As the level of penetration of intermittent renewable energy sources increases in power systems, energy supply side reliability decreases. In this context, the flexibility afforded by electric loads associated with energy storage such as space heaters, air conditioners or water heaters becomes a crucial asset as these loads can be deferred or anticipated to mitigate energy supply variability. We consider the case of an aggregator coordinating a very large number of small residential electric space heating loads. The aggregator pursues two possible distinct objectives over a fixed time interval: (i) Reducing/increasing the loads mean energy requirements; (ii) Achieving a fixed mean load power demand rate. Both control problems are approached via a mean field prescriptive linear quadratic (LQ) game framework. (i) is solved using a nonstandard LQ game with cost coefficients involving a time integral of an error signal. (ii) is solved using a novel inverse mean field equilibrium approach. Based on joint work with A. Kizilkale, R. Salhab and Q. Lénet.