This paper deals with the scheduling of real-time periodic tasks executed on heterogeneous multicore platforms. Each processor is composed of a set of multi-speed cores with limited energy resources. A reconfigurable system is sensible to unpredictable reconfiguration events from related environment, such as the activation, removal or update of tasks. The problem is to handle feasible reconfiguration scenarios under energy constraints. Since any task can finish execution before achieving its worst-case execution time (WCET), the idea is to distribute this execution on different processor cores for meeting related deadlines and reducing energy consumption. The methodology consists in using lower processor speeds first to consume less energy. If the system is still non-feasible after reconfiguration, then we adjust the task periods as a flexible solution or migrate some of them to the least loaded processors. Accordingly, an integer linear program (ILP) is formulated to encode the execution model that assigns tasks to different cores with optimal energy consumption, thereby realizing energy-efficient computing/green computing. The potency and effectiveness of the proposed approach are rated through simulation studies. By measuring the energy consumption cost, our solution offers better than 11% of gain than recently published methods and improves by 85% the overall number of adjusted periods.