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

## TL;DR

This paper introduces an integral control approach within a mean-field game framework to coordinate large-scale energy storage loads in smart grids, enhancing robustness against modeling errors and fluctuations from renewable sources.

## Contribution

It formulates a linear quadratic mean field game with integral control for energy storage coordination, establishing Nash equilibrium existence and proposing algorithms for near-optimal solutions.

## Key findings

- Robustness to mismodeling demonstrated in simulations
- Effective coordination of thermal loads in smart grids
- Algorithmic solutions for near Nash equilibria

## 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.