International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976
ISSN 0976 – 6553(Online) Volume 5, Issue...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print),
ISSN 0976 – 6553(Online) ...
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40220140505002

  1. 1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 8 GENETIC ALGORITHM APPROACH FOR THE OPTIMAL COORDINATION OF OVER CURRENT RELAYS ABSTRACT Operating times of over current relays can be greatly reduced and proper coordination can be obtained if a proper choice of Plug Setting (PS) and Time Setting Multiplier (TMS) is made. Over Current Relay (OCR) characteristic is inherently non-linear in nature. Classical Optimization methods such as steepest decant method, non-linear programming have limitations in searching for an absolutely optimal settings and sometimes get trapped in local optimal settings. This paper systematically exploits the Genetic Algorithms (GA) tool to solve this complex and non-convex optimization problem. Key Words: Genetic algorithm, optimal over current relay coordination, power system protection. I. INTRODUCTION Shunt fault is characterized by the sudden increase in current which is sensed by the overcurrent relays [1, 2]. Directional overcurrent relays have become the economic alternative to protect sub-transmission and distribution systems [3-5]. In a protection environment, each relay should get sufficient opportunity to protect the equipment which it is supposed to protect. In case the primary protection fails to clear the fault, the backup protection should be made to clear the fault. Both primary and backup protection must be properly coordinated for minimum disruption of power supply to the system. The basic objective of relay coordination is to avoid mal operation of relays which happens to be the major concern for power system protection [5, 6]. The problem of optimum coordination of OCRs is generally modelled as an LPP in which pick up value of currents (PS) of relays are assumed to be known and operating time of each relay is considered as a linear function of its TMS [5]. A. Sudha Dept of Electrical Engg., K. D. K. College of Engg., Nagpur, India Dr. R. M. Moharil Dept. of Electrical Engg., Yashwantrao Chavan College of Engg., Nagpur, India Dr. P. Devnani Dept of Electrical Engg., S. R. M. College of Engg., for Women, Nagpur, India INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME: www.iaeme.com/ijeet.asp Journal Impact Factor (2014): 6.8310 (Calculated by GISI) www.jifactor.com IJEET © I A E M E
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 9 In this paper, a comparative study has been made after carrying out optimal relay coordination using GA to two typical cases: PS fixed as a discrete integer and finding TMS, finding both PS and TMS with suitable modification in the mathematical model of the problem. II. PROBLEM FORMULATION The coordination problem of directional OCRs in a ring fed distribution system, can be seen as an optimization problem, where the sum of operating times of relays of the system is to be minimized [8-10] )1(min ,. 1 kii m i tWz ∑= = Where m is the number of relays, t i, k is the operating time of relay Ri, for a fault at k and Wi is the weight assigned for operating time of the relay Ri In distribution systems where the lines are short and are of equal length, equal weight (=1) is assigned for operating times of all relays [5, 6, 9, 11]. The objective function defined in (1) has to be minimized under the below mentioned five constraint sets. A. Constraint set I – Coordination Criteria Fault is sensed by primary as well as back up relay simultaneously. In order that the back-up relay does not mal-operate, primary relay has to be given sufficient time to act and clear the fault. And back up relay has to act in case the primary relay fails to operate. If Rj is the primary relay for fault at k, and Ri is the backup relay for the same fault, then the coordination constraint can be stated as )2(,, ttt kjki ∆≥− Where, t j, k is the operating time of primary relay Rj for a fault at k, t i,k is the operating time for backup relay Ri for the same fault and ∆t is the coordination time interval. B. Constraint set II – Relay characteristics Over current relays are named on the type of characteristic they tend to exhibit. However, OCRs are governed by the general characteristic given in equation (3) and the details of the nomenclature is as per the details mentioned in Table I [1,6,9,12,13,14]. Where, opt indicates the operating time of the relay, TMS indicates the time multiplier setting PS is the plug setting. I relay is the current seen by the relay. )3( 1)( )( − = γ λ PSI TMS t relay op
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 10 TABLE I VALUES OF λ AND γ FOR DIFFERENT TYPES OF OCR C. Constraint set III – Limits on the Relay Operating Time Constraint imposed due to the restriction on the operating time of relays can be mathematically stated as )4(max,,min, ikii ttt ≤≤ Where, t i, min is the minimum operating time of relay at location i, for fault at any point in the zone of operation t i, max is the maximum operating time of relay at location i, for fault at any point in the zone of operation D. Constraint set IV – Limits on the TMS of the Relays The limits on the TMS of relays can be stated as )5(max,min, iii TMSTMSTMS ≤≤ Where, TMS i, min is the minimum value of TMS of relay Ri TMS i, max is the maximum value of TMS of relay Ri TMS i, min and TMS i, max are 0.025, 1.2 respectively [12] E. Constraint set V – Limits on the PS of the Relays The limits on the PS of relays can be stated as )6(max,min, iii PSPSPS ≤≤ Where, PS i, min is the minimum value of PS of the relay Ri; PS i, max is the maximum value of PS of the relay Ri PS i, min and PS i, max are selected as the rule of thumb [12]; PS ≥ 1.25 times maximum load current and PS ≤ 0.67 times minimum fault current OCR type Λ Γ Instantaneous Operating time is fixed. No Intentional time delay can be introduced. Definite time Operating time is predefined but time delay can be introduced. Inverse definite minimum time 0.14 0.02 Very inverse 13.5 1 Extremely Inverse 80 2
