## A Mean Field Game Approach to Equilibrium Pricing, Optimal Generation, and Trading  in Solar Renewable Energy Certificate Markets

#### Sebastian JaimungalUniversity of Toronto

SREC markets are a market-based system designed to incentivize solar energy generation. A regulatory body imposes a lower bound on the amount of energy each regulated firm must generate via solar means, providing them with a certificate for each MWh generated.
Regulated firms seek to navigate the market to minimize the cost imposed on them, by modulating their SREC generation and trading activities. As such, the SREC market can be viewed through the lens of a large stochastic game with heterogeneous agents, where agents interact through the market price of the certificates. We study this stochastic game by solving the mean-field game (MFG) limit with sub-populations of heterogeneous agents. Our market participants optimize costs accounting for trading frictions, cost of generation, SREC penalty, and generation uncertainty. Using techniques from variational analysis, we characterize firms' optimal controls as the solution of a class of McKean-Vlasov FBSDE and determine the equilibrium SREC price. We further prove uniqueness and existence of the fixed-point problem for the measure flow and that the MFG strategy has the $\epsilon$-Nash property for the finite player game. Finally, we numerically solve the MV-FBSDEs and conclude by demonstrating how firms behave in equilibrium using simulated examples.
[ joint work with Arvind Shrivats and Dena Firoozi ]

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