Modelling the charging probability of electric vehicles as a gaussian mixture model for a convolution based power flow analysis

Abstract

This paper presents an approach for modelling the charging probability of electric vehicles as a Gaussian mixture model. The model is built up by assembling adapted multivariate normal probability density functions. This is done because the expectation maximization algorithm fails finding maximum likelihood estimates in respect of the charging power of the generated charging profiles. This Gaussian mixture model enables for capturing the charging profiles comprehensively with a few parameters and therefore it enables for calculating the charging probability dynamically for individual parameter intervals. The underlying assumptions about battery capacity, consumption, charging infrastructure, type of weekday and settlement structure determine the generation of the charging profiles. The proposed approach makes these parameters available for the density. Thereby, the provision of the charging profiles gets obsolete. This density can be used for a convolution based power flow analysis which offers benefits regarding the computational effort and random access memory usage compared to Monte Carlo-like simulations.