To address the impact of the randomness of distributed photovoltaic (PV) output and load demand on the economic operation of the power system

this paper proposes a robust optimization strategy for the cooperative game of virtual power plants (VPP) considering multi-agent interaction. Under the electricity trading and reactive power auxiliary service markets

an optimal operation model of the distribution network based on the price-quota curve and an optimal operation model of the VPP based on peer-to-peer (P2P) energy exchange are established respectively. Under the distributionally robust optimization based on the kullback-leibler (KL) divergence

with the electricity price formulated by the distribution network and the grid-connected power determined by the VPP as the interaction variables

the profit distribution balance among different market entities is achieved through the interactive between the distribution network and the VPP. On this basis

according to the decision-making information obtained from the interactive between the distribution network and the VPP

the profit distribution for each VPP is carried out based on the Nash bargaining model

and the alternating direction method of multipliers (ADMM) is adopted for distributed solution to realize the cooperative game among multiple VPP. The example simulation conducted on an urban distribution system verifies the effectiveness of the strategy proposed in this paper.