Event-Based Optimization Within the Lagrangian Relaxation Framework for Energy Savings in HVAC Systems

Optimizing HVAC operation becomes increasingly important because of the rising energy cost and comfort requirements. In this paper, an innovative event-based approach is developed within the Lagrangian relaxation framework to minimize an HVAC's day-ahead energy cost. To solve the HVAC optimization problem based on events is challenging since with time-dependent uncertainties in weather, cooling load, etc., the optimal policy is not stationary. The nonstationary policy space is extremely large, and it is time consuming to find the optimal policy. To overcome the challenge, we develop an event-based approach to make the nonstationary optimal policy stationary in the planning horizon. The key idea is to augment state variables to include the time-dependent variables that make the optimal policy nonstationary and then define events based on the extended state variables. In addition, we develop within the Lagrangian relaxation framework a Q-learning method where Q-factors are used to evaluate event-action pairs and to obtain the optimal policy. Numerical results demonstrate that, as compared with time-based approaches, the event-based approach maintains similar levels of energy costs and human comfort, but reduces computational efforts significantly and has a much faster response to events.