Abstract
Economic dispatch (ED) problem exhibits highly nonlinear characteristics, such as prohibited operating zone, ramp rate limits, and non-smooth property. Due to its nonlinear characteristics, it is hard to achieve the expected solution by the classical methods. To overcome the challenging difficulty, this paper proposes an improved firefly algorithm (FA) to solve economic dispatch (ED) problem. The improved FA employs two strategies to enhance the search ability and avoid the premature usually suffered from in standard FA. The first one is based on the distance information among the fireflies, and it adjusts the light absorption coefficient adaptively. The other one is a decreasing strategy for the randomization parameter. Additionally, a crossover operation is employed to create potential solution with high diversity. The designs are able to enhance the search ability and performance of FA, which have been demonstrated on six benchmark functions. To validate the proposed algorithm, we also use three different systems to demonstrate its efficiency and feasibility in solving ED problem. The experimental results show that the proposed FA method was capable of achieving higher quality solutions in ED problems.
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References
Victoire TAA, Jeyakumar AE (2004) Hybrid PSOSQP for economic dispatch with valve-point effect. Electr Power Syst Res 71(1):51–59
Merkle D, Middendorf M (2003) Ant colony optimization with global pheromone evaluation for scheduling a single machine. Appl Intell 18(1):105–111
Dodu JC, Martin P, Merlin A, Pouget J (1972) An optimal formulation and solution of short-range operating problems for a power system with flow constraints. Proc IEEE 60(1):54–63
Parikh J, Chattopadhyay D (1996) A multi-area linear programming approach for analysis of economic operation of the indian power system. IEEE Trans Power Syst 11(1):52–58
Lowery PG (1966) Generating unit commitment by dynamic programming. IEEE Trans Power Appar and Syst PAS-85(5):422–426
Selvakumar AI, Thanushkodi K (2007) A new particle swarm optimization solution to nonconvex economic dispatch problems. IEEE Trans Power Syst 22(1):42–51
Yang X-S, Hosseini SSS, Gandomi AH (2012) Firefly algorithm for solving non-convex economic dispatch problems with valve loading effect. Appl Soft Comput 12(3):1180–1186
Chiang C-L (2007) Genetic-based algorithm for power economic load dispatch. IET Gener, Transm Distrib 1(2):261–269
Lin W-M, Cheng F-S, Tsay M-T (2002) An improved tabu search for economic dispatch with multiple minima. IEEE Trans Power Syst 17(1):108–112
Favuzza S, Graditi G, Sanseverino ER (2006) Adaptive and dynamic ant colony search algorithm for optimal distribution systems reinforcement strategy. Appl Intell 24(1):31–42
Lee KY, Sode-Yome A, Park J-H (1998) Adaptive Hopfield neural networks for economic load dispatch. IEEE Trans Power Syst 13(2):519–526
dos Santos Coelho L, Mariani VC (2013) Improved firefly algorithm approach applied to chiller loading for energy conservation. Energy Build 59:273–278
Kazem A, Sharifi E, Hussain FK, Saberi M, Hussain OK (2013) Support vector regression with chaos-based firefly algorithm for stock market price forecasting. Appl Soft Comput 13(2):947–958
Mohammadi S, Mozafari B, Solimani S, Niknam T (2013) An adaptive modified firefly optimisation algorithm based on Hong’s point estimate method to optimal operation management in a microgrid with consideration of uncertainties. Energy 51:339–348
Sulaiman MH, Daniyal H, Mustafa MW (2012) Modified firefly algorithm in solving economic dispatch problems with practical constraints. In: IEEE international conference on power and energy (PECon), pp 157–161
Pourakbari-Kasmaei M., Rashidi-Nejad M. (2011) An effortless hybrid method to solve economic load dispatch problem in power systems. Energy Convers Manag 52(89):2854–2860
Cai J, Li Q, Li L, Peng H, Yang Y (2012) A hybrid CPSOSQP method for economic dispatch considering the valve-point effects. Energy Convers Manag 53(1):175–181
Mohammadi-ivatloo B, Rabiee A, Ehsan M (2012) Time-varying acceleration coefficients IPSO for solving dynamic economic dispatch with non-smooth cost function. Energy Convers Manag 56:175–183
Niknam T, Narimani MR, Azizipanah-Abarghooee R (2012) A new hybrid algorithm for optimal power flow considering prohibited zones and valve point effect. Energy Convers Manag 58:197–206
Chalermchaiarbha S, Ongsakul W (2013) Stochastic weight trade-off particle swarm optimization for nonconvex economic dispatch. Energy Convers Manag 70:66–75
