Nonparametric Probabilistic Unbalanced Power Flow With Adaptive Kernel Density Estimator

Abstract

This paper presents a nonparametric algorithm to estimate probability density functions of power flow outputs in unbalanced distribution systems. The proposed algorithm is based on an adaptive kernel density estimation. As the main advantage, the proposed algorithm is: 1) applicable for power flow problems with unknown classes of probability distributions for output random variables; 2) highly accurate; 3) non-time-consuming; 4) capable of modeling uncertainties of distributed generators; 5) able to provide complete statistical information on the probabilistic power flow problem; and 6) applicable to unbalanced power distribution systems. The proposed nonparametric estimator is applied to the IEEE 13-bus and IEEE 37-bus test cases, which consist of wind farms and photovoltaic units. We use several statistical parameters to compare outcomes of the proposed nonparametric estimator with results obtained by the 2n + 1 point estimation, and unscented transforms methods. In addition, probability density functions of power flow output variables are plotted using the proposed algorithm, Monte-Carlo simulation, and diffusion methods, and the results are compared.