A flexibility product for electric water heater aggregators on electricity markets

Electric thermal loads, such as those for space heaters, water heaters and air conditioners,vdue to their association with energy storage, are deferrable. Thus, they can become an effective tool to compensate for the mismatches between power generation and power demand induced by renewable sources. Load reduction and load increase may appear to be equivalent to generation increase and generation withdrawal, but there is a significant difference in the associated post-load-control energy rebound phenomena. These phenomena can provoke undesirable post-load-control changes in the demand dynamics. The contribution of this paper is twofold. First, we define a flexibility product that load aggregators could propose that would involve a mean energy increase or decrease offer for a price and also guarantee bounds on the post-load-control deviations from normal. Second, we provide aggregators with the mathematical tools to specify the maximum load relief or increase possible under specific constraints on post-control recovery dynamics. The analysis rests on successive solutions of a linear program and exploits recent results on load control based on mean field game theory. We consider the case of aggregate electric water heater loads.