Power economic dispatch (ED) plays an important role in energy saving in power system operations. The penalty function method is widely used to handle equality constraints involved in ED problems. However, it is sometimes difficult to select the optimal penalty coefficients. To solve this problem, a Two-Stage strategy is proposed in this paper to handle equality constraints in artificial bee colony algorithm (ABC)-based ED problems, called as TSABC. Two groups of onlooker bees are employed in the first stage to search for feasible solutions satisfying all constraints. Then, in the second stage, a novel searching strategy with dynamic bounds for the elements of the solutions is introduced to keep the constraints always satisfied during the optimization process. The TSABC method does not require more control parameters and is easy to implement. Both based on basic ABC algorithm, the Two-Stage strategy is compared with the penalty function method (PFABC) for handling equality constraints in both static and dynamic economic dispatch problems. The comparative analysis reveals that the proposed TSABC method has merit in terms of effectiveness, reliability and solution quality.
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The authors would like to thank the editors and anonymous referees for their invaluable comments and suggestions. This work is supported by the National Natural Science Foundation of China (No. 51476028 and No. 51876035) and the scholarship from China Scholarship Council under the Grant CSC No. 201706090049.
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Conflict of interest
The authors declare that they have no conflict of interest.
All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Declaration of Helsinki and its later amendments or comparable ethical standards.
Human and animals rights
This article does not contain any studies with animals performed by any of the authors.
Informed consent was obtained from all individual participants included in the study.
Attaviriyanupap P, Kita H, Tanaka E, Hasegawa J (2002) A hybrid ep and sqp for dynamic economic dispatch with nonsmooth fuel cost function. IEEE Trans Power Syst 17(2):411–416CrossRefGoogle Scholar
AydıN D, ÖZyöN S (2013) Solution to non-convex economic dispatch problem with valve point effects by incremental artificial bee colony with local search. Appl Soft Comput 13(5):2456–2466CrossRefGoogle Scholar
Aydin D, Özyön S, Yaşar C, Liao T (2014) Artificial bee colony algorithm with dynamic population size to combined economic and emission dispatch problem. Int J Electr Power Energy Syst 54:144–153CrossRefGoogle Scholar
Basu M (2013) Artificial bee colony optimization for multi-area economic dispatch. Int J Electr Power Energy Syst 49:181–187CrossRefGoogle Scholar
Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338CrossRefzbMATHGoogle Scholar
Gaing ZL (2003) Particle swarm optimization to solving the economic dispatch considering the generator constraints. IEEE Trans Power Syst 18(3):1187–1195CrossRefGoogle Scholar
Hemamalini S, Simon SP (2010) Artificial bee colony algorithm for economic load dispatch problem with non-smooth cost functions. Electr Power Compon Syst 38(7):786–803CrossRefGoogle Scholar
Hemamalini S, Simon SP (2011) Dynamic economic dispatch using artificial bee colony algorithm for units with valve-point effect. Int Trans Electr Energy Syst 21(1):70–81Google Scholar
Homaifar A, Qi CX, Lai SH (1994) Constrained optimization via genetic algorithms. Simulation 62(4):242–253CrossRefGoogle Scholar
Irisarri G, Kimball L, Clements K, Bagchi A, Davis P (1998) Economic dispatch with network and ramping constraints via interior point methods. IEEE Trans Power Syst 13(1):236–242CrossRefGoogle Scholar
Jadhav H, Roy R (2013) Gbest guided artificial bee colony algorithm for environmental/economic dispatch considering wind power. Expert Syst Appl 40(16):6385–6399CrossRefGoogle Scholar
