In the small-cell networks (SCNs) with multiple small-cell base stations (ScBSs), the joint design of beamforming vectors, user scheduling and ScBS sleeping is investigated with the constraints on proportional rate. A long-term grid-energy expenditure minimization problem is formulated for the considered SCNs, which are powered by the smart grid and natural renewable energy. Since the scheduled user indicators are coupled with the beamforming vectors, the formulated problem is challenging to handle. In order to decouple the beamforming vectors from the scheduled user indicators, the Lyapunov optimization technique is used. As a result, a practical two-scale algorithm is proposed to allocate the user scheduling indicators and ScBS sleeping variables at the coarse-grained granularity (frame) as well as obtain the beamforming vectors at the fine-grained granularity (slot). Numerical results are used to verify the performance of the proposed two-scale algorithm.