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Multi-terminal modular multilevel converter (MMC) power transmission is the current development trend in DC transmission. However, owing to its fast control and dynamic characteristics, it may interact with the other inductive devices or the grid and cause stability issues. This paper describes the use of the impedance analysis method in the frequency domain to analyze system stability. First, the multi-harmonic linearization method is used to model the impedance of a three-terminal MMC system. To make the model more accurate, the modeling considers the effect of frequency coupling caused by an asymmetric controller and the AC sampling site position. This paper then proposes an equivalent method of the grid impedance for the three-terminal system that can accurately judge the stability of the grid-connected system when the AC side is coupled. This work provides a theoretical basis for the prediction and suppression of the oscillation of MMC grid-connected system with coupling on the AC side. Finally, a three-terminal MMC model is built in Matlab/Simulink and the Nyquist stability criterion is used to verify the correctness of the analysis. [ABSTRACT FROM AUTHOR]