Optimal Day-ahead Charging Scheduling of Electric Vehicles through an Aggregative Game Model

Zhaoxi Liu*, Qiuwei Wu, Shaojun Huang, Lingfeng Wang, Mohammad Shahidehpour, Yusheng Xue

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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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.
Original languageEnglish
JournalIEEE Transactions on Smart Grid
Issue number5
Pages (from-to)5173-5184
Publication statusPublished - 2017

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  • Aggregative game model
  • Day-Ahead Market
  • Electric vehicles (EVs)
  • Game theory
  • Nash equilibrium


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