  4. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 11 III. GENETIC ALGORITHM Genetic algorithm begins and ends like any other optimization technique. It starts with the definition of design variables and objective function. And it ends after testing for convergence. However, in between the algorithm is different [17]. In GA, the design variables are represented as strings of binary numbers. If each design variable x i, i = 1, 2,…, n is coded in string of length q, a design vector is represented using a string of total length of nq. This is achieved by placing the strings of all the variables side by side. Thus a chromosome is formed. GA essentially starts with a group of chromosomes called population. In numerical optimization using GA, basic operations of natural genetics like reproduction, crossover and mutation are applied. Reproduction is a process in which the individuals are selected based on their fitness values relative to that of the population. Individuals with higher fitness values are selected for mating and subsequent genetic action. After reproduction, crossover operation takes place. Crossover is a process of generating new set of chromosomes called offsprings from the parent chromosomes. The parents and the offsprings form a new population. Mutation is applied after crossover. Mutation is an occasional, random alteration of a binary digit in a string, The chromosome obtained after mutation is performed replaces original chromosome in the population. GA basically finds the optimum of an unconstrained problem [16], [19]. To solve a constrained optimization problem, we need to transform the original constrained problem into an unconstrained problem. Transformation methods are the simplest and the most popular optimization methods of handling constraints. The constraints can be included in the objective function with the help of penalty method [18]. IV. APPLICATION OF GA The flow chart of GA is given in Appendix A. From (3), it is clear that the objective function is of minimization type, a large number is taken as penalty. It is described by the following algorithm 1. Set penalty =10000 (a large number). 2. Set k = 1 (start with the first chromosome of the population. 3. Take kth chromosome. 4. Calculate the objective function for the kth chromosome. 5. n=1 6. If nth constraint is violated for the kth chromosome z(k) = z(k) + penalty 7. Set penalty =10000 (a large number). 8. Set k = 1 (start with the first chromosome of the population. 9. Take kth chromosome. 10. Calculate the objective function for the kth chromosome.
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 12 11. n=1 12. If nth constraint is violated for the kth chromosome, z(k) = z(k) + penalty 13. n=n+1 14. If n > number of constraints then go to step 9 or else go to step 6. 15. k=k+1 16. If k > population size then go to step 11 or else go to step 6. 17. Return objective function value for the chromosome. With this when the population is sorted according to the objective function, values of the chromosomes in the population, the chromosomes with higher value of objective function (for which one or more constraints are violated) go the bottom and are automatically discarded in the next iteration. V. IMPLEMENTATION OF THE ABOVE METHOD The problem is first converted into unconstrained optimization problem. As the objective function, coordination constraints and operating time constraints are written using relay characteristics (3), the relay characteristic constraint gets automatically incorporated in the objective function, coordination constraints and operating time constraints. The constraints due to bounds on TMS and PS, are taken care of by defining the lower and upper limit of variables representing TMS and PS of relays, respectively, in the GA program. The constraints due to operating time of relays, and the constraints due to coordination criteria, are included in the objective function using penalty method, thus the problem gets converted into a unconstrained optimization problem. Number of bits to represent each parameter is decided and then a population of suitable number of chromosomes is generated randomly. The value of variables in each chromosome is bounded by lower and upper limits as described above. After this, the generations (iterations) of GA are sorted. The population is passed through the fitness function (objective function). Then the population is sorted according to the fitness. As the objective function is of minimization type the chromosome giving minimum value is most fit chromosome. This chromosome has been treated as elite chromosome in the paper. The proposed method was tested for several systems and one illustration is presented here in this paper. The chromosomes with higher fitness value survive and are called parent chromosomes. These are used for mating. Pairs of parent chromosomes are made for mating. Using the pairs of parent chromosome, crossover is performed. For each pair the crossover site is selected randomly. One pair (two parent chromosomes) generates two offsprings after crossover. All the parent chromosomes and all offsprings are placed together to form the population for the next generations. The population for all generations is maintained the same. Mutation is applied after crossover. The number of mutations to be performed is decided by mutation rate which is one of the GA parameters to be supplied at the beginning of the program. For each mutation the chromosome is selected randomly. The bit to be mutated is again selected randomly.
