École Nationale Supérieure de
Techniques Avancées

Abstract

The transition to renewable energy requires determining the optimal time for conven- tional generators to exit the electricity market in favor of renewable generators. Building on the work of Peter Tankov and his fellow researchers, we define a model of the electri- city market that considers four types of generators : coal and gas generators leaving the market, gas generators and wind generators entering the market. The agents interact with each other through the market price, determined by matching supply and demand. We have taken advantage of the mean field game theory through a relaxed model and have determined the Nash equilibrium defined beforehand. We added a carbon tax to make the model more realistic and we explained the improvements made to make the program more efficient. We have illustrated our model through the German electricity market. We will see that subsidies are necessary to have a significant penetration of wind generators, but taking into account the sales of guaranteed capacity by conventional generators would allow to decrease the price during the periods when consumption is the most important. An increase in the carbon tax would allow Germany to meet its environmental goals by 2038.