Generation following with thermostatically controlled loads via alternating direction method of multipliers sharing algorithm

A fundamental requirement of the electric power system is to maintain a continuous and instantaneous balance between generation and load. The intermittency and uncertainty introduced by renewable energy generation requires expanded ancillary services to maintain this balance. In this paper, we examine the potential of thermostatically controlled loads (TCLs), such as refrigerators and electric water heaters, to provide generation following services in real-time energy markets (1-5 min). Previous research in this area has primarily focused on the development of centralized control schemes with an aggregate TCL model. An objective of our approach is to enable each TCL to model and control its dynamics independently and to use distributed convex optimization techniques to allow a central aggregator to influence, but not directly control, the behavior of the population. To control the non-linear dynamics of hysteretic dead-band systems in a manner suitable for convex optimization, we introduce an alternative control trajectory representation of the TCLs and their discrete input signals. This approach allows us to approximate the control of a TCL as a convex program and to produce a solution that can be interpreted stochastically for implementation. To perform distributed optimization across large populations of TCLs, we apply a variation of the alternating direction method of multipliers (ADMM) algorithm. The objective of the distributed optimization algorithm is to enable an aggregator to coordinate with a population of TCLs and to increase or decrease the total power demand according to a control signal. We include experimental results in which different populations of TCLs with varying levels heterogeneity are optimized to provide 5-min ahead generation following services. We numerically demonstrate the algorithm's potential for controlling a TCL population's power demand within a definable error tolerance.