On aggregating thermostatically controlled loads based on energy losses

In this paper we revisit the problem of modeling a large population of residential thermostatically controlled loads (TCLs) as a single reserve, from the perspective of an Aggregator. Our model tracks and controls individual TCLs based on the heat stored in their thermal capacity and their corresponding thermal resistive losses, using the heat pump to compensate for lost energy in order to maintain TCLs around desired reference temperatures. We show that, under reasonable approximations, the energy loss dynamics can be easily tied to a common outside temperature, whose random fluctuations are in one to one correspondence with the available reserve capacity. This approach greatly simplifies any stochastic optimization of the TCLs as an aggregate resource compared to the state of the art.