Affine adaptive robust model for local energy community operations in energy, reserve, and regulation markets

This paper proposes an Affine Adaptive Robust Optimization (AARO) framework for the optimal day-ahead and real-time operation of a Local Energy Community (LEC) participating in energy, reserve, and regulation markets under uncertainty in photovoltaic (PV) generation, demand, and reserve activation. Uncertainties are modeled using normalized deviation variables bounded by polyhedral uncertainty sets, with a budget-of-uncertainty parameter to control the level of conservatism. Linear Decision Rules (LDRs) are employed to express real-time regulation and resource dispatch decisions as affine functions of uncertain parameters, transforming the two-stage adaptive robust problem into a tractable min–max mixed-integer linear program (MILP). The resulting two-stage structure is efficiently solved using the Column-and-Constraint Generation (C&CG) algorithm. The model jointly optimizes here-and-now decisions (day-ahead energy and reserve schedules) and wait-and-see decisions (real-time regulation services and flexibility deployment) to minimize operational costs under worst-case uncertainty realizations. Numerical results for a PV–BESS–HES-equipped LEC demonstrate that the proposed framework ensures feasible, cost-effective, and market-responsive operation across a wide range of uncertainty levels. As the budget of uncertainty increases, the LEC shifts toward greater self-sufficiency, reducing grid dependence while increasing the utilization of internal flexibility resources. Sensitivity analysis indicates that battery energy throughput is a critical driver of long-term profitability, with high-cycle systems yielding up to 26% higher cumulative revenue over a 15-year period. The proposed affine model provides a scalable, distribution-free robustness tool for multi-market LEC operation under deep uncertainty.