Unmanned Aerial wireless Communication Systems (UASs), featuring the low cost and flexible deployment of unmanned aerial vehicles (UAVs), have attracted intensive attention recently to provide wireless communication services in some specific scenarios, e.g., disaster areas and temporary hotspots. Nonetheless, due to UAVs’ limited on-board energy storage, the provisioning of wireless communications can deplete their carried energy, consequently landing on the ground. To mitigate this issue, harvesting solar energy to power UAVs is a promising alternative solution. However, the essential dynamics of solar energy can seriously affect communication performance in UASs. In this paper, we explore dynamic solar energy to supply a UAS with an aerial base station (BS) and aim to minimize the long-term time-averaged energy consumption of the UAS. Particularly, we formulate a Long-term time-averaged Energy Consumption minimization problem (LEC) by jointly taking into account transmission power and data rate. Considering that LEC is time-coupling nonlinear programming (NLP), we reformulate a relaxed online optimization problem, called STP (single-time slot problem), by employing Lyapunov optimization theory. Then, we develop a joint power and rate control algorithm to solve STP. Particularly, we theoretically show that the proposed algorithm can achieve (D/V + C)-approximation and guarantee stability. Extensive simulation results have shown the performance gain, in terms of stability and throughput, achieved by the proposed algorithm.