In this paper, we study the grid energy consumption of a hybrid energy powered base station system equipped with a renewable source and a battery. We focus on the energy storage element that is prone to irreversible aging mechanisms, thus requiring precise management that takes into account both energy cost and constraints preventing fast battery degradation. We propose a Battery Aging and Price-Aware (BAPA) algorithm that brings down the grid energy consumption of the operator while including battery degradation constraints. We decompose the problem into three subproblems: Resource allocation problem, grid energy purchase problem and power allocation problem. We show that our algorithm performs very close to optimality (up to 99%) and outperforms a benchmark algorithm.