Optimal Power Flow in DC Networks Using the Whale Optimization Algorithm

This paper presents a solution method for the optimal power flow (OPF) problem in direct current (DC) networks. The method implements a master-slave optimization that combines a whale optimization algorithm (WOA) and a numerical method based on successive approximations (SA). The objective function is to reduce the power losses considering the set of constraints that DC networks represent in a distributed generation environment. In the master stage, the WOA determines the optimal amount of power to be supplied by each distributed generator (DG) in order to minimize the total power losses in the distribution lines of the DC network. In the slave stage, the power or load flow problem is solved in order to evaluate the objective function of each possible configuration proposed by the master stage. To validate the efficiency and robustness of the proposed model, we implemented three additional methods for comparison: the ant lion optimizer (ALO), a continuous version of the genetic algorithm (CGA), and the algorithm of black hole-based optimization (BHO). The efficiency of each solution method was validated in the 21- and the 69-node test systems using different scenarios of penetration of distributed generation. All the simulations, performed in MATLAB 2019, demonstrated that the WOA achieved the greatest minimization of power losses, regardless of the size of the DC network and the level of penetration of distributed generation.