algorithm for relay coordination

Evolutionary Algorithm for Protection Relay Setting Coordination K.K.Li, C. W. So Hong Kong Polytechnic University Abstract- The protection relay setting coordination manages the protection relay operations to clear a system f a d t in several steps of contingence. Relays which are missoordinated will trip out unnecessary circuits resulting in electric supply interruption. The Time Coordination Method (TCM) which formulates the coordination of relay settings into a set of constraint equations and objective function is developed to manage the relay settings. The protection system coordination is a highly constrained optimization problem and conventional methods fail in searching for the global optimum. This paper presents the application of Evolutionary Algorithm (EA) in optimizing the protection relay setting coordination in comparison with other intelligent methods. The result shows that Evolutionary Algorithm is an effective tool to search the optimum protection setting with maximum constraint satisfactions.

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Initialization Generation

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Objective Value Evaluation

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INTRODUCTION The protection relay setting coordination manages the protection relay operations to clear a system fault in several steps of contingence. Relays which are mis-coordinated will trip out unnecessary circuits resulting in electric supply interruption. The Time Coordination Method (TCM) [l] is developed to manage the relay settings. It formulates the coordination of relay settings into a set of constraint equations and objective function, which are optimized by the Evolutionary Algorithm (EA). EA is a novel technique for solving highly constrained discrete optimization problems [2] such as protection relay coordination. This problem is difficult to be solved by conventional optimization technique such as linear programming or steeper descend gradient search [2]. This paper presents the application of Evolutionary Algorithm on the protection relay setting Coordination. The results show that EA effectively searches for the optimum protection relay settings with maximum constraint satisfactions. ALGORITHM 11. EVOLUTIONARY Evolutionary Algorithm (EA) is one branch of the Evolutionary Computation. It can search for the optimum solution for a highly constrained problem. The flow chart for EA is shown in Fig 1.

4 Yes End of EA Fig. 1 Evolutionary Algorithm Processes Flowing Diagram A. Initialization The initialization process of EA is similar to all Evolutionary Computational Methods such as Genetic Algorithm and Evolutionary Programming. It provides the starting points for the EA to search for the optimized solution. The greater number of points to start, the higher is the chance to search for the global optimum solution. The initialization of the TCM generates a set of relay settings and formulated a column vectorX,as shown in equation (1).

Where

kjis the j setting in relay n.

X*=

0-7803-6338-8/00/$10.00(~)2000IEEE

Note For example, if RI is Inverse Definite Multiple Time Lag (IDMTL) Overcurrent (OC) Relay, RIslis the Current Setting Multiplier (CSM) and RI, is the Time Multiplier (TM) of R,.

(1)

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The dimension of X,,is the summation of all protection relay settings in the TCM to be processed. Typically, EA requires pure random initialization. It can broaden the search area and increase the chance of searching out the global optimum solution. Unfortunately, protection setting coordination is a highly constrained problem. The pure random generated relay settings very often fail due to constraint violations [3]. For example, a random generated relay settings may not satisfy the operation time margin between upstream and downstream relays [l] under fault conditions. Any insufficient relay operation time margin may cause unnecessary system supply interruption, which is classified as a constraint violation case. Those initialized relay settings with constraint violations will be discarded. Another set of relay settings will be generated and it will be tested against the constraint violations as before. The successful rate of a pure random initialized protection relay settings without any constraint violation may be calculated in the equation (2).

NJU)

N=gm

(21

Where n is the number of relays in the power system, m is the number of settings in relay n, N,(ij) is the number of setting steps of relay i setting j which satisfy the constraint violations, N,&) is the number of settable steps of relay i settingj, N is the successfil rate of the protection relay settings without constraint violations.

For example, if the total number of relays is 10. Each relay has two settings with 100 steps in each setting range. If the chance to satisfy the constraints is only 10% in each setting range, thus N = (1O h OO)20 = 1x 1 From equation 2, if the number of relays is increasing, the successful rate of the initialized relay settings without constraint violations will decrease and approaches to zero. To maximize the successful rate, the setting pusher technique is developed [l] to push the random generated protection settings from unfeasible solution region to feasible solution region. The processing of EA introduce the continuous improvement to relay settings in which some constraint violation cases are corrected to within the constraint violation limits. A small number of constraint violations is thus allowed at initialization stage. In the TCM, the maximum number of constraint violations is defmed. It counts the number of constraint violations for the initialized relay setting during constraint checking. If the checked number of constraint violations of the initialized relay settings is greater than the pre-defined value, it will be discarded. Otherwise, it

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will be put into the eligible pool for TCM process. The number of constraint violations will be reflected on the objective value. The initialization process will be terminated after the pre-defined number relay settings are initialized.

