With the generalization of cloud infrastructures usage, energy consumption has become a major issue. Scheduling heuristics have been proposed to optimize the resource usage of data center so as to take down the energy consumption. This paper tackles the problem with a different approach by taking into consideration the availability of renewable energy. First we formalize the green energy aware scheduling problem (GEASP) and propose a global model based on constraint programming as well as a search heuristic to solve it efficiently. The proposed model integrates the various aspects inherent to the dynamic planning in a data center: heterogeneous physical machines, various application types (i.e., active or online applications and batch applications), actions and energetic costs of turning ON/OFF physical machines, interrupting/resuming batch applications, CPU and RAM resource consumption, tasks migration, migration costs, and integration of green energy availability. The model can therefore reduce both the costs related to energy consumption and the carbon footprint of a data center. We evaluate the model against the state-of-the-art framework PIKA on real-world workload and solar power traces.