Fuzzy Stochastic Programming Method: Capacitor Planning in Distribution Systems With Wind Generators

Capacitor planning in a distribution system (DS) must account for forecasted load and planned wind generators (WGs). In some DSs with large penetration, WGs support a significant part of the total load on an average and the power flow reverses to the substation during high-wind-low-load conditions. With annual forecasts of peak loads and generations being probabilistic in nature with differing probability distribution functions, their proper representation in a capacitor planning exercise is imperative. In this work, using probabilistic models of load and wind generation, we propose a stochastic capacitor planning formulation for DSs. The proposed formulation minimizes the total cost of newly located and sized capacitors and the annual energy loss in a DS while considering limits on load bus voltages. The starting state of the optimization process has forecasted loads, planned WGs, and inadequate capacitors that results in lower voltage limit violations. In order to handle this infeasible state in a stochastic optimization formulation, fuzzy models are used to represent load bus voltage constraints. The proposed fuzzy stochastic programming method that combines stochastic programming and fuzzy optimization procedure is solved using a robust mixed integer linear programming solver. Results on a 70-bus system are reported, compared, and discussed.