A mean field model for the development of renewable capacities

TL;DR

This paper develops a mean field model to analyze how subsidies influence the capacity of renewable energy production, considering competitive markets, cannibalization effects, and capacity adjustments over time.

Contribution

It introduces a novel mean field framework with explicit equilibrium formulas and numerical methods for renewable capacity development under subsidies.

Findings

Explicit formulas for long-term equilibrium capacities

Optimal subsidy levels for desired capacity targets

Numerical methods for simulating capacity evolution

Abstract

We propose a model based on a large number of small competitive producers of renewable energies, to study the effect of subsidies on the aggregate level of capacity, taking into account a cannibalization effect. We first derive a model to explain how long-time equilibrium can be reached on the market of production of renewable electricity and compare this equilibrium to the case of monopoly. Then we consider the case in which other capacities of production adjust to the production of renewable energies. The analysis is based on a master equation and we get explicit formulae for the long-time equilibria. We also provide new numerical methods to simulate the master equation and the evolution of the capacities. Thus we find the optimal subsidies to be given by a central planner to the installation and the production in order to reach a desired equilibrium capacity.