Digital protection for power systems pdf


    Digital Protection for Power Systems - Ebook download as PDF File .pdf) or read book online. Digital Protection for Power Systems A. T. Johns & S. K. Salman. Digital protection is based on the use of computers in power line relaying. Inspec keywords: power transformer protection; power system protection; power ISBN: ; e-ISBN: ; Page count: ; Format: PDF. Operating voltages and currents flowing through a power system are usually at The first two subsystems are generally common to all digital protective.

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    Digital Protection For Power Systems Pdf

    as the literature for the courses: Power System Protection, Digital Signal Processing for Power Also I will appreciate receiving from you the pdf files of the. Vol Digital Protection and Signalling DOWNLOAD PDF 2 Power system protection Several simple logic circuits are depicted in Figure. Digital protection is based on the use of computers in power line relaying. html view,bcoz of i cn't read it plz i want this book in pdf formate. please.

    About this book Introduction Digital Signal Processing in Power System Protection and Control bridges the gap between the theory of protection and control and the practical applications of protection equipment. Understanding how protection functions is crucial not only for equipment developers and manufacturers, but also for their users who need to install, set and operate the protection devices in an appropriate manner. After introductory chapters related to protection technology and functions, Digital Signal Processing in Power System Protection and Control presents the digital algorithms for signal filtering, followed by measurement algorithms of the most commonly-used protection criteria values and decision-making methods in protective relays. A large part of the book is devoted to the basic theory and applications of artificial intelligence techniques for protection and control. Fuzzy logic based schemes, artificial neural networks, expert systems and genetic algorithms with their advantages and drawbacks are discussed. AI techniques are compared and it is also shown how they can be combined to eliminate the disadvantages and magnify the useful features of particular techniques. The information provided in Digital Signal Processing in Power System Protection and Control can be useful for protection engineers working in utilities at various levels of the electricity network, as well as for students of electrical engineering, especially electrical power engineering. It may also be helpful for other readers who want to get acquainted with and to apply the filtering, measuring and decision-making algorithms for purposes other than protection and control, everywhere fast and on-line signal analysis is needed for proper functioning of the apparatus.

    Related Work Osorno, Bruno[2] provided a review of microprocessor based protective relay MBPR systems with emphasis on differential equation algorithms. The application of protection relaying in power systems, using MBPR systems, based on the differential equation algorithm are valued more than the protection relaying based on any other algorithms, because the algorithm has the advantages of accuracy and easy implementation.

    MBPR differential equation approach can tolerate some errors caused by power system abnormality such as DC offset. It is widely implemented in the protections for lines, transformers, buses, motor, and other equipment in power systems. However, the parameters for system description algorithms are obtained from power system current i t or voltage v t , which are abnormal values under fault or distortion situations.

    So the error study for the algorithm is considered necessary. Amin Zamani, Tarlochan S. Sidhu, Amirnaser Yazdani [3] explained that one of the major challenges associated with microgrid protection is to devise an appropriate protection strategy that is effective in the grid- connected as well as islanded mode of operation. They proposed a protection strategy based on microprocessor- based relays for low-voltage microgrids.

    Further, the structure of a new relay enabling the proposed protection strategy was presented. One of the salient feature of the developed protection scheme is that it does not require communications or adaptive protective devices.

    Moreover, it is to a large extent independent of the fault current magnitude and the mode of operation. John J. Novak, Richard D. Kirby [4] explained that improvements in protection and control via communications methods used to exchange digital bits DBs among devices are common in progressive utilities in high-voltage substations.

    These improvements are now being incorporated into the process-sensitive electric power distribution systems of large industrial plants. Gary H. Fox[5] discussed the issues that can exist when applying multifunction microprocessor-based protective relays in switchgear that has alternating current ac control voltage rather than a direct current dc -battery-based control bus. He recommended several techniques for overcoming these issues. End- users sometimes report unexpected circuit breaker tripping and significant financial consequences due to process discontinuity.

    Although these relays comply with the latest IEC and IEC standards and associated subsets, they have to be installed by switchboard manufacturers, whoever they are, in air insulated or Gas Insulated switchgear. Improper installation rules can sometimes result in unexpected tripping. Tingfang, Yang ; Xin, Yang[7] proposed a generalizing modern microprocessor-based relay protection at the power transmission line and a design of relays based on ARM processor was put forward.

