A mean field game model of an electricity market with consumers minimizing energy cost through dynamic battery usage

• This work contains a model of an electricity market consisting of consumers who own batteries that they charge and discharge in an optimal way. The goal of each individual customer is to minimize their total electricity cost, not by changing how much they consume, but by utilizing an optimal strategy for their battery usage. For each consumer we therefore have a value function. Since all consumers are assumed to be equal, their associated value functions are also equal. The optimization problem to determine the optimal battery usage depends on the electricity price, which in turn depends on the total electricity consumption. The consumption is given as a solution to a Kolmogorov forward equation, which involves the battery usage. Hence the Hamilton-Jacobi-Bellman and Kolmogorov equations need to be solved together as a coupled system of PDEs. We devise a numerical scheme for this system and show some simulations. We also prove a result on the existence and uniqueness of solutions to the system of PDEs.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Mean field games

mfg

optimal control

electricity market

existence theorem

Matematik

Mathematics

Publication and Content Type

vet (subject category)

ovr (subject category)