Four-level, two-stage hierarchical robust model for optimizing home-community-distribution energy systems

This paper proposes a four-level, two-stage robust optimization with decision-dependent uncertainty for integrated optimization of home energy management system, community energy management system, and distribution system operator operations. The principal challenge addressed is the coordinated optimization of interconnected layers under renewable and demand uncertainties, where independent optimization causes voltage violations, feeder congestion, and under-utilization of prosumer flexibility. Two-stage robust optimization with decision-dependent uncertainty links first-stage scheduling and second-stage real-time adjustments with uncertainty sets that adapt to operational decisions, reducing conservatism while preserving feasibility across scenarios. The framework enforces grid-aware home energy management system schedules, coordinates peer-to-peer trading at the community level, and incorporates distribution system operator constraints to maintain network stability. A scalable Benders-type decomposition is developed to handle decision-dependent uncertainties in large systems. Case studies on IEEE 69-bus and 119-bus test systems demonstrate Two-stage robust optimization with decision-dependent uncertainty's effectiveness: achieving cost reductions of 6.3% at the home energy management system schedules, coordinates peer-to-peer trading at the community level, and incorporates distribution system level, 8.5% at the community energy management system level, and 1.2% for the distribution grid, alongside improved voltage stability and reduced grid stress. The method manages over 60 prosumers, with peer-to-peer trading lowering grid imports by 20% and voltage deviations by 22%; a 30% flexible-load share yields a 5% reduction in total system cost and a 3.6% decrease in grid stress.