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.
Highlights
Most engineering and scientific optimization problems in the real world involve multiple objective functions with different meanings and non-commensurable units, making it difficult to simultaneously optimize multiple objectives [1,2]
In recognition of the disadvantages in those previously proposed methods, we propose a multi-objective firefly algorithm with a novel constraint processing approach (MOFA-constraints-prior Pareto-domination approach (CPA)) to solve the constrained Multi-objective optimal power flow (MOOPF) problem
Mean CPU Time/T max Researchers have encountered great difficulties in handling the inequality constraints of dependent variables when dealing with large-scale, multi-constrained MOOPF problems
Summary
Most engineering and scientific optimization problems in the real world involve multiple objective functions with different meanings and non-commensurable units, making it difficult to simultaneously optimize multiple objectives [1,2]. MOEA/D algorithm with repair strategy and penalty function for constraints processing to solve the MOOPF problem. The authors used the non-dominated sorting multi-objective gravitational search algorithm (NSMOGSA) to solve the MOOPF problem, its applicability to large systems remains to be tested due to the effectiveness of the proposed algorithm is only tested on a standard IEEE 30-bus power system [16]. In [19], the authors presented the application of a new effective meta-heuristic optimization method, namely, non-dominated cuckoo search algorithm (NSCS). It is necessary to propose alternative methods to effectively deal with constraints on the dependent variables of MOOPF problems. In recognition of the disadvantages in those previously proposed methods, we propose a multi-objective firefly algorithm with a novel constraint processing approach (MOFA-CPA) to solve the constrained MOOPF problem.
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