This paper introduces the scheduling of frame-based real-time tasks in partitioning schemes for multiprocessor systems powered by rechargeable batteries. In frame-based real-time systems, a set of tasks must execute in a frame, and the whole frame is repeated. This system model is widely used in real-time communication, real-time imaging and a lot of other real-time/embedded systems. Nowadays, many of these systems are powered by rechargeable batteries. Scheduling real-time tasks on these rechargeable systems is an important yet largely ignored issue. The problem for uniprocessor systems had been studied in (A. Allavena and D. Mosse, 2001), in which an algorithm of complexity O(N) was proposed for determining the feasibility of the task set. However, it poses a challenge when doing so in a rechargeable multiprocessor system considering different characteristics of the batteries. In this paper, we first show this problem to be NP-hard, and then propose efficient algorithms to overcome it. The simulation results have shown that our algorithms exhibit very good behaviors and they can be considered as solutions to the problem.