    The test results show the design of the microprocessor- based protection has good performance. Problem Formulation Electrical Power System protection is required for protection of both user and the system equipment itself from fault, hence electrical power system is not allowed to operate without any protection devices installed. Power system fault is defined as undesirable condition that occurs in the power system.

    These undesirable conditions such as short circuit, current leakage, ground short, over current and over voltage. The functional security of the power grid depends upon the successful operation of thousands of relays that may be used in protective scheme for preventing the power system from cascading failures. The failure of one relay of the protective scheme to operate as intended may imbalance the stability of the entire power grid and hence it may lead the whole system to blackout.

    In fact, major power system failures during a transient disturbance are more likely to be caused by unnecessary protective relay tripping rather than by the failure of a relay to take action. In other words, the performance of protective relay or system is very important to be known especially in smart power grid.

    In other words, the performance of protection system is measured by several criteria including reliability, selectivity, speed of operation, etc. Reliability has two aspects: dependability and security. Dependability is known as the degree of certainty that a relay system will operate correctly when there is a fault on the system.

    Security is the degree of certainty that a relay will operate unnecessary even when there is no fault on the system. Originally, electromechanical relays were used to protect power system. Most relays used either electromechanical attraction or electromechanical induction principle for their operation.

    These relays were classified as amplitude comparators or as phase comparators. When solid state technology was introduced, amplitude and phase comparison were implemented using discrete components including vaccum tubes.

    Solid state relays appeared as the technology poised to replace electromechanical relays. Devices using electron tubes were studied but never applied as commercial products, because of the limitatons of vacuum tube amplifiers.

    Computer hardware technology has tremendously advanced since early s and new generations of computers tend to make digital computer relaying a viable and better alternative to the traditional relaying systems. The additional features offered by microprocessor technologies encouraged the evolution of relays that introduced many changes to the industry. Design and implementation of a teleprotection system with digital and Abstract: Safe and un-interrupted power transmission requires a widespread use of control and protection equipment to avoid fault propagation In this report, a new type of power system is proposed where a wide-area Frequency stability and digital protection coordination of multi-source Full Paper.

    Power System Protection, Volumes - Knovel ; Digital protection systems. Adaptive protections. Power system protection. Protection of electrical equipment.

    Relaying communications. When the steady state conditions on the power system are such that power The document points out the limitation that existing digital protective relays generally have in IEEE Std Individual locations within the m e m o r y may be electrically erased and r e p r o g r a m m e d with the chip in situ. Can be used for storing relay settings. Erasure of flash memory is restricted to large fractions o f the on-chip memory rather than individual locations.

    Flash memory is likely to feature highly in future numeric relays for storing program memory and relay setting data. The flexibility of this device simplifies the shop-floor production of numeric relays, as well as allowing for easy on-site upgrades of relay software. An example 8 bit number is where the leading '1' is referred to as the most significant bit, or msb, and the trailing '0' is the least significant bit or isb.

    To convert a binary number into decimal, it is necessary to calculate the decimal equivalent of each binary position. A simple way of encoding unsigned binary numbers is given below: Using this representation, the highest number is decimal. Since it is laborious to refer continually to binary numbers explicidy, a shorthand notadon has been developed which splits 8 bit binary numbers into two 4 bit 'nibbles' note also that 8 bits are usually referred to as 'bytes' and 2 bytes, on a 16 bit microprocessor, are called a 'word'.

    Note that a hexadecimal representation gives no indication of what the binary n u m b e r really represents, it merely makes handling binary numbers easier for humans.

    Digital technology 11 To allow negative numbers, the twos complement representation is used. In this representation, the msb is taken as negative: Stricdy speaking this is 'integer' twos complement. Another form is fractional twos complement: The advantage of fractional over integer arithmetic is seen if the numbers shown above are squared.

    However, any fractional n u m b e r can be squared to yield a representable result. Finally, an increase in dynamic range may be achieved with the use of floating point representation. Here, numbers are represented in the form: Typically the mantissa, M, is represented with 10 bits and the exponent, E, is represented with 6 bits thus using 16 bits in total.