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Tech. rep., Technical report-tr06, Erciyes University, Engineering Faculty, Computer Engineering DepartmentGoogle Scholar
Karaboga D, Basturk B (2008) On the performance of artificial bee colony (abc) algorithm. Appl Soft Comput 8(1):687–697CrossRefGoogle Scholar
Karaboga D, Ozturk C, Karaboga N, Gorkemli B (2012) Artificial bee colony programming for symbolic regression. Inf Sci 209:1–15CrossRefGoogle Scholar
Koodalsamy C, Simon SP (2013) Fuzzified artificial bee colony algorithm for nonsmooth and nonconvex multiobjective economic dispatch problem. Turk J Electr Eng Comput Sci 21(Sup. 1):1995–2014CrossRefGoogle Scholar
Liao X, Zhou J, Ouyang S, Zhang R, Zhang Y (2013) An adaptive chaotic artificial bee colony algorithm for short-term hydrothermal generation scheduling. Int J Electr Power Energy Syst 53:34–42CrossRefGoogle Scholar
Lin C, Viviani G (1984) Hierarchical economic dispatch for piecewise quadratic cost functions. IEEE Trans Power Appar Syst PAS 103(6):1170–1175CrossRefGoogle Scholar
Malik TN, ul Asar A, Wyne MF, Akhtar S (2010) A new hybrid approach for the solution of nonconvex economic dispatch problem with valve-point effects. Electr Power Syst Res 80(9):1128–1136CrossRefGoogle Scholar
Niknam T, Azizipanah-Abarghooee R, Zare M, Bahmani-Firouzi B (2013) Reserve constrained dynamic environmental/economic dispatch: A new multiobjective self-adaptive learning bat algorithm. IEEE Syst J 7(4):763–776CrossRefGoogle Scholar
Özyön 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 65:397–407CrossRefGoogle Scholar
Panigrahi C, Chattopadhyay P, Chakrabarti R, Basu M (2006) Simulated annealing technique for dynamic economic dispatch. Electric Power Compon Syst 34(5):577–586CrossRefGoogle Scholar
Park JB, Jeong YW, Shin JR, Lee KY (2010) An improved particle swarm optimization for nonconvex economic dispatch problems. IEEE Trans Power Syst 25(1):156–166CrossRefGoogle Scholar
Secui DC (2015a) The chaotic global best artificial bee colony algorithm for the multi-area economic/emission dispatch. Energy 93:2518–2545CrossRefGoogle Scholar
Secui DC (2015b) A new modified artificial bee colony algorithm for the economic dispatch problem. Energy Convers Manag 89:43–62CrossRefGoogle Scholar
Singh NJ, Dhillon J, Kothari D (2018) Multi-objective thermal power load dispatch using chaotic differential evolutionary algorithm and powell’s method. Soft Comput 22(7):2159–2174CrossRefGoogle Scholar
Sinha N, Chakrabarti R, Chattopadhyay P (2003) Evolutionary programming techniques for economic load dispatch. IEEE Trans Evol Comput 7(1):83–94CrossRefGoogle Scholar
Somuah C, Khunaizi N (1990) Application of linear programming redispatch technique to dynamic generation allocation. IEEE Trans Power Syst 5(1):20–26CrossRefGoogle Scholar
Victoire TAA, Jeyakumar AE (2005a) Deterministically guided pso for dynamic dispatch considering valve-point effect. Electr Power Syst Res 73(3):313–322CrossRefGoogle Scholar
Victoire TAA, Jeyakumar AE (2005b) A modified hybrid ep-sqp approach for dynamic dispatch with valve-point effect. Int J Electr Power Energy Syst 27(8):594–601CrossRefGoogle Scholar
Walters DC, Sheble GB (1993) Genetic algorithm solution of economic dispatch with valve point loading. IEEE Trans Power Syst 8(3):1325–1332CrossRefGoogle Scholar
Wood AJ, Wollenberg BF (2012) Power generation, operation, and control. Wiley, HobokenGoogle Scholar
Xia X, Elaiw A (2010) Optimal dynamic economic dispatch of generation: a review. Electric Power Syst Res 80(8):975–986CrossRefGoogle Scholar
Yaşar C, Özyön S (2011) A new hybrid approach for nonconvex economic dispatch problem with valve-point effect. Energy 36(10):5838–5845CrossRefGoogle Scholar
Zaman M, Elsayed SM, Ray T, Sarker RA (2016) Evolutionary algorithms for dynamic economic dispatch problems. IEEE Trans Power Syst 31(2):1486–1495CrossRefGoogle Scholar