Stochastic Modeling of Power Demand Due to EVs Using Copula

The driving patterns characterizing electric vehicles (EVs) are stochastic and, as a consequence, the electrical load due to EVs inherits their randomness. This paper presents a Monte Carlo procedure for the derivation of load due to EVs based on a fully stochastic method for modeling transportation patterns. Under the uncontrolled domestic charging scenario three variables are found to be crucial: the time a vehicle leaves home, the time a vehicle arrives home, and the distance traveled in between. A detailed transportation dataset is used to derive marginal cumulative distribution functions of the variables of interest. Since the variables are statistically dependent, a joint distribution function is built using a copula function. Subsequently, simulated EV trips are combined with a typical charging profile so that the energy contribution to the system is computed. The procedure is applied to analyze the effect of the EV load on the national power demand of The Netherlands under different market penetration levels and day/night electricity tariff scenarios.