Application of the Vortex Search Algorithm to the Phase-Balancing Problem in Distribution Systems

Abstract

This article discusses the problem of minimizing power loss in unbalanced distribution systems through phase-balancing. This problem is represented by a mixed-integer nonlinear-programming mathematical model, which is solved by applying a discretely encoded Vortex Search Algorithm (DVSA). The numerical results of simulations performed in IEEE 8-, 25-, and 37-node test systems demonstrate the applicability of the proposed methodology when compared with the classical Cuh & Beasley genetic algorithm. In addition, the computation times required by the algorithm to find the optimal solution are in the order of seconds, which makes the proposed DVSA a robust, reliable, and efficient tool. All computational implementations have been developed in the MATLAB® programming environment, and all the results have been evaluated in DigSILENT© software to verify the effectiveness and the proposed three-phase unbalanced power-flow method.

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

“…The set of constraints for the phase-balancing problem is typically associated with the operative conditions of the network, that is, the power balance equations and the voltage regulation bounds [2]. These equations are as follows:…”

“…Three-phase distribution grids are responsible for providing electrical energy to residential, commercial, and industrial areas at medium-and low-voltage levels [1,2]. These grids are typically unbalanced owing to the following factors: (i) line configurations are non-symmetric because the transposition criteria are not applicable owing to the short length of the lines (few tens of kilometers) [3]; and (ii) the nature of loads can be single-, two-, and three-phase, which results in intrinsic imbalances in the currents through the lines and voltages in the nodes [4].…”

“…These grids are typically unbalanced owing to the following factors: (i) line configurations are non-symmetric because the transposition criteria are not applicable owing to the short length of the lines (few tens of kilometers) [3]; and (ii) the nature of loads can be single-, two-, and three-phase, which results in intrinsic imbalances in the currents through the lines and voltages in the nodes [4]. The main problem arising from the general unbalanced nature of three-phase networks is the large power losses in the distribution stage (distribution lines and transformers); these losses cause increments in the final billing of the electricity service for all the end-users, which is permitted by regulatory entities within an acceptable range [2]. In Colombia, the power losses of distribution systems range from 6% to 18%, depending on the geographic location of the distribution systems (i.e., rural or urban areas) as well as the level of investment in maintenance activities on the physical layer of the distribution network [5].…”

“…Owing to the importance of strategies for reducing the amount of energy loss in electrical distribution networks, multiple well-known approaches have been established. Some of these include (i) optimal sizing and installation of distributed generation [7]; (ii) optimal installation and sizing of reactive power compensators [5]; (iii) optimal grid reconfiguration [8]; and (iv) optimal phase-balancing strategies [2]. Each of the aforementioned methodologies can help distribution companies in significantly reducing the amount of power loss.…”

“…As indicated by existing literature, the problem of phase balancing has been solved using multiple optimization approaches, including the classical Chu and Beasley genetic algorithms [12][13][14][15]; tabu search algorithm [16,17]; ant colony optimization [18,19]; immune optimization algorithm [20]; branch and bound and convex methods [4,21]; bat optimization algorithm [22]; vortex search algorithm [2]; particle swarm optimization methods [8,23,24]; differential evolution algorithm [25]; and simulated annealing optimization method [26]. The main characteristics of these approaches are the hybridization of metaheuristic discrete optimization methods (with binary and integer codifications) with three-phase power flow methods, which are typically based on sweep iterative backward/forward power flow methods, and the minimization of the amount of power loss for a particular load condition, which typically corresponds to the peak load condition.…”