Price Control for Heterogeneous Thermostatically Controlled Loads in Communication and Computation Delay Environments

In this paper, we examine the potential of thermostatically controlled loads (TCLs) to provide demand response services in real-time energy markets (15 minutes) to optimize the tradeoff between the electricity bills and occupants' comfort requirements. A distributed optimization scheme is presented based on the derived second-order thermal dynamics and heterogeneous TCL models, in which a central controller is allowed to collect information from and broadcast control signals to TCLs. However, due to the real-time consideration, traditional synchronized computation does not scale well with the problem size, as the speed of the algorithm is limited by the slowest agent. This is particularly true in a heterogeneous network where the computing nodes experience different computation and communication delays. To perform distributed optimization in the presence of delay, we apply an asynchronous distributed alternating direction method of multipliers (ADMM) where the central controller makes decisions when it receives information from a predefined number of TCL in the population. Through rigorous theoretical results we show that the proposed algorithm converges to the optimal solution. We also provide numerical results in which different populations of TCLs with varying levels heterogeneity are optimized.