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Novel Hybrid Algorithm Based on Combined Particle Swarm Optimization and Imperialist Competitive Algorithm for Non-Convex CHPED Solution

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Abstract

This paper presents a novel hybrid approach by integrating the imperialist competitive algorithm (ICA) with particle swarm optimization (PSO) method to deal with the combined heat and power economic dispatch (CHPED) problem with the bounded feasible operating region. Unlike many previous methods, this approach takes the valve-point effects explicitly into account as an absolute sinusoidal term in the conventional polynomial cost function. The efficiency and feasibility of the hybrid scheme are evaluated on three small (with three different scenarios), medium and large test systems. The simulation results suggest the superior performance of the proposed hybrid algorithm in finding optimum solutions compared to other existing methods.

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Abbreviations

i :

The index of conventional thermal units.

j :

The index of cogeneration units.

k :

The index of heat-only units

\({P}_{i}^{p}\) :

The power output of the ith conventional thermal unit.

\({P}_{j}^{c},{H}_{j}^{c}\) :

The power and thermal output of the jth cogeneration unit

\({H}_{k}^{h}\) :

The thermal output of the kth heat-only unit

\({N}_{p}\) :

The number of conventional thermal units

\({N}_{c}\) :

The number of cogeneration units

\({N}_{h}\) :

The number of heat-only units

\({\alpha }_{i},{\beta }_{i}\;and\;{ \gamma }_{i}\) :

The cost coefficients of the ith conventional thermal unit.

\({\lambda }_{i}\;and\;{\rho }_{i}\) :

The cost coefficients representing valve point effects of the ith conventional thermal unit.

\({a}_{j},{b}_{j},{c}_{j},{d}_{j}, {e}_{j},\;and\;{f}_{j}\) :

The cost coefficients of the jth cogeneration unit.

\({a}_{k},{b}_{k}\;and\;{c}_{k}\) :

The cost coefficients of the kth heat-only unit.

\({P}_{\text{demand}}\) :

The system power demand

\({H}_{\text{demand}}\) :

The system thermal demand

\({{P}_{i}^{p,max}, P}_{i}^{p,min}\) :

The upper and lower limit of power output of the ith conventional power-only unit.

\({{H}_{k}^{h,max}, H}_{k}^{h,min}\) :

The upper and lower limit of power output of the kth heat-only unit

\({C}_{i}({P}_{i}^{p})\) :

The fuel cost of the conventional thermal unit i

\({C}_{j}({P}_{j}^{c},{H}_{j}^{c})\) :

The cost function of the cogeneration unit j

\({C}_{k}({H}_{k}^{h})\) :

The cost of the heat-only unit k

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Acknowledgements

This work was financially supported by the general project of natural science research in Colleges and universities of Jiangsu Province (Project Nos. 21KJD10004, 16KJD580001), the general project of philosophy and social sciences research in Colleges and universities in Jiangsu Province (Project No. 2021SJA1642), the collaborative education project of industry university cooperation of the Ministry of Education (Grant No. 202101056007), the project of Jiangsu Institute of Educational Technology (Grant No. 2021JSETKT064) and the Jiangsu Industry University Research Cooperation Project (Grant Nos. BY2020545, BY2020547), the Nantong Science and technology projects(Grant Nos. JCZ21059, JC2018148, GY12015024.

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Authors and Affiliations

  1. School of Mechanical Engineering, Nantong Institute of Technology, Nantong, 226002, China

    Yuwei Yang, Jie Gao & Hai Gu

  2. School of Electrical Engineering, Science and Research, Islamic Azad University, Tehran, Iran

    Hashem Imani Marani

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Correspondence to Hashem Imani Marani.

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Yang, Y., Gao, J., Gu, H. et al. Novel Hybrid Algorithm Based on Combined Particle Swarm Optimization and Imperialist Competitive Algorithm for Non-Convex CHPED Solution. J. Electr. Eng. Technol. 18, 1–13 (2023). https://doi.org/10.1007/s42835-022-01143-x

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