عنوان مقاله [English]
In this paper, real-coded genetic algorithm with smart mutation (RCGA-SM) is proposed to solve the economic dispatch (ED) problem. In the proposed method, the required controlling process is accomplished on the total amount of chromosomes and consequently there is no need to use penalty cost function for controlling sum of variables in solving economic dispatch problem. This method will begin to explore the optimal answer just within the logic and acceptable zone in addition to its capability in reducing the search range. In order to show the performance and the efficiency of the proposed method, the ED problem considering several constraints is solved in 6, 15, and 40 units systems through the proposed technique. The proposed coding could effectively escapes from infeasible solutions. Thereby search efficiency and solution quality are dramatically improved. The obtained results are compared with other advanced technical algorithms, which well depicts the superiority of the RCGA-SM technique over the others compared methods.
 N. Ghorbani , S. Vakili, E. Babaei and A. Sakhavati, “Particle Swarm Optimization with Smart Inertia Factor for Solving Nonconvex Economic Load Dispatch Problems” Int. Trans. Electr. Energ. Syst. 24, pp. 1120–1133, 2014.
 Ghorbani, N., and Babaei, E., “Exchange market algorithm for economic load dispatch,” Electrical Power and Energy Systems, Vol. 75, pp. 19–27, 2016.
 Afzalan E, Joorabian M. Emission. reserve and economic load dispatch problem with non-smooth and non-convex cost functions using epsilon-multi-objective genetic algorithm variable. Electrical Power and Energy Systems Vol. 52, pp. 55-67, 2013.
 Sinha N, Chakrabarti R, Chattopadhyay PK. Evolutionary programming techniques for economic load dispatch. IEEE Trans EvolComput Vol. 7, No. 1, pp. 83–94, 2003.
 Secui, D. C.,“A new modified artificial bee colony algorithm for the economic dispatch problem,”Energy Conversion and Management, Vol. 89, pp. 43–62, 215.
 Abroa, A. G., and Mohamad-Saleh, G., “Enhanced probability-selection artificial bee colony algorithm for economic load dispatch, ” A comprehensive analysis, Engineering Optimization, Vol. 46, No. 10, pp. 1315-133, 2013.
 Arul, R., Ravi, G., and Velusami, S., “An improved harmony search algorithm to solve economic load dispatch problems with generator constraints,”Electr. Eng., Vol. 96, No.1, pp. 55-63, 2013.
 Arul R, Ravi G, Velusami S.“Non-convex economic dispatch with heuristic load patterns, valve point loading effect, prohibited operating zones, ramp-rate limits and spinning reserve constraints using harmony search algorithm,”Electr. Eng., Vol. 95, pp. 53-61, 2013.
 Srinivasa-Reddy, A., and Vaisakh, K., “Shuffled differential evolution for economic dispatch with valve point loading, ” effects. Elect. Power and Energy Syst., Vol. 46, pp. 342–52, 2013.
 Duvvuru N, Swarup KS. “A Hybrid Interior Point Assisted Differential Evolution Algorithm for Economic Dispatch. IEEE Trans. Power Syst., Vol. 26, No. 2, pp. 541-549, 2011.
 Abdullah, M. N., Abu-bakr A. H., Abd-rahim, N., and Mokhlis, H., “Modified Particle Swarm Optimization for Economic-Emission Load Dispatch of Power System Operation,”Turk J. Elec. Eng. & Comp. Sci., Vol. 23, pp. 2304-2318, 2015.
 Yuan, X., Ji, B., Zhang, SH., Tian, H., Chen, Z., “An improved artificial physical optimization algorithm for dynamic dispatch of generators with valve-point effects and wind power, ”Energy Conversion and Management, Vol. 82, pp. 92–105, 2014.
 Chaturvedi, K. T., Pandit, M., Srivastava, L., “Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch,”IEEE Trans. Power Syst., Vol. 23, No. 3, pp. 1079-87, 2008.
 Z. L. Gaing, Particle swarm optimization to solve the economic dispatch considering the generator constraints, IEEE Trans. Power Syst., Vol. 118, No. 3, pp. 1787-1195, 2003.
 Vlachogiannis, J. G., Lee, K. Y., “Closure to Discussion onEconomic load dispatch—A comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO,”Trans. Power Syst., Vol. 2, No. 1, pp. 591-592, 2010.
 Bhattacharya, A., Chattopadhyay, P. K., “Biogeography-based optimization for different economic load dispatch problems,”IEEE Trans. Power Syst., Vol. 25, No. 2, pp. 1064–1077, 2010.
 krishnasamy, U., Nanjundappan, D., “Hybrid weighted probabilistic neural network and biogeography-based optimization for dynamic economic dispatch of integrated multiple-fuel and wind power plants,”Electrical Power and Energy Systems, Vol. 77, pp. 385–394, 2016.
