In this paper, the overvoltage problems that might arise from the integration of photovoltaic (PV) panels into low-voltage (LV) distribution networks is addressed. A distributed scheme is proposed that adjusts the reactive and active power output of inverters to prevent or alleviate such problems. The proposed scheme is model-free and makes use of limited communication between the controllers in the form of a distress signal only during emergency conditions. It prioritizes the use of reactive power, while active power curtailment is performed only as a last resort. The behavior of the scheme is studied using dynamic simulations on a single LV feeder and on a larger network composed of 14 LV feeders. Its performance is compared with a centralized scheme based on the solution of an optimal power flow (OPF) problem, whose objective function is to minimize the active power curtailment. The proposed scheme successfully mitigates overvoltage situations due to high PV penetration and performs almost as well as the OPF-based solution with significantly less information and communication requirements.