The use of renewable energy (RE) sources is a promising solution to reduce grid power consumption and carbon dioxide emissions (CO2e) of cellular networks. However, the benefit of utilizing RE is limited by its highly intermittent and unreliable nature leading to mismatch between generation and base station (BS) needs, resulting in low savings in grid power. To address the above challenges, we propose a novel base station time resource allocation technique using data storage at user equipments (UEs) to optimally utilize renewable energy to reduce grid power consumption. The proposed approach transforms the surplus RE (in excess of the BS power requirements) to excess data delivered to the users and stored in UE data storages, to draw from in deficit periods (when RE generation is lesser than BS requirements) to reduce grid power. Though the proposed approach is applicable to any application that utilizes UE data buffer, we formulate the problem for mobile video and propose a algorithm for RE aware BS resource allocation during mobile video download, as the latter will dominate wireless traffic and hence BS power consumption. Our experimental results using sample solar and BS utilization traces demonstrate the ability of the proposed approach to reduce grid power consumption by increasing solar power utilization while satisfying user QoS requirements.