Comparative Analysis of Metaheuristics for Solving the Optimal Power Flow With Renewable Sources and Valve-Point Constraints

Abstract

The Optimal Power Flow (OPF) problem, used to obtain efficient operation conditions with the lowest cost or the minimum power loss in electrical power systems, is a non-polynomial problem that becomes even harder to analyze when considering renewable energy sources (RES) with uncertain behavior. Therefore, establishing a manageable number of RES scenarios in the modeling is essential for optimizing cost-effective solutions, including those with constraints such as the valve-point effect and prohibited operational zones. This work compares three differential evolution algorithm (DEA) variants and four well-known metaheuristics: the Particle Swarm Optimization (PSO), the Bio-geographical Based Optimization (BBO), the Artificial Bee Colony Optimization (ABC), and the Non-dominated Sorting Genetic Algorithm II (NSGA-II). The metaheuristics are compared: 1) to determine the one with the best performance considering RES; 2) to establish an approach to minimize and find the best set of scenarios representing variable RES; 3) to compare the success rate of convergence of the penalized function against the real objective function. Results show that BBO and PSO optimization are the best choices for solving the classic objective function of OPF. On the other hand, the DE/best/1 (DEAB) algorithm demonstrates the best performance when the valve-point effect with prohibited zones is considered. DEAB presents the largest weighted cumulative rating (WCR) and the second-best weighted cumulative successful rate (WCSR) for all the evaluated criteria.

Keywords

• Differential evolution algorithm
• electrical power systems
• optimal power flow
• renewable energy sources
• stochastic modelling