The paper addresses the real-time xed-priority scheduling problem for battery-powered embedded systems whose energy storage unit is replenished by an environmental energy source. In this context, a task may meet its deadline only if its cost of energy can be satis ed early enough. Hence, a scheduling policy for such a system should account for properties of the source of energy, capacity of the energy storage unit and tasks cost of energy. Classical fixed-priority schedulers are no more suitable for this model. Based on these motivations, we propose PFPasap an optimal scheduling algorithm that handles both energy and timing constraints. Furthermore, we state the worst case scenario for non concrete tasksets scheduled with this algorithm and build a necessary and su cient feasibility condition for non concrete tasksets. Moreover, a minimal bound of the storage unit capacity that keeps a taskset schedulable with PFPasap is also proposed. Finally, we validate the proposed theory with large scale simulations and compare our algorithm with other existing ones.