Modified Invasive Weed Optimization with Dual Mutation Technique for Dynamic Economic Dispatch Essay Example

Modified Invasive Weed Optimization with Dual Mutation Technique for Dynamic Economic Dispatch Essay Dynamic economic dispatch (DED) is one of the main functions of power system operation and control. It determines the optimal operation of units with predicted load demands over a certain period of time with an objective to minimize total production cost while the system is operating within its ramp rate limits.This paper presents DED based on Invasive Weed Optimization (IWO) technique for the determination of the global or near global optimum dispatch solution. In the present case, load balance constraints, operating limits, valve-point loading, ramp constraints, and network losses using loss coefficients are incorporated. Numerical results for a sample test system (10- unit) have been presented to demonstrate the performance and applicability of the proposed method. Index Terms dynamic economic dispatch, invasive weed optimization algorithm, non-smooth cost function, valvepoint effect.I. INTRODUCTION NE of the most important aspects of power system operation is its obligation to su pply power to the customers economically [1]. Power system economic load dispatch is the process of allocating generation among the available generating units subject to load and other operational constraints such that the cost of operation is minimum [2], [3]. And now a day’s quality requirements of power utilities are so severe, that the operators have to sort out possible means of minimizing the production cost so as to offer the most competitive price to its customers.This has led to the adoption of system models and other operational constraints more analogous to real life situations. Traditional optimization techniques can never accurately model the system according to mathematical solutions [4],[5]. To solve the DED problem, it is assumed that a thermal unit commitment has been *Corresponding Author Renu Sharma is with Dept of ICE, Siksha ‘O’ Anusandhan University1, Bhubaneswar, Orissa, 751030 INDIA(e-mail: [emailprotected] com) Niranjan Nayak is with Elec trical Engg Dept, Siksha ‘O’ Anusandhan University1,Bhubaneswar,Orissa,751030INDIA(e-mail: iranjannayak. el. [emailprotected] com) Krishnanand K. R is with MDRC, Siksha ‘O’ Anusandhan University1, Bhubaneswar, Orissa, 751030 INDIA(e-mail: [emailprotected] com), P. K. Rout is with Dept of EEE, Siksha ‘O’ Anusandhan University1, Bhubaneswar, Orissa, 751030 INDIA(e-mail: [emailprotected] com), O 978-1-4673-0136-7/11/$26. 00  ©2011 IEEE previously determined [6]. DED considers the constraints imposed on the systems by the generator ramp rate limits because mathematically DED is considered as second–order dynamic optimization problem [6].To extend the life of equipments, the gradients for temperature and pressure inside the boiler and turbine should be kept within the limit. This mechanical constraint is transformed into a limit on the rate of increase or decrease of electrical power output . This limit is called ramp rate limit which disti nguishes DED from static economic dispatch problem [7]. The DED can be solved by dividing the total load dispatch period into a number of small intervals, during that period load demand is assumed to be constant, and the system is considered to be time invariant for that period.Traditional approach of a DED with N units and T time intervals would require the solution of an optimization problem of size N? T— a considerably more complex task. Recently, hybrid EPsequential quadratic programming (SQP) [6], deterministically guided PSO [8], and hybrid PSO-SQP [9] methods were proposed to solve the DED problem with non-smooth fuel cost functions. Simulated Annealing (SA) [10] has also been employed for the solution of the DED problem.The DED problem becomes heavily constrained as these utilize the traditional approach of a DED, in which power generation is coordinated for the entire dispatch period. Differential Evolution (DE) is also applied to solve these DED problems [11]. It is also a stochastic method to solve multi dimensional problems to find the global optimum value. The Invasive Weed Optimization technique [12] is a stochastic optimization method that is based on the simulation of production, mutation and spatial propagation of weeds. The philosophy behind the technique is justified by the fact that eeds exhibit uncanny adaptability and persistence in reproduction despite imposition of adverse conditions, including many methods to destroy them. It applies the seeding and mutation of the parent plant with varying the standard deviation keeping the mean at the parent plant. The dual mutation presented in this paper