Assuming non-ideal circuit power consumption at the energy harvesting (EH) nodes, we propose two practical protocols that optimize the performance of the harvest-then-transmit wireless powered communication networks (WPCNs) under two different objectives: (1) proportional fair (PF) resource allocation, and (2) sum rate maximization. These objectives lead to optimal allocations for the transmit power by the base station (BS), which broadcasts RF radiation over the downlink, and optimal durations of the EH phase and the uplink information transmission phases within the dynamic time-division multiple access (TDMA) frame. Compared to the max-sum-rate protocol, the PF protocol attains a higher level of system fairness at the expense of the sum rate degradation. The PF protocol is advantageous over the max-sum-rate protocol in terms of system fairness regardless of the circuit power consumption, whereas the uplink sum rates of both protocols converge when this power consumption increases.