Economic Operation of Thermostatic Loads Under Time Varying Prices: An Optimal Control Approach

In this paper, we consider the problem of optimal precooling of thermostatic loads by a load serving entity (LSE) under time varying electricity prices. Specifically, we propose a low complexity dynamic programming based algorithm for controlling the switching of heating, ventilation, and cooling (HVAC) units such that the cost of cooling is minimized while ensuring that the resultant temperatures do not violate the comfort constraints of consumers. Specifically, our algorithm makes use of two facts: first, the price of electricity vary discretely in time; and second, the cost-optimal state trajectory under fixed electricity price and ambient temperature, with given initial and final states, can be characterized explicitly in closed-form. We validate our algorithm with a set of numerical simulation studies using real market prices of electricity from the New York and Texas electricity markets. In addition, we also provide an approximation mechanism to implement this optimization algorithm in HVAC systems that have ON-OFF switching constraints.