A Probabilistic Approach for Multiobjective Optimal Allocation of Voltage Regulators and Capacitors in Three-Phase Unbalanced Distribution Systems Part I: Theoretical aspects

Capacitors and series voltage regulators are widely used 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, and is usually 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 problem’s input data, primarily the load demands, this paper formulates and solves the multi-objective optimization problem in probabilistic scenarios. To reduce the computational efforts, a linearized form of the equality constraints of the optimization model is used, and a microgenetic algorithm-based procedure is applied as a solution method. This paper, which reports the theoretical aspects of the method, is a companion paper to a paper of the same title, Part II [1], in which the proposed approach is tested on the IEEE 34-node unbalanced distribution system.