With the advancement of power systems, the integration of a substantial portion of renewable energy often leads to frequent voltage surges and increased fluctuations in distribution networks (DNs), significantly affecting the safety of DNs. Active distribution networks (ADNs) can address voltage issues arising from a high proportion of renewable energy by regulating distributed controllable resources. However, the conventional mathematical optimization-based approach to voltage reactive power control has certain limitations. It heavily depends on precise DN parameters, and its online implementation requires iterative solutions, resulting in prolonged computation time. In this study, we propose a Volt-VAR control (VVC) framework in ADNs based on multi-agent reinforcement learning (MARL). To simplify the control of photovoltaic (PV) inverters, the ADNs are initially divided into several distributed autonomous sub-networks based on the electrical distance of reactive voltage sensitivity. Subsequently, the Multi-Agent Soft Actor-Critic (MASAC) algorithm is employed to address the partitioned cooperative voltage control problem. During online deployment, the agents execute distributed cooperative control based on local observations. Comparative tests involving various methods are conducted on IEEE 33-bus and IEEE 141-bus medium-voltage DNs. The results demonstrate the effectiveness and versatility of this method in managing voltage fluctuations and mitigating reactive power loss.