With the implementation of the “coal to electricity” project

the heat pump load in the distribution network increases significantly. Standing in the point of heat pump users

cooperative game mode is used for heat pumps joining in day-ahead dispatching of distribution network. In order to accurately describe the polymerization flexibility of the heat pump load cluster

this paper uses the constraint space superposition method based on Minkowski Sum

and describes the heat pump cluster as a “virtual synchronous machine” or “virtual energy storage” model by looking for its maximal inner cube or rectangular pyramid simplification constraint. Furthermore

a method of income distribution among users based on approximated Shapley Value is proposed. The validity of the proposed method is verified by the case based on IEEE 33 mode system.