Wind Farm Portfolio Optimization under Network Capacity Constraints

Hélène Le Cadre (1) , Anthony Papavasiliou (2) , Yves Smeers (2)

1 CMA - Centre de Mathématiques Appliquées
2 UCL - Université Catholique de Louvain = Catholic University of Louvain

In this article, we provide a new methodology for optimizing a portfolio of wind farms within a market environment, for two Market Designs (exogenous prices and endogenous prices). Our model is built on an agent based representation of suppliers and generators interacting in a certain number of geographic demand markets, organized as two tiered systems. Assuming rational expectation of the agents with respect to the outcome of the real-time market, suppliers take forward positions, which act as signals in the day-ahead market, to compensate for the uncertainty associated with supply and demand. Then, generators optimize their bilateral trades with the generators in the other markets. The Nash Equilibria resulting from this Signaling Game are characterized using Game Theory. The Markowitz Frontier, containing the set of efficient wind farm portfolios, is derived theoretically as a function of the number of wind farms and of their concentration. Finally, using a case study of France, Germany and Belgium, we simulate the Markowitz Frontier contour in the expected cost-risk plane.

Mots clés: Game Theory; Market Design; Markowitz Frontier; Renewable Capacity Investment

Domaines: Recherche opérationnelle [math.OC]; Économie et finance quantitative [q-fin]; Sciences de l'ingénieur [physics]; Machine Learning [stat.ML]

Hélène Le Cadre, Anthony Papavasiliou, Yves Smeers. Wind Farm Portfolio Optimization under Network Capacity Constraints. European Journal of Operational Research, 2015, 247 (2), pp.560-574. ⟨10.1016/j.ejor.2015.05.080⟩. ⟨hal-01007992v4⟩