Fast Point Estimate Method for Correlated Multimodally Distributed Input Variables

Uncertainties in the electricity grid grow, so the need for alternatives to deterministic load flow approaches come up. The Point Estimate Method (PEM) as an approximate probabilistic load flow method calculates the statistical moments of the output variables using the statistical moments of the input variables. Afterwards, the probability density functions (PDF) and cumulative density functions (CDF) are determined using expansion methods. Due to the combination of different renewable energy sources (RES) at the same grid node, correlated multimodally distributed input variables may result. An enhancement to the two-PEM (2m-PEM) and expansion method in order to consider correlated multimodally distributed input variables is presented. The new method consists of a sensitivity analysis and a modified 2m-PEM to be applicable for large grids with multiple multimodal distributed variables. The proposed algorithm is demonstrated in a test grid and verified through the comparison of the results using Monte Carlo Simulation (MCS) as reference method.