A Probabilistic Approach for Voltage Regulators and Capacitor Placement in Three-Phase Unbalanced Distribution System

Capacitors and voltage series regulators are widely used in distribution systems to improve the system behaviour. A mixed integer, non-linear, constrained optimization problem can be formulated for an optimal allocation of these devices. This problem is frequently solved in deterministic scenarios with Genetic Algorithms. However, the distribution systems are probabilistic in nature, leading to inaccurate and in some cases conservative deterministic solutions. This paper proposes a new probabilistic method to solve the allocation problem. The method is based on the use of a Micro-Genetic Algorithm. Two different techniques based on the linearized form of the constraints of the probabilistic optimization model and on the Point Estimate Method were tested and compared to reduce the computational efforts. The proposed approaches were tested on the IEEE 34-node unbalanced distribution system.