  6. 6. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. At this point, an iteration of GA is complete. criteria in this paper and hence the chromosome that results at the end of stopping gives the result. VI. ILLUSTRATIONS Fig. 1: Single line diagram of a 6 bus, 7 line system Fig. 1 shows a test system having 6 transformers. It is a 150 kv, 100 MVA system. sec. The CTI is assumed to be 0.4 sec analysis. The constraints due to bounds on TMS were taken care by defining the lower and the upper limits of the variables x 1 to x 14. The constraints due to bounds on PS were taken care by defining the lower and the upper limits of the variables TMS of OCRs 1 to 14 and x 15 to x 28 The objective function formed by (1) and (3 1)/( 14.0 min 02.0 24 24 1 − = += ∑ irelay i i xI x z I relay is the current seen by the relay under consideration. Coordination constraints were formed by (2) and (3), and relay operating time constraints were formed by (2) and (4). The constraints due to bounds on TMS and PS of relays were formed using (5) and (6), respectively. Line between Buses B1 – B2 B1 – B3 B3 – B4 B4 – B5 B5 – B6 B6 – B2 B6 – B1 Electrical Engineering and Technology (IJEET), ISSN 0976 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 13 At this point, an iteration of GA is complete. Number of iterations is used as the stopping in this paper and hence the chromosome that results at the end of stopping gives the result. Single line diagram of a 6 bus, 7 line system a test system having 6 buses, 7 lines with 14 OCRs, two generators and two . It is a 150 kv, 100 MVA system. The minimum operating time of relay is taken as 0.2 CTI is assumed to be 0.4 sec. The currents seen by the relays were obtained by short circuit onstraints due to bounds on TMS were taken care by defining the lower and the upper . The constraints due to bounds on PS were taken care by defining the lower and the upper limits of the variables x 15 to x 28. i.e. x 1 to x 14 were taken to represent the 28 were taken to represent the PS of the OCRs 1 to 14. ve function formed by (1) and (3) is: )7( 1 is the current seen by the relay under consideration. Coordination constraints were formed by (2) and (3), and relay operating time constraints were formed by (2) and (4). The constraints due to bounds on TMS and PS of relays were formed TABLE II LINE DATA Line between Buses R (pu) X (pu) V (kV) B2 0.0018 0.0222 150 B3 0.0018 0.0222 150 B4 0.0018 0.02 150 B5 0.0022 0.02 150 B6 0.0022 0.02 150 B2 0.0018 0.02 150 B1 0.0022 0.0222 150 B4 Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), used as the stopping in this paper and hence the chromosome that results at the end of stopping gives the result. , two generators and two The minimum operating time of relay is taken as 0.2 obtained by short circuit onstraints due to bounds on TMS were taken care by defining the lower and the upper . The constraints due to bounds on PS were taken care by defining the were taken to represent the were taken to represent the PS of the OCRs 1 to 14. Coordination constraints were formed by (2) and (3), and relay operating time constraints were formed by (2) and (4). The constraints due to bounds on TMS and PS of relays were formed
  7. 7. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 14 TABLE III LOAD CURRENT AND CT DATA Relay Number Load Current (A) CT ratio (A/A) Relay Number Load Current (A) CT ratio (A/A) 1 104 150:1 8 109 150:1 2 166 200:1 9 118 150:1 3 125 150:1 10 110 150:1 4 180 250:1 11 135 200:1 5 129 150:1 12 122 150:1 6 114 150:1 13 125 150:1 7 141 200:1 14 166 200:1 TABLE IV PRIMARY AND BACKUP RELAY PAIRS AND FAULT CURRENTS P/B relays Fault currents (A) Primary Relay Backup Relay Primary Relay Backup Relay 1 6 2682 2682 2 1 5428 828 2 7 5428 1571 3 2 3505 3505 4 3 1769 1769 5 4 1103 1103 6 5 4936 340 6 14 4936 1565 7 5 4184 337 7 13 4184 816 8 7 4933 1563 8 9 4939 640 9 10 1174 1174 10 11 2589 2589 11 12 3655 3655 12 13 5431 828 12 14 5431 1573 13 8 2492 2492 14 1 4184 816 14 9 4184 337 Table II, Table III and Table IV give the line data, load current data and the fault currents as obtained from the short circuit analysis respectively.
