In this paper, we propose feasibility and schedulability tests for a real-time scheduling problem under energy constraints. We first introduce the problem and show how to model it using timed automata. We propose then a feasibility test based on CTL model checking and schedulability tests for EDF and fixed priority algorithms. Our approach also permits to generate a feasible schedule if one exists and otherwise to find the good characteristics of a battery to make the problem feasible. It is finally possible to generate schedules that optimize some criteria, such as the number of mode switching (battery charge or discharge), the minimal and the maximal energy level, or the number of preemptions. The approach is illustrated by some experiments using the model checking tool U PPAAL.