Dealing with Uncertainty in the Smart Grid: A Learning Game Approach

Hélène Le Cadre (1) , Jean-Sébastien Bedo (2)

1 CMA - Centre de Mathématiques Appliquées
2 Orange Labs [Paris]

In this article, the smart grid is modeled as a decentralized and hierarchical network, made up of three categories of agents: suppliers, generators and microgrids. To optimize their decisions concerning prices and traded power, agents need to forecast the demand of the microgrids and the fluctuating productions of the generators. The biases resulting from the decentralized learning could create imbalances between demand and supply leading to penalties for suppliers and for generators. We analytically determine prices that provide generators with a guarantee to avoid such penalties, transferring risk to the suppliers. Additionally, we prove that collaborative learning, through a grand coalition of suppliers in which information is shared and forecasts aligned on a single value, minimizes the sum of their average risk. Simulations, run for a large sample of parameter combinations using external and internal regret minimization, show that the convergence of the collaborative learning strategy is clearly faster than that resulting from distributed learning. Finally, we analyze the suppliers' individual incentives to enter into a grand coalition and the tightness of the learning algorithm's theoretical bounds.

Mots clés: Distributed Learning; Information; Regret; Learning Game Theory

Domaines: Optimisation et contrôle [math.OC]; Machine Learning [stat.ML]

Hélène Le Cadre, Jean-Sébastien Bedo. Dealing with Uncertainty in the Smart Grid: A Learning Game Approach. 2015. ⟨hal-00740893v7⟩