Multivariate Stochastic Modeling of Plug-in Electric Vehicles Demand Profile Within Domestic Grid

Abstract

A copula-based stochastic approach is proposed to derive the load demand of a fleet of domestic commuter plug-in electric vehicles (PEVs). Employing a copula, a multivariate distribution can be constructed by specifying marginal univariate distributions, and afterwards choosing a copula to provide a dependence structure among variables. The copula function does not constrain the choice of the marginal distribution. At first, appropriate non-Gaussian probability density functions are fitted to the gathered datasets. The datasets include home arrival time, daily travelled distance, and home departure time of randomly selected private internal combustion engines (ICE) vehicles. Then, the dependence structure is modeled using a student’s t copula distribution to generate random samples required in the Monte Carlo simulation. In each iteration, extraction of the charging profile is carried out for the individual PEVs in order to derive the hourly aggregated load profile of the fleet. Afterwards, probability density function of the aggregated load of the PEVs within each hour is estimated by applying the Monte Carlo simulation. Eventually, the expected value of the hourly load demand can be calculated regarding the achieved power distributions. The PEVs are supposed to be charged through a distribution transformer. Consequently, the profile of the power delivered through the transformer to the PEVs is attained, which in turn can be useful for various distribution system applications such as network planning, load management, and probabilistic load flow as well as sitting and sizing issues.