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Optimal management and integration of electric vehicles to the grid: Dynamic programming and game theory approach

This paper provides a Dynamic Programming (DP) approach to optimally manage the charging schedule of electrical vehicles (EV) based on a decentralized global optimization frame given by the use of a Game Theory approach. The paper provides a detailed explanation of a forward induction DP algorithm and shows its adaptation to the problem of optimal charging of one EV with the corresponding constraints of limiting power consumption, minimal and maximal states of charge, desired states of charge, etc. The extension to multiple EVs is provided by the adaptation of a N-person non-cooperative game approach. In this game, the payoff of each player is based on a utility function that aims to reduce the distance between the total load and the average load, achieving load curve flattening.