Digital Protection for Power Systems

Contents
About the Authors
Preface
Abbreviations and Terminologies
Figure captions
Table captions
1 Introduction
1.1 Historical background
1.2 Performance and operational characteristics of digital protection
1.2.1 Reliability
1.2.2 Flexibility
1.2.3 Operational performance
1.2.4 Communication capability
1.2.5 Adaptability
1.2.6 Cost/benefit considerations
1.2.7 Other features and functions
1.3 Basic structure of digital relays
1.4 Summary
References
2 Mathematical background to protection algorithms
2.1 Introduction
2.2 Finite difference techniques
2.3 Interpolation formulas
2.3.1 Forward interpolation
2.3.2 Backward interpolation
2.3.3 Central difference interpolation
2.4 Numerical differentiation
2.5 Curve fitting and smoothing
2.5.1 Least-squares error (LSE) method
2.5.2 Smoothing
2.6 Fourier analysis
2.6.1 The Fourier series
2.6.2 The Fourier transform
2.6.3 Discrete Fourier transform and its inverse
2.6.4 Short-time Fourier transform
2.7 Walsh function analysis
2.7.1 Definition of Walsh functions
2.7.2 Some fundamental properties of Walsh functions
2.7.3 Discrete representation of Walsh functions
2.7.4 The Walsh series
2.8 Relationship between Fourier and Walsh coefficients
2.9 Wavelet analysis
2.9.1 Mother wavelets
2.9.2 Continuous wavelet transform
2.9.3 Discrete wavelet transform
2.9.4 Wavelet packet Transform
2.10 S transform
2.10.1 Derivation of ST through CWT
2.10.2 Derivation of ST through STFT
2.10.3 Relationship between ST and FT
2.10.4 The instantaneous frequency
2.10.5 The discrete ST
2.11 Basic principles of differential evolution
2.11.1 General formulation of DE algorithm
2.11.2 Procedure of executing DE algorithm
2.12 Summary
References
3 Basic elements of digital protection
3.1 Introduction
3.2 Basic components of a digital relay
3.3 Signal conditioning subsystem
3.3.1 Transducers
3.3.2 Surge protection circuits
3.3.3 Analogue filtering
3.3.4 Analogue multiplexers
3.4 Conversion subsystem
3.4.1 The sampling theorem
3.4.2 Signal aliasing error
3.4.3 Sample and hold circuit
3.4.4 Digital multiplexing
3.4.5 Digital-to-analogue conversion
3.4.6 A/D conversion
3.5 Digital relay subsystem
3.6 Microprocessor-based digital relay
3.7 Summary
References
4 Sinusoidal wave-based algorithms
4.1 Introduction
4.2 Sample and first-derivative method
4.2.1 Basic formulation
4.2.2 Calculation of an approximation to the signal derivatives
4.2.3 Error analysis
4.2.4 Practical considerations
4.3 First- and second-derivative method
4.3.1 Mathematical formulation
4.4 Two-sample technique
4.4.1 Prediction of values of peak (or magnitude) of signal waveforms
4.4.2 Determination of phase angle between waveforms
4.5 Three-sample technique
4.6 Extracting the phasor of signals from data samples received over Ethernet network with variable jitter
4.7 An early relaying scheme
4.8 Summary
References
5 Fourier analysis, Walsh function-based, and S-transform techniques
5.1 Introduction
5.2 Determination of the phasor at the fundamental frequency using Fourier-analysis-based algorithms
5.2.1 The full-cycle window algorithm
5.2.2 Fractional-cycle window algorithms
5.2.3 Fourier transform-based algorithm
5.2.4 Improved DFT-based phasor estimation algorithm
5.3 Walsh-function-based algorithms
5.3.1 Basic principles
5.3.2 Development of basic algorithm
5.3.3 Algorithm for Walsh function determination
5.3.4 Estimation of the amplitude and phase angle of fundamental components
5.3.5 Determination of Walsh coefficients for pure sinusoidal waveforms
5.4 Mimic circuit
5.4.1 Principles of mimic filter
5.4.2 Digital mimic filter
5.4.3 Adaptive mimic filter algorithm
5.5 Application of S-transform to the protection of transmission lines
5.5.1 Analysis of faulted power network signals using S-transform
5.5.2 Implementation of S-transform to the protection of transmission lines
5.6 Summary
References
6 Least squares-based methods
6.1 Introduction
6.2 Integral LSQ fit
6.2.1 Basic assumptions
6.2.2 Determination of unknown coefficients
6.2.3 Implementation of the algorithm
6.3 Power series LSQ fit
6.3.1 Basic assumptions
6.3.2 Shifted waveform
6.3.3 Approximating the shifted waveform by a power series
6.4 Multivariable series LSQ technique
6.4.1 Basic assumptions
6.4.2 Derivation of the multivariable series
6.5 Recursive least square technique
6.6 Determination of measured impedance estimates
6.7 Summary
References
7 Differential equation-based techniques
7.1 Introduction
7.2 Representation of transmission lines with capacitance neglected
7.2.1 Single-phase to ground fault
7.2.2 Phase-to-phase and three-phase faults
7.3 Differential equation protection with selected limits
7.3.1 Basic principles
7.3.2 Digital harmonic filtering by selected limits
7.3.3 Graphical interpretation of digital filtering by integration over selected limits
7.3.4 Filtering of multiple harmonic components
7.4 Simultaneous differential equation techniques
7.4.1 Lumped series impedance-based algorithms
7.4.2 Single PI section transmission line model-based algorithms
7.4.3 Development of the algorithm and basic assumptions
