## 1 Introduction  
In recent years, the integration of renewable energy photovoltaic power generation has seen rapid growth [1, 2, 3]. Nevertheless, faults or disturbances in the power grid can cause the voltage at the PCC of photovoltaic stations to decline. Grid-connected systems must possess a certain degree of LVRT capability. Figure 1 illustrates that, when the voltage dip falls within the range indicated above the dashed line, the photovoltaic system continues to operate without disconnecting from the grid, supplying reactive current to stabilize the PCC voltage. Owing to its precise replication of synchronous generator inertia and damping, the VSG has emerged as the leading control approach for grid-tied inverters. The concept of a virtual synchronous generator, which entails incorporating the inertia and damping characteristics of a synchronous generator into the control strategy of grid-connected inverters, was first introduced in literature [4]. Subsequently, literature [5, 6] crafted the -droop control equation for the VSG by mirroring the primary frequency and voltage control mechanisms of synchronous generators, thereby decoupling the active and reactive power loops. However, no intervention was made on the virtual synchronism and power angle, leading to issues with power angle stability. Literature [7] bolstered the power angle stability of the VSG system through the application of the virtual power angle increment technique. In literature [8], the VSG control methodology was integrated into the LVRT strategy for renewable energy systems, successfully enabling LVRT via a dual-mode switching control mechanism for inverters. Lastly, in literature [9], by establishing a VSG model for permanent magnet direct-drive wind turbines, a new power compensation setpoint during LVRT scenarios was introduced. It was pointed out that when the grid voltage dip is not severe, active power can be maintained constant while an appropriate amount of reactive power is increased, thereby enhancing resource utilization beyond the original setpoint. The aforementioned research on VSG control strategies and their LVRT capabilities assumes a three-phase symmetrical voltage sag scenario in the power grid. Yet, in real-world operations, unbalanced load power and various faults in distribution networks often lead to unbalanced and harmonically disturbed grid voltage sags during power system short-circuit faults, challenging the maintenance of balanced and stable grid-connected currents in VSG systems. To tackle this, literature [10] introduces a technique that integrates virtual impedance with phasor current limiting for direct voltage-controlled VSG systems, efficiently constraining both transient and steady-state fault currents. However, this approach assumes a single fault in the grid and neglects complex faults characterized by harmonic-laden unbalanced voltage sags. Literature [11] employs a DSOGI to extract positive and negative sequence components of the grid voltage, achieving balanced grid-connected currents by suppressing the negative sequence component of the grid-connected current. This control strategy performs well under low harmonic grid voltage conditions, but its efficacy in acquiring grid frequency and phase using a traditional DSOGI-PLL diminishes when the grid voltage contains significant harmonics. This paper investigates the LVRT control strategy for VSG under harmonic-containing asymmetric voltage sags in the power grid. The objective is to improve traditional control strategies to stabilize grid-connected currents when the grid voltage contains harmonic interference or a certain degree of imbalance. Firstly, an LC-type VSG control model is established to analyze the impact of grid voltage, particularly under unbalanced sags, on the grid-connected currents during the LVRT of the VSG. Secondly, the traditional DSOGI-PLL is improved to achieve good filtering performance in grids with rich harmonics.