Storage Management in a Shared Solar Environment with Time-Varying Electricity Prices

Internet of Things technologies will enable smart energy planning, which in turn will expedite the adoption of renewable energy (RE). In this paper, we propose a mathematical framework to optimize the use of RE in a shared solar environment featuring households with access to several RE generators. We consider location and time-dependent electricity prices, and formulate an optimization problem to minimize the energy cost incurred by the households over a finite planning horizon. The proposed framework accounts for transmission losses and battery inefficiencies. We then proposed two approaches to solve the formulated optimization problem. The first approach is based on quadratic programming, and is used to obtain a precision-controllable solution, requiring discretization in time and convex relaxation. The second approach is based on variational methods, which are used to tackle the problem directly in continuous time, thus obtaining a solution in closed form after introducing reasonable simplifications. To ensure full cooperation, we finally derive a fair energy allocation policy, which allocates RE to each household in proportion to its capital investment. The obtained analytical results allow us to evaluate the relationship between achievable performance, RE production, transmission losses, and price variability. Extensive simulations are used to verify the derived analytical results, illustrate the characteristics of the proposed strategies and compare their achievable performance.