Improved Genetic Algorithm for Phase-Balancing in Three-Phase Distribution Networks: A Master-Slave Optimization Approach

Abstract

This paper addresses the phase-balancing problem in three-phase power grids with the radial configuration from the perspective of master–slave optimization. The master stage corresponds to an improved version of the Chu and Beasley genetic algorithm, which is based on the multi-point mutation operator and the generation of solutions using a Gaussian normal distribution based on the exploration and exploitation schemes of the vortex search algorithm. The master stage is entrusted with determining the configuration of the phases by using an integer codification. In the slave stage, a power flow for imbalanced distribution grids based on the three-phase version of the successive approximation method was used to determine the costs of daily energy losses. The objective of the optimization model is to minimize the annual operative costs of the network by considering the daily active and reactive power curves. Numerical results from a modified version of the IEEE 37-node test feeder demonstrate that it is possible to reduce the annual operative costs of the network by approximately 20% by using optimal load balancing. In addition, numerical results demonstrated that the improved version of the CBGA is at least three times faster than the classical CBGA, this was obtained in the peak load case for a test feeder composed of 15 nodes; also, the improved version of the CBGA was nineteen times faster than the vortex search algorithm. Other comparisons with the sine–cosine algorithm and the black hole optimizer confirmed the efficiency of the proposed optimization method regarding running time and objective function values.

An Improved Crow Search Algorithm Applied to the Phase Swapping Problem in Asymmetric Distribution Systems

“…The optimal phase swapping problem in ADSs is represented by a mixed-integer nonlinear programming (MINLP) model [16]. The binary variables are the decision variables, which correspond to the connections set for each load presented in the system [8].…”

“…The product between the magnitudes of the voltages and the trigonometric functions makes the objective function nonlinear and nonconvex [16]. The structure of the objective function makes advanced numerical optimization techniques necessary to minimize it efficiently [15].…”

“…These power losses can exceed the capacity required to supply the demand, cause equipment to age, and increase investment and operating costs for network operators [7,9]. The importance of reducing power losses in distribution networks has established multiple approaches, such as (i) optimal placement and sizing of distributed generation [10], (ii) optimal capacitor placement and sizing [11], (iii) optimal network reconfiguration [12], (iv) optimal conductor sizing in distribution networks [13], (v) optimal power system restoration [14], and (vi) optimal phase swapping [15,16]. These strategies can significantly help distribution companies to reduce the number of power losses.…”

“…In the specialized literature, the balance phase problem, with the minimizing power losses approach, has been solved using different optimization methods, including the Chu and Beasley genetic algorithms [8,16,[21][22][23][24], particle swarm optimization [9], mixedinteger convex optimization [25], bat optimization algorithm [26], differential evolution algorithm [27], simulated annealing optimizer [28], and vortex search algorithm [15], among others.…”

“…The master defines the connection of the loads to the nodes. The slave is typically a power flow tool that allows one to revise and exploit the solution space through the power losses calculation [16].…”