Optimal HVAC Energy and Regulation Reserve Scheduling in Power Markets

This paper considers the optimal scheduling of the hourly energy consumed and regulation reserve capacity offered by a Heating, Ventilation and Air-Conditioning (HVAC) system participating in a day-ahead electricity market. We formulate an Integrated hourly energy and regulation reserve Scheduling and Deployment (ISD) problem that optimizes the hourly costs and benefits resulting from the power consumed, the regulation reserve capacity offered, the occupant thermal comfort utility, and the expected Intra-Hour Costs (IHCs) due to HVAC's imperfect tracking of the regulation signal broadcasted by the Independent System Operator every few seconds. Addition of the IHCs to the objective function is the major innovation of this paper. It enables optimal HVAC scheduling to internalize expected regulation signal tracking error cost traded-off against incremental occupant thermal discomfort that may result from perfect tracking. The cost causation circle closes by noting that a high hourly regulation reserve offer may result in higher expected IHCs by increasing the associated tracking error and the incremental occupant discomfort. The paper's innovation is achieved by (i) estimating an analytic function of the hourly HVAC scheduling decision and state variables that approximates the expected IHCs, and (ii) including this exogenously estimated analytic function in the objective of the hourly ISD optimization problem. Non-convexities introduced to the optimization problem resulting from high fidelity HVAC model and the inclusion of the expected IHCs, are addressed efficiently through piecewise convex relaxations that provide tight optimality bounds. Extensive numerical results are provided to demonstrate the applicability and performance of the proposed approach.