An improved real-coded genetic algorithm with random walk based mutation for solving combined heat and power economic di
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ORIGINAL RESEARCH
An improved real‑coded genetic algorithm with random walk based mutation for solving combined heat and power economic dispatch A. Haghrah1 · M. A. Nekoui1 · M. Nazari‑Heris2 · B. Mohammadi‑ivatloo2,3 Received: 14 July 2019 / Accepted: 30 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Combined heat and power economic dispatch (CHPED) is an energy management problem that minimizes the operation cost of power and heat generation while a vast variety of operational constraints of the system should be met. The CHPED is a complicated, non-convex and non-linear problem. In this study, a new real-coded genetic algorithm with random walk-based mutation (RCGA-CRWM) is under study, which is effective in solving large-scale CHPED problem with minimum operation cost. In the presented optimization method, a simple approach is introduced to combine the positive features of different probabilistic distributions for the step size of random walk. Using the presented approach, while the genetic algorithm is speeded up, the premature convergence is also avoided. After verifying the performance of the presented method on the benchmark functions, two large-scale and two medium-scale case studies are used for determining the algorithm strength in solving the CHPED problem. Despite the fact that the complexity of the CHPED rises dramatically by increasing its dimensionality, the algorithm has solved the problems accurately. The application of RCGA-CRWM method improves the results of the CHPED problem in terms of both operation cost and convergence speed in comparison with other optimization methods. Keywords Combined heat and power (CHP) · economic dispatch · real-coded genetic algorithm · random walk · complex optimization problem List of symbols i Index of the thermal units j Index of the CHP units k Index of the boilers aj , bj , cj , dj , and fj Cost coefficients of the jth CHP plant 𝛼i , 𝛽i , and 𝛾i Cost coefficients of the ith thermal plant * B. Mohammadi‑ivatloo [email protected] A. Haghrah [email protected] M. A. Nekoui [email protected] M. Nazari‑Heris [email protected] 1
Faculty of Electrical Engineering, K. N. Toosi University of Technology, Tehran, Iran
2
Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran
3
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
𝜆i and 𝜌i Coefficients of the valve-point influence of the ith thermal plant. ak , bk , and ck Cost coefficients of the kth boiler Ci Power production cost of the ith thermal unit Cj Power production cost of the jth CHP unit Ck Power production cost of the kth boiler p Pi Power generation of the ith conventional plant Pcj Power generation of the jth CHP unit Hjc Heat generation of the jth CHP unit Hkh Heat generation of the kth boiler Pd Power demand Hd Heat demand pmin Pi Minimum power generation of the ith conventional power unit pmax Pi Maximum power generation of the ith conventional pow
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