The high penetration of renewable energy sources in modern distribution networks poses challenges for grid voltage regulation. In this study, a multi-agent distributed voltage control strategy based on the proximal Jacobian alternating direction method of multipliers (PJ-ADMM) is proposed for distribution power systems with a high penetration of photovoltaic (PV) resources coordinated with battery energy storage systems (BESS). In this context, all active and reactive power outputs of the PV are locally optimized through smart inverters to improve the grid voltage with minimum power loss. Uncertainties associated with the solar energy generation and load demands are considered in the defined scenarios. This study consists of two phases. In the first phase, the voltage control problem is formulated as an optimization problem to regulate the voltages within an acceptable limit with fast convergence. In the second phase, a coordinated voltage control strategy for smart PV inverters and BESS is proposed to allocate the power capacity of the battery energy storage systems and the active power loss reduction. Finally, the proposed method is tested on modified IEEE 13-bus, 33-bus and 141-bus distribution systems using MATLAB/Simulink and MATPOWER. A comparison of the results of the voltage profiles with and without the control algorithm demonstrated the efficacy, robustness, and scalability of the distributed scheme for voltage improvement and optimal utilization of PV power under different scenarios.