    The penalty of using floating point arithmetic is the extra processing required to perform simple operations such as addition, multiplication etc. At the time of writing, no numeric relays use floating point arithmetic.

    However, this reflects upon the current high cost of microprocessors which can process floating point numbers at the speeds required for protection. It is likely that future relays will use this number representation.

    Microprocessors may be programmed at three basic levels: Here the specific codes to provide a given instruction, e. This m e t h o d of programming is very time-consuming and tedious and is m e n t i o n e d here for completeness. Suitable only for very simple programs. Assembly language programming. This allows the machine codes to be addressed symbolically by a simple mnemonic. The programmer writes a series of mnemonics to perform the desired task.

    This program is then assembled into the relevant machine codes using another computer program called an assembler. This m e t h o d is quicker to develop than machine code programming but is still tedious for long programs. However, resulting code is very efficient. Parts of numeric relay programs, where it is essential that the microprocessor executes the code as quickly as possible, are programmed in assembly language. High level language programming. A computer program written in a high level language such as Basic, Fortran, C, Pascal etc is far easier to understand than an assembly language program since the programs read similar to English.

    It is thus easier to develop the code and far simpler to write long programs. However, the resulting code is generally less efficient than for the previous two methods, i. Statements written in the high level language are converted into machine code by a program called a compiler. The non-time critical parts of a relay program are usually p r o g r a m m e d in a high level language.

    This process is referred to as analogue to digital conversion and is perform by special hardware. In practice, useful power system signals are bipolar, i.

    To simplify the following discussion on conversion, analogue signals are taken to be unipolar, i. However, the general principles may be extended to include bipolar conversion. Analogue " Output Figure 1. A basic circuit for a 4 bit DAC is shown in Figure 1. It is seen that the weighting resistors connected to each of the data lines increase in binary progression.

    The gain of the operational amplifier is given by: The negative gain of the amplifier is compensated by making the buffering amplifiers inverting. If more than one data line is active, then the analogue output voltage is the sum of the two Vout s calculated from the above expression. Thus the voltage at the output is directly proportional to the binary n u m b e r represented by the data lines.

    The feedback resistors across the operational amplifier ensure that 14 Power system protection the largest binary number corresponds to highest analogue voltage. By increasing the number of data line inputs, and progressively increasing the series resistor values, DACs of 8, 10, 12, 14 and 16 bits may be implemented.

    A comparator is similar to an operational amplifier and, as used in this circuit, will give an output of '1', or high, if the analogue input voltage is greater than the DAC output, and an output of'0', or low, otherwise. Note, because of the AND gate, the clock signal will not reach the counter unless the comparator output is high. Thus the DAC output is zero, the comparator output is high and, in turn, the clock pulses will pass into the counter.

    Assuming the analogue input to be non-zero, as the counter increments, the output of the DAC appears as a ramp. When the DAC voltage exceeds the analogue input voltage, the comparator output will go low and prevent the clock pulses reaching the counter.

    Thus the binary counter digital output lines now hold the nearest digital value corresponding to the analogue input. Digital technology 15 The ramp ADC is rarely used in practice since the conversion time, the time required to ascertain the digital equivalent value of the input analogue signal, increases with the input voltage.

    To make the conversion fast, very high speed clock pulses are required which introduce other problems. The binary counter is replaced by a slightly more complicated logic arrangement which will be referred to as a successive approximation register. Prior to the conversion, all data lines are set to zero.

    It is seen that on the first clock cycle the DAC goes to half of its maximum output, this is equivalent to setting high the most significant bit of the data bus, D3. On the next clock cycle the successive approximation logic senses that the DAC output is still lower than the input signal since the comparator output is high.

    Thus, the D2 data line is now set high. I0 Successiveapproximation converter I.. V Enable 16 Power system protection A n a l o g u e Input 7" "'' The fourth clock cycle results in DO being set high and yields the digital result: It is seen that a successive approximation ADC individually tests each bit of the output data lines in turn; thus the time taken to convert is always fixed at the number of bits multiplied by the internal clock period.