removes the monotony of the conventional weed optimization algorithm and causes multiple mutation distributions to contribute to the variety of the seeds produced in parallel in a particular iteration step.This causes the algorithm to search for global optimum through the hyperspace created by the problem at hand more stochastically. Even th e selection of the mutation process for a particular plant at a particular iteration has been randomized to overcome the demerit of single distribution method used in conventional IWO. The proposed time-varying process of mutation is such that there is very less chance of missing the global optimum value for high dimensional problems and also make searching very fast. A high dimensional problem, in hich each parameter has a different impact numerically on the total output of the system, is not vulnerable to yielding solutions easily to an algorithm that follows a definite distribution. So, a dual mutation technique can yield better solutions than a single one for problems like DED. instantaneous. However, under practical circumstances ramp rate limit restricts the operating range of all the online units for adjusting the generator operation between two operating periods. The generation may increase or decrease with corresponding upper and downward ramp rate limits.So, units are cons trained due to these ramp rate limits as mentioned below. If power generation increases, P ih Ph i 1 (7) If power generation decreases, A. Problem formulation (8) P h 1 P d DRi i ih The objective function corresponding to the production cost where P h-1 is the power generation of unit i at previous hour i can be approximated to be a quadratic function of the active and UR and DR are the upper and lower ramp rate limits i i power outputs from the generating units. Symbolically, it is respectively.The inclusion of ramp rate limits modifies the represented as generator operation constraints (6) as follows. Minimize Fc where II. FORMULATION OF THE PROBLEM d URi  ¦Ã‚ ¦ F k 1 i 1 T NG ih (Pih ) $ (1) Fi h (Pi h ) a i Pi2h bi Pi h ci , i 1,2,3, , NG (2) dispatch. The cost function for unit with valve point loading effect is calculated by using is the expression for cost function Fi h (Pi h ) a i Pi2h b i Pi h c i e i sin f i h Pimin h Pi h (3) Where ei and fi are the cost coefficients c orresponding to valve point oading effect. Due to the valve point loading the solution may be trapped in the local minima and it also increases the non-linearity in the system. This constrained DED problem is subjected to a variety of constraints depending upon assumptions and practical implications. These include power balance constraints to take into account the energy balance; ramp rate limits to incorporate dynamic nature of DED problem and prohibited operating zones. These constraints are discussed as under. A. )Power Balance Constraints or Demand Constraints: This constraint is based on the principle of equilibrium between total system generation (? ) and total system loads (PD) and losses (PL). That is,  ¦P i 1 NG ih P Dh P Lh (4) where PLh is obtained using B- coefficients, given by PLh  ¦Ã‚ ¦ P B P ih ij i 1 j 1 NG NG jh (5) A. 2)The Generator Constraints: The output power of each generating unit has a lower and upper bound so that it lies in between these bounds. This constraint is represented by a pair of inequality constraints as follows: Pi min d Pih d Pi max 6) where, Pimin and Pimax are lower and upper bounds for power outputs of the ith generating unit in MW. A. 3) The Ramp Rate Limits: One of unpractical assumption that prevailed for simplifying the problem in many of the earlier research is that the adjustments of the power output are max( , ? ) ? min( , ? ) (9) A. 4) Fitness Function To evaluate the fitness of each individual in the population in order to minimize the fuel costs while satisfying unit and system constraints, the following fitness-function model is adopted for simulation in this article: ?F (P ) + ? ? ? P ? f =? 2 2 ? P ? P P . +? ? (10) . . . where ? and ? are penalty parameters. The penalty term reflects the violation of the equality constraint and assigns a high cost of penalty function. The Prlim is defined by P ( ) ? DR , P lt; P ( ) ? DR P ( ) + UR , P gt; P ( ) + UR P = P , otherwise (11) III MODIFIED INVASIVE WEED OPTIMIZATION Invasive Weed Optimization is a numerical stochastic search algorithm simulating the natural behaviour of weed colonizing in search domains for optimization of mathematically modeled systems.Adapting with their environments, invasive weed cover spaces of opportunity left behind by improper tillage; followed by enduring occupation of the field. They reproduce rapidly by making seeds and raise their population. Their behaviour changes with time as