Enhancement to the combination of point estimate method and Gram-Charlier Expansion method for probabilistic load flow computations

Due to growing uncertainties in the grid, probabilistic load flow methods achieve more attention. The Point Estimate Method (PEM) was introduced in 1975 first and was enhanced since then. In a first step, this paper evaluates the applicability of the method considering different input data to analyze the limitations of the method. Different input data exist through the diversity of generators and loads with diverse characteristics. Discrete probability mass functions (PMF) and continuous probability distribution functions (PDF), e.g. Normal, Weibull and Student-t distributions are considered for input data with different standard deviations. The statistical moments are calculated with the PEM. Often the evaluation of statistical moments is not sufficient, but rather the PDF and cumulative distribution function (CDF) of the output variables are of interest. Therefore, the method can be extended by expansion methods. Nowadays, Gram-Charlier Expansion (GCE), Edgeworth- and Cornish-Fisher-Expansions are mainly used. This paper shows that the existing expansion methods cannot deal with discrete PMF as they lead to PDF and CDF with multimodality. Therefore, this paper amplifies the method to determine the PDF and CDF of the output variables with given discrete PMF as input variables. In addition, modifications are shown to reduce the computational burden regarding a greater amount of input data in a large grid.