Abstract: In order to improve the throughput and user capacity of the downlink non-orthogonal multiple access & power line communication (NOMA-PLC) system, this paper proposes incorporating NOMA technology into the PLC channel with lognormal fading, and studies the optimal power allocation scheme. Assuming that the downlink NOMA-PLC system contains multiple NOMA clusters, and each cluster operates in an independent resource block, the optimal power allocation problem in the system and rate maximization is equivalent to the minimum power consumption problem of each cluster, and each NOMA cluster is equivalent to a virtual orthogonal multiple access (OMA) user to obtain the effective channel gain of the user in a closed form. Then, the proposed fast water injection algorithm is used to solve the sum rate maximization problem, and finally the global optimal power allocation scheme is obtained and analyzed by Monte-Carlo simulation. The simulation results show that compared with the traditional OMA-PLC system, the NOMA-PLC power allocation scheme proposed in this paper has significantly improved performance in terms of system outage probability, minimum power consumption of the transmitter, and average sum-rate.