In this paper, we study the performance of nonorthogonal multiple access (NOMA) scheme in wireless-powered communication networks (WPCN) focusing on the system energy efficiency. We consider multiple energy-harvesting user equipments (UEs) that operate based on harvest-then-transmit protocol. The uplink information transfer is carried out by using powerdomain multiplexing, and the receiver decodes each UE's data in such a way that the UE with the best channel gain is decoded without interference. In order to determine optimal resource allocation strategies, we formulate optimization problems considering two models, namely half-duplex operation and asynchronous transmission, based on how downlink and uplink operations are coordinated. In both cases, we have concave-linear fractional problems, and hence Dinkelbach's method can be applied to obtain the globally optimal solutions. Thus, we first derive analytical expressions for the harvesting interval, and then we provide an algorithm to describe the complete procedure. Simulation results are included to justify the theoretical characterizations. In fact, we observe that broadcasting at higher power level is more energy efficient for WPCN with uplink NOMA.