Probabilistic load flow computation using saddle-point approximation

The purpose of this paper is to present a new cumulant-based method, based on the properties of saddle-point approximation (SPA), to solve the probabilistic load flow (PLF) problem for distribution networks with wind generation.

This technique combines cumulant properties with the SPA to improve the analytical approach of PLF calculation. The proposed approach takes into account the load demand and wind generation uncertainties in distribution networks, where a suitable probabilistic model of wind turbine (WT) is used.

The proposed procedure is applied to IEEE 33-bus distribution test system, and the results are discussed. The output variables, with and without WT connection, are presented for normal and gamma random variables (RVs). The case studies demonstrate that the proposed method gives accurate results with relatively low computational burden even for non-Gaussian probability density functions.

The main contribution of this paper is the use of SPA for the reconstruction of probability density function or cumulative distribution function in the PLF problem. To confirm the validity of the method, results are compared with Monte Carlo simulation and Gram–Charlier expansion results. From the viewpoint of accuracy and computational cost, SPA almost surpasses other approximations for obtaining the cumulative distribution function of the output RVs.