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In the present day, when centralized energy storage technology is becoming increasingly mature, the cooperative energy sharing framework between the combined cooling, heating, and power (CCHP) systems and a shared energy storage provider (SESP) can effectively promote the local consumption of renewable energy and reduce the social energy cost. In this study, the optimal operation models of CCHP and SESP are first developed by considering the electric energy trading of the CCHP and the SESP. Then the CCHP–SESP cooperative operation model is established based on Nash bargaining theory, followed by equating it into two subproblems of coalition social energy cost minimization and electric energy trading payment negotiation. The alternating direction method of multipliers approach is introduced to solve the energy‐sharing problems in a distributed way. Numerical simulation results show the effectiveness of the proposed energy‐sharing framework. Simulation results show that the proposed bargaining‐based energy‐sharing framework can significantly reduce the social energy cost and improve the utilization rate of energy storage resources. [ABSTRACT FROM AUTHOR]