4.4 Varying the DFT Window Size 2007.4.5 Frequency Estimation Based on LSE 2017.4.6 IIR Notch Filter 2037.4.7 Small Coefficient and/or Small Arithmetic Errors 2037.5 Phasor Estimation 2057.5.1 Introduction 2057.5.2 The PLL Structure 2077.5.3 Kalman Filter Estimation 2097.5.4 Example of Phasor Estimation using Kalman Filter 2117.6 Phasor Estimation in Presence of DC Component 2127.6.1 Mathematical Model for the Signal in Presence of DC Decaying 2137.6.2 Mimic Method 2147.6.3 Least-Squares Estimator (LSE) 2157.6.4 Improved DTFT Estimation Method 2167.7 Conclusions 224References 2248 Spectral Estimation 2278.1 Introduction 2278.2 Spectrum Estimation 2278.2.1 Understanding Spectral Leakage 2298.2.2 Interpolation in Frequency Domain: Single-Tone Signal 2328.3 Windows 2368.3.1 Frequency-Domain Windowing 2368.4 Interpolation in Frequency Domain: Multitone Signal 2408.5 Interharmonics 2438.5.1 Typical Interhamonic Sources 2468.5.2 The IEC Standard 61000-4-7 2478.6 Interharmonic Detection and Estimation Based on IEC Standard 2508.7 Parametric Methods for Spectral Estimation 2548.7.1 Prony Method 2548.7.2 Signal and Noise Subspace Techniques 2628.8 Conclusions 269References 2709 Time-Frequency Signal Decomposition 2719.1 Introduction 2719.2 Short-Time Fourier Transform 2749.2.1 Filter Banks Interpretation 2749.2.2 Choosing the Window: Uncertainty Principle 2769.2.3 The Time-Frequency Grid 2799.3 Sliding Window DFT 2809.3.1 Sliding Window DFT: Modified Structure 2829.3.2 Power System Application 2829.4 Filter Banks 2849.4.1 Two-Channel Quadrature-Mirror Filter Bank 2889.4.2 An Alias-Free Realization 2909.4.3 A PR Condition 2909.4.4 Finding the Filters from P(z) 2929.4.5 General Filter Banks 2949.4.6 Harmonic Decomposition Using PR Filter Banks 2959.4.7 The Sampling Frequency 2989.4.8 Extracting Even Harmonics 2989.4.9 The Synthesis Filter Banks 3009.5 Wavelet 3009.5.1 Continuous Wavelet Transform 3019.5.2 The Inverse Continuous Wavelet Transform 3059.5.3 Discrete Wavelet Transform (DWT) 3059.5.4 The Inverse Discrete Wavelet Transform 3089.5.5 Discrete-Time Wavelet Transform 3089.5.6 Design Issues in Wavelet Transform 3139.5.7 Power System Application of Wavelet Transform 3169.5.8 Real-Time Wavelet Implementation 3189.6 Conclusions 319References 31910 Pattern Recognition 32110.1 Introduction 32110.2 The Basics of Pattern Recognition 32210.2.1 Datasets 32310.2.2 Supervised and Unsupervised Learning 32310.3 Bayes Decision Theory 32310.4 Feature Extraction on the Power Signal 32410.4.1 Effective Value (RMS) 32410.4.2 Discrete Fourier Transform 32510.4.3 Wavelet Transform 32510.4.4 Cumulants of Higher-Order Statistics 32510.4.5 Principal Component Analysis 32610.4.6 Normalization 32710.4.7 Feature Selection 32810.5 Classifiers 32910.5.1 Minimum Distance Classifiers 32910.5.2 Nearest Neighbor Classifier 32910.5.3 The Perceptron 33010.5.4 Least-Squares Methods 33410.5.5 Multilayer Perceptron 33710.5.6 Support Vector Machines 34210.6 System Evaluation 34810.6.1 Estimation of the Classification Error Probability 34910.6.2 Limited-Size Dataset 35010.7 Pattern Recognition Examples in Power Systems 35010.7.1 Power Quality Disturbance Classification 35010.7.2 Load Forecasting in Electric Power Systems 35110.7.3 Power System Security Assessment 35310.8 Conclusions 353References 35311 Detection 35511.1 Introduction 35511.2 Why Signal Detection for Electric Power Systems? 35511.3 Detection Theory Basics 35611.3.1 Detection on the Bayesian Framework 35611.3.2 Newman-Pearson Criterion 35711.3.3 Receiving Operating Characteristics 35811.3.4 Deterministic Signal Detection in White Gaussian Noise 35811.3.5 Deterministic Signals with Unknown Parameters 36311.4 Detection of Disturbances in Power Systems 36811.4.1 The Power System Signal 36811.4.2 Optimal Detection 36911.4.3 Feature Extraction 37011.4.4 Commonly Used Detection Algorithms 37011.5 Examples 37111.5.1 Transmission Lines Protection 37111.5.2 Detection Algorithms Based on Estimation 37311.5.3 Saturation Detection in Current Transformers 37711.6 Smart-Grid Context and Conclusions 380References 38112 Wavelets Applied to Power Fluctuations 38312.1 Introduction 38312.2 Basic Theory 38412.3 Application of Wavelets for Time-Varying Generation and Load Profiles 38512.3.1 Fluctuation Analyses with FFT 38512.3.2 Methodology 38612.3.3 Load Fluctuations 38712.3.4 Wind Farm Generation Fluctuations 38912.3.5 Smart Microgrid 39012.4 Conclusions 392References 39213 Time-Varying Harmonic and Asymmetry Unbalances 39513.1 Introduction 39513.2 Sequence Component Computation 39613.3 Time-Varying Unbalance and Harmonic Frequencies 39713.4 Computation of Time-Varying Unbalances and Asymmetries at Harmonic Frequencies 39813.5 Examples 40113.5.1 Inrush Current 40113.5.2 Voltage Sag 40413.5.3 Unbalance in Converters 40713.6 Conclusions 410References 411Index 413