Robust Energy Scheduling of Interconnected Smart Homes with Shared Energy Storage under Quadratic Pricing

In this paper, we propose a novel robust framework for day-ahead energy scheduling of interconnected smart homes with shared energy storage system (ESS), taking into account users' behavior uncertainty. The objective is minimizing the total energy payment for each user while satisfying the constraint on the feasibility of energy transactions between users and the power grid in presence of data uncertainty. Unlike most existing robust scheduling frameworks that assume a linear cost function for energy purchased from the grid, our design presents a tractable robust optimization scheme to solve the energy scheduling problem with a more realistic quadratic cost function. We model device/comfort constraints as well as contractual obligations imposed by the power grid restricting the users' energy consumption to a maximum level at each time slot. Thus, in our problem, uncertainty affects both the quadratic objective function and linear contractual constraints. To solve the resulting problem, we first formulate a deterministic model of the scheduling problem, then establish a min-max robust counterpart, and finally apply some mathematical transformations to solve the equivalent problem. We also deal with the conservatism of the robust control algorithm and flexibility of the method for application to different settings. The validity and effectiveness of the proposed approach is verified by simulation results.