the colony become dense leaving lesser opportunity of life for the ones with lesser fitness. B. Details about the algorithm: B. 1 Initialization A random initial population is being dispersed over the D dimensional problem space uniformly within the lower and the upper limit which is considered as the initial solution.B. 2 Reproduction A potential solution represented by a row vector in the population of weeds (represented by the whole matrix) is allowed to produce seeds depending on its own fitness as compared to the lowest and highest fitness in the population at that iteration point. The number of seeds shows linear increase in production from minimum possible seed production to its maximum being a function of the fitness of the plant. So, a plant will produce seeds based on its fitness, the colonys lowest fitness and highest which increases linearly as shown in the figure 1. Fig. Reproduction of seeds in proposed invasive weed optimization algorithm nonlinear modulation index. ?initial(k) and ? final(k) are initial and final standard deviations respectively. The conventional IWO follows a singular mutation process. The mutated plants are obtained from parent plants which act as the mean of the normal distribution. ?m M ? ,? t (15) The equation describing this behavior is: ?plant ?min  § ? ceil ? ? plant u max ? ? max  © ?min ? min  · ? ? ? (12) where ? min and ? max are the set values for minimum and maximum number of seeds which can be produced, respectively. ?min and ? ax are the minimum and ma ximum of the objective function values for a particular set of population for a given iteration, respectively. ?plant is the number of seeds to be produced for a given plant whose objective function value is ? plant. This makes the procedure to concentrate on the highest fitness values in the search domain and hence increases convergence towards the group best value. The fittest weeds survive and reproduce in the next generation whereas the worst ones are eliminated from the growth process. B. 3 Spatial Dispersal Randomness and adaptation in the algorithm is provided in this part.The generated seeds are being randomly distributed over the D dimensional search space by normally distributed random numbers with mean equal to zero; but varying variance. The well-known normal distribution has a probability density function which can be represented as (x ? )2 where ? mis the mutated plant, ? is a random number which follows normal distribution with mean as ? and standard deviations as in the set of ? t. In this modified Invasive Weed algorithm, the mutation follows a dual strategy. The mutation strategy is selected randomly using a uniform random variable.A mutation process selection factor (Pm) is used to bias the mutation towards a particular distribution. For mutation of the seed, the parent weed of that seed itself is the mean for the normal distribution and the standard deviation of the random function used is given by ? t(k) which is time-varying with respect to time step t. The seeds (or vectors) that satisfy the selection using Pm undergo either the simple Gaussian mutation or they are mutated by a shifted and scaled Gaussian mutation operation. This operation gives a parallel probable search strategy to the algorithm.The mutated seeds produced by both the methods carry out parallel search in the D dimensional search space following their respective probabilistic mutation distributions. ?m ( 1 ? t )? ?M(? t )? t? (16) y f ( x) e 2? ? 2? 2 (13) where x is the random variable,  µ is the mean and ? is the standard deviation. This means that seeds will be randomly distributed such that they abode near to the parent plant which results in a thorough search around the parental domain. However, standard deviation (? ), of the random function will be reduced from a previously defined initial value, ? initial, to a final value, ? inal, for each variable in every generation as the procedure converges to the best fitness value. For each variable in the kth position of the weed, standard deviation is given by ? t(k) (itermax t)n (itermax )n (? initial(k) ? final(k) ) ? final(k) (14) where itermax is the maximum number of iterations, ? t(k) is the standard deviation at the present time step (t) and n is the where ? m is the mutated seed, ? is the original seed of the parent weed , ? is the scaling factor and ? is a random number which follows normal distribution with mean as zero and standard deviations as in the set of ? . The shifting and scali ng being dependent on the number of iterations completed makes the algorithm more explorative in the beginning of the iteration. This implies that the mutated seed dispersion is well spread all across the D dimensional space limited by ? min and ? max in the