Distributionally Robust Chance-Constrained Building Load Control under Uncertain Renewables

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. However, the time-varying PV generation is not perfectly known when the system operator decides the HVAC control schedules. To consider the unknown uncertain PV generation, in this paper, we formulate a distributionally robust chance-constrained (DRCC) building load control problem under two typical ambiguity sets: moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the DRCC problem under Wasserstein ambiguity set, we utilize the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known big-M MILP reformulations. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained formulation to achieve a reasonable trade-off between operational risk and costs. We derive tractable reformulations/algorithm under both ambiguity sets. Using real-world data, we conduct computational studies to demonstrate the effectiveness of the solution approaches and the efficiency of the solutions.