The increasing penetration of renewable energy sources is impacting the operation of the distribution grid. Whilst they are currently placing a burden on the distribution grid, it is generally agreed that these sources could also be used for active grid control, thereby contributing to a stable and secure grid. Smart photovoltaic inverters can contribute to active grid control, by expanding their features with added functions. In this paper, we develop a novel grid voltage support algorithm for smart photovoltaic inverters, based on distributed optimization and peer-to-peer communication. The Jacobi-Proximal Alternating Direction Method of Multipliers is applied in this paper to locally optimize reactive power compensation and active power curtailment of each inverter participating in the voltage control. We propose the use of a push-sum gossip protocol to enable peer-to-peer data interchange between inverters. We also use strategies to improve the robustness of the proposed algorithm: an acceleration strategy, a feedback strategy and an anti-windup strategy. A case study is presented, demonstrating the fast convergence of the algorithm and its ability to solve the voltage problems.