beginning. Later, as the iteration progresses, the standard deviation value gradually decreases and the algorithm becomes more exploitative in nature, thereby making maximum use of the existing superior solutions for local search. The seeds are now considered as grown weed plants which have undergone mutation.B. 4 Selection If the plant produce inferior seeds, then it would not survive, otherwise the seeds which are superior among their population, can cover a large area in huge numbers. Thus, there is a need of some kind of competition between plants for limiting maximum number of plants in a colony for practical implementation of the algorithm in a machine with limited memory. After passing a few iterations, the number of plan ts in a colony will reach its maximum by fast reproduction, however, it is expected that the fitter plants have been reproduced more than undesirable plants.By reaching the maximum number of plants in the colony, Pmax, a mechanism for eliminating the plants with poor fitness in the generation is applied. When the maximum number of weeds in a colony is reached, each weed is allowed to produce seed as mentioned in reproduction. The produced seeds are then allowed to spread over the search area. When all seeds have found their position in the search area they are ranked together with their parents (as a colony of weeds). Next, weeds with lower fitness are eliminated to reach the maximum allowable population in a colony.In this way, plants and offspring are ranked together and the ones with better fitness survive and are allowed to replicate. This mechanism gives a chance to the plants with lower fitness to reproduce, and if their offspring has a good fitness in the colony then they can survive. The population control mechanism also is applied to their offspring to the end of a given run, realizing competitive exclusion and better selection. C. Invasive Weed Optimization for solving DED problem The IWO algorithm applied for solving the DED problem is summarized below: C. Generation of initial Condition: Within the range specified for each generating unit, initial conditions have to be generated randomly. In the DED problem, the initial population is the initial random real power outputs of the generators. The population is denoted as Pik, where N is the total number of generating units (i = 1,2,†¦N) and k shows the time intervals (in hours) (k = 1,2†¦. 24). A single potential schedule can be denoted as: Potential Schedule PN ,1 ? (17)  »  » P , k PN , k  » i  »  » P ,24 PN ,24  » i ?A single schedule can be passed to the objective function to estimate the cost per day using the mathematical input-output relations of the system. To ac commodate each schedule as a row vector in the population, the schedules are reshaped as row vectors and a population of such row vectors is formed as given below. Population P ,1 i 1 1 1 ? P 11 PN ,1 P 1k PN , k P 124 PN , 24 ? 1, 1, 1,  »  «  »  « r r r  « P ,r1 PN ,1 P ,rk PN , k P ,r24 PN , 24  » 1 1 1  »  «  »  «  « P NP P NP P NP P NP P NP P NP  » 1,1 1, k 1, 24 N ,1 N ,k N , 24 ?  ¬ (18) where NP is the population size (r = 1, 2, †¦, NP). After generating initial population each individual (each row) is evaluated by passing to the fitness function and the cost is calculated. C. 2 Reproduction: After calculating the cost of each individual, the individual (the row) which gives the minimum cost and satisfies all the constraints is selected as the best individual. The individual having the highest objective value including the penalties is considered as the most inferior solution.Then a linear slope is computed accordin g to which the plants in the population reproduce. The individual giving less cost will reproduce more and the individual giving high cost will reproduce less. C. 3Mutation and dispersal: The feasible solutions for the generating units are mutated using the probabilistic dual mutation so that the new generating units will satisfy all the constraints and get the least cost. The mutation is done according to the time-varying standard deviation. The mutation process should be such that the new generating unit should not deviate much from the parent. C. Evaluation of each plant: Each individual or plant in the population is evaluated using the fitness function of the problem to minimize the fuel-cost function. The automatic satisfaction of power balance constraint is attempted by allocating the biggest generator the mismatched power. This step is applied only when the loss coefficients are not considered. In case of transmission losses, the loss itself being a function of generated powe r cannot be used easily to find the mismatched power. Equation (10) is used to evaluate the schedule inclusive of penalty for each schedule in the population.C. 5Termination Criteria: When the iterations are completed, the program is terminated and the best dispatch schedule is stored which satisfies all the constraints. IV SIMULATION RESULTS AND DISCUSSIONS Here the IWO technique is applied to solve the DED for 10 unit system to validate the effectiveness of the algorithm. The experiment is carried out on a computer having Intel Core 2 Duo processor with 3 GHz clock-speed and 3GB RAM. The simulation software used for this purpose was MATLAB 7. 