Online Convex Optimization of Multi-Energy Building-to-Grid Ancillary Services

In this article, buildings with several sources of flexibility, subject to multiple energy requirements, and having access to different electricity markets are considered. A two-level algorithm for optimizing the building's energy management under uncertainty and limited information is presented in this article. A mixed-integer linear program scheduling level is first used to set an energy management objective for every hour using only averaged data. Then, an online convex optimization (OCO) algorithm is used to track in real time the objective set by the scheduling level. For this purpose, a novel penalty-based OCO algorithm for time-varying constraints is developed. The regret of the algorithm is shown to be sublinearly bounded above. This ensures, at least on average, the feasibility of the decisions made by the algorithm. A case study in which the two-level approach is used on a building located in Melbourne, Australia, is presented. The approach is shown to satisfy all constraints 97.32% of the time while attaining a positive net revenue at the end of the day by providing ancillary services to the power grid.