Coordinated robust planning of multi-energy microgrids with P2P trading: A variational inequality based distributed approach

The coordinated planning of multi-energy microgrids (MEMGs) plays a pivotal role in improving energy efficiency within peer-to-peer (P2P) energy markets. However, source-demand uncertainty introduces energy fluctuations that jeopardize system stability, and the multi-agent coupling structure of planning models often depends on convexity assumptions to enable tractable distributed solutions. To tackle these challenges, this paper develops a coordinated planning framework for multiple MEMGs that integrates P2P energy sharing with stochastic source-load modeling. The multi-agent cost minimization problem is formulated under mixed-integer programming (MIP) settings. Then, a monotone variational inequality (MVI)-driven equilibrium model is constructed to capture interactions among MEMGs, and an alternative optimization procedure (AOP) is incorporated to address the non-convexity arising from integer variables. Subsequently, a distributed adaptive prediction–correction algorithm with theoretical convergence guarantees is developed to solve the multi-block MVI formulation with minimal information exchanged. Additionally, the generalized Nash bargaining solution is employed to ensure incentive compatibility and fair profit distributions among MEMG investors. Numerical experiments demonstrate the effectiveness and advantages of the proposed framework in enhancing efficiency, safeguarding privacy, and fostering cooperation.