In this paper, we investigate the downlink of large-scale MIMO systems considering two practical constraints related to system power. More precisely, we consider a non-negligible circuit power consumption and we impose a per-antenna power constraint due to limitations on the linearity of the RF power amplifier. Hence, a sum-rate maximization problem considering the two constraints is formulated for conjugate beamforming and zero forcing beamforming. Next, we propose efficient greedy antenna selection and power allocation algorithms in order to heuristically solve the formulated problem with reasonable computational complexity. Simulation results show the efficiency of the proposed algorithms compared to random antenna selection and optimal brute force antenna selection.