In response to the issue of low terminal voltage in distribution transformer areas due to the excessive supply radius and rapid load growth, a battery energy storage-based low voltage governance method is proposed. This approach employs a bipolar control strategy, utilizing the coordinated control of a bidirectional buck-boost converter and a three-phase full-bridge inverter. By integrating a fuzzy PI control method optimized with Chaotic Particle Swarm Optimization (CPSO) and model predictive control, this method effectively addresses the low voltage problem in distribution transformer areas. The DC/DC section implements a CPSO-optimized fuzzy PI voltage and current dual closed-loop control, which dynamically adjusts the quantization and proportional factors, significantly enhancing the tracking speed and stability of the DC bus voltage. The DC/AC section employs single vector model current predictive control to dynamically regulate the voltage amplitude and frequency, effectively elevating the voltage in the distribution transformer area.Simulink simulations demonstrate that this strategy can rapidly restore the voltage amplitude within the allowable fluctuation range for various degrees of voltage sag: 90%-95% (mild), 80%-90% (moderate), and below 80% (severe). Additionally, the overshoot of the DC bus voltage is nearly eliminated, with the voltage distortion rate reduced to as low as 1.18%, meeting the requirements of the distribution system.