Hélène Le Cadre (MINES ParisTech) & Jean Sébastien Bedo (Orange Lab)

In this article, the smart grid is modeled as a decentralized and hierarchical network, made of three categories of agents: producers, providers and microgrids. To optimize their decisions concerning the energy prices and the traded quantities of energy, the agents need to forecast the energy productions and the demand of the microgrids. The biases resulting from the decentralized learning might create imbalances between demand and supply, leading to penalties for the providers and for the producers. We determine analytically prices that provide to the producers a guarantee to avoid such penalties, reporting all the risk on the providers. Addition- ally, we prove that collaborative learning, through a grand coalition of providers where information is shared and forecasts aligned on a single value, minimizes their average risk. Simulations, run for a large sample of parameter combinations, lead us to observe that the convergence times of the collaborative learning strategy are clearly superior to times resulting from distributed learning, using external and internal regret minimization. Furthermore, a grand coalition has 98% (resp. 85%) of chances to emerge under internal (resp. external) regret minimization.