Establishing a suitable closed-loop transfer function model for the grid-connected PMSG system is the key basis in performing inter-harmonic characteristics analysis. Multiple closed-loop transfer functions can be constructed when different components of the converter controller are taken into account. However, the effect of different components of the converter controller on inter-harmonic stability analysis is not clear. In this paper, the complete transfer function, considering different loops, is first given. Based on the complete closed-loop transfer function, the DC-link, PLL and voltage forward-feed are removed step by step to derive different closed-loop transfer functions. The inter-harmonic related poles of different closed-loop transfer functions are further calculated to analyze the effect of closed-loop transfer functions on inter-harmonic characteristics analysis. Finally, by performing time domain simulation, the correctness of the theoretical analysis results is verified. The results show that under the conditions of a weak AC system, each loop of the converter control system will reduce the stability of the inter-harmonic in the sub-synchronous frequency range and influence the inter-harmonic oscillation frequency. The transfer function needs to consider the influence of each loop to accurately calculate the inter-harmonic stability of the system.