Digital Power System Protection

Transcription

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2 Digital Power System Protection S.R. Bhide Associate Professor of Electrical Engineering Visvesvaraya National Institute of Technology Nagpur Delhi

3 Digital power system protection S.R. Bhide 2014 by PHI Learning Private Limited, Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN The export rights of this book are vested solely with the publisher. Published by Asoke K. Ghosh, PHI Learning Private Limited, Rimjhim House, 111, Patparganj Industrial Estate, Delhi and Printed by Star Print-O-Bind, F-31, Okhla Industrial Area Phase I, New Delhi

4 To the memomy of My Parents Pushpa and Ramkrishna Bhide

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6 Contents Preface xi 1. Evolution of Power System Protection and the Emergence of Digital Relaying Evolution of OC Relay from an Ammeter Evolution of a Directional Relay from a Wattmeter The Birth of Transistor Start of a Revolution Architecture of the Modern Digital Relay 4 2. Digital Signal Processing Basics and Architecture of Numerical Relay Introduction to Digital Signal Processing The DSP Signal Processing Chain Analog to Digital Converters Quantization Error ADC Types Sampling Need for Sample and Hold Circuit Shannon s Sampling Theorem and Aliasing Anti-aliasing Filter Design of Anti-aliasing Filter Numerical Example Functional Block Diagram of Numerical Relay 24 Review Questions 27 v

7 vi Contents 3. Algorithms Based on Undistorted Single Frequency Sine Wave Mann and Morrison Algorithm Historical Perspective Derivation of the Sample and Derivative (Mann & Morrison) Algorithm Instantaneous OC Relay Based on Mann and Morrison Algorithm Simulation of the Mann and Morrison Algorithm in Spreadsheet Simulation of Mann and Morrison Algorithm in MATLAB Three-Sample Technique Determination of Frequency of the Signal Determination of Amplitude of the Signal Determination of Phase of the Signal Summary of Three Sample Algorithm Excel Spreadsheet for Simulation of Three-Sample Algorithm MATLAB Program for Simulating Three-Sample Algorithm First and Second Derivative Algorithm Excel Spreadsheet for Simulation of First and Second Derivative Algorithm MATLAB Simulation of First and Second Derivative Algorithm Two-Sample Technique Spreadsheet for Two-Sample Technique MATLAB Simulation of Two-Sample Technique 54 Review Questions Algorithms Based on Solution of Differential Equation Differential Equation Algorithm Justification for Lumped Series R-L Model Excel Spreadsheet Implementation of the Differential Equation Algorithm MATLAB Implementation of Differential Equation Algorithm Solution of Differential Equation Algorithm Using Numerical Integration MATLAB Implementation of Solution of Differential Equation Algorithm Using Numerical Integration Trapezoidal Rule for Numerical Integration Simpson s Rule for Numerical Integration MATLAB Script of Implementation of Solution of Differential Equation Algorithm Using Numerical Integration Application of Differential Equation Algorithm to Three-Phase Line Ground Fault Protection of Three-Phase Line Using Phase Quantities Ground Fault Protection of Three-Phase Line Using Sequence Quantities Phase Fault Protection of Three-Phase Line Using Phase Quantities 81

8 Contents vii Phase Fault Protection of Three-Phase Lines Using Sequence Quantities Elimination of Specific Harmonics by Integration between Selected Limits 84 Review Questions Algorithms Based on Least Squared Error (LSQ) LSQ Technique Average is Best Value in LSQ Sense LSQ and Pseudo-Inverse Relation between LSQ and Pseudo-Inverse LSQ Algorithm by Sachdev MATLAB Implementation of LSQ Algorithm 96 Review Questions Discrete Fourier Transform Introduction to Concept of Spectrum Generalised Fourier Series Dirichlet Conditions Fourier Series in Trigonometric Form Fourier Series in Exponential Form Fourier Coefficients are Best in LSQ Sense Summary of Fourier Series Applications of Fourier Analysis Fourier Series for a Recurring Pulse Recurring Pulse to Non-recurring Pulse Discrete Fourier Transform Development Implicit Assumption behind Windowed Fourier Transform Meaning of N Samples Collected in a Window Redundancy of DFT DFT as a Mapping Numerical Calculation of DFT Coefficients Sliding DFT Algorithm Modified DFT MATLAB Program for Sliding Modified Recursive DFT Algorithm 129 Review Questions FFT and Goertzel Algorithm What is the Motivation for FFT? FFT by Decimation-in-Time (DIT) Numerical Problem on FFT (DIT) Fast Fourier Transform by Decimation-in-Frequency Numerical Problem on FFT (DIF) MATLAB Implementation of FFT: Decimation-in-Time 150

