Imputation schemes for the cooperative game in the hybrid power system planning

Game theory is a good way to model the hybrid power system planning, by taking the wind power, photovoltaic generation and storage batteries as players. It is illustrated that the grand cooperation of all the three players can achieve the maximum total economic benefit. However, that how to assign the gains from the cooperation is an essential problem in the cooperative game, and is thus the topic of this paper. The constraints for the core that any imputation of this cooperative game should satisfy are given in this paper to attempt to achieve a mutually acceptable basis for an agreement, such that all the players are interested to cooperate. A modified index of propensity to disrupt is used to test the cooperation strength of a given imputation scheme. Furthermore, four specific imputation schemes including the equal assignment, the generation capacity based assignment, the Shapley value and the equal disruption propensity based imputations, are proposed and analyzed, and the last two schemes are illustrated to be the best.