Comparative Analysis of the Particle Swarm Optimization and Primal-Dual Interior-Point Algorithms for Transmission System Volt/VAR Optimization in Rectangular Voltage Coordinates

Abstract

Optimal power flow (OPF) is one of the most widely studied problems in the field of operations research, as it applies to the optimal and efficient operation of the electric power system. Both the problem formulation and solution techniques have attracted significant research interest over the decades. A wide range of OPF problems have been formulated to cater for the various operational objectives of the power system and are mainly expressed either in polar or rectangular voltage coordinates. Many different solution techniques falling into the two main categories of classical/deterministic optimization and heuristic/non-deterministic optimization techniques have been explored in the literature. This study considers the Volt/VAR optimization (VVO) variant of the OPF problem formulated in rectangular voltage coordinates, which is something of a departure from the majority of the studies, which tend to use the polar coordinate formulation. The heuristic particle swarm optimization (PSO) and the classical primal-dual interior-point method (PDIPM) are applied to the solution of the VVO problem and a comparative analysis of the relative performance of the two algorithms for this problem is presented. Four case studies based on the 6-bus, IEEE 14-bus, 30-bus, and 118-bus test systems are presented. The comparative performance analysis reveals that the two algorithms have complementary strengths, when evaluated on the basis of the solution quality and computational efficiency. Particularly, the PSO algorithm achieves greater power loss minimization, whereas the PDIPM exhibits greater speed of convergence (and, thus, better computational efficiency) relative to the PSO algorithm, particularly for higher-dimensional problems. An additional distinguishing characteristic of the proposed solution is that it incorporates the Newton–Raphson load flow computation, also formulated in rectangular voltage coordinates, which adds to the efficiency and effectiveness of the presented solution method.

Particle Swarm Optimization for an Optimal Hybrid Renewable Energy Microgrid System under Uncertainty

“…Based on its own and the swarm's collective flight experiences, a particle can be viewed as an autonomous intelligent agent that "flies" around a multi-dimensional issue space in pursuit of the best solution to the optimisation problem. Three n-dimensional vectors make up each particle i in the swarm (with n being the dimensionality of the search space, R n ), which, at time, t, can be represented as the current location, X i t , the previous best position, pbest i , and the velocity, V i t [18]. The iterative velocity update, which modifies each particle's position to guide the entire swarm towards the best solution to the optimisation issue, is the fundamental portion of the PSO method, as shown in Equation (28).…”

“…One crucial aspect of the PSO algorithm is the social interaction and information sharing that occurs amongst the particles in the swarm. The swarm's collective behaviour is what allows the program to search as efficiently as possible [18]. Figure 2's flowchart presents the standard PSO algorithm.…”