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

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

A mirror descent approach for Mean Field Control applied to Demande-Side management

We consider a finite-horizon Mean Field Control problem for Markovian models. The objective function is composed of a sum of convex and Lipschitz functions taking their values on a space of state-action distributions. We introduce an iterative algorithm which we prove to be a Mirror Descent associated with a non-standard Bregman divergence, having a convergence rate of order 1/ \sqrt K. It requires the solution of a simple dynamic programming problem at each iteration. We compare this algorithm with learning methods for Mean Field Games after providing a reformulation of our control problem as a game problem. These theoretical contributions are illustrated with numerical examples applied to a demand-side management problem for power systems aimed at controlling the average power consumption profile of a population of flexible devices contributing to the power system balance

Distributed Control Design for Balancing the Grid Using Flexible Loads

International audienceInexpensive energy from the wind and the sun comes with unwanted volatility, such as ramps with the setting sun or a gust of wind. Controllable generators manage supply-demand balance of power today, but this is becoming increasingly costly with increasing penetration of renewable energy. It has been argued since the 1980s that consumers should be put in the loop: " demand response " will help to create needed supply-demand balance. However, consumers use power for a reason, and expect that the quality of service (QoS) they receive will lie within reasonable bounds. Moreover, the behavior of some consumers is unpredictable, while the grid operator requires predictable controllable resources to maintain reliability. The goal of this chapter is to describe an emerging science for demand dispatch that will create virtual energy storage from flexible loads. By design, the grid-level services from flexible loads will be as controllable and predictable as a generator or fleet of batteries. Strict bounds on QoS will be maintained in all cases. The potential economic impact of these new resources is enormous. California plans to spend billions of dollars on batteries that will provide only a small fraction of the balancing services that can be obtained using demand dispatch. The potential impact on society is enormous: a sustainable energy future is possible with the right mix of infrastructure and control systems