Parzen Window Density Estimator-Based Probabilistic Power Flow with Correlated Uncertainties

This paper presents a numerical-based algorithm to solve the probabilistic power flow problem. Parzen window density estimator is used to efficiently estimate probabilistic characteristics of power flow outputs. Correlations between wind generation, load, and plug-in hybrid electric vehicle charging stations are taken into account. The proposed algorithm works properly for random variables with various probability distribution functions and is very useful when limited information is available for each random variable. The algorithm is tested on the IEEE 14-bus and IEEE 118-bus systems considering correlated and uncorrelated conditions. Comparison between the proposed algorithm with 2n, \text{2n} + 1 point estimation methods as well as Monte Carlo simulation and linear diffusion method are provided. In addition, probability density and cumulative distribution functions are determined using the proposed algorithm, diffusion method, and the combined Cumulants and Gram-Charlier for \text{2n} + 1 point estimation method. Error indices are introduced to evaluate all random variables in a single benchmark. Simulation results show the effectiveness of the proposed algorithm to provide complete statistical information for probabilistic power flow outputs