Ozyon S, Aydin D (2013) Incremental artificial bee colony with local search to economic dispatch problem with ramp rate limits and prohibited operating zones. Energy Convers Manag 65:397–407
Vlachos A, Apostolopoulos T (2011) Application of the firefly algorithm for solving the economic emissions load dispatch problem. Int J Comb 2011:23
Sulaiman MH, Mustafa MW, Zakaria ZN, Aliman O, Rahim SRA (2012) Firefly algorithm techniquefor solving economic dispatch problem. In: IEEE international Power engineering and optimization conference (PEDCO) melaka, malaysia, pp 90–95
Yang X-S (2009) Firefly algorithms for multimodal optimization. In: Stochastic algorithms: foundations and applications, SAGA, vol 5792, pp 169–178
Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(2324):2325–2336
Bratton D, Kennedy J (2007) Defining a standard for particle swarm optimization. In: IEEE symposium on swarm intelligence, pp 120–127
Zhan Z-H, Zhang J, Li Y, Chung HS-H (2009) Adaptive particle swarm optimization. IEEE Trans Syst Man Cybern B: Cybern 39(6):1362–1381
Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: World congress on nature biologically inspired computing NaBIC, pp 210–214
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248
Tarasewich P, McMullen PR (2002) Swarm intelligence: power in numbers. Commun ACM 45(8):62–67
Sinha N, Chakrabarti R, Chattopadhyay PK (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Comput 7(1):83–94
Walters DC, Sheble GB (1993) Genetic algorithm solution of economic dispatch with valve point loading. IEEE Trans Power Syst 8(3):1325–1332
Park J-B, Lee K-S, Shin J-R, Lee KY (2005) A particle swarm optimization for economic dispatch with nonsmooth cost functions. IEEE Trans Power Syst 20(1):34–42
Chiang C-L (2005) Improved genetic algorithm for power economic dispatch of units with valve-point effects and multiple fuels. IEEE Trans Power Syst 20(4):1690–1699
dos Santos Coelho L, Mariani VC (2006) Combining of chaotic differential evolution and quadratic programming for economic dispatch optimization with valve-point effect. IEEE Trans Power Syst 21(2):989–996
Wang S-K, Liu C-W, Chiou J-P (2006) Non-smooth/non-convex economic dispatch by a novel hybrid differential evolution algorithm. IET Gener, Transm Distrib 1(5):793–803
Vlachogiannis JG, Lee KY (2009) Economic load dispatch - a comparative study on heuristic optimization techniques with an improved coordinated aggregation-based PSO. IEEE Trans Power Syst 24(2):991–1001
Meng K, Wang HG, Dong Z, Wong K-P (2010) Quantum-inspired particle swarm optimization for valve-point economic load dispatch. IEEE Trans Power Syst 25(1):215–222
dos Santos Coelho L, Mariani VC (2008) Particle swarm approach based on quantum mechanics and harmonic oscillator potential well for economic load dispatch with valve-point effects. Energy Convers Manag 49(11):3080–3085
Reddy AS, Vaisakh K (2013) Shuffled differential evolution for economic dispatch with valve point loading effects. Int J Electr Power Energy Syst 46:342–352
Ling SH, Iu HH-C, Chan KY, Lam HK, Yeung BCW, Leung FH (2008) Hybrid particle swarm optimization with wavelet mutation and its industrial applications. IEEE Trans Syst Man Cybern B: Cybern 38(3):743–763
Liu D, Cai Y (2005) Taguchi method for solving the economic dispatch problem with nonsmooth cost functions. IEEE Trans Power Syst 20(4):2006–2014
Selvakumar AI, Thanushkodi K (2008) Anti-predatory particle swarm optimization: Solution to nonconvex economic dispatch problems. Electr Power Syst Res 78(1):2–10
Chaturvedi KT, Pandit M, Srivastava L (2008) Self-organizing hierarchical particle swarm optimization for nonconvex economic dispatch. IEEE Trans Power Syst 23(3):1079–1087
Bhattacharya A, Chattopadhyay PK (2010) Solving complex economic load dispatch problems using biogeography-based optimization. Expert Syst Appl 37(5):3605–3615
Alsumait JS, Sykulski JK, Al-Othman AK (2010) A hybrid GAPSSQP method to solve power system valve-point economic dispatch problems. Appl Energy 87(5):1773–1781
ping Chen Y, Peng W-C, Jian M-C (2007) Particle swarm optimization with recombination and dynamic linkage discovery. IEEE Trans Syst Man Cybern B: Cybern 37(6):1460–1470
Vlachogiannis JG, Lee KY (2006) A comparative study on particle swarm optimization for optimal steady-state performance of power systems. IEEE Trans Power Syst 21(4):1718–1728
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Chen, G., Ding, X. Optimal economic dispatch with valve loading effect using self-adaptive firefly algorithm. Appl Intell 42, 276–288 (2015). https://doi.org/10.1007/s10489-014-0593-2
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DOI: https://doi.org/10.1007/s10489-014-0593-2