Hybrid energy powered cellular networks are key for proposing green and cost-efficient wireless networks. Yet, the related energy management imposes severe challenges to efficiently manage the power allocation between the Renewable Energy (RE) source, the batteries and the smart power grid. The energy storage element (i.e., battery) is prone to irreversible aging mechanisms, requiring intelligent management that takes into account both the energy cost and requirements preventing battery degradation. In this work, we include this important constraint before proposing an energy management and base stations switch off algorithm for a partially RE-equipped cellular network in a variable electricity price environment. Results show that our algorithm outperforms a benchmark algorithm with a gain up to 20% in terms of electric bill reduction and enhances the battery life time by 35%.