A Genetic Based Fault Location Algorithm for Transmission Lines

Transcription

1 A Genetic Based Fault Location Algorithm for Transmission Lines K. M. EL-Naggar Assistant Professor, College of Technological Studies, Kuwait Summary Overhead transmission lines are parts of the electric power system where fault probabilities are generally higher than that of other system components. One of the main objective of protective system is to detect faults on transmission lines as fast as possible. Another important job is to locate this fault point accurately. Therefore, it is very important to have a fast reliable methods that can detect and locate faults on transmission lines in order to reduce the time needed to resume the service to consumers. This paper presents a new method based on Genetic Algorithms (GAs) for locating fault point on power transmission lines. Genetic Algorithms (GAs) have recently received much attention as robust stochastic search algorithms for various optimization problems. This class of methods is based on the mechanism of natural selection and natural genetics which combines the notion of survival of fittest. Random and yet structured search and parallel evaluation of the points in search space. The construction of a simple genetic algorithm for any problem can be summarized in four main tasks to be done: first, the parameters coding, second, the selection or reproduction stage, third, determination of the probabilities controlling the genetic operators, finally, fitness function design and solution evaluation. The process starts with random generation of a population. A population consists of a set of strings. The population may be of any size according to the accuracy required. The problem variables are coded using suitable coding system. The strength of an individual is the objective function, Fitness Function, that must be optimized. After evaluation, strings are subjected to a set of genetic operators for generating new search points and a stochastic assignment to control the genetic operators. One of the advantages of GA is the using of stochastic operators instead of deterministic rules to search the solution. This means that GA does not need a continues search space. GA hops randomly from point to point in search space and this allows it to escape from local optimum points in which some of other algorithms might land. Another advantage is that GA deals with nonlinear functions direct without any linearzation. A practical case study is presented in this work to evaluate the performance of the proposed method. The short circuit current mathematical model for different fault locations is presented. The simulated short circuit current is sampled at sending end terminals. The current samples are used to set up an over-determine system of equations in state space form. The system state will be the transmission line length up-to the fault point. The problem is then formulated as an optimization problem. The goal is to minimize the error in estimated state parameter. Finally, GA is used to find the optimum solution for the formulated optimization problem. The effects of GAs parameters and operators, such as population size, crossover, mutation probabilities and fitness functions are studied. Effects of estimation process parameters such sampling rate and sampling window size on the accuracy of the estimated fault location are also presented and evaluated. Results obtained for different fault locations and different fault inception instants show that the algorithm can identify and locate faults in over head transmission systems with a very high degree of accuracy. In conclusions a new application of GAs in the area of power system analysis and protection is presented and tested. Results obtained show that the technique can be used as a fast on-line efficient alternative for conventional optimization techniques in the area of power system analysis and protection. A GENETIC BASED FAULT LOCATION ALGORITHM FOR TRANSMISSION LINES

