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Energies 2018, 11(12), 3438; https://doi.org/10.3390/en11123438

Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach

1
Key Laboratory of Network control & Intelligent Instrument, Chongqing University of Posts and Telecommunications, Ministry of Education, Chongqing 400065, China
2
Chongqing Key Laboratory of Complex Systems and Bionic Control, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
3
Key Laboratory of Communication Network and Testing Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
4
Department of Electrical and Computer Engineering, University of Idaho, Moscow, ID 83844, USA
*
Author to whom correspondence should be addressed.
Received: 15 November 2018 / Revised: 28 November 2018 / Accepted: 6 December 2018 / Published: 8 December 2018
(This article belongs to the Section Energy Economics and Policy)
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Abstract

Known as a multi-objective, large-scale, and complicated optimization problem, the multi-objective optimal power flow (MOOPF) problem tends to be introduced with many constraints. In this paper, compared with the frequently-used penalty function-based method (PFA), a novel constraint processing approach named the constraints-prior Pareto-domination approach (CPA) is proposed for ensuring non-violation of various inequality constraints on dependent variables by introducing the Pareto-domination principle based on the sum of constraint violations. Moreover, for solving the constrained MOOPF problem, the multi-objective firefly algorithm with CPA (MOFA-CPA) is proposed and some optimization strategies, such as the crowding distance calculation and non-dominated sorting based on the presented CPA, are utilized to sustain well-distributed Pareto front (PF). Finally, in order to demonstrate the feasible and effective improvement of MOFA-CPA, a comparison study between MOFA-CPA and MOFA-PFA is performed on two test systems, including three bi-objective optimization cases and three tri-objective optimization cases. The simulation results demonstrate the capability of the MOFA-CPA for obtaining PF with good distribution and superiority of the proposed CPA for dealing with inequality constraints on dependent variables. In addition, some quality indicators are used to evaluate the convergence, distribution, and uniformity of the PFs found by the MOFA-CPA and MOFA-PFA. View Full-Text
Keywords: multi-objective optimal power flow problem; multi-objective firefly algorithm; constraints-prior Pareto-domination approach; quality indicator multi-objective optimal power flow problem; multi-objective firefly algorithm; constraints-prior Pareto-domination approach; quality indicator
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Chen, G.; Yi, X.; Zhang, Z.; Lei, H. Solving the Multi-Objective Optimal Power Flow Problem Using the Multi-Objective Firefly Algorithm with a Constraints-Prior Pareto-Domination Approach. Energies 2018, 11, 3438.

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