B. Generation The EA is responsible for the generation of new relay settings. It is carried out by mutation, which is different from genetic algorithm [4] and evolutionary programming [5]. For generation n of the k relay settingsX f i ] , the n + l generation of k relay settings X,,+,F/ is generated by equation (3).

X,,FI = X f i I + ofiI=(

onsin FI = JP

d w x~fiIfl(OY1)

(3)

}

- ~.)(xnrki) +Y

where /7

is the scale factor for EA mutation.

y is the offset for EP mutation. @(XJk-n is the objective value of the relay settings XJk-1. N(0,l) is the Gaussian normal distribution noise. PmJk] is a mutation enabling matrix. a,@] is a step matrix. The step matrix 0 Jk] is calculated before mutation process. This is generated from the objective value @(X,@J of the protection setting XJk] and each entry ,[RI is independent of the others. The mutation enabling matrix Pmfi] is designed to decrease the number of relay settings alternation in each mutation process. It is found that a larger number of relay setting altemation will result in a larger number of constraint violations. For the Genetic Algorithm, the single point crossover operator [6] may provide smooth relay setting alteration and introduce smaller number of constraint violations, but the speed of searching for the optimum relay setting is slow. If multi-point crossover operator is applied, the relay setting altemations in each generation is greater and will caused larger number of constraint violations. Consequently, the Genetic Algorithm fails in the Time Coordination Method application. At the end of generation, the new generated relay settings and the old relay settings will undergo a selection process to select the better relay settings for the next generation. The EA uses stochastic selection via a tournament [5]. Each new generated relay settings face competition against a preselected number of opponents and receives a ''win" if it is at least as good as its opponent in each encounter. Selection then eliminates those sets of relay settings with the least wills.

C. Objective Value Evaluation The objective value evaluation is taking the key-roll in the TCM. It generates all system constraints according to the system configurations, fault types and fault locations [ 11. The constraint checking is playing the important part in the objective value evaluation. It checks the relay settings satisfaction in all constraints and counts the number of constraint violations. The number of constraint violations is a punishment to the relay settings as it is reflected in the objective value. The larger number of constraint violations scores higher objective value resulting in less chances to survive in the next generation.

D. Termination The termination of the EA process is similar to the other evolutionary computation methods, such as evolutionary programming, by applying the fixed number of generations. As EA introduce continuous improvement process, the occurrence of the global optimum solution cannot be predicted. Unlike Genetic Algorithm which generates offspring mainly by crossover operator, EA generates relay settings by mutation. It can get rid of the pre-mutual dominance which is the solution trapped in the local optimum. For some other optimization algorithms, the termination is by monitoring the difference of the objective values between two consecutive generations approaching to the pre-defined value. This technique fails in the TCM because the local optimum relay settings always last for several number of generations which satisfies the termination criteria but it is not the best optimum solution. 111.

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B -us B7 0 IDMTL Phase Fault / Earth Fault Overcurrent Relay Fig. 2 Typical distribution network

Table 1 Circuit Parameters

SIMULATION

The control parameter of EA are as follows: Number of generations - EA termination criteria. Population size - The number of sets of relay settings in each generation. Mutation Probability - To generate the mutation enabling matrix h J k ] .

Note : All values are per-unit @U) at IOOMVAbase and all Lines are working at 11kV.