2 K. M. EL-Naggar Assistant Professor, College of Technological Studies, Kuwait SUMMARY This paper presents a new method for on-line computation of fault location in transmission lines. The proposed method uses digital set of short circuit current measurements for estimating fault location. These digital current samples are used to construct a set of overdetermine system of equations. The estimation problem is then solved using Genetic Algorithms (GAs) optimization technique to find the fault distance. GAs are powerful optimization techniques based on natural selection and natural population genetics. The effects of GAs parameters and operators, such as population size, crossover, mutation probabilities and fitness functions as well as the effects of sampling rate and sampling window size are studied. A practical case study is presented in this work to evaluate the proposed method. Results are reported and conclusions are drown. INTRODUCTION Overhead transmission lines are parts of the electric power system where fault probabilities are generally higher than that of other system components. One of the main objective of protective system is to detect faults on transmission lines as fast as possible. Another important job is to locate this fault point accurately. Therefore, it is very important to have a fast reliable methods that can detect and locate faults on transmission lines in order to reduce the time needed to resume the service to consumers. Several methods have so far been proposed, most of these methods are based on state estimation techniques. Static estimation techniques such as least error squares and least absolute value were proposed in many references. Sachdaev and Baribeu () proposed a method based on least error square estimation technique that uses the voltage and current samples at sending end to calculate the impedance up to the fault point. The fault distance is then calculated by assuming that the line reactance is proportional to the line length to the fault point. Dynamic state estimation techniques are presented as well in some references. Ismail and EL-Naggar (2) proposed the use of dynamic filter to estimate the fault location on-line. The method uses the digital voltage and current samples at sending end to calculate the line impedance and accordingly the fault distance. Sheng and Elangovan (3) presented a method based on discrete Fourier transform that uses voltage and currents samples at both ends of the transmission line. Methods based on Artificial Neural networks and expert systems have been recently presented. Fukui and Kawakami (4) presented a method based on expert systems. The method estimates the fault section using the information from protective relays and circuit breakers. EL-Sharkawy and Niebour (5) presented a review for the methods based on Artificial neural network as used for faults detection. The reference discusses the advantage and disadvantage of these methods in this area. Methods based on GAs for fault section estimation in sub-transmission networks are also presented by Wen and Han (6). This paper presents a new method based on GAs for locating fault point on transmission lines. GAs have recently received much attention as robust stochastic search algorithms for various optimization problems. This class of methods is based on the mechanism of natural selection and natural genetics which combines the notion of survival of fittest. Random and yet structured search and parallel evaluation of the points in search space. GAs have been successfully applied in the area of power systems analysis to solve many complicated optimization and estimation problems as presented by Nims et-al (7), Paterni et-al (8) and EL- Naggar and Yossef (9). In this work the short circuit current is sampled at sending end terminals. The current samples are used to set up an over-determine system of equation in state space form. The system state will be the transmission line length up-to the fault point. The problem is then formulated as an optimization problem. The goal is to minimize the error in estimated state parameter. Finally, GA is used to find the optimum solution for the formulated optimization problem. PROBLEM FORMULATION The power system shown in the Appendix is used in this study. The system consists of a generator feeding a load center through two transformers and a short transmission line. The Transmission Line is 50 miles long, the line capacitance is neglected. The fault is assumed to occur at different lengths from the sending end. Neglecting resistance, the symmetrical short circuit current that flow in the transmission line can be written as: i t) = Esin( ωt + θ) + e xdeq ) + e x ( t / τ d t / τd ( ( x deq deq xdeq x deq )

3 () where i(t) is the instantaneous symmetrical short circuit current E is the machine terminal voltage θ is the voltage phase angle T d is the transient short circuit time constant T d is the sub-transient short circuit time constant x d eq = x d + x T + (x T.L )*L. x d eq = x d + x T + (x T.L. )*L x d eq = x d + x T + (x T.L )*L. x T.L. is the transmission line reactance/mile x T is the transformer reactance L is the transmission line length up to the fault point Assuming the fault occurs at length L from the sending end and the current waveform is sampled at equal time intervals, t, we will have a set of (m) samples, i(t ), i(t 2 ),,i(t m ) available at t, t 2, t m, where t is an arbitrary time reference. We can write the following discrete system of equations in state space form : [ Z ] = [ f ( x ) ] + [ e ] (2) where: [Z] is the m x current samples vector [f(x)] is the m x information vector (x) is the parameter to be estimated, namely L [e] is the mx measurements error vector that highly fitted strings receive a higher number of copies in the next generation. This is also means that strings with a higher fitness will have a probability of contributing one or more offspring in the next generation. Reproduction can carried out in a variety of ways. In this study, the process is carried out using roulette wheel technique. In this technique each string in the old population has a slot sized in proportional to its fitness. Thus, more highly fitted strings receive a higher number of copies in the next generation. Crossover is performed on two strings at a time that are selected from the population at random. Crossover involves choosing a random position in the two strings and swapping the bits that occur after this position. In one generation the crossover operation is performed on a specified percentage of the population. This is defined at the initialization stage as crossover probability. Mutation, the last Genetic operator, is needed because even though reproduction and crossover effectively search and recombine extant notion, occasionally they may become over-zealous and loose some potentially useful genetic material. In artificial GA mutation protects against such an irrecoverable loss. Mutation operator is performed randomly on less than 5% of the bits. In binary coding system the selected bits are changed from 0 to and vice versa. Mutation process is used to escape from probable local optimum. After mutation the new generation is completed and the procedure begins again with fitness evaluation of strings (0). INTRODUCTION TO GENETIC ALGORITHMS Coding Genetic Algorithm is a search technique based on the concept of the natural selection and natural population genetics. The construction of a simple 0genetic algorithm for any problem can be summarized in four main tasks to be done: first, the parameters coding, second, the selection or reproduction stage, third, determination of the probabilities controlling the genetic operators, finally, fitness function design and solution evaluation. The process starts with random generation of a population. A population consists of a set of strings. The population may be of any size according to the accuracy required. The population size remains constant throughout the whole process. Each string in GAs may be divided into a number of sub-strings. The number of sub-strings, usually, equals to the number of the problem variables. The problem variables are coded using suitable coding system. The strength of an individual is the objective function, Fitness Function, that must be optimized. After evaluation, strings are subjected to three major operators, reproduction, crossover and mutation. Reproduction is Simply a process in which individuals are copied into mating pool according to its fitness value. Copying strings according to their fitness means In this study the problem parameter is the length (L). The parameter is coded in binary using 2 bits. Thus the string length will be only 2 bits. An eighty strings are generated randomly to form the initial population. It is important to mention that the number of strings is chosen by trail and error. The optimum number is different from problem to another. Fitness Function Fitness Function is the function that responsible for evaluation of the solution at each step. The objective here is to minimize the estimation error. Two different functions are used in this work to evaluate the quality of the solution. Each function will be used and the solution obtained using both of them will be evaluated. Sum of Square Errors Fitness Function (FF). Starting with equation (2), each of this vector equation can be rewritten as: Z i F i (x) = e i ; i=,2, m (3)

