A probabilistic approach for multiobjective optimal allocation of capacitors in distribution systems based on genetic algorithms

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 multi-objective optimization problem, and is usually solved in deterministic scenarios. However, distribution systems are stochastic in nature, which leads to inaccurate deterministic solutions. To take into account the unavoidable uncertainties that affect the problem´s input data (mainly the load demands), this paper formulates a probabilistic multi-objective optimization problem. To reduce the computational efforts, a linearized form of the equality and inequality constraints of the multi-objective optimization model is used, and a proper micro-genetic algorithm (μGA)-based procedure is applied as a 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 the reduced computational effort and accuracy of the results.