Insurance contract for high renewable energy integration

The increasing penetration of renewable energy poses significant challenges to power grid reliability. There have been increasing interests in utilizing financial tools, such as insurance, to help end-users hedge the potential risk of lost load due to renewable energy variability. With insurance, a user pays a premium fee to the utility, so that he will get compensated in case his demand is not fully satisfied. A proper insurance design needs to resolve the following two challenges: (i) users' reliability preference is private information; and (ii) the insurance design is tightly coupled with the renewable energy investment decision. To address these challenges, we adopt the contract theory to elicit users' private reliability preferences, and we study how the utility can jointly optimize the insurance contract and the planning of renewable energy. A key analytical challenge is that the joint optimization of the insurance design and the planning of renewables is non-convex. We resolve this difficulty by revealing important structural properties of the optimal solution, using the help of two benchmark problems: the no-insurance benchmark and the social-optimum benchmark. Compared with the no-insurance benchmark, we prove that the social cost and users' total energy cost are always no larger under the optimal contract. Simulation results show that the largest benefit of the insurance contract is achieved at a medium electricity-bill price together with a low type heterogeneity and a high renewable uncertainty.