  Pressure on ancillary reserves, i.e.frequency preserving, in power systems
has significantly mounted due to the recent generalized increase of the
fraction of (highly fluctuating) wind and solar energy sources in grid
generation mixes. The energy storage associated with millions of individual
customer electric thermal (heating-cooling) loads is considered as a tool for
smoothing power demand/generation imbalances. The piecewise constant level
tracking problem of their collective energy content is formulated as a linear
quadratic mean field game problem with integral control in the cost
coefficients. The introduction of integral control brings with it a robustness
potential to mismodeling, but also the potential of cost coefficient
unboundedness. A suitable Banach space is introduced to establish the existence
of Nash equilibria for the corresponding infinite population game, and
algorithms are proposed for reliably computing a class of desirable near Nash
equilibria. Numerical simulations illustrate the flexibility and robustness of
the approach.
