## 1 Introduction  
As clean and renewable energy, wind power has broad application prospects, and will become more important in the future energy consumption pattern [1, 2, 3, 4]. Since wind turbines cannot provide short-circuit current as conventional synchronous generators do, with the increasing penetration of wind power integrated to the grid [5, 6], the equivalent strength of the grid reduces gradually, and the grid tends to become a weak grid [7, 8]. The characteristics of the weak grid are mainly reflected in the following two aspects [9]: (i) in the electromechanical perspective, the grid lacks rotating masses, causing frequency instability with the high-penetration integration of wind power [10]; (ii) in the electrical perspective, the poor voltage-supporting capability of the grid will lead to abnormal interactions between wind turbines and the grid, such as the low-frequency oscillation, sub-synchronous oscillation, and harmonic oscillation, which endangers the safe and stable operation of the grid [11]. In order to cope with the high-penetration integration of large-scale wind power, the following three challenges need to be overcome: (1) wind turbines participate in the grid regulation, i.e., inertial response and primary frequency regulation; (2) the stable operation of wind turbines under weak grid conditions; (3) the LVRT of wind turbines when the short-circuit fault occurs [12]. The control of wind power converters is the key to influence the grid-connected performance of wind turbines. At present, the conventional control strategy of wind power converters adopts the PLL to orientate with the grid, and realizes power regulation by adjusting the injected current. The conventional converter control strategy makes the converter exhibit the current source characteristics [13], thus it is called the current source (CS) control. Under the CS control, since wind turbines act as constant power sources and have no responses to frequency fluctuations from the grid, the integration of high-penetration wind power reduces the equivalent inertia of the grid, which is not conducive to the frequency stability of the power system [14]. On the other hand, when designing the current control loop of a wind power converter, the influence of the grid impedance is usually ignored. However, the effective bandwidth of the current loop decreases with the increase of the grid impedance, causing abnormal interactions between the PLL and the current control loop, which will lead to oscillations and instability [15]. Although introducing the auxiliary control loop to the existing CS control structure can simulate the inertial response function and suppress oscillations of wind turbines, this kind of control strategy exhibits poor adaptability in practical applications [16]. By simulating the dynamic equation of the synchronous generator (SG), the VS control directly controls the amplitude and phase of the converter's output voltage, and has the function of PLL-less autonomous grid-synchronization. In addition, the VS control can be viewed as a grid-forming control strategy [17]. At present, the existing virtual synchronous generator (VSG) control method [18] and power synchronization control method [19] that imitate the motion equation of the synchronous generator can be regarded as the VS control. These two VS control methods, setting the output power as the control target, are suitable for converters with stable and controllable input power, but have limitations in the application to PMSG-based wind turbines with intermittent and fluctuating input of wind power. The author proposes a novel VS control strategy by employing the inherent dynamics of the GSC's DC-link capacitor to automatically synchronize the grid in [20]. Moreover, the functions of autonomous inertial response and stable operation under weak grid conditions are achieved at the same time. However, this paper [20] does not study the primary frequency regulation and LVRT of the PMSG-based wind turbine.