Robust Analysis and Optimal Control of Flexible Interconnected Microgrids Considering Wind and Solar Uncertainty

High penetration of wind and photovoltaic (PV) generation increases renewable uncertainty and real-time balancing pressure in active distribution networks. To address this problem, this paper proposes a two-stage robust optimization method for day-ahead and real-time scheduling of a flexibly interconnected multi-microgrid (MMG) system enabled by a flexible interconnection device (FID). The proposed framework jointly optimizes power purchase from the upper-level distribution network, micro-gas turbine output, energy storage system (ESS) operation, and FID-based bidirectional power exchange, thereby coordinating local temporal flexibility and inter-microgrid spatial flexibility. A polyhedral uncertainty set is used to model wind and PV forecast errors, and the problem is solved by the column-and-constraint generation (C&CG) algorithm. Case studies on a two-microgrid system show that, compared with independent operation under traditional robust optimization, the proposed method reduces real-time balancing cost, wind and PV curtailment, and total operating cost by 98.96%, 95.84%, and 0.59%, respectively. Sensitivity analysis further verifies the economy–robustness trade-off under different uncertainty budgets and forecast deviation levels.