9 viii Contents 7.5 MATLAB Implementation of FFT: Decimation-in-Frequency Motivation for Goertzel Algorithm The Goertzel Algorithm Implementation of Goertzel Algorithm in MATALB 158 Review Questions Windowing and Spectral Leakage The Fourier Machine Windowing without Spectral Leakage Windowing Leading to Spectral Leakage Spectral Leakage from Time Domain Viewpoint Spectral Leakage from Frequency Domain Viewpoint Windowed and Sampled Signal 168 Review Questions Introduction to Digital Filtering Introduction to Filters What is a Digital Filter? Why Digital Filtering? FIR and IIR Filters Running Average as FIR Filter: 5-Point Running Average Filter Impulse Response of 5-Point Running Average Filter Frequency Response of a 2-Point Running Average FIR Filter Frequency Response of 2-Point Running Average Filter Using Z-transform Frequency Response of a 3-Point Running Average Filter Frequency Response of 3-Point Running Average Filter Using Z-transform Frequency Response of 4-Point Running Average Filter Using Z-transform MATLAB Program for Plotting Frequency Response of N-Point Running Average Filter Introduction to Infinite Impulse Response (IIR) Filters 191 Review Questions Digital Filter Design Filter Specifications Relation between Linear Phase and Symmetry of Filter Coefficients for FIR Filter Design of FIR Filter Using Frequency Sampling Method Numerical Problem on Design of FIR Filter Using Frequency Sampling Method Bilinear Transformation Design of IIR Filter Using Bilinear Transformation 204

10 Contents ix Warping of Frequency Pre-Warping of Frequency During Design Step by Step Design of Iir Filter Using Bilinear Transformation Review of Formulas Derived Numerical Problem on Design of IIR Filter Design of a Digital Resonator Using Pole Zero Placement Understanding the z Plane Placement of Pole Placement of Zeros Expression for H(z), the Frequency Domain Transfer Function Numerical Problem on Design of Digital Resonator 213 Review Questions Synchrophasors Introduction The Phasor The Synchrophasor as per IEEE Std C The Synchrophasor in Steady State Conditions The Synchrophasor in Transient Conditions Synchrophasor under Dynamic Conditions Total Vector Error (TVE) Frequency and Rate of Change of Frequency (ROCOF) Time Tagging (Stamping) of the Synchrophasor Dissemination of the Time Stamp: IRIG-B Standard Synchrophasor Reporting Rates Block Diagram of the Synchrophasor Enabled Digital Relay or Phasor Measurement Unit (Pmu) Two Alternatives for Sampling Off-nominal Frequency Operation of the PMU A Demonstration of Error Caused by Off-nominal Frequency Operation Analytical Expression for Effect of Off-nominal Frequency Operation A MATLAB Script to Demonstrate Off-nominal Frequency DFT Synchrophasor Applications 234 Review Questions Removal of DC Offset Why Decaying DC Offsets are Created? What is the Effect of Decaying DC Offsets up on Relays? Mimic Impedance Method of Removal of DC Offset Immunity of LSQ Method to Decaying Dc Offset Immunity of Differential Equation Algorithm to Dc Offsets Digital Mimic Impedance Based Filter 240

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