Reachable-Set Decomposition for Real-Time Aggregation of Multi-Zone HVAC Fleets
Aggregating building heating, ventilation, and air-conditioning (HVAC) fleets can provide substantial real-time flexibility to power systems. However, practical deployment requires scalable characterization of multi-zone, multi-period flexibility and guaranteed feasible disaggregation as temperature states and exogenous inputs are revealed sequentially. This paper develops an offline-online reachable-set decomposition framework that combines offline temporal decomposition with a scalable online fleet coordination policy. Offline, backward reachable sets encode remaining-horizon feasibility as per-period state constraints, while tailored polytopic inner approximations provide tractable representations of these sets for thermally coupled multi-zone buildings. Online, aggregate flexibility is computed through parallel, single-period building-level linear programs followed by the fleet-level closed-form Minkowski summation of power intervals, thereby avoiding operations on high-dimensional full-horizon sets. The resulting endpoint profiles enable a closed-form, time-causal policy that disaggregates any aggregate HVAC power command within the reported interval while preserving recursive feasibility. Case studies show that, relative to the considered fixed full-horizon baselines, the proposed framework captures greater aggregate flexibility by recomputing per-period intervals using the latest state and exogenous information, while maintaining feasible disaggregation under sequentially revealed uncertainty. Its building-separable computation further enables scalable implementation for large fleets of multi-zone buildings.