The application of renewable energy is a promising solution to realize the Green Communications. However, if the cellular systems are solely powered by the renewable energy, the weather dependence of the renewable energy arrival makes the systems unstable. On the other hand, the proliferation of the smart grid facilitates the loads with two-way energy trading capability. Hence, a hybrid powered cellular system, which combines the smart grid with the base stations, can reduce the grid energy expenditure and improve the utilization efficiency of the renewable energy. In this paper, the long-term grid energy expenditure minimization problem is formulated as a stochastic optimization model. By leveraging the stochastic optimization theory, we reformulate the stochastic optimization problem as a per-frame grid energy plus weighted penalized packet rate minimization problem, which is NP-hard. As a result, two suboptimal algorithms, which jointly consider the effects of the channel quality and the packet reception failure, are proposed based on the successive approximation beamforming (SABF) technique and the zero-forcing beamforming (ZFBF) technique. The convergence properties of the proposed suboptimal algorithms are established, and the corresponding computational complexities are analyzed. Simulation results show that the proposed SABF algorithm outperforms the ZFBF algorithm in both grid energy expenditure and packet delay. By tuning a control parameter, the grid energy expenditure can be traded for the packet delay under the proposed stochastic optimization model.