 Wu C, Lou Y, Lou P and Xiao H. DG location and capacity optimization considering several objectives with cloud theory adapted GA. Int Trans ElectrEnergSyst, Vol. 24, No. 8, pp. 1076–1088, 2014.
 Ghorbani, N., Babaei, E., “Exchange Market Algorithm. Applied Soft Computing, Vol. 19, pp. 177–187, 2014.
 J. B. Park, Y. W. Jeong, J. R. Shin and K. Y. Lee, An Improved Particle Swarm Optimization for Nonconvex Economic Dispatch Problems, IEEE Trans. Power Syst., Vol. 25, No. 1, pp. 156-166, 2010.
 I. G. Damousis, A. G. Bakirtzis, and P. S. Dokopoulos, Network-constrained economic dispatch using real-coded genetic algorithm, IEEE Trans. Power Syst., Vol. 18, No. 1, pp. 198–205, 2003.
 N. Amjady, H. Nasiri-Rad, Nonconvex economic dispatch with AC constraints by a new real coded genetic algorithm, IEEE Trans. Power Syst., Vol. 24, No. 3, pp. 1489–1502, 2009.
 I. Ciornei and E. Kyriakides, A GA-API Solution for the Economic Dispatch of Generation in Power System Operation, IEEE Trans. Power Syst., Vol. 27, No. 1, pp. 233-242, 2012.
 S .Pothiya, I. Ngamroo, W. Kongprawechnon, Ant colony optimization for economic dispatch problem with non-smooth cost functions, Int. J. Electr. Power Energy Syst., Vol. 32, No. 5, pp. 478–487, 2010.
 H. Lu, P. Sriyanyong, Y.H. Song, T. Dillon, Experimental study of a new hybrid PSO with mutation for economic dispatch with non-smoothcost function, Int. J. Electr. Power Energy Syst., Vol. 32, No. 9, pp. 921–935, 2010.
 K. T. Chaturvedi, M. Pandit, and L. Srivastava, Self-Organizing Hierarchical Particle Swarm Optimization for Nonconvex Economic Dispatch, IEEE Trans. Power Syst., Vol. 23, No. 3, pp. 1079-1087, 2008.
 J. G. Vlachogiannis and K. Y. Lee, Closure to Discussion onEconomic load dispatch—A comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO, IEEE Trans. Power Syst., Vol. 25, No. 1, pp. 591-592, 2010.
 A.Pereira-Neto, C. Unsihuay, O. R. Saavedra, Efficient evolutionary strategy optimization procedure to solve the nonconvex economic dispatch problem with generator constraints, IEE Proc. Gener. Transm. Distrib., V0l. 152, No. 5, pp. 653–660, 2005.
 B. K. Panigrahi, V. R. Pandi, Bacterial foraging optimisation: Nelder–Mead hybrid algorithm for economic load dispatch, IET Gener. Transm. Distrib., Vol. 2, No.4, pp. 556–565, 2008.
 K. Meng, H.G.Wang, Z.Y.Dong, K. P. Wong, Quantum-inspired particle swarm optimization for valve-point economic load dispatch, IEEE Trans. Power Syst., Vol. 25, No. 1, pp. 215–222, 2010.
 A. Bhattacharya, P. K. Chattopadhyay, “Hybrid differential evolution with biogeography-based optimization for solution of economic load dispatch,” IEEE Trans. Power Syst., Vol. 25, No. 4, pp. 1955-1964, 2010.
 J. S. Alsumait, J. K. Sykulski, A. K. Al-Othman, A hybrid GA–PS– SQP method to solve power system valve-point economic dispatch problems, Appl. Energy, Vol. 87, No. 5, pp. 1773–1781, 2010.
 Labbi Y, Attous D B,.Gabbar H, Mahdad B and Zidan A, A new rooted tree optimization algorithm for economic dispatch with valve-point effect, Electrical Power and Energy Systems, Vol. 79, pp. 298–311, 2016
 Dubey H M, Pandit M and Panigrahi B K, A Biologically Inspired Modified Flower Pollination Algorithm for Solving Economic Dispatch Problems in Modern Power Systems, Cognitive Computation, Vol. 7, No. 5, pp, 594-608, 2015.
 Hosseinnezhad V, Rafiee M, Ahmadian M, TaghiAmeli MT. Species-based quantum particle swarm optimization for economic load dispatch. Int J Electr Power Energy Syst. Vol. 63, pp. 311–22, 2014.