Full-duplex (FD) allows the exchange of data between nodes on the same temporal and spectrum resources, however, it introduces self interference (SI) and additional network interference compared to half-duplex (HD). Power control in the FD networks, which is seldom studied in the literature, is promising to mitigate the interference and improve the performance of the overall network. In this work, we investigate the random and deterministic power control strategies in the FD networks, namely, constant power control, uniform power control, fractional power control and ALOHA-like random on-off power control scheme. Based on the obtained coverage probabilities and their robust approximations, we show that power control provides remarkable gain in area spectrum efficiency (ASE) and energy efficiency (EE), and improves the fairness among the uplink (UL) and downlink (DL) transmissions with respect to the FD networks. Moreover, we evaluate the minimum SI cancellation capability to guarantee the performance of the cell-edge users in FD networks. Generally, power control is helpful to improve the performance of the transmission for long distance in the FD networks and reduce the requirement of SI cancellation capability.