Optimal Day-Ahead Charging Scheduling of Electric Vehicles Through an Aggregative Game Model

Abstract

The electric vehicle (EV) market has been growing rapidly around the world. With large scale deployment of EVs in power systems, both the grid and EV owners will benefit if the flexible demand of EV charging is properly managed through the electricity market. When EV charging demand is considerable in a grid, it will impact spot prices in the electricity market and consequently influence the charging scheduling itself. The interaction between the spot prices and the EV demand needs to be considered in the EV charging scheduling, otherwise it will lead to a higher charging cost. A day-ahead EV charging scheduling based on an aggregative game model is proposed in this paper. The impacts of the EV demand on the electricity prices are formulated with the game model in the scheduling considering possible actions of other EVs. The existence and uniqueness of the pure strategy Nash equilibrium are proved for the game. An optimization method is developed to calculate the equilibrium of the game model through quadratic programming. The optimal scheduling of the individual EV controller considering the actions of other EVs in the game is developed with the EV driving pattern distribution. Case studies with the proposed game model were carried out using real world driving data from the Danish National Travel Surveys. The impacts of the EV driving patterns and price forecasts on the EV demand with the proposed game model were also analysed. Index Terms-Aggregative game model, day-ahead market, electric vehicles (EVs), game theory, Nash equilibrium. NOMENCLATURE A. Indices and Sets: t, τ Index of time intervals. T Set of time intervals for planning. v, v , v , i, φ Index of electric vehicles (EVs). V Set of EVs in the game. Φ Set of EVs with driving pattern realizations according to the driving pattern distribution of set V. δ Cardinality of set T .

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