Point-Estimate Method for Probabilistic Power Flow in Unbalanced and Distorted Distribution Systems

In this paper, a probabilistic power flow (PPF) for unbalanced and distorted distribution systems based on the Point-Estimate Method (PEM) is proposed. The uncertainties of loads and photovoltaic (PV) generations are taken into consideration. The normal and Beta distributions are used for describing the probability density function (PDF) and cumulative distribution function (CDF) of the input stochastic variables –load powers and solar irradiance, respectively. For obtaining the PDFs and CDFs of the output variables of interest the Gram-Charlier (GC) expansion series are used. The proposed method is tested on the IEEE 13- and 37-bus test systems, and accuracy of the results is validated by comparing the results with those obtained using the Monte Carlo simulation (MCS) method. It is shown that the PEM-based approach provides effective, robust and high-quality solutions.