In this article, we propose a centralized battery energy storage-based medium-voltage multiwinding dynamic voltage compensator (DVC) for balance and unbalance operations. In this topology, the compensation voltage is added to the grid side through the transformer, and the primary side of the transformer is shunted by multiple windings to support the voltage sag on the medium-voltage distribution systems. According to the symmetrical and asymmetrical grid-side voltage sags, the positive- and negative-sequence mathematical models of DVC as well as their voltage-current double closed-loop control strategies are developed. As for the dc bias caused by circulating current between the primary windings of each phase of the multiwinding transformer, circulating current suppression algorithm is added to the positive- and negative-sequence inner current loops. Simulation and experimental results are performed to verify the effectiveness and superiority of the proposed methodology on voltage support.