In this paper, we analyze the performance of cooperative power domain non-orthogonal multiple access (NOMA) in power line communication (PLC) networks. Due to the high signal attenuation of the source to user links, a relay aids communication from the source to two users. With half-duplex transmission, the source transmits a superimposed symbol in the first phase. The relay utilizes amplify-and-forward (AF) and decode-and-forward (DF) protocol on the received superimposed signal and forwards it to the users in the second phase. We derive analytic expressions for the outage probability and the system throughput of the proposed system under a PLC log-normal channel with impulsive noise. Based on the results for AF NOMA relaying case, we analyze the system performance at high signal-to-noise ratio (SNR) and derive closed-form lower and upper bounds for the outage probability. Simulation results show an improvement in the outage probability and the system throughput performance of the AF and DF NOMA schemes compared to the NOMA without relaying transmission and conventional orthogonal multiple access scheme. Furthermore, the impact of the channel variance is highlighted in the results. It is shown that the DF NOMA has a better outage probability than the AF NOMA scheme for low channel variance scenarios (i.e., less branches and connected loads in the PLC network). However, as the channel variance increases, AF NOMA scheme has similar outage probability performance as the DF NOMA scheme. In addition, it is shown that the system throughput is enhanced when the relay employs DF relaying compared to AF relaying.