An integral control formulation of mean field game based large scale coordination of loads in smart grids

Abstract

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.

Distributed Control of Clustered Populations of Thermostatic Loads in Multi-Area Systems: A Mean Field Game Approach

“…This new mathematical paradigm, first introduced in [19,20], approximates the population size of the responsive agents as infinite and allows to characterize the desirable equilibrium solution through two coupled partial differential equations (rather than several optimality conditions, one for each single agent). Mean field games have been recently used to characterize the flexible operation of TCLs, considering for example random switches between their ON/OFF states [21], formally demonstrating the existence of suitable equilibrium solution [22] and evaluating the capability of the loads to provide ancillary services in a market framework [23].…”

Lax connection and conserved quantities of quadratic mean field games

“…Mean Field Game (MFG) is a rather recent theoretical framework specifically developed to address complex problems of game theory when the number of players becomes large [1][2][3][4]. Accordingly, they have natural applications in various fields, ranging from finance [5][6][7] to sociology [8][9][10] and engineering science [11][12][13], and more generally whenever optimization issues involve a large number of coupled subsystems.…”

Smart Distributed Energy Storage Controller (smartDESC)

“…The approach used in smartDESC is closer to [20], except that in producing the microscopic device-wise actions to attain the global objectives, the recent theory of Mean Field (MF) control theory [21] is applied. Devices are attributed an individual cost function which encapsulates conflicting objectives: local customer comfort and safety, but with compulsory global objectives enforced on the mean behavior of the population of devices [22,23].…”