Cumulant Based Stochastic Reactive Power Planning Method for Distribution Systems With Wind Generators

Proliferation of wind generators (WGs) requires a change in distribution system planning techniques as WGs have intermittent and uncertain output. This paper proposes a Cumulant based stochastic optimal reactive power planning method for distribution systems with high penetration of WGs. Uncertainties in the output of WGs and load forecasts are modeled using probability density functions (PDFs). With a stochastic framework, an optimization challenge is formulated to minimize the total costs of new capacitors and the total annual energy loss. The optimization problem is then solved by using the Logarithmic Barrier Interior Point Method (LBIPM). At the optimal solution, LBIPM provides a linear relationship between the cumulants of independent variables (load and wind power) and the cumulants of the dependent system parameters. The Cumulant method offers a generous advantage in speed, while maintaining acceptable accuracy, as compared to the computationally cumbersome traditional Monte Carlo simulation (MCS) method. The method is tested on 7-bus, 33-bus, and 129-bus systems. The results are reported and discussed. The performance and accuracy are assessed by comparing the results with those from MCS method.