    ADCs usually have an 'end-of-conversion' signal which is commonly connected to an interrupt line of the microprocessor to inform when a conversion has finished and that the converted value is available for processing. Although other types of ADC are available, successive approximation ADCs are the preferred type for protection relays. Other types include flash converters which are designed to have very fast conversion times 1. To eliminate this source of error, the input analogue signals are passed Digital technology 17 through sample and hold SH amplifiers which, upon c o m m a n d from the microprocessor, hold the input signal at a constant analogue level for the duration of the conversion.

    This is shown in Figure 1. Immediately prior to a conversion being made, the microprocessor opens the switch and the previous analogue voltage is held on the capacitor and thus the output remains constant - the hold mode. The two amplifiers in Figure 1. Figure I. In relays requiring multi-channel inputs, such as a distance relay where a minimum of 6 channels 3 voltage, 3 current are used, a device called a multiplexer is used to switch each of the input channels to the input of the ADC sequentially.

    Thus, it is c o m m o n for each analogue input channel to have its own SH amplifier. A typical digital relay analogue input stage is shown in Figure 1. Note that the multiplexer MUX is under the control of the microprocessor and that the SH amplifiers are all selected simultaneously into either the sample or hold modes. T h e correct n u m b e r of bits for a given relay d e p e n d s upon the application.

    A relay will work correctly with an over-specified ADC, i. An example is given here o f how an ADC may be specified for a distance relay. Consider a distance relay which has a minimum setting impedance of 4 relative to the relay.

    Digital Protection for Power Systems - Free Download PDF

    For a distance relay, the current rather than the voltage inputs will have the greater dynamic range. Suppose that the relay must operate for a m i n i m u m current level of 25mA and this can be represented by 1 digital level.

    H e n c e for a bipolar signal, the dynamic range is Thus, a 14 bit converter would be required for this situation. In general, most high p e r f o r m a n c e numeric relays use 12, 14 or 16 bit ADCs.

    Prior to the introduction o f 16 bit microprocessors, 8 bit microprocessors were standard, but not ideally suited to processing 12 or 14 bit values. Thus, the advent o f 16 bit microprocessors was instrumental in the progress o f numeric relays. O n e o f the first 16 bit processors on the market was the Intel which was launched in T h e series is o n e o f the most successful family o f processors ever p r o d u c e d due to its widespread use in IBM PCs usually as the , or Another popular processor launched a r o u n d the same time as the was the Motorola which, like the , has been continually updated.

    Although the emerging processor technology was suited to the development of numeric relays, there still existed a problem o f digital multiplication. Any numeric relay, o t h e r than the most simple application, will execute a large n u m b e r o f multiplications whilst performing its protection function.

    Since multiplication o n a microprocessor was, at the time, achieved by a series o f shifts and additions which took a relatively large n u m b e r o f clock cycles to execute, this led to relay algorithms being very conservative in the n u m b e r o f multiplications used since multiplications used up processing time. Note that all the calculations p e r f o r m e d by the relay must be completed in the time between ADC samples. A typical multiplication time for a standard 16 bit microprocessor in was xs.

    A stop-gap in the problem o f digital multiplication was the e m e r g e n c e o f hardware multipliers HMs , single VLSI chips which were dedicated to the task o f multiplying 16 bit numbers and could p r o d u c e a result in, typically, lOOns. HMs were originally launched in the mid s but it took several years before prices d r o p p e d significantly.

    Despite the fast multiplication time of the HM, the effective multiplication rate was a lot slower since the microprocessor had to spend time sending data to and from the HM. A significant step forward was made by the launch, in , o f the Texas Instruments TMS range o f 16 bit digital signal processors.

    T h e TMS differs from conventional 16 bit microprocessors by having a hardware multiplier integrated directly onto its chip. T h e architecture o f the TMS range was especially designed for digital signal processing DSP , for example it is possible to perform a multiplication and an addition, a c o m m o n operation 20 Power system protection in DSP as will be shown later, in one instruction cycle. Over the past 10 years, there has been a steady growth in the performance of digital signal processors and they are now available from several manufacturers.

