# Low-Loss Active Grid Impedance Cancellation in Grid-Connected Inverters with LCL Filter
## 4 Simulation Results  
In this section, the simulation study is to verify the control functions of the LV-VSC, and conduct comparative evaluations between CASE I and CASE II as described in Section 3. The simulation is implemented in PSIM software. The parameters are given in Table 1, in which the dc capacitance of the LV-VSC is chosen to be large enough to mitigate the double frequency ripple at the dc side, and the LCL filter parameters are designed based on the criterion in reference [4]. The current control parameters are chosen properly according to reference [11]. To validate the effectiveness of inverter current control against PCC voltage distortion, a 300 W rectifier load is in shunt at the PCC in the following simulation.  
Figure 13 presents the inverter output performance under different grid conditions when only active damping function (\(R_{v}=30\)\(\Omega\)) of the LV-VSC in Section 3.1.2 is activated. It indicates that the active damping function in the LV-VSC is helpful to stabilize the grid-connected inverter with an LCL filter in relatively strong grid condition. At \(L_{g}=0.04\) pu (4 mH), the total harmonic distortion (THD) of grid current is sustained at THDi = 1.69%, which benefits from the unit PCC VFFC and PR+HC current regulator. However, with the increase of grid inductance, the grid current is highly distorted due to poor stability under the weak grid condition. To counteract such negative effect of grid impedance on the inverter output performance, ac voltage regulation of the LV-VSC introduced in Section 3.1.1 is activated. Figure 14 shows the simulation results with the grid impedance cancellation function of the LV-VSC enabled. As expected, both the inverter stability and high injected power quality  
Figure 11: Comparative frequency response of the open loop transfer function (CF: cutoff frequency; PM: phase margin). (**a**) without the compensator (CASE I); (**b**) with the proposed compensator (CASE II).  
Figure 12: Reshaped well-damped GC-VSI with the grid impedance cancellation.  
are guaranteed even under very weak grid condition. That matches with the theoretical analysis in Section 3. Figure 15 simulates the dynamic operation of dc capacitor voltage regulation in the LV-VSC. The dc capacitor voltage tracks the reference command at 30 V gradually.  
Figure 14: Simulation results under different grid conditions when both active damping function and grid impedance cancellation function of the proposed LV-VSC are enabled (CASE II).  
Figure 13: Simulation results under different grid conditions when only active damping function of the proposed LV-VSC is enabled.  
Figure 15: The dynamic response of dc capacitor voltage regulation in the proposed LV-VSC.  
To further demonstrate the importance of grid impedance cancellation, the inverter output performance with traditional current control method (CASE I) is also examined in simulation. To offer a fair comparison, the current control parameters in CASE I are kept the same with the proposed method (CASE II). Figure 16 shows the inverter output performance under different grid conditions for CASE I. It can be seen that the inverter stability becomes poor with the increase of grid inductance, which matches well with the theoretical analysis in Figure 11a. The poor performance in the extremely weak grid (i.e., \(L_{g}\) = 0.20 pu (10 mH)) would be disastrous because other devices at the same PCC exposes to the highly distorted PCC voltage. This problem is addressed successfully by using the proposed grid impedance cancellation method (CASE II), as indicated in Figure 14.