For distribution networks with a high penetration of photovoltaic (PV) systems, overvoltage is a common and major issue that needs be addressed to not only assure reliable and secure system operation, but also to fully utilize PV generation capacity. A new real power capping method is proposed in this paper to prevent overvoltages by adaptively setting the power caps for PV inverters in real time. The proposed method can maintain voltage profiles below a preset upper limit while maximizing the PV generation and fairly distributing the real power curtailments among all the PV systems in the network. As a result, each of the PV systems in the network has equal opportunity to generate electricity and shares the responsibility of voltage regulation. The method does not require global information and can be implemented either under a centralized supervisory control scheme or in a distributed way via consensus control. Both steady state and dynamic simulation studies under various scenarios have been carried out on a 33-bus distribution system and the IEEE 13-bus test feeder to verify the effectiveness of the method.