A Probabilistic Approach for Optimal Capacitor Allocation in Three-Phase Unbalanced Distribution Systems

The problem of choosing the optimal location and size for shunt capacitors in unbalanced distribution systems can be formulated as a mixed, non-linear, constrained optimization problem and is usually solved in deterministic scenarios. However, distribution systems are stochastic in nature, leading thus to inaccurate deterministic solutions. To take into account the unavoidable uncertainties which affect the problem input data (mainly the load demands), this paper formulates a probabilistic optimization model. To reduce the computational efforts, a linearized form of the equality and inequality constraints of the optimization model is used, and a proper genetic algorithm-based procedure is applied as solution method. The proposed approach is tested on the IEEE 34-node unbalanced distribution system in order to demonstrate the effectiveness of the procedure in terms of reduced computational efforts and accuracy of the results.