This paper proposes an energy management framework for cellular heterogeneous networks (HetNets) supported by dynamic solar powered drones. A HetNet composed of a macrocell base station (BS), micro cell BSs, and drone small cell BSs are deployed to serve the networks' subscribers. The drones can land at pre-planned locations defined by the mobile operator and at the macrocell BS site where they can charge their batteries. The objective of the framework is to jointly determine the optimal trips of the drones and the MBSs that can be safely turned off in order to minimize the total energy consumption of the network. This is done while considering the cells' capacities and the minimum receiving power guaranteeing successful communications. To do so, an integer linear programming problem is formulated and optimally solved for three cases based on the knowledge level about future renewable energy statistics of the drones. A low complex relaxed solution is also developed. Its performances are shown to be close to those of the optimal solutions. However, the gap increases as the network becomes more congested. Numerical results investigate the performance of the proposed drone-based approach and show notable improvements in terms of energy saving and network capacity.