7. The data for the simulation of DED problem was taken from [13].The proposed IWO algorithm uses 8 control parameters like initial population size, maximum seed population, minimum seed population, modulation index(n), mutation process selection factor (Pm), initial standard deviation , final standard deviation and number of generations. By taking 25 trials, the best solution obtained for the problem is compared with the recently reported best results. The parameters taken for the IWO algorithms are: Initial population size(NP) = 20, maximum seed population(? max) = 10, minimum seed population(? in) = 4, modulation index(n) = 3, mutation process selection factor (Pm)= 0. 5, initial standard deviation(? initial) = 5, final standard deviation(? final) = 10-2 and number of generations(itermax)= 1000. Problem : Ten Unit System The 10 unit DED is done using this method to validate the effectiveness of the algorithm. The results are compared with the results given in [14]. The data for this is taken as given in [13]. The dispatch horizon is chosen as one day with 24 intervals. The parameters taken for this problem are P = 20, Max_P = 10, Min_P = 4, NG = 1000.The DED problem of the ten-unit system is solved by the proposed method in order to compare the results of the proposed method with Artificial Immune System (AIS) optimi zation as reported in the literature [14]. The load demand of the system is divided in the 24 intervals. The system data for the ten-unit system is taken from [13]. The simulation results are tabulated in Table 1. Table 2 provides comparison of the optimal system costs obtained from ?P 1,1  «  «  «Pk 1,  «  «  «P  ¬ 1,24 cost value $/h different methods. The convergence curve for the best solution of proposed IWO approach is shown in Fig 2.For the scalability of the problem the loss component B is taken into account and hence the equality constraint becomes more difficult to handle. The total time interval is divided into 24 hours and load pattern is taken according to that. The minimum total fuel cost obtained by the proposed method is 2,519,528$/24 hr compare to the best result so far by AIS as 2,519,700 $/24 hour with a difference of saving 172. 0 $/24 hr. generation schedule which results in lower generating cost per day. . x 10 7 7 6 IWO Convergence curve 5 4V C ONCLUSION 3 Dynamic Economic Dispatch is a complex optimization problem whose importance may increase as competition in 2 power generation intensifies due to deregulated power markets. This paper introduces a new modified IWO method 1 for the ramp rate limits and valve-point effect constrained 0 DED problem solution. The modified invasive optimization 0 500 1000 1500 2000 2500 3000 3500 4000 4500 No. of iterations implements dual probabilistic mutation and achieves better optimization by stochastically covering the hyperspace to Fig. 2. Simulation result of 10-generators system search.The comparisons of the results with other published techniques are reported in the literature. The results clearly indicate the superiority of the proposed technique in obtaining Table 1. Best solution of the proposed method Hours 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 P1(MW) 150. 4915 151. 0248 155. 2633 159. 7511 153. 4732 153. 2182 204. 7939 195. 8612 272. 4122 297. 0429 319. 9452 385. 5101 313. 0808 234. 2543 184. 2666 151. 6680 154. 6041 162. 0087 240. 4552 310. 5014 258. 4640 181. 6952 150. 3830 150. 2623 P2(MW) 135. 1026 135. 0950 143. 0757 144. 3443 140. 9293 175. 776 174. 3308 252. 7589 326. 0599 399. 7379 469. 1870 464. 6516 428. 3641 355. 0360 279. 4530 202. 1231 140. 3212 186. 1483 255. 0652 330. 0797 318. 5077 241. 5924 174. 7700 136. 0135 P3(MW) 150. 2901 177. 6299 251. 5504 311. 8992 281. 3345 333. 7739 336. 7093 338. 2089 338. 9737 336. 7214 338. 6820 337. 5278 339. 1240 339. 9914 339. 9695 306. 4620 283. 4979 304. 0022 311. 6329 339. 9473 338. 8327 259. 7133 228. 2250 153. 5858 P4(MW) 98. 7395 111. 1656 156. 9066 199. 1548 249. 0843 283. 4221 291. 9328 298. 8934 298. 1071 299. 6439 299. 3690 294. 7837 295. 8531 295. 9855 295. 8928 281. 926 261. 6619 288. 1384 299. 1992 291. 5209 299. 9920 260. 7732 246. 8937 240. 0228 P5(MW) 121. 4557 169. 9773 179. 2562 188. 7567 227. 5455 225. 7110 234. 1186 226. 3429 242. 6844 240. 