This paper investigates and discusses the interaction stability issues of a wind farm with weak grid connections, where the wind turbines (WTs) are controlled by a new type of converter control strategy referred to as the voltage source (VS) control. The primary intention of the VS control method is to achieve the high-quality inertial response capability of a single WT. However, when it is applied to multiple WTs within a wind farm, its weak-grid performance regarding the stability remains concealed and needs to be clarified. To this end, a frequency domain model of the wind farm under the VS control is first developed. Based on this model and the application of a stability margin quantification index, not only the interactions between the wind farm and the weak grid but also those among WTs will be systematically assessed in this paper. A crucial finding is that the inertial response of VS control has negative impacts on the stability margin of the system, and the dominant instability mode is more related to the interactions among the WTs rather than the typical grid-wind farm interaction. Based on this knowledge, a stabilization control strategy is then proposed, aiming for stability improvements of VS control while fulfilling the demand of inertial responses. Finally, all the results are verified by time-domain simulations in power systems computer aided design/electromagnetic transients including DC(PSCAD/EMTDC).