  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 first studies deterministic optimization,
robust optimization, and stochastic optimization to minimize 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 distributionally robust optimization (DRO) method is
proposed to enhance the robustness of the optimal schedule against the
uncertainty of probabilistic prediction errors. The schedule is optimized under
the worst-case distribution within an ambiguity set defined by the Wasserstein
metric. 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 making in demand response programs.
