This paper deals with the real-time scheduling in a reconfigurable multi-core platform powered by a rechargeable battery. A reconfiguration scenario is defined as an operation that allows the addition-removal-modification of tasks which may result in timing unfeasibility. Such a system may face several scenarios: i) increased power consumption that, in the worst case, may surpass the available energy budget, ii) increased computing demand, which may lead to the violation of real-time constraints, and iii) increased memory demand, potentially exceeding the provided memory capacity. To prevent these problems during the execution, a new scheduling strategy is necessary. The proposal is based on the assignment of tasks to different processor cores to satisfy these constraints simultaneously after any reconfiguration scenario. The effectiveness and performance of the designed approach are evaluated through simulation studies. An intelligent tool named Reconf-Pack is developed in our research laboratory to support this new proposed approach and to simulate it over randomly generated tasks.