Discriminatory Price Mechanism for Smart Grid
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We consider a scenario where the retailers can select different prices to the users in a smart grid. Each user's demand consists of an elastic component and an inelastic component. The retailer's objective is to maximize the revenue, minimize the operating cost, and maximize the user's welfare. The retailer wants to optimize a convex combination of the above objectives using a price signal. The discriminations across the users are bounded by a parameter η. We formulate the problem as a Stackelberg game where the retailer is the leader and the users are the followers. However, it turns out that the retailer's problem is non-convex and we convexify it via relaxation. We show that even though we use discrimination the price obtained by our method is fair as the retailers selects higher prices to the users who have higher willingness for demand. We also consider the scenario where the users can give back energy to the grid via net-metering mechanism.
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