The use of economic incentives has been proposed to manage user demand in smart grids that integrate renewable sources of energy to compensate for the intrinsic uncertainty in the prediction of the supply generation. We address the problem of synthesizing optimal energy pricing strategies, while quantitatively constraining the risk due to uncertainty for the network operator and guaranteeing quality-of-service for the users. We use Ellipsoidal Markov Decision Processes (EMDP) to model the decision-making scenario. These models are trained with measured data and allow to quantitatively capture the uncertainty in the prediction of energy generation. We then cast the constrained optimization problem as the strategy synthesis problem for EMDPs, with the goal to maximize the total expected reward constrained to properties expressed using the Probabilistic Computation Tree Logic (PCTL), and propose a novel sound and complete synthesis algorithm. An experimental comparison shows the effectiveness of our method with respect to previous approaches presented in the literature.




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