The TCM also has a set of control parameters to be set and are described in [11. To demonstrate the effectiveness of EA in Protection Setting Coordination, a typical distribution network with 8 circuits and each circuit is protected by a IDMTL Phase Fault / Earth Fault Overcurrent Relay as shown in Fig. 2 for study. The circuit parameters are listed in Table 1. Systems Parameters EA SurvivalSize EA Offsety

EA EA

ScaleFactor p Mutation Factor

Values 10 0 0.9 0.1

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Population No. of Objective Generations Value ‘Size 500 0.000670 30 500 0.000650 50 500 0.000730 I00

Simulation Time per Generation for Pentium II 350MHz 0.912 sec I.728 sec 3.563 sec

The optimum solution among these simulation cases occurs in case 2 with the smallest objective value. The relay settings are shown in Table 4. The optimum relay settings can protect the system with fastest fault clearance time, maximum operation time margin and minimum number of constraint violations for all system conditions [13. Table 4 Optimum Protection Relay Settings Line

Phase Fault CSM I TM

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Earth Fault CSM I TM

a & ] . The mutation enabling matrix Pm&] is controlled by the Mutation Factor 0.1. The PmJk] is generate in each EA generation by comparing the Mutation Factor and random numbers. The larger population size also allow more sets of protection settings survives in. each generation and the divergent effect is reflected on the maximum objective values in Fig 3, 4, 5 and 6. The divergent effect should be limited and specific to the problem. In case 2, the divergent effect is the minimum. V. CONCLUSION The Evolutionary Algorithm is successfully applied in the Time Coordination Method for protection setting coordination. The results show that the population size and the number of generations should be pre-determhate by several trials. The number of relays forms the problem domain and imposes the divergent effect, which can be suppressed by the selection of the correct population size. The future work would be the development on a method to find out the right population size and the number of generations automatically. VI. ACKNOWLEDGEMENTS The authors would like to thank the Hong Kong Polytechnic University for supporting the research and publishing this work.

VII. The population size is the number of sets of relay settings in each generation to be processed. Obviously, a larger population size would use more computation power. Thus, case 1 is the fastest and the case 3 is the slowest. To examine the EA performance, all trails are recorded as shown in Fig. 3, 4, 5 and 6. Fig.3 shows the best, average and m a x i “ objective values recorded in each generation for the first 100 generations in case 1. From 21’‘ to 93“‘ generations, it is found that the best objective values are improved significantly. Beyond 93“ generations, the improvements becomes less significant. When all individuals are improved, the better relay settings is prepared by EA and stored in several sets of relay settings. Eventually, the new best relay settings are generated. This improvement is carrying on for the first 300 generations as shown in Fig 4. In Fig 4 , s and 6, the improvement becomes minimum, and the average and the best objective value becomes almost constant for the last 200 generations. Beyond 450 generations, the trend of improvement for both average and best objective values becomes flat. Typical effect also occurs in several other trials on the case. Therefore, 500 generations is selected to be the tetmination criteria. The Survival Size is controlled the tournament size and 10 is recommended by D.B. Fogel [SI. The Offset and Scale Factor is set to 0 and 0.9 and they control the step matrix

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REFERENCE

[11 C W So, K K Li, ‘Time Coordination Method for Power

[2]

[3]

[4] [5]

[6]

System Protection by Evolutionary Algorithm”, 1999 IEEE Industry Application society Annual Meeting, Phoenix Arizona, U.S.A., 3-7 October 1999, Session 53, paper no 53.4. R Salomon, “Evolutionary Algorithms and Gradient Search Similarities and Differences”, IEEE Transactions on Evolutionary Computation, Volume 2, July 1998, pp 45-55. C.W. So, K.K. Li, K.T. Lai, K.Y. Fung, “Overcurrent Relay Grading Coordination Using Genetic Algorithm”, IEE APSCOM-97 International Conference, Hong Kong, November 11-14,1997, Vol. 1, pp. 283-287. D.E. Goldberg, “Genetic Algorithm in Search, optimization and Machine Learning”, Addison-Wesley, Reading MA, 1989 D.B. Fogel, “An analysis of evolutionary programming”, Proc. of the First Cod. on Evolutionary Programming, Evolutionary Programming Society, La Jolla, CA, 1992, pp 43-5 1. C.W. So, K.K. Li, K.T. Lai, ICY. Fung, ‘Application of Genetic Algorithm for Overcurrent Relay Coordination’,IEE 6”’ Intemational Conference on Developments in Power System Protection, Nottingham, UK,March 1997, pp. 66-69

Fig 3 EA performance case lin the first 100 generations

Fig 5 EA performance for case 2

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