With the advance of the photovoltaic panel technology, the infrastructure equipment of cellular networks with solar energy sources has attracted extensive interests. It is expected that base stations (BSs) and relay stations (RSs) with renewable energy will play important roles in reducing the power consumption from electrical grids in future green cellular networks. Inspired by this technology trend, this paper considers a heterogeneous green cellular network, in which a part of RSs is powered by solar energy sources to represent the incremental deployment for the infrastructure with renewable energy in the near future. We formulate a new relay selection and power allocation problem with Mixed Integer Linear Programming to select solar-powered RSs and grid-powered RSs, such that the total grid power consumption is effectively minimized in decode-and-forward cooperative communication networks. We design an algorithm to derive the optimal solution, and also devise an efficient distributed algorithm to reduce the computational cost. The simulation results demonstrate that the algorithms can effectively reduce the total grid power consumption with different channel conditions, different deployments of RSs in a network, and different available power levels in solar-powered RSs. In addition, the problem model and the proposed algorithms can be extended to support hybrid energy sources.