Copula-based integration of electric vehicles into a smart grid using MILP

This paper presents an approach to integrate electric vehicles into a smart grid formulated by a mixed integer linear programming (MILP) model. Modelling the driving patterns of the electric vehicles has to consider their variability. Therefore, a stochastic approach is used to model electric vehicle usage. The variables used to describe the mobility behaviour are strongly correlated. Hence, a copula function is used to create a multivariate probability distribution of the variables, taking into account the correlations among variables as well as the marginal distributions of the individual variables. Additionally, differences between the mobility behaviour of five groups of people with different occupational activities are considered. Afterwards, a simulation is carried out to assess the impact of electric vehicles on the smart grid from the perspective of an energy supplier operating the local energy production. An uncontrolled, a controlled and a bidirectional charging strategy are analysed. The uncontrolled strategy leads to increased energy demand in the evening during peak demand and more than 20% increased grid demand of the smart grid. In the controlled strategies, more charging demand is satisfied with locally produced energy. The bidirectional strategy furthermore cuts the grid demand in the morning and evening during peak electricity demand.