This paper is a first study focusing on a single-machine platform powered solely by renewable energy, showing how by simply adding an energy storage device, even a small battery, can greatly facilitate task scheduling by providing the energy needed to complete tasks. Our objective is to minimize the number of periods required to complete a bag of tasks under energy constraints. We investigate two settings, with and without energy losses (both during charging and discharging). For each case, we analyze the computational complexity of the problem and provide algorithms that are either optimal when parameters permit or approximate when limited battery capacity prevents overcoming strong inapproximability barriers.