This paper proposes an energy management framework for cellular heterogeneous networks (HetNets) supported by dynamic drone small cells. A 3-tier HetNet is considered where macrocell, on/off switching micro cells, and solar-powered drone small cells are deployed to serve the networks' subscribers. In addition to energy harvesting, the drones can power their batteries via a charging station located at the macrocell site. Pre-planned locations are identified by the mobile operator for possible drones' placement. The objective of the framework is to optimally determine the positioning of the drones in addition to the micro cells status that can be turned off in order to minimize the daily energy consumption of the network. The framework takes also into account the cells' capacity and quality of service (QoS) metric defined by the minimum received power. An integer linear programming problem is formulated to optimally determine the network status during a time blocked period. The performance of this online scheme shows important advantages in terms of energy efficiency and connectivity compared to the traditional case without drones specially when the network is congested.