A Static Mean Field Game for Optimal Renewable Energy Investment

Abstract

We develop a static mean field game formulation for optimal wind energy capacity siting in Alberta, Canada. The revenue model for agents is based on the expected wind resource at a location and the covariance of this wind resource with other locations. Agents choose locations to maximize long-run revenue while accounting for spatial correlations in wind resource availability. Spatial wind dependence is incorporated through an empirically calibrated covariance structure, combining a PCA-based component estimated from historical weather station data with a parametric residual kernel, to capture variability across locations. The equilibrium investment problem can be formulated as a quadratic program, which we solve for four policy scenarios that progressively restrict the feasible siting area, incorporating viewscape and transmission constraints beyond a baseline of minimal siting restrictions. These policy and infrastructure-driven land use restrictions are represented as constraints on the agents' action space, allowing us to examine their economic implications through a comparison of the MFG equilibria across policy scenarios.Our findings highlight the trade-off between regulatory land use objectives and economic efficiency in the use of renewable energy resources in the short and long term, and provide quantitative insights into how policy design shapes the spatial distribution and financial performance of wind investments. The static MFG formulation could be used to inform electricity system planning including, transmission planning and renewable energy development planning.