Multi-microgrids distributed peer-to-peer energy trading in distribution system considering uncertainty risk

•The cooperative energy trading model for MMGs in the distribution network under uncertainty is developed.•The CVaR theory is used to quantify the energy trading risks brought by uncertainty.•The Nash negotiation theory is used to realize the distribution of benefits and payment of network fees.•A distributed Bi-CADMM is used to compute the cooperative energy trading model. The cooperative energy trading model for multi-microgrids in the distribution network systems under uncertainty is investigated in this paper, which permits peer-to-peer (P2P) energy trading under the system network constraints. The model is formulated as a two-stage problem, i.e. cooperative welfare maximization problem based on the conditional value at risk (CVaR) (P1) and market clearing problem based on the Nash Bargaining theory (P2). In the first stage, the CVaR is used to quantify the risk of uncertainty of source and load, and a stochastic optimization model is formed to identify energy scheduling and reactive power control. The bi-level nested alternating direction method of multiplier based on consistent communication (Bi-CADMM) is offered as a privacy-preserving technique for solving P1. Then, the second stage determines the mutual payments of the microgrids (MGs) and network usage charges for the distribution systems operator (DSO) according to the negotiation coefficient in the form of centralized solving technology. Case studies on a modified IEEE-33 system with 4-MGs show that the Bi-CADMM has strong convergence performance and can guarantee the sub-optimal and feasible solution compared with the centralized technology first. The final results also show that the decision-makers with different preferences can determine the degree of conservatism of the scheduling through the risk factor to deal with the uncertainty, and the suggested energy trading model is beneficial in terms of lowering participants' costs and improving voltage security.