The virtual synchronous generator (VSG) is a promising technology for future utility grids, since it can mimic the output characteristics of a synchronous generator, which provides the necessary inertia to a utility grid. However, the large-scale application of VSGs is limited due to the harmonic interaction between VSGs and the utility grid. Therefore, in order to investigate the stability issue as well as improve the practical application for large-scale power stations, the harmonic interaction mechanism between the VSG cluster and the utility grid is addressed. Firstly, the output impedance model of a single VSG is established, and it is found that the resonance frequency is related to parameters including the output filter, controller, and grid impedance. On this basis, the capacitor current control for a grid-connected inverter based on a VSG is proposed to enhance the resonance suppression. Furthermore, the output impedance of the VSG cluster is established, which reveals the harmonic interaction characteristics between the VSG cluster and the utility grid. In addition, in order to suppress the resonance and improve the stability, an inner-loop control strategy of VSG is introduced. Finally, the simulation and experimental results verified the correctness of the established modeling and analysis of the harmonic interaction between the clustered VSGs and the utility grid. The results show that the proposed impedance model is correct and can predict the resonant point accuracy (which is around 2.3 kHz in the simulation and experimental cases). The total harmonic distortion (THD) can be reduced to 3.2% which meets the requirements of IEEE standard 519.