Digital Protection for Power Systems (2nd Edition)
2: School of Electronic and Electrical Engineering, University of Bath, UK
Electric power systems have become much more complex in the past years, due to the integration of distributed generation including renewable energy sources and the challenges caused by intermittency of renewables. This complexity makes power systems potentially more vulnerable. However, use of computerbased protection methods (i.e., digital protection relays) supported by communication technology have helped in protecting electrical networks from faults to which they are subjected to.
This second edition of the book covers a comprehensive introduction to the protection of electrical power systems using digital protective relays. The new edition offers a thorough revision and update, and comprehensive additional material. Chapters treat the mathematical background of protection algorithms including, sinusoidalwavebased algorithms, Walsh function and STransformbased techniques, least squares and differential equationbased techniques, travelling wavebased protection, protection of transformers, digital line differential protection, a comparison between digital protection algorithms, and importantly, protection of networks with distributed generation including renewable energy resources.
The book is written for researchers in electrical engineering and power engineering, in industry, utilities and universities, and for advanced students. The treatment is logically structured, covering mathematics and principles for the development and implementation of the major algorithms underlying different protection techniques. These techniques can be applied to protection of generator transformers, lines, switchgear and cable circuits: the main components of transmission and distribution systems with and without integrated distributed energy sources including renewables.
 Book DOI: 10.1049/PBPO165E
 Chapter DOI: 10.1049/PBPO165E
 ISBN: 9781839530432
 eISBN: 9781839530449
 Page count: 399
 Format: PDF

Front Matter
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1 Introduction
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This chapter begins by presenting a historical background of digitalbased relays in section 1.1. This is followed by discussing the performance and operational characteristics of digital protection in section 1.2. Such characteristics include reliability, flexibility, operational performance, communication capability, adaptability, cost/benefit consideration and other features and functions. The chapter is then concluded in section 1.3 by explaining the basic structure of digital relays, which highlighted that a digital relay, unlike conventional relays, consists of two main parts: hardware and software.

2 Mathematical background to protection algorithms
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Digital protection devices involve extensive use of numerical techniques, which are implemented in real time. Such methods are often specific to digital protection and as such are often alien to engineers trained in the development and application of previous generations of analogue or electromagneticbased protection devices.
To understand the principles underlying digital protection technology, it is necessary to briefly review the mathematical basis of numerical algorithms. The topics covered in this chapter therefore include finite differences, numerical differentiation, curve fitting and smoothing, Fourier analysis, Walsh analysis, and the relationship between Fourier and Walsh coefficients. It is not the intention that the material presented should be highly rigorous in the mathematical sense, but rather that it should give a working knowledge of the numerical techniques used and thus provide a basis for the work on specific protection algorithms that are presented in later chapters.

3 Basic elements of digital protection
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Operating voltages and currents flowing through a power system are usually at kilovolt and kiloampere levels. However, for digital processing, it is necessary to reduce the primary measurands to manageable levels. Therefore, the analogue signals are converted to digital form, thereby allowing subsequent digital processing to be performed to determine the circuit state.

4 Sinusoidal wavebased algorithms
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The algorithms covered in this chapter assume that the postfault current and voltage waveforms are sinusoidal. This assumption is not, of course, generally valid, particularly when Extra High Voltage (EHV) or Ultra High Voltage (UHV) network applications are involved. However, in practice, the signals processed are often prefiltered and, in lower voltage distribution systems in particular, the waveforms often very quickly attain a nominally sinusoidal form. Historically, algorithms developed for use in applications where the signals processed are nominally sinusoidal were the first to emerge [1, 2]. Most of the early work involved applying the technique to the calculation of transmissionline faultloop impedances. However, the methods are equally applicable to determining the magnitude and phase of relaying currents for differential protection of lines and plants.
All sinusoidalbased algorithms are designed to predict either the peak or squared peak of the compared waveforms. They may be loosely classified into two broad groups that use sample and first derivative (or first and second derivative), and that use two or three samples to predict the peak or squared peak values.