4 By squaring the individual errors and adding them together, we will end up with the following equation: m F sum = e i i= 2 (4) Since the objective of GAs is to maximize the objective function, it is necessary to map the error square function (F sum ) into minimization fitness function(ff) as: FF = (5) + F sum where is a small constant (= in this work) to avoid overflow problems if F sum goes to zero Minimax fitness function (FF2). In this case, the fitness function is set to minimize the maximum individual error. Thus we can write FF2 as: 2 = e max FF (6) + where e max is the maximum individual error in each generation. TEST RESULTS The Genetic algorithm described in this paper is implemented in FORTRAN77 and extensively tested using the system in the Appendix. Equation () is used to generate current samples needed. The samples generated are then fed to the GA program to estimate the fault distance (L). The two fitness functions FF and FF2, proposed earlier, are used to evaluate the GA solution. GA parameters and probabilities are obtained by trail and error at each case study and held constant (0). In this study it is found that the best values for crossover probability and mutation probability are 0.95 and respectively. Different study cases are performed and samples of the resulted are presented and discussed in this section. The first study case evaluates the effect of the data window size considered. Table summarizes the results of this case. The data window size is varied between and 0 cycles in step of one cycle at a sampling rate of 500 Hz. The corresponding number of samples is given in the same table. The fault exact location is 20 miles the phase angle is assumed to be 0 degrees. It is clear that the best window sizes are 2, 4, 0 and. Considering the calculation time, the window size 0 can be excluded and the remaining window sizes are used for further studies. TABLE - Estimated fault location (L) in miles Exact Fault location = 20 miles θ = 0 o, sampling rate = 500 Hz #of Widow L using FF L using FF2 Samples size In the next study case the three windows,2 and 4 are used with different sampling rates. Sampling rates used started from 500 Hz and ended-up at 4000 Hz in step of 500 Hz. Extensive runs show that the window size gives the best results with both FF and FF2 when compared with the results obtained using window sizes of 2 and 4. A sample of the results is given in table 2 (window size = only). This table shows the results obtained when the window size is fixed at and the exact fault location is 20 miles. Results obtained show that both FF gives results with high accuracy, except with 7 and 8 samples which give unacceptable results. It can be concluded that,, 2 and 4 samples can be used for further studies as they have appreciable errors. In the third case study the effect of phase angle is studied, here only samples within one cycle are used to reduce the computational effort. Table 3 shows this case study and it is clear that FF success in estimating the fault distance with a high degree of accuracy. TABLE 2 - Estimated fault location (L) in mile Exact Fault location = 20 miles θ = 0 o, Window size = cycle #of Samples Sampling Rate L using FF L using FF