    The following table summarises the state-of-the-art for Table I. Moore Introduction T h e processing o f signals which have b e e n converted to digital form - digital signal processing - is now c o m m o n p l a c e and this subject area is likely to grow m o r e important in the future. T h e purpose o f this chapter is to give an elementary grounding in digital signal processing including the process and limitations o f sampling, digital filtering and spectral analysis.

    Quite unusually for this subject, little reference is made to mathematics, and so there are limitations to the depths o f explanation, Further details may be found in the references at the e n d o f the chapter. However, when this representation is used, the very nature o f the waveform has been changed and it is important that this distinction is understood. If a 50Hz waveform is displayed on a standard oscilloscope, then the trace o f the waveform is said to be continuous;, that is, at every point in time, there is a distinct value which represents the 50Hz waveform.

    If it is possible to examine a small section o f the waveform in great detail, then it would always appear to be continuous, no matter how closely the waveform is examined.

    All power system waveforms are continuous, as are the waveforms from a m i c r o p h o n e or a record player. Note that, in the context o f electrical engineering, analogue waveforms are continuous. W h e n waveforms are converted to digital form, then they will no longer be continuous. Table 2. At, say, 3ms, the digital representation of the waveform is and remains so until a time o f 4ms at which point it changes to Another term for this representation is a discrete time signaL This is distinct from the continuous waveform representation o f the sine wave where, between 3ms and 4ms, there are an infinite n u m b e r o f values, since a continuous waveform may be infinitely subdivided.

    Despite the a p p a r e n t differences between the two waveform representations, the discrete values are said to be a unique representation o f the original sine wave. T h a t is to say that only the original sine wave, and not any o t h e r waveform, may be converted to produce the set o f digital values shown in table 2.

    However, this may not always be the case, as will be shown in the next section. In Table 2.

    Digital Protection for Power Systems

    T h e reciprocal of sampling frequency is referred to as the sampling interval. T h e sampling frequency is not chosen arbitrarily and, in general, is a governing factor in the design of the digital protection relay hardware and will be discussed later.

    However, an important relationship exists between the sampling frequency and the frequency o f the waveform to be sampled; this relationship is referred to as the sampling theorem see, for example, References 1 or 2. Succinctly stated, the sampling t h e o r e m says that the sampling frequency must be greater than twice the highest frequency to be sampled.

    If this rule is disobeyed, then the unique digital representation of the original continuous waveforms is lost and an effect called aliasing occurs. T h e effect o f aliasing is that two different continuous waveforms, when sampled, can appear as the same digital representation. Although this may appear unlikely, a simple exercise will show this to be true.

    Figure 2. T h e vertical dotted lines represent the exact instant of sampling and, where a sampling operation has occurred on each o f the sine waveforms, a square box is drawn to indicate that a sample has been made.

    The waveform in Figure 2. It does not matter that the samples of b do not closely approximate a sine wave; this is merely how a discrete time signal appears when drawn on a graph. This is achieved by the use of an analogue filter which is designed to remove any frequencies exisdng on the input signal which are greater than half the sampling frequency; such filters are referred to as anti-aliasingfilters.

    Note that 24 Power system protection almost without exception, digital protection relays process only the power system frequency i. Thus, it is imperative that the anti-aliasing filter removes any frequencies that would 'fold down' to 50Hz after sampling. When referring to discrete time signals, it is c o m m o n to refer to a specific set of values as being a sequence.

    In Figure 2. Commonly, Tis omitted in this description since it is always implied and, as in Figure 2. Note that the original continuous waveform is described as x t where t is the continuous time variable. The most efficient way of filtering out nonHz components is by the use of a digital filter, i.

    Although the use of an analogue anti-aliasing filter was discussed earlier, it is far better to use digital filters rather than analogue types since digital filters have a shorter group delay which leads to shorter relay operating times.

    Group delay is the time taken for a signal to pass through the filter. Both Figures 2. If it were necessary to describe the pertinent information contained in Figure 2. Clearly, it is preferable to describe the information, in this case, as a time domain description.

    The use of time domain and frequency domain representations is interchangeable and, in general, it is purely a matter of convenience that dictates which representation is used.

    It can be seen from Figure 2. In fact, this is not entirely true in the general sense, since in the frequency domain, phase as well as magnitude information is required for a complete description. Hence, if magnitude and phase information are available, then the time domain may be derived. The same is true in reverse, that frequency domain information may be derived from only a dine domain description, although this is less easy to see intuitively.

