## 1 Introduction  
Renewable energy generation has received much attention in recent years [1; 2]. As a power interface between renewable energy sources and the grid, voltage source converters (VSCs) have been increasing the penetration in power systems [3]. However, due to the geographical distribution characteristics of renewable energy sources, the long transmission lines of the grid result in grid impedance that cannot be neglected [4] which makes the power grid become a weak grid. Under a weak grid, the interaction between the VSC and the grid easily causes oscillation problems and brings new challenges to the safe and stable operation of power systems [5; 6; 7]. The stability analysis methods of VSC grid-connected system oscillation are mainly divided into two categories, that is, the eigenvalue analysis method based on state space and the impedance analysis method based on frequency domain theory [8; 9; 10]. The eigenvalue analysis method relies on detailed models and parameters of converters and grids which is difficult to adapt to the large-scale grid-connected analysis of renewable energy. The impedance analysis method considers the VSC and grid as two independent subsystems, the system stability can be analyzed using only the port characteristics of the two subsystems [10; 11]. Depending on the coordinate system used for modeling, there are two types of impedances, that is, dq-domain impedance in a synchronous rotating coordinate system [12; 13] and sequence-domain impedance in a stationary coordinate system [14; 15]. Based on the impedance model, the generalized Nyquist criterion is usually used for stability analysis. These methods can identify whether the grid-connected VSC is stable and provide a qualitative evaluation for stability. However, they cannot quantitatively evaluate the system stability, and cannot evaluate the difference in the system stability with different parameters. The stability level of the grid-connected VSC system is different when the control parameters of the VSC are different. If the controller parameters are not designed properly, it will affect the system stability and even cause oscillations [16]. Current loop and phase-locked loop (PLL) are key components in VSCs, the former is responsible for regulating the output power accurately and flexibly, and the latter is responsible for the synchronization between VSC and the power grid. The control parameters of both components can significantly affect the interactions between VSC and the power grid [17]. Moreover, the parameter analysis for the current control loop further indicates that the damping characteristics of the VSC will be reduced by an excessively small proportional coefficient of the current controller which is harmful to the stable operation of VSC [18; 19]. For the influence of PLL on system stability, [20; 21] indicated that inappropriate PLL parameters can lead to negative resistance of VSC which can decrease the stability of VSC. Therefore, determining the appropriate parameters for the control of VSCs is essential to prevent oscillations in advance [22]. To address the oscillations caused by the interaction between VSCs and weak grids, scholars have proposed solutions based on parameter optimizations of current loops and PLL. A parameter optimization method for VSC current loop control was proposed in [23] which uses the system stability margin as a constraint. [24] limited the selection range of the control parameters based on the relationship between frequency domain indicators and current control parameters, thereby optimizing the parameters of the current control loop. An adaptive PLL parameter design method was proposed to ensure sufficient phase angle margin by adjusting PLL parameters in real time [25]. However, the existing methods did not give the principle of control parameters selection according to the different stability margins of the system nor can quantify the stability level of the system.