High levels of penetration of distributed photovoltaic generators can cause serious overvoltage issues, especially during periods of high power generation and light loads. There have been many solutions proposed to mitigate the voltage problems, some of them using battery energy storage systems (BESS) at the PV generation sites. In addition to their ability to absorb extra power during the light load periods, BESS can also supply additional power under high load conditions. However, their capacity may not be sufficient to allow charging every time when power absorption is desired. Therefore, typical PV/BESS may not fully prevent over-voltage problems in power distribution grids. This work develops a cooperative state of charge control scheme to alleviate the BESS capacity problem through Monte Carlo tree search based reinforcement learning (MCTS-RL). The proposed intelligent method coordinates the distributed batteries from other regions to provide voltage regulation in a distribution network. Furthermore, the energy optimization process during the day hours and the simultaneous state of charge control are achieved using model predictive control (MPC). The proposed approach is demonstrated on two test cases, the IEEE 33 bus system and the practical medium size distribution system in Alberta Canada.