To address the issue of common-mode ground circulating current in non-isolated flexible interconnected devices, a low-frequency circulating current suppression strategy designed for multi-terminal converters was investigated. A mathematical model of low-frequency ground circulating currents for these multi-terminal converters was developed, while simplified circuit analysis was performed to clarify the key factors and mechanisms governing low-frequency circulation. Building on this analysis, a suppression strategy utilizing a multi-mode proportional resonant controller was introduced, coupled with an improved modulation algorithm which injected corrected voltage signals to accomplish closed-loop suppression for low-frequency circulating currents in multi-terminal converters. Lastly, MATLAB/Simulink simulations were conducted to verify the efficacy and rapid dynamic response of the presented strategy, thereby offering technical support for the flexible interconnection of distribution networks featuring high penetration of renewable energy.