Allocation of Capacitors and Voltage Regulators in Unbalanced Distribution Systems: A Multi-objective Problem in Probabilistic Frameworks

Abstract

Abstract Capacitors and series voltage regulators are used extensively in distribution systems to reduce power losses and improve the voltage profile along the feeders. This paper deals with the problem of contemporaneously choosing optimal locations and sizes for both capacitors and series voltage regulators in three-phase, unbalanced distribution systems. This is a mixed, non-linear, constrained, multi-objective optimization problem that usually is solved in deterministic scenarios. However, distribution systems are stochastic in nature, which can lead to inaccurate deterministic solutions. To take into account the unavoidable uncertainties that affect the input data related to the problem, in this paper, we have formulated and solved the multi-objective optimization problem in probabilistic scenarios. To address the multi-objective optimization problem, algorithms were used in which all the objective functions were combined to form a single function. These algorithms allow us to transform the original multi-objective optimization problem into an equivalent, single-objective, optimization problem, an approach that appeared to be particularly suitable since computational time was an important issue. To further reduce the computational efforts, a linearized form of the equality constraints of the optimization model was used, and a micro-genetic algorithm-based procedure was applied in the solution method.