    Techniques for transferring between time and frequency domains will be described in Section 2.

    Digital Protection for Power Systems

    However, as discussed in Section 2. And so the question arises, how is a filter described in the time domain? This question will be answered shordy after another important feature of filters is examined. Suppose that the waveform of Figure 2. Since the. I1 Input Fi,to, ] b Output Amplitude 1. This process, which is impractical for most purposes, uses the frequency d o m a i n to calculate the time d o m a i n answer. T h e r e is a m a t h e m a t i c a l process which can be used to calculate the resulting filter output without any reference to the frequency domain.

    This process is referred to as convolution a n d it uses a characteristic o f the filter called its impulse responsein o r d e r to calculate the resulting output waveform. Thus, the o u t p u t signal from the filter is result of convolvingthe input signal with the filter impulse response.

    T h e impulse response is the time d o m a i n description o f a filter which was q u e r i e d earlier. T h e impulse response o f a filter is as unique as its frequency response but, as Section 2. W h e n describing filters, frequency responses are far m o r e useful than impulse responses, as Figure 2. Indeed, analogue convolution may only be described in terms of integral calculus and will not be explained here and the filter response to an impulse, a very narrow isolated pulse of great magnitude, can only be approximated.

    This in some way explains why the frequency domain is preferred for describing filters. However, when the internal mechanisms of digital filters are examined, the concepts of impulse responses and convolution are immediately apparent, hence the foregoing discussion.

    Furthermore, digital filters have very clearly defined impulse responses and the digital equivalent of convolution is easy to understand without having to resort to complicated mathematics. II b Same filter with larger impulse applied 2. This particular input sequence is the digital equivalent o f the impulse described earlier. Note that the impulse is as narrow as possible. T h e o u t p u t o f the filter, the impulse response, is also shown and is seen to consist, for this specific filter, o f a sequence o f 8 values which somewhat resemble a decaying sine wave.

    Note that the filter o u t p u t is also scaled by a factor o f 2, yet its o t h e r characteristics, such as shape and length o f response, remain unchanged. In general, the o u t p u t o f a digital filter is the summation of the individual responses o f the filter to each sample in the input sequence. Each isolated response to the first 5 inputs samples is shown individually at the correct point in time; the filter o u t p u t is simply the sum o f all the relevant parts o f the responses at a given point in time.

    Note that the values o f h[k] are usually referred to as the filter coefficients. In the filter example of Figure 2. A m o r e general expression for digital convolution is: N y[n].

    Note that digital convolution is achieved by a series o f multiplication and addition operations which are easily i m p l e m e n t e d on a microprocessor. Although N c a n be large, it cannot be infinitely large since, in order to implement the filter, a total of N multiplications and N additions must be performed between sampling instants.

    A filter of this type is, thus, referred to as a finite impulse response FIR filter. FIR filters have the property that their group delays are never greater than NT where T is the sampling interval. Furthermore, when designing FIR filters, the group delay may be used as a design parameter.

    This is very important for digital protection relay applications since the group delay will directly influence the relay operating time and, generally, is kept to a minimum. Although digital filters have been explained in relation to their impulse responses, when designing a digital filter, the starting point is a frequency response of the desired filter.

    The difficulty then is to find the impulse response which corresponds to the desired frequency response the derivation of the frequency response from the impulse response is covered in Section 2. Latterly, the design of FIR filters has been revolutionised by the development of an optimal filter design program by Parks and McLellan see Reference 2 for more details , referred to as the Remez exchange method.

    The Remez exchange program is given the desired frequency response and the filter length from which the optimal filter coefficients are calculated. Ironically, this technique is of limited use in protection applications where filter lengths are of critical importance see Section 2. IIR filters cannot be implemented via Equation 2. Instead an equation which uses both past values of the filter input and output is used: Since previous values of the filter output are used in Equation 2.

    The main drawback to the use of IIR filters in digital protection relays is that the group delay cannot be specified in the design process. This makes their use in protection somewhat onerous and, in general, FIR filters are usually the preferred type; however, there is an important exception to this which will be discussed in Section 2. This leads to the question: The answer to this question is yes, the technique to be used is called the Fourier transform, which is named after its inventor, Jean BaptisteJoseph Baron de Fourier.

