A novel chaotic flower pollination algorithm for function optimization and constrained optimal power flow considering renewable energy sources

Abstract

This study presents an improved chaotic flower pollination algorithm (CFPA) with a view to handle the optimal power flow (OPF) problem integrating a hybrid wind and solar power and generate the optimal settings of generator power, bus voltages, shunt reactive power, and tap setting transformers. In spite of the benefits of FPA, it encounters two problems like other evolutionary algorithms: entrapment in local optima and slow convergence speed. Thus, to deal with these drawbacks and enhance the FPA searching accuracy, a hybrid optimization approach CFPA which combines the stochastic algorithm FPA that simulates the flowering plants process with the chaos methodology is applied in this manuscript. Therefore, owing to the various nonlinear constraints in OPF issue, a constraint handling technique named superiority of feasible solutions (SF) is embedded into CFPA. To confirm the performance of the chaotic FPA, a set of different well-known benchmark functions were employed for ten diverse chaotic maps, and then the best map is tested on IEEE 30-bus and IEEE 57-bus test systems incorporating the renewable energy sources (RESs). The obtained results are analyzed statistically using non-parametric Wilcoxon rank-sum test in view of evaluating their significance compared to the outcomes of the state-of-the-art meta-heuristic algorithms such as ant bee colony (ABC), grasshopper optimization algorithm (GOA), and dragonfly algorithm (DA). From this study, it may be established that the suggested CFPA algorithm outperforms its meta-heuristic competitors in most benchmark test cases. Additionally, the experimental results regarding the OPF problem demonstrate that the integration of RESs decreases the total cost by 12.77% and 33.11% for the two systems, respectively. Thus, combining FPA with chaotic sequences is able to accelerate the convergence and provide better accuracy to find optimal solutions. Furthermore, CFPA (especially with the Sinusoidal map) is challenging in solving complex real-world problems.