5 Fourier analysis, Walsh functionbased, and Stransform techniques
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This chapter is focused on presenting digital relaying algorithms that are based on Fourier, Walsh, and Stockwelltransform (Stransform) analyses. From the point of view of this discussion, Fourier analysis includes Fourier series and Fourier transformbased methods, while Walsh analysis includes Walsh series only. Removal of decaying DC components (DDCs) from fault currents using mimic circuits is also presented, which covered the principles of mimic filter, digital mimic filter, and adaptive mimic filter (AMF).
The basic assumption used in Fourier and Walsh seriesbased methods is that the waveform that results from a fault condition (voltage and/or current) is assumed to be periodic within the interval, say, from t _{0} to t _{0} + T, where T is the period of the fundamental component. This assumption enables the waveform to be expanded by either Fourier or Walsh series. The fundamental component is then extracted and then used to calculate either the impedance to the fault or differential current quantities.
In the case of the Fourier transform method, no assumption as to the nature of the faulted waveform is necessary. Both the voltage and current waveforms within the data window are transformed to the frequency domain. These transformed quantities are then used to calculate the apparent impedance to the fault.
In the case of the Stransform, again no assumption is made on the nature of the faulted waveform. The phasor values of the fundamental frequency components of voltage and current faulted signals are determined by calculating the fundamental voice of the Stransform.

6 Least squaresbased methods
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In this chapter, we shall discuss techniques used to fit faulted current and voltage waveforms, each to a sinusoidal waveform containing a fundamental component, a decaying/constant direct current (DC) component and/or harmonics.
These techniques use the least squares (LSQ) method to minimise the fitting error, and all have the common goal of extracting the fundamental components of voltage and current waveforms, to calculate the impedance to the fault or the comparison of currentbased signals in digital differential protection.

7 Differential equationbased techniques
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In this chapter, no special assumption will be made with regard to the content of faulted current and voltage waveforms. The fundamental approach, which is common to all algorithms covered in this chapter, is based on the fact that all protected equipment can be normally represented by differential equations of either first or second order. The methods are described by reference to transmission line protection, since it is in this application that they are mainly used. However, the methods can easily be extended to other items of plant. For the purposes of this chapter, we shall assume the line length is such that shunt capacitance can either be neglected or be lumped into a single 'equivalent' value.

8 Fundamentals of TWbased protection
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This chapter is devoted mainly to discuss fundamentals of the TWbased protection schemes and its application to transmission lines and busbars.
In section 8.2, derivation of mathematical representation of the transmission line based on its treatment as a distributed component is discussed. This is extended to drive the mathematical representation of TWs in assumed lossless singlephase lines and threephase transposed lines.
Superimposed quantities generated by a fault on transmission line and their properties are discussed under section 8.3. The discussion included explaining the polarity of superimposed quantities versus fault, interrelation between the superimposed voltage and current quantities versus fault location, behaviour of relaying signals at the relay and fault locations and superimposed component elliptical trajectories.
Section 8.4 devoted to discuss Bergeron's equations and derive these equations for single and threephase lines.
The discriminant function, which can be used to differentiate between internal and external (or forward and backward) faults with respect to the terminal of a transmission line, is introduced in section 8.5. The discussion included single and threephase lines.
TW differential protection based on ETW is covered under section 8.6. The coverage included ETW, and WT and reconstruction of ETW. This approach is used to resolve the problem related to the contradiction between sampling frequency and communication traffic, which makes achieving high sensitivity and high reliability at the same time difficult.
Finally, the TWbased busbar protection is discussed under section 8.7. This covered the basic principles of busbar protection scheme discussing faultgenerated TWs, analysis of the characteristics directional TWs and the criterion of TWbased busbar protection. The discussion then concluded by explaining the implementation of TWbased busbar protection scheme.

9 TW protective schemes
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The previous chapter laid down the foundation of TW protective methods. This chapter is designed to extend knowledge about TW techniques by presenting the underlying principles of some specific implementations. Information on the further development of specific products is available from manufacturers' literature.