  8. 8. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 15 VII. RESULTS AND DISCUSSIONS TABLE V RESULTS OBTAINED BY NLP AND GA METHODS Relay No Conventional method Modified GA PS TMS PS TMS 1 0.5 0.29 0.512 0.3043 2 1.25 0.31 1.228 0.2917 3 1.25 0.26 1.324 0.2543 4 1.25 0.19 1.243 0.1851 5 0.75 0.18 0.612 0.1700 6 1.25 0.26 1.122 0.2711 7 0.75 0.54 0.325 0.5316 8 0.75 0.24 1.149 0.2387 9 1.0 0.17 0.436 0.1865 10 1.25 0.19 1.015 0.1895 11 1.25 0.21 1.345 0.2014 12 1.25 0.3 0.989 0.2890 13 0.75 0.23 0.302 0.2207 14 0.25 0.51 0.233 0.5278 O.F 17.38 15.69 The problem of relay coordination was solved in a conventional manner as a constrained non linear programming problem using the function available in MATLAB and the results are tabulated in Table V. Later the same problem is solved using a modified objective function developed as in (7) for GA. GA parameters used are as follows: Population size is 256, No. of bits per parameter is 8, Crossover rate is 0.5 (50%), Mutation is 0.1(10%)
  9. 9. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 16 The results obtained are also tabulated in Table V. The objective function obtained in modified GA is less compared to the conventional NLP approach. Table VI gives the operating time of back up and primary relays for a typical near end fault and it is seen that the coordination constraint is met in all the cases. No constraint is violated and the objective function which is the total operating time is less than in the modified method. TABLE VI OPERATING TIME OF BACKUP AND PRIMARY RELAYS FOR NEAR END FAULTS Back Up relay Primary Relay Relay No. Operation Time (Sec) Relay No. Operation Time (Sec) 6 1.121 1 0.817 1 1.017 2 0.718 7 0.948 2 0.659 2 1.033 3 0.768 3 1.033 4 0.923 4 1.069 5 0.89 5 1.036 6 0.914 14 0.956 6 0.664 5 1.031 7 0.664 13 1.088 7 0.784 7 1.057 8 0.768 9 1.057 8 0.884 VIII. CONCLUSION In this paper, a novel method of applying GA to relay coordination problem has been developed. A systematic procedure for formulation of the problem as an optimization problem has been proposed. Firstly the problem is solved as a constrained NLPP in this paper. The constraints were included in the objective function and then solved using GA. The algorithm is tested on several systems and one illustration is presented. The results obtained were found satisfactory. The proposed method can be applied to any system easily.
