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An improved particle swarm optimization with clone selection principle for dynamic economic emission dispatch

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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., \(P^{\mathrm{best}}\)) at every generation. The fittest particles in \(P^{\mathrm{best}}\) 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.

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Acknowledgements

The authors acknowledge the support from the National Natural Science Foundation of China under Grants 61762001, Creative Research Groups of the Natural Science Foundation of Guizhou of China under Grants Qian Jiao he KY zi 2019069 and 2018034, Provincial Science and Technology Foundation of Guizhou of China under Grants Qian ke he LH zi 20177047, and Innovation Foundation of Nanjing Institute of Technology under Grants CKJC201603.

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Authors and Affiliations

  1. School of Science, Anshun University, Anshun, 561000, Guizhou, China

    Shuqu Qian & Huihong Wu

  2. University of Engineering of Nanjing, Nanjing, 211167, China

    Guofeng Xu

Authors
  1. Shuqu Qian
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  2. Huihong Wu
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  3. Guofeng Xu
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Correspondence to Shuqu Qian.

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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 Helsinki Declaration and its later amendments or comparable ethical standards. This article does not contain any studies with animals performed by any of the authors.

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Appendix

Appendix

See Tables 13, 14, 15, 16, 17, 18, 19.

Table 13 5-unit generator coefficients
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Table 14 5-unit B matrix
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Table 15 10-unit generator coefficients
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Table 16 10-unit B matrix \((\times 10^{-6})\)
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Table 17 15-unit generator coefficients
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Table 18 15-unit B matrix \((\times 10^{-5})\)
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Table 19 24-h power demands
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Qian, S., Wu, H. & Xu, G. An improved particle swarm optimization with clone selection principle for dynamic economic emission dispatch. Soft Comput 24, 15249–15271 (2020). https://doi.org/10.1007/s00500-020-04861-4

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