10 Digital differential protection of transformers
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This chapter gives a brief general review of the principles of transformer differential protection (TDP). This is followed by an explanation of the application of digital techniques and the algorithms that have been developed specifically for the application of transformer protection. The algorithms covered include finiteduration impulse response (FIR) filters, leastsquares (LSQ) curve fitting, the digital Fourier algorithm, and the fluxrestrained current differential algorithm.
Finally, the basic hardware arrangement for implementing digital techniques for the protection of transformers is described. It is, however, important to note that closely similar techniques can be applied to the protection of generators, although, in this case, the transformation ratio of currents is the same on each side of the protected zone.

11 Digital line differential protection
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This chapter is devoted to discuss the digital line differential protection, which include twoterminal lines as well as multiterminal and tapped lines.
Currentbased differential schemes are discussed in section 11.2, which include the basic principles of line current differential protection for twoterminal and multiterminal lines, FM current differential protective scheme, and modal currentbased protection scheme.
To overcome the problems associated with differential schemes, the composite voltage and currentbased scheme is introduced in section 11.3. This included the basic operating principles and the formation of terminal signals.
Application of WPT to protection of tapped transmission line is covered in section 11.4. The selection of mother wavelet and scale that suits this application is highlighted. This is followed by covering the basic description of the developed protection scheme.

12 Comparison between digital protection algorithms
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Most protection functions are performed by digital relays using the fundamental components of voltage and current signals fed to the relays. During a fault condition, voltage and current signals are distorted. They usually contain, in addition to the fundamental component, a decaying DC and harmonics components. The fundamental components of voltage and current signals can be extracted from the samples of their respective faulted signals using digital filters. Ideal digital filters are expected to extract the correct fundamental component of a signal, i.e., without time delay and with exact amplitude and phase values. However, real digital filters cannot fulfil the ideal concept despite the advancements that have been made in digital technologies. Digital filters can be represented mathematically as discussed in Chapters 46, and therefore they are also called "Digital filtering algorithms (DFAs)." Such filters include two and threesample techniques, fullcycle Fourier (FCF), halfcycle Fourier (HCF), fullcycle Walsh (FCW), least squares error (LSE), cosine (COS), modified cosine filter (MCF) and mimicbased techniques.
The factors that affect the performance of a digital filter include (i) existing harmonic components, (ii) the exponentially decaying DC component and (iii) the processing window used. The first two factors depend mainly on the DFA used while the last one depends on the size of the adopted data window.
This chapter discusses the evaluation methodology of DFAs and introduces performance and sensitivity indices, which are considered the necessary tools required to facilitate such an evaluation. This is followed by highlighting the application of performance and sensitivity indices and finally comparing the performance of number of DFAs currently used in extracting fundamental components from faulted voltage and current signals. The considered algorithms include FCF, FCW, COS, LSE and adaptive mimic filter (AMF)based algorithms.

13 Protection of distribution networks with distributed generation including renewables
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This chapter focuses on discussing the application of digital protection techniques to distribution networks (DNs) with high penetration of distributed generation (DGn) including renewable energy sources (RESs). Prior to the introduction of DGn to DNs, DNs act as a mean of passing electrical power from transmission system to consumers/load centres connected to them. Thus, such networks are described as passive networks and the power flow in these networks is unidirectional. Consequently, the philosophy used in designing the protection systems for these networks is based on these two basic properties of the networks, i.e. being passive and with unidirectional power flow. However, the integration of DGn into DNs has transformed DNs into active networks and their power flow to bidirectional. This in turn has led to several problems to the current protection systems already installed in DNs.
Therefore, the impact of DGn on the protection of associated networks is thoroughly discussed. This is followed by a detailed discussion of the protection problems caused by high penetration of DGn into DNs. Such problems include blinding of protection, sympathetic tripping (false tripping of feeders), loss of mains (LOMs) or islanding condition, loss of coordination and autoreclosing problem.
The solutions of the protection problems identified above are then extensively discussed. They are classified into four types, namely, individual solutions to particular problems, solution to feeder protection, zonesbased solution to DN and smart gridbased solutions.

Back Matter
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