An Extended Mean Field Game for Storage in Smart Grids

We consider a stylized model for a power network with distributed local power generation and storage. This system is modeled as network connection a large number of nodes, where each node is characterized by a local electricity consumption, has a local electricity production (e.g. photovoltaic panels), and manages a local storage device. Depending on its instantaneous consumption and production rates as well as its storage management decision, each node may either buy or sell electricity, impacting the electricity spot price. The objective at each node is to minimize energy and storage costs by optimally controlling the storage device. In a non-cooperative game setting, we are led to the analysis of a non-zero sum stochastic game with $N$ players where the interaction takes place through the spot price mechanism. For an infinite number of agents, our model corresponds to an Extended Mean-Field Game (EMFG). In a linear quadratic setting, we obtain and explicit solution to the EMFG, we show that it provides an approximate Nash-equilibrium for $N$-player game, and we compare this solution to the optimal strategy of a central planner.Comment: 27 pages, 5 figures. arXiv admin note: text overlap with arXiv:1607.02130 by other author

Regression Monte Carlo for Microgrid Management

We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We introduce a methodology to solve microgrid management problem using different variants of Regression Monte Carlo algorithms and use numerical simulations to infer results about the optimal design of the grid.Comment: CEMRACS 2017 Summer project - proceedings

Regression Monte Carlo for microgrid management

We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We build on the mathematical model introduced in [14] and optimize the diesel consumption under a “no-blackout” constraint. We introduce a methodology to solve microgrid management problem using different variants of Regression Monte Carlo algorithms and use numerical simulations to infer results about the optimal design of the grid

Regression Monte Carlo for microgrid management

We study an islanded microgrid system designed to supply a small village with the power produced by photovoltaic panels, wind turbines and a diesel generator. A battery storage system device is used to shift power from times of high renewable production to times of high demand. We build on the mathematical model introduced in [14] and optimize the diesel consumption under a “no-blackout” constraint. We introduce a methodology to solve microgrid management problem using different variants of Regression Monte Carlo algorithms and use numerical simulations to infer results about the optimal design of the grid