5 TABLE 3 - Estimated fault location (L) miles Exact Fault location = 20 miles θ = 0 o, window size = cycle θ (degree) L using FF L using FF The last set of results is summarized in Table 4. In this table the window size is fixed at cycle, the sampling frequency is constant and equals 500 Hz. and samples are always used while the fault distance is varied between 0 and 40 miles in step of 5 miles. Examining this table reveals that both FF give results with almost the same degree of accuracy. The maximum error occurs at 5 miles is about 4 %, while the minimum error occurs at 25 miles (FF) and equals about 0.4%. Although results obtained In many cases using both fitness functions are very close, but FF is preferred because it gives less error in most cases. It can be concluded that if FF were used with in the specified ranges, the estimation process error would be always in acceptable range. It should be noted also, that although some window sizes, other than cycle, could give results with a better accuracy, but using a window size of cycle gives the algorithm the advantage when used in an on-line applications. In this paper the application of Genetic Algorithms in the area of power system protection is presented. Genetic Algorithm is successfully applied to the problem of estimating fault location. The proposed method based on digital measurement of short circuit current waveform at sending end. The problem is formulated as an optimization problem. Simulated short circuit current waveforms with different window sizes are generated and sampled to test the proposed algorithm. Genetic algorithm is then used to find the optimum fault distance. The identification problem is solved using two different Genetic fitness functions. Results obtained show that the technique can be used as on-line method for determination of fault location in only one cycle with a very high degree of accuracy. APPENDIX () G T T.L. T Generator Data Transformer Data 25 MVA, 3.8 KV 30 MVA, 3.8/69 KV X d =.7 p.u. X T = 0.0 p.u. X d = p.u T.L. Data X d = 0.85 p.u Lenght=50miles T d=0.027 Z/mile = 0.2+j0.8 ohms T d=0.26 TABLE 4- Estimated fault location (L) miles Variable Fault location, θ = 0 o window size = cycle, samples Actual fault L using FF L using FF2 Location (mile) CONCLUSIONS REFERENCES. M.S. Sachdaev and M.A. Baribeu, Nov-Dec. 979, A New Algorithm for Digital Impedance Relay., IEEE Tran. on Power Apparatus & Systems, Vol. PAS-98, No.6, pp Hanafy M. Ismail and Khaled M. EL-Naggar, May 999, A Dynamic On-Line Fault Location Algorithm Based on A Discrete Filter for HV Transmission Lines, Third Regional Conference of CIGRE Committees in Arab Countries, Doha, Qatar, Vol. 2, pp Lino Bo Sheng and S. ELangovan, 998, A Fault Location Algorithm for Transmission Lines, Electric Machines & Power Systems Journal, Vol. 26, pp

6 4. C.Fukui and J. Kawakami,, 986, An Expert System for Fault section estimation Using Information from Protective Relays and Circuit Breakers, IEEE. Trans. Power Delivery, PWRD- (4), pp M. EL-Sharkawy and D. Niebur, 996, Artificial Neural Networks With Applications to Powe Systems, IEEE Power Engineering Socity, A Tutorial Course. 6. Fushuuan Wen, Zhenxiang Han, 995, Fault Section Estimation In Power Systems Using Genetic Algorithm, Electric Power System Research Journal, Vol.34, pp J.W. Nims, A.A. EL-Kieb and R.E. Smith,, 997, Contingency Ranking for Voltage Stability Using A Genetic Algorithm, Electric Power System Research Journal, Vol.43, pp Pierre Paterni et-al.., Feb. 999, Optimal Location Of Phase Shifters in the French Netwok by Genetic Algorithm, IEEE Trans. on Power Systems, Vol.4, No., pp Khaled M.EL-Naggar and Hosam K.M.Youssef, 999, Synchronous Machine Parameter Estimation Using A New Genetic Based Algorithm, International Journal of Energy Research, Vol. 23, pp D.E. Goldberge, Ma. 989, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesely, Reading.. William D.Stevenson, Gringer, Jhon J., 994, Power System Analysis, McGro-Hill-International Edition.