  10. 10. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 17 APPENDIX A Yes Yes Select bit position for mutation, complement the bit, m = m + 1 No Fig. 2: Flowchart of genetic algorithm No Define test function Enter the number of Parameters Enter the Number of iterations “n” Define GA Parameters Create initial population Iter = 1 Evaluate the cost for each chromosome Sort the cost & associated parameters Is iter > n Form pairs for mating & Set k= 1 Pick up kth pair for mating Select crossover site Perform crossover, k =k + 1 Is k > n pair Select chromosome for mutation Is selected chromosome elite Is m > nmut iter = iter + 1 m = 1 Display Output Stop Yes No Yes Start
  11. 11. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 5, May (2014), pp. 08-18 © IAEME 18 REFERENCES [1] A. S. Noghabi, H. R. Mashhadi, and J. Sadeh, “Optimal Coordination of Directional Overcurrent Relays Considering Different Network Topologies in Using Interval Linear Programming”, IEEE Trans. On Power Delivery, Vol 25, July 2010, pp 1348-1354. [2] P. P. Bedekar, S. R. bhide, “Optimum Coordination of Directional Overcurrent Relays using the Hybrid GA-NLP Approach”, IEEE Trans. On power Delivery, Vol 26, January 2011, pp. 109-119. [3] A. S. Noghabi, J. Sadeh,and H. R. Mashhadi, “Considering Different Network Topologies in Optimal Relay Coordination Using a Hybrid GA”, IEEE Trans. On Power Delivery, Vol 24,October 2009, pp 1857-1863. [4] B.Chattopadhyay, M.S.Sachdev, and T.S.Sidhu, “An online relay coordination algorithm for adaptive protection using linear programming technique,” IEEE Trans.on Power Deiveryl, vol. 11, no. 1, Jan 1996, pp.165-173. [5] P. P. Bedekar, S. R. Bhide, and V. S. Kale, “Optimm Time Coordination of Overcurrent Relays in Distribution System Using Big-M (Penalty) Method”, WSEAS Transactions on Power System, Vol. 4, Issue 11, November 2009, pp. 341-350. [6] A.J.Urdaneta, H.Restrepro, S. Marquez and J.Sanchez, “Optimal coordination of directional overcurrent relays in interconnected power systems,” IEEE Trans.Power Del., vol. 3, no. 3 July 1988, pp.903– 911. [7] H. Zeienldin, El-Saadany, and M. A. Salama, “A novel problem formulation for directional over current relay coordination,” Large Engineering Systems Conference on Power Engineering July 2004 (LEECOPE-04),pp-48-52, Halifax, Canada, 48-52. [8] A.J.Urdaneta, H.Restrepro, S. Marquez and J.Sanchez, “Coordination of directional overcurrent relay timing using linear programming” IEEE Trans.Power Del., vol. 11, no. 1, Jan. 1996, pp.122-129. [9] H. K. Karegar, H. A. Abyaneh, V. Ohis, and M. Meshkin, “Pre-processing of the optimal Coordination of Overcurrent Relays”, Electric Power System Research, Vol 75, 2005, pp. 134-141. [10] S. A. Soman, “Lectures on Power System Protection,” available at www.cdeep.iitb.ac.in/NPTEL, module 4 & 5. [11] C. W. So and K. K. Li , “Overcurrent Relay Coordination by Evolutionary Programming ”, Electric Power System Search, Vol 53, 2000, pp. 83-90. [12] So C.W. and Li K.K., “Time Coordination Method for Power System Protection by Evolutionary Algorithm”, IEEE Transactions on Industry Application”, Vol -36, No.-5, September-October 2000, pp. 1235-1240. [13] Y. G. Paithankar, and S. R. Bhide, Fundamentals of Power System Protection, 2nd edition”, Printice- Hall of India Pvt Ltd., New Delhi, 2010. [14] J. J. Blackburn, Protective Relaying: Principles and Applications, 2nd edition”, Marcel Dekker, Inc., New York. [15] P. Shankara Iyer, Operations Research, Tata McGraw Hill Publishing Company Limited, New Delhi, 2009. [16] D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning, New Delhi, India: Dorling Kindersley (Indai) Pvt. Ltd., 2008. [17] R. L. Haupt and S. E. Haupt, Practical Genetic Algorithm, 2nd ed. Hoboken, NJ:Wiley,2004. [18] K. Deb, Optimization for Engineering Design – Algorithms and Examples, New Delhi, Indian Prentice Hall of India Pvt. Ltd., 2006. [19] S.S. Rao, Engineering Optimization – Theory and Practice, 3rd ed. New Delhi, India: New Age International Pvt. Ltd. 1998. [20] MATLAB optimization Toolbox. [22] Dr.T.Ananthapadmanabha, H Pradeepa, Likith Kumar. M. V, Maruthi Prasanna.H.A., Veeresha.A.G. and Pradeep N, “Optimal DG Placement using Multiobjective Index and its Effect on Stability and Field Relays”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2013, pp. 202 - 218, ISSN Print : 0976-6545, ISSN Online: 0976-6553. [21] Prachi R. Shinde, Madhura Gad and Prof. S.U. Kulkarni, “Genetic Algorithm Approach into Relay Co-Ordination”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 3, 2013, pp. 35 - 42, ISSN Print : 0976-6545, ISSN Online: 0976-6553.

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