In this paper, we consider a wireless communication system, where a full-duplex hybrid access point (HAP) transmits to a set of cellular users (CUs) in the downlink channel, while receiving data from a set of energy-constrained communication devices like user equipments (UEs) in the uplink channel. The HAP has a massive antenna array, while all CUs and UEs nodes are equipped with single antenna each. Time switching protocol is adopted, where channel estimation, wireless power transfer, and information transfer between UEs, CUs and full-duplex HAP are performed in two phases. By adopting maximum ratio combining/maximum ratio transmission (MRC/MRT) and zero-forcing (ZF) processing at the HAP, the uplink and downlink achievable rate expressions in the large-antenna limit and approximate results that hold for any finite number of antennas are derived. Moreover, the optimum energy beamformer and time-split parameter at the HAP are found to maximize the downlink sum-rate under a constraint on uplink sum-rate. Our findings reveal that our proposed energy beamforming with ZF and MRC/MRT processing for information transfer achieves up to 47% and 14% average sum rate gains as compared with the suboptimum energy beamformer, respectively.