    The process of moving between the time domain and the frequency domain, or vice-versa, is referred to as transforming. Quite often, the impetus for performing Fourier transforms is the need to have a knowledge of the frequency spectrum of some time domain waveform, hence the section rifle, spectral analysis.

    Note that the frequency domain graphs are shown as having both positive and negative frequency spectrums. When the Fourier transform is used for spectral analysis of time domain waveforms such as power system voltage and current waveforms, the positive and negative frequency information from the Fourier transform will be identical.

    Thus, it is easier to consider all frequency spectrums as being purely positive.

    The Fourier transform not only allows conversion from time to frequency domain but, also, through the use of the inverse Fourier transform, can convert from the frequency domain to the rime domain.

    However, it is the former process of time to frequency conversion which is of interest in this context and further references to Fourier transforms will assume time to frequency conversion. In c o m m o n with the discussion on continuous convolution, the abstract use of Fourier transforms on continuous waveforms involves integral calculus which, again, will not be described here.

    However, the Fourier transform may be adapted for use on discrete time signals - as such it is referred to as the discreteFourier transform or DE'I'. A typical use for the DEr is to analyse the time domain waveform of Figure 2.

    This is of particular relevance to protection where it is clearly advantageous to estimate the 50Hz component of a power system waveform corrupted by noise.

    In practice, the DFT, for transforming from rime to frequency domains, is implemented as two equations: Note the similarity of Equation 2. Equation 2. These are simply related to the more familiar magnitude and phase description.

    All frequencies evaluated arc harmonically related to the lowest, non d. The second harmonic frequency is twice the fundamental frequency, the third harmonic is three times the fundamental etc. For example, consider an input sequence consisdng of 20 samples taken at a sampling frequency of 1kHz.

    Specifically these are shown in Table 2. Although digital multiplication on a computer is now relatively quick, it is always beneficial to use efficient algorithms which reduce the number of operations, be they multiplication or otherwise.

    An efficient algorithm for the computation of the DFT has been developed which reduces the number of arithmetic operations required. This redundancy is that the same operation, e. The exact operation of the Digital signal processing 35 FFT will not be discussed here, but a comprehensive description may be found in Reference 3. The FFT becomes more efficient as Nincreases. Simply, the FFT calculates all of the frequency spectrum; this may not always be required for the protection function.

    Indeed, as stated earlier, it is usually only the 50Hz component which is of interest, although occasionally other components may render useful information, e.

    The DFT, however, may be evaluated for only one frequency c o m p o n e n t and hence it is the DFT equation, or its variant, which is found in protection applications. This is achieved by performing an FFT on the filter impulse response. An example of this is shown in Figure 2. A large number of points for the F F r are used to give good frequency resolution, this is why the frequency response almost appears to be continuous.

    When the n u m b e r of points in an impulse response is less than the number of points in the FFT, the unused points are set to zero. In general, with FIR-type digital filters, there is no readily available analogue counterpart and thus the use of FIR digital filtering is an advantage in itself since frequency responses may be achieved that would otherwise be impossible.

    However, the use of digital filtering in protection relays poses some problems. Consider the FIR filter impulse response of Figure 2. Examination of the frequency response shows that it has a pass band centred on 50Hz and excellent rejection of harmonics.

    As such it would appear to be an ideal filter for a protection relay. However, due to its group delay of 20ms, a relay using this filter would be unable to operate correctly, and consistently, until 20ms after the occurrence of the fault and is consequently unable to give ultra-high-speed performance.

    Thus, the group delay is 3ms and ultra-high-speed operation is now a possibility. However, examination of its frequency response reveals a less favourable situation with the passband of the filter centred at Hz.

    Thus the fundamental problem of digital relay filter design is choosing an optimum balance between frequency response and operating time. The discussion regarding digital filters concentrated on filters with coefficients that have fixed values. There is another important class of filters called adaptive filters where the coefficients vary in time according to some controlling influence. Adaptive filters are useful because the characteristics of power system signal distortion u n d e r fault conditions vary according to the type of fault.

