Distributionally robust optimal scheduling of multi-microgrid considering asymmetric bargaining

•A two-stage distributionally robust model is constructed to improve the robustness of the scheduling plan.•To ensure stability and sustainability of the cooperative operation, an asymmetric bargaining method is proposed to quantify the contribution of each microgrid to the cooperative alliance from the perspectives of energy and the environment, aiming to achieve a fair distribution of the cooperative benefit.•The proposed optimal scheduling method of the multi-microgrid can guarantee the robustness, economy and privacy of the system. Cooperative operation of microgrids (MGs) is conducive to increasing the absorption rate of renewable energy and decreasing carbon emissions, but the scheduling of the multi-microgrid (MMG) is challenged due to the uncertainty of wind and solar output and the distribution of the income after energy trading. Based on this, a MMG optimal scheduling method on the basis of the distributionally robust method and asymmetric bargaining method is proposed. Firstly, according to Nash negotiation theory, an optimization model of cooperative operation is established, and it is equivalently transformed into easy-to-solve sub-problems of minimizing the MMG operating cost and maximizing the benefit of power trading. Secondly, to cope with the uncertainty of wind and solar output, the minimization model of the distributionally robust optimal form is established, and the alternating direction multiplier method (ADMM) of nested column constraints generation (C&CG) method is employed to solve the model in a distributed manner, which can ensure the equilibrium between robustness and economy of the scheduling scheme and the optimal economic benefit; to realize a fair distribution of cooperative income, an unsymmetrical bargaining method is presented to calculate bargaining factor with electric energy contribution and carbon emissions reduction of each MG as indicators, and the ADMM is used to solve the maximization model in a distributed manner so as to ensure a reasonable and optimal distribution of income. Lastly, the validity of the program is verified by arithmetic simulation.