An improved particle swarm optimization with clone selection principle for dynamic economic emission dispatch
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METHODOLOGIES AND APPLICATION
An improved particle swarm optimization with clone selection principle for dynamic economic emission dispatch Shuqu Qian1 · Huihong Wu1 · Guofeng Xu2
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, an improved particle swarm optimization algorithm (PSOCS) that integrates with a clone selection (CS) principle of artificial immune system is proposed to solve dynamic economic emission dispatch (DEED) problem. Classical particle swarm optimization method is easy to fall into stagnation when no particle discovers a position that is better than its previous best position. To overcome the disadvantage, the CS mechanism is used to evolve the personal best swarm (i.e., P best ) at every generation. The fittest particles in P best will be cloned independently and proportionally to their fitness. In order to force PSOCS jump out of stagnation, a hybrid mutation scheme (called R/1orCB/1) is developed to mutate the clones generated. A constrain-handling approach is utilized to repair infeasible solutions for enhancing the ability of adapting to the DEED problem with various strong constraints. In numerical experiments, the proposed PSOCS is applied to solve three test cases (5-unit, 10-unit, and 15-unit systems) with nonsmooth fuel cost and emission functions. Simulation results indicate that the PSOCS can find the high-quality solutions for the DEED problem, when compared with the most recent methods reported in the literature. Keywords Dynamic economic emission dispatch · Particle swarm optimization · Clonal selection principle · Strong constraints · Hybrid mutation
1 Introduction Economic dispatch (ED) is a key problem of power system optimal operation. It is necessary to build models for the electricity dispatching principles and plans in order to ensure fair competition and real-time ED by various power generation enterprises. In recent years, the research on ED mainly focuses on the optimal start–stop problem of the units and the spot market daily power generation plan. However, the study on the power system dispatching model and related algorithm Communicated by V. Loia.
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Shuqu Qian [email protected] Huihong Wu [email protected] Guofeng Xu [email protected]
1
School of Science, Anshun University, Anshun 561000, Guizhou, China
2
University of Engineering of Nanjing, Nanjing 211167, China
is an important topic related to applied mathematics. In order to solve the ED problem, the selection of optimization methods is particularly important issue. A number of scholars have tried to mix different optimization algorithms to form a hybrid intelligent optimization algorithm. The hybrid intelligent optimization algorithm could fully utilize the advantages of various algorithms, complement each other’s advantages, and overcome the flaws in a single intelligent optimization algorithm with satisfying results. In Neto et al. (2017), in order to improve the global searching capability and prevent the convergence to local minima, the greedy randomized adapti
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