A novel multi-stage robust optimization model for carbon-free microgrid scheduling with decision-dependent uncertainty sets via adaptive benders decomposition

The integration of renewable energy sources into carbon-free microgrids introduces operational challenges due to uncertainties in generation and demand. Traditional robust optimization methods rely on static uncertainty sets, often producing overly conservative or infeasible solutions. This paper presents a novel two-stage robust optimization framework that explicitly models decision-dependent uncertainties (DDUs), where uncertainty sets dynamically adapt to operational decisions such as energy storage dispatch, EV charging schedules, and hydrogen fuel cell operations. Unlike static approaches, this method captures how system actions influence uncertainty bounds, enabling a realistic balance between conservatism and risk. Advanced polyhedral uncertainty sets are employed to dynamically represent evolving uncertainty ranges, effectively linking operational decisions to uncertainty management. To solve this complex problem, an enhanced Benders decomposition algorithm is developed, integrating adaptive optimality and feasibility cuts that remain valid under dynamic uncertainty adjustments, ensuring computational tractability and global optimality—a limitation in traditional methods like Column-and-Constraint Generation. The framework is validated on 33-bus and 69-bus microgrids under grid-connected and islanded modes. Results show a 7–12 % increase in operational costs compared to static robust optimization but demonstrate significant improvements in reliability: 15–20 % reduction in load shedding during islanded operation, voltage deviations constrained below 0.02 p.u., and 5–8 % higher renewable energy utilization. By dynamically aligning uncertainty management with operational decisions, the method mitigates conservative biases while enhancing resilience. This work provides a practical, decision-responsive optimization tool for carbon-free microgrids, advancing robust energy management systems that address real-world uncertainties. The framework supports grid operators in balancing operational risks, cost efficiency, and reliability, offering a critical pathway for sustainable power system transitions.