Optimal HVAC Scheduling under Temperature Uncertainty using the Wasserstein Metric

The heating, ventilation and air condition (HVAC) system consumes the most energy in commercial buildings, consisting over 60% of total energy usage in the U.S. Flexible HVAC system setpoint scheduling could potentially save building energy costs. This paper proposes a distributionally robust optimal (DRO) HVAC scheduling method that minimizes the daily operation cost with constraints of indoor air temperature comfort and mechanic operating requirement. Considering the uncertainties from ambient temperature, a Wasserstein metric-based ambiguity set is adopted to enhance the robustness against probabilistic prediction errors. The schedule is optimized under the worst-case distribution within the ambiguity set. The proposed DRO method is initially formulated as a two-stage problem and then reformulated into a tractable mixed-integer linear programming (MILP) form. The paper evaluates the feasibility and optimality of the optimized schedules for a real commercial building. The numerical results indicate that the costs of the proposed DRO method are up to 6.6% lower compared with conventional techniques of optimization under uncertainties. They also provide granular risk-benefit options for decision-makinz in demand response programs.