    Since the type of fault is not predictable, an adaptive filter will always give an optimal filter response to the fault, although in addition to filter group delay, the time for the filter to adapt needs to be considered. However, currently there is much interest in the area of Kalman filtering, which is an IIR-based adaptive filter.

    I 1 12 point sine wave based filter -frequency and impulse responses 38 Power system protection The factors to be considered in designing digital filters for protection relays are: During a fault, when there is a significant change of voltage at the fault point, waves will be generated which travel from the fault point into the adjoining power network travelling waves.

    This effect is particularly prevalent in overhead ehv applications where it causes corruption of relaying quantities. The dominant frequency of the travelling waves will be influenced by the position of the fault. Power system harmonics are inevitable. Rejection of harmonic effects is best achieved by using protection algorithms which are immune to such effects. Removal of low order harmonics, particularly the third, by filtering will lead to an increase in operating time.

    Exponential offsets. These can occur in genuine response to a fault condition, or can be induced in transducers, particularly current and voltage transformers CVTs. As such, it is better to remove actively all exponential offsets from whatever cause. This implies that digital filters with d. Even with the use of high speed processors such as the TMS family as described in Section 1.

    Between each sample, the relay has to filter all the measured signals, run the protection algorithm and reach a decision regarding the fault.

    This dme available is referred to as real-time. Clearly, a digital protection relay cannot operate correctly if it is unable to complete all the required tasks within the real-time constraint. One approach to increasing the real-time available for protection processing is to lower the sampling frequency.

    However, lowering the sampling frequency also lowers the passband required of the analogue anti-aliasing filters and, as a consequence, will increase the group delay of these filters since a sharper cutoff is required.

    In essence the total relay filtering function has been moved from digital to analogue circuitry.

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    Since digital filters are more efficient in terms of group delay than analogue types, the net effect of lowering the sampling frequency is to increase relay operating time. Note that ultra-high-speed relays, as a rule, use high sampling frequencies which allow very simple and basic anti-aliasing filters with correspondingly short group delays.

    The favoured approach to solving real-time problems is to increase the processing capability by providing more than one processor. A typical digital ultra-high-speed relay has three processors, two digital signal processors for data acquisition, digital filtering and protection algorithm execution, and a more conventional microprocessor to perform the scheme logic including monitoring the relay elements, communicating with other relays, tripping and implementing time delays where appropriate.

    An alternative approach to increase real-time, but without affecting hardware considerations, is to perform the sampling and digital filtering as normal, but perform the protection Digital signal processing 39 algorithm at half the sampling frequency. This increases available real-time, but delays the operating time by only one sampling interval. Ohlg,n and Dr R. Aggarwal Introduction This chapter introduces the final e l e m e n t o f background knowledge required for the r e m a i n d e r o f this book.

    It begins with the general subject o f digital communications, explaining transmission types, protocols, error handling and networks, and concludes with a description o f the transmission medium o f fibre optics, a technology which is increasingly found within the substation environment. It is therefore important first to answer the questions: In the field o f substation automation we can divide the communication into information and commands.

    We can f u r t h e r m o r e structure both the information and the commands into different levels o f importance. This in turn will give the r e q u i r e m e n t for the accuracy or the quality o f the information as well as when it should be sent.

    On-line information with short response time and high resolution is required for commands o f breakers whereas statistical data is not time-critical. Instead o f on-line information immediately transferred, the data can be regularly stored until requested. To where the data information and commands are sent can basically be divided into four locations: Today, some utilities are implementing mobile workplaces for both the operator and engineer. T h e o p e r a t o r on duty can, for example, monitor the power system from h o m e using a portable PC.

    For remote communication the available media is normally already given. This could be utility-owned microwave and power line carrier, or the telephone Digital communications and fibre optics 41 system. Today the available s p e e d on these systems is normally between and bps, although in s o m e cases a n d 19 can be obtained. With the increased use of fibre optics a n d satellite c o m m u n i c a t i o n s the t e l e p h o n e companies are now able to offer data transmission at speeds greater than 1 Mbps.

    T h e user of the information d e t e r m i n e s how it should be sent and presented. Too m u c h information is often worse than too little.

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