7.5 Improvements of the performance of differential equation algorithm
7.6 Summary
References
8 Fundamentals of TW-based protection
8.1 Introduction
8.2 The transmission line as a distributed component
8.2.1 TWs in assumed lossless single-phase lines
8.2.2 Three-phase transposed lines
8.3 Superimposed quantities and their properties
8.3.1 Polarity of superimposed quantities versus fault location
8.3.2 Interrelation between the superimposed voltage and current quantities versus fault location
8.3.3 Behaviour of relaying signals at the relay and fault locations
8.3.4 Superimposed component elliptical trajectories
8.4 Bergeron's equations
8.4.1 Single-phase lines
8.4.2 Three-phase lines
8.5 Discriminant functions
8.5.1 Single-phase lines
8.5.2 Three-phase lines
8.6 TW differential protection based on equivalent TW
8.6.1 Equivalent travelling wave
8.6.2 Reconstruction of ETW using WT
8.7 TW-based busbar protection
8.7.1 Basic principles of busbar protection scheme
8.7.2 Implementation of busbar protection scheme
8.8 Summary
References
9 TW protective schemes
9.1 Introduction
9.2 Bergeron's-equation-based scheme
9.2.1 Principles of internal fault detection
9.3 Ultra-high-speed polarity comparison scheme
9.3.1 Basic operating principle
9.3.2 Description of typical implementation
9.4 Ultra-high-speed wave differential scheme
9.4.1 Operating principles
9.4.2 Basic description of the scheme
9.4.3 Digital implementation of wave differential scheme
9.4.4 General description of the digital relay
9.5 Discriminant function-based scheme
9.5.1 Operating principles
9.6 Superimposed component trajectory-based scheme
9.6.1 Basic principles
9.6.2 Sense of trajectories versus fault direction
9.6.3 Extension of trajectories approach to signals including TW components
9.7 TW-based protective scheme for double-transmission line circuit
9.7.1 Operating principles
9.7.2 Propagation of the TWs in double-transmissionline circuit
9.7.3 Basic description of the protection scheme algorithm
9.8 TW-based protective scheme for UHVDC transmission lines
9.8.1 Operating principles
9.8.2 The overall protection scheme
9.9 TW-based protective scheme that uses wavelet technique
9.9.1 The adapted WT
9.9.2 Detection of TWs using modulus maxima of the WT
9.9.3 The overall protection scheme
9.10 Summary
References
10 Digital differential protection of transformers
10.1 Introduction
10.2 Principles of transformer protection
10.2.1 Basic principles
10.2.2 Biased differential relaying
10.2.3 Harmonic-restrained differential relay
10.3 FIR filter-based algorithms
10.3.1 FIR filter characteristics
10.3.2 Extraction of fundamental and second-harmonic components
10.3.3 Discrimination between inrush and internal fault currents
10.4 LSQ curve fitting-based algorithms
10.4.1 Basic assumptions and algorithm derivation
10.4.2 Basis of discrimination between inrush and internal fault currents
10.5 Fourier-based algorithm
10.5.1 Filtering of harmonics
10.6 Flux-restrained current differential relay
10.6.1 Development of the algorithm
10.7 Enhancement of TDP to improve its security and dependability
10.7.1 Types of faults to which power transformers are subjected
10.7.2 Securing TDP against external faults
10.8 Wavelet-based transformer protection methods
10.9 Basic hardware of microprocessor-based transformer protection
10.10 Summary
References
11 Digital line differential protection
11.1 Introduction
11.2 Current-based differential schemes
11.2.1 Basic principles of line current differential protection
11.2.2 Frequency modulation current differential protective scheme
11.2.3 Modal current-based protection scheme
11.3 Composite voltage- and current-based scheme
11.3.1 Basic operating principles
11.3.2 Formation of terminal signals
11.4 Application of wavelet to protection of tapped transmission line
11.4.1 Selection of mother wavelet and scale
11.4.2 Basic description of the protection scheme
11.5 Summary
References
12 Comparison between digital protection algorithms
12.1 Introduction
12.2 Evaluation methodology of DFAs during fault condition
12.2.1 Voltage and current signals following a fault condition
12.2.2 Performance and sensitivity indices
12.2.3 Evaluation of the frequency response of DFAs
12.2.4 Evaluation of the time response of DFAs
12.3 Application of PIs and sensitivity analysis
12.3.1 Evaluation of phasor estimation
12.3.2 Evaluation the performance of DFAs using PIs
12.4 Summary
References
13 Protection of distribution networks with distributed generation including renewables
13.1 Introduction
13.2 Protection of distribution networks with distributed generation including renewable energy resources
13.2.1 Impact of distributed generation on the protection of associated networks
13.2.2 Protection problems caused by high penetration of distributed generation
13.3 Solution of protection problems of distribution networks with high penetration of distributed generation
13.3.1 Individual solutions to specific problems
13.3.2 Solution to feeder protection
13.3.3 Zones-based protection solution for the whole network
13.3.4 Smart grid-based solutions
13.4 Summary
References
Index
Back Cover