An integral control formulation of Mean-field game based large scale coordination of loads in smart grids
For power grid operators, this provides a theoretically grounded method to use distributed loads for frequency regulation, though the approach is incremental over existing mean-field game formulations.
The paper formulates the tracking of aggregate energy content of electric thermal loads as a mean-field game with integral control, proving existence of Nash equilibria and proposing algorithms for near-optimal coordination. Simulations demonstrate robustness to model mismatches.
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.