In this study, the authors study the power efficiency optimisation in wireless-powered full-duplex relay (WFR) systems, where the entire transmission process can be partitioned into wireless power transfer phase (WP) and full-duplex information transmission phase (FP). For WFR systems with same source transmit power, where the source transmit powers of WP and FP are same, they first prove that the power efficiency is a strictly concave function over the time-switching factor, and an optimal time allocation scheme is proposed to maximise the power efficiency. Then, for the given time-switching protocol, the optimal power allocation strategy is obtained by analysing the derivative of the power efficiency with respect to the transmit power. Finally, they propose the joint power and time allocation scheme. For WFR systems with different source transmit power, where the source transmit powers of WP and FP are different, the optimal time allocation scheme and optimal power allocation strategy are derived by studying the derivative of the power efficiency. Furthermore, the joint power and time allocation scheme is proposed to maximise the power efficiency. Simulation results are presented to validate the authors' proposed schemes for the WFR systems.