Building Load Control Using Distributionally Robust Chance-Constrained Programs with Right-Hand Side Uncertainty and the Risk-Adjustable Variants

Abstract

Aggregation of heating, ventilation, and air conditioning (HVAC) loads can provide reserves to absorb volatile renewable energy, especially solar photo-voltaic (PV) generation. In this paper, we decide HVAC control schedules under uncertain PV generation, using a distributionally robust chance-constrained (DRCC) building load control model under two typical ambiguity sets: the moment-based and Wasserstein ambiguity sets. We derive mixed integer linear programming (MILP) reformulations for DRCC problems under both sets. Especially, for the Wasserstein ambiguity set, we use the right-hand side (RHS) uncertainty to derive a more compact MILP reformulation than the commonly known MILP reformulations with big-M constants. All the results also apply to general individual chance constraints with RHS uncertainty. Furthermore, we propose an adjustable chance-constrained variant to achieve tradeoff between the operational risk and costs. We derive MILP reformulations under the Wasserstein ambiguity set and second-order conic programming (SOCP) reformulations under the moment-based set. Using real-world data, we conduct computational studies to demonstrate the efficiency of the solution approaches and the effectiveness of the solutions. Summary of Contribution: The problem studied in this paper is motivated by a building load control problem that uses the aggregation of heating, ventilation, and air conditioning (HVAC) loads as flexible reserves to absorb uncertain solar photovoltaic (PV) generation. The problem is formulated as distributionally robust chance-constrained (DRCC) programs with right-hand side (RHS) uncertainty. In addition, we propose a risk-adjustable variant of the DRCC programs, where the risk level, instead of being predetermined, is treated as a decision variable. The paper aims to provide tractable reformulations and solution algorithms for both the (general) DRCC and the (general) adjustable DRCC models with RHS uncertainty.