Incorporating Delayed Temperature Dynamics into Residential Air Conditioner Models for Grid Frequency Regulation

Aggregations of residential air conditioners can be controlled to provide important services to the grid, such as frequency regulation. To facilitate such applications, it is essential that models used to represent air conditioners capture their key dynamics. Using house temperature measurements, we demonstrate that there is a delay between the time instant at which an air conditioner switches and the time when the regulated indoor temperature starts moving in the opposite direction, a phenomenon that is not captured by existing models commonly used by power system researchers. We show that this delayed temperature evolution is dependent upon the outdoor temperature and model this relation using a quadratic curve fit to the available data using a robust linear least-squares method in order to address the presence of heteroscedasticity. We extend a commonly used house model that captures both air and mass temperature dynamics in order to account for the aforementioned temperature delays. We assess the impacts that these temperature delays can have on the performance of an existing model-based controller. We develop a new model of aggregate air conditioner dynamics that captures the delays, and modify the controller to incorporate this model. We show that our new controller is able to achieve better frequency regulation performance without compromising user comfort.