The paper considers the concept of a charging station for an Unmanned Aerial Vehicles (UAV, drone) fleet. The special feature of the station is its autonomy understood as independence from a constant energy source and an external module for managing its operation. It is assumed that the station gives the possibility to charge batteries of many drones simultaneously. However, the maximum number of simultaneously charged drones is limited by a temporary total charging current (i.e. there is a power limit). The paper proposes a mathematical model of charging a single drone battery. The problem of finding a schedule of charging tasks is formulated, in which the minimum time of the charging process for all drones is assumed as the optimization criterion. Searching for a solution to this problem is performed by an autonomous charging station with an appropriate computing module equipped with a Variable Speed Processor (VSP). To that end an appropriate algorithm is activated (i.e. a computational job), the execution of which consumes a certain amount of limited energy available to the charging station. In the paper we consider energy-aware execution of an implementation of an evolutionary algorithm (EA) as a computational job. The possibility of saving energy by controlling the CPU frequency of a VSP is analyzed. A characteristic feature of the processor is the non-linear relationship between the processing rate and electric power usage. According to this relationship, it turns out that slower execution of the computational job saves electrical energy consumed by the processor.