## 4 Performance Assessment under Distorted Weak Grid Condition
### Simulation Results
Under the ideal grid voltages, this scheme provides reasonable current waveforms without the harmonic resonant controllers incorporated in the orders of 5 th, 7 th, 11 th, and 13 th. However, as shown in Figure 21, as soon as the resonant controllers start at 0.5 s, the system instantly becomes unstable, which accords closely with the stability analysis given in Figure 8.  
In order to validate the stability analyses of the integral-resonant state feedback controller shown in Figures 9-13, the simulation results are presented. Figure 22 shows the simulation results for the integral-resonant state feedback controller with \(L_{1}=1.7\) mH, \(L_{2}=1.0\) mH, and \(C_{f}=4.5\) uF without the grid impedance in Case 1. Test grid voltages are the same as Figure 17a. As can be clearly observed in Figure 22, the grid currents are quite sinusoidal without negative impact from the distorted grid voltages, resulting in the THD value of 3.96%. The simulation results for the integral-resonant state feedback controller under the grid impedance change and distorted grid are shown in Figures 23 and 24 for the weak grid condition, in which all the conditions including the grid distortion are the same as Figure 17. The parameters of the current controller are properly designed under distorted grid condition and \(L_{g}=0\). It is worth noting that the measured grid voltages in Figure 23a are different from Figure 17a since \(L_{g}\) produces additional inductive voltage drop by the grid current as is shown in Figure 15. Clearly, the instability of the direct current controller is observed in Figure 18 with the same level of weak grid. On the contrary, the output currents of the full-state feedback controller in Figure 23a shows stable sinusoidal waveforms with the THD value reduced to 2.16%. The full-state feedback control is tested further under more severe weak grid conditions with \(L_{g}\) increased to 14 mH in Figure 15:0 Though the voltages at the PCC contain more distorted harmonics due to the weak grid, the current controller can still produce stable high-quality injected currents with the THD of 2.09%. These results well match up the stability analysis given in Figure 15:1 In terms of current quality, the THD value of current is smaller as \(L_{g}\) is increased. This complies well with the frequency responses in Figure 5, in which the resonance frequency of the LCL filter is smaller as \(L_{g}\) is increased. Figure 15:2 Simulation result for direct grid current controller with \(L_{1}=1.7\) mH, \(L_{2}=1.0\) mH, and \(C_{f}=30\) μF under ideal grid voltages without grid impedance in Case 3. Figure 15:3 Simulation results for integral-resonant state feedback controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 4.5 μF under distorted grid voltages and \(L_{g}\) = 7 mH in Case 1: (**a**) Distorted grid voltages; (**b**) Grid-side three-phase currents. Figure 15:4 Simulation results for integral-resonant state feedback controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 4.5 μF under distorted grid voltages without grid impedance in Case 1: (**a**) Grid-side three-phase currents; (**b**) FFT result for \(a\)-phase grid-side current. To investigate the stability and current control performance for larger variation of the grid impedance, Figure 25 shows the simulation result when \(L_{g}\) is increased to 21 mH in Case 1 under distorted grid. In this Case, the system loses the stability. From the simulation tests in Figures 18 and 25, it is confirmed that the use of the state feedback controller provides a more flexible option to design a current control of an LCL-filtered inverter system in the environment of uncertain grid impedance under distorted weak grid condition because the stability region is extended.