9616 242. 9848 229. 4 335 240. 1859 227. 1472 242. 4442 240. 8853 235. 3062 235. 3486 231. 5476 242. 3394 242. 1989 237. 9403 189. 6318 140. 3746 P6(MW) 98. 3668 121. 7723 109. 5705 149. 3983 137. 0117 153. 2218 156. 2518 156. 3649 157. 5010 159. 0699 159. 4658 155. 8409 159. 8308 159. 9426 157. 2568 109. 0791 140. 0261 154. 0252 153. 5088 159. 2086 158. 2292 150. 6278 108. 5308 126. 6570 P7(MW) 101. 6669 125. 648 129. 1000 117. 4661 127. 3838 129. 4003 125. 2603 129. 1870 129. 8214 125. 5839 125. 6191 129. 6900 129. 8789 129. 2933 129. 9828 105. 1355 122. 7111 129. 9112 126. 4452 129. 0948 128. 3704 129. 7649 122. 1082 109. 8106 P8(MW) 81. 1441 61. 0316 76. 2356 83. 2820 98. 8998 105. 5534 119. 0414 104. 9613 118. 1167 119. 5519 116. 3985 119. 6392 116. 5446 119. 9611 93. 6535 118. 0159 90. 5640 112. 0406 106. 4538 115. 1262 119. 9239 105. 6221 83. 2299 72. 3638 P9(MW) 76. 6946 49. 8180 44. 1354 54. 6277 59. 9467 73. 0904 71. 2933 78. 4389 56. 4680 69. 5797 78. 5597 75. 6848 79. 8530 78. 4228 62. 935 51 . 3785 42. 2058 65. 9938 56. 7163 79. 6004 78. 6781 62. 4106 36. 7102 43. 8847 41. 7367 29. 8035 41. 7912 33. 3706 44. 0918 43. 3930 41. 7012 53. 9213 54. 8869 54. 1215 44. 2887 50. 5046 54. 0427 54. 9820 50. 0674 32. 3056 48. 8717 38. 8290 54. 3642 49. 8063 51. 5183 46. 9295 23. 9500 36. 4389 5000 P10(MW)) Table 2. Comparison of results for problem Total fuel cost ($/24hr) 2,519,528 2,519,700 2,572,200 2,585,400 Cost difference with proposed approach ($/24 hr) -172 52672 65872 [14] M. Basu, Artificial immune system for dynamic economic dispatch, Electrical Power and Energy Systems, vol. 3, pp. 131-136,2011. VII BIOGRAPHIES Prof. Renu Sharma received her BE in Electrical and Electronics from BIET,Davangere, Karnataka and MEE degree from the Jadavpur University, India in 1998 and in 2006 respectively. Presently, she is working as an Associate Professor and HOD in the ICE Department, ITER, Siksha ‘O’ Anusandhan University. She is pursuing her PhD in Power Systems and her field of interest includes Evolutionary Computation, Biomedical Instrumentation and Soft Computing Techniques Applied to Power System Optimisation. Prof Niranjan Nayak received his M. Tech. egree from VSSUT, Burla in the Power System Engg Presently, he is working as an Asst. Professor and in the Electrical Engg Department, ITER, Siksha ‘O’Anusandhan University. He ispursuing his PhD inControl Systems and his field of interest includes Soft Computing Application to Power System Control , Power Quality and Renewable Energy. Method Proposed IWO AIS [14] PSO[14] EP[14] VI REFERENCES [1]. K. P. Wong and Y. W. Wong, â€Å"Genetic and genetic/simulated-annealing approaches to economic dispatch,† IEE Proc. Gener. Transm. Distrib. , vol. 141, no. 5, September 1994. K. P. Wong and C.C. Fung, â€Å"Simulated annealing based economic dispatch algorithm,† IEE Proc. -C, vol. 140, no. 6, November 1993. W. G. Wood, â€Å"Spinning reserve constrained static and dynamic ec onomic dispatch,† IEEE Trans. PAS, pp. 381, February 1982. X. S. Han, H. B. Gooi and D. S. Kirschen,â€Å"Dynamic economic dispatch: Feasible and optimal solutions,† IEEE Trans. Power Systems, vol. 16, no. 1, pp. 22–28, February 2001. S. Kirkpatrick, G. D. Gelatt, Jr. , and M. P. 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Syst. , vol. 34, no. 5, pp. 577–586, May 2006. R. Balamurugan and S. Subramanian,â€Å"Differential Evolution-based Dynamic Economic Dispatch of Generating Units with Valve-point Effects†, Electric Power Components and Systems,vol. 36:pp. 828–843, 2008. A. R. Mehhrabian, C. Lucas, A novel numerical optimization algorithm inspired from weed colonization, Ecological Informatics, Elsevier Science, vol. , pp. 355-366, 2006. M. Basu, Dynamic economic emission dispatch using nondominated sorting genetic algorithm- II, Electrical Power and Energy Systems vol. 30 ,pp. 140-149, 2008. [2]. [3]. [4]. [5]. [6]. Krishnanand K. R. received h is BTech in Electrical and Electronics from the Biju Patnaik University of Technology and is currently working as a Senior Research Associate (SRA) in Siksha ‘O’ Anusandhan University. His field of interest includes Evolutionary Computation, Digital Protection, Power Quality and Application of Soft Computing Techniques to Power System Optimisation. 7] [8] [9] Dr(Prof)P. K. Rout received his ME degree from the Thiagarajar College of Engineering, Madurai, Tamilnadu, India in 1995 and PhD from the Biju Patnaik University of Technology, Rourkela, Orissa, India in 2010. Presently, he is working as a Professor and HOD in the Department of Electrical and Electronics Engineering, SOA University, Bhubaneswar, Orissa, India. His interests are in Soft Computing Applications to Power System Control, Power Quality and Renewable Energy. [10] [11] [12] [13]