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Massively distributed antenna system is a promising architecture to enhance the system performance in future broadband wireless access beyond the Long Term Evolution (LTE) and Long Term Evolution Advanced (LTE-A) standards. Reduction of the power consumption of such systems is an important issue in their practical realization. This paper presents a technique to optimize the power consumed by a massively distributed antenna system in a multiuser downlink scenario subjected to throughput constraints. More specifically, the power consumed under the target sum-capacity constraint is optimized. We use zero-force beam forming scheme to simplify our analysis and derive optimal rate allocation among the users. Simulation results confirm that the energy consumption can be reduced considerably while the throughput constraint is satisfied.