## 4 Performance Assessment under Distorted Weak Grid Condition
### Simulation Results
The same integral-resonant state feedback control method is applied for the different set of the LCL parameters given in Case 2 with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 10 \(\mu\)F. Figure 26 shows the simulation results under distorted grid voltages without the effect of the grid impedance in Case 2. The grid current waveforms are satisfactory with the THD of 3.86%. Figure 27 shows the simulation results with an extra \(L_{g}\) of 7 mH in Case 2 under the same voltage conditions of Figure 17a. As shown in Figure 10, the poles of the closed-loop current control still remain inside the stable region when \(L_{g}\) varies from 0 to 7 mH. As a result, high-quality sinusoidal grid-injected currents can be obtained, which well demonstrates the validity of the stability analysis. The THD value is much smaller than that of Figure 26 due to additional inductance. Figure 15:5 Simulation result for integral-resonant state feedback controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 4.5 \(\mu\)F under distorted grid voltages and \(L_{g}\) = 14 mH in Case 1. Figure 15:6 Simulation result for integral-resonant state feedback controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 4.5 \(\mu\)F under distorted grid voltages and \(L_{g}\) = 21 mH in Case 1. The grid impedance is further increased under more severe weak grid level. Figure 28 shows the simulation results when \(L_{g}\) increases to 14 mH in Case 2. According to the analysis in Figure 10, the integral-resonant state feedback controller designed for the LCL parameter set of Case 2 shows unstable currents for this value of the grid impedance. As the final LCL parameter set, low region resonance frequency of Case 3 in Table 1 is considered, where \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 30 uF are given. The state feedback current controller is designed for the given LCL filter set to produce a good grid-side current at the stiff grid condition as shown in Figure 15:7 However, as presented in Figure 11, low region resonance frequency of the LCL filter is extremely sensitive to uncertainty caused by the weak grid condition, causing the instability by only small grid impedance change. Figure 30 demonstrates this situation, in which \(L_{g}\) is suddenly increased from 3 mH to 7 mH in Case 3 at 0.5 s. While stable currents are observed with 3 mH of \(L_{g}\), the change to 7 mH of \(L_{g}\) produces unstable grid currents. From the performance assessment of two types of current controls with harmonic compensator, it is clearly confirmed that the state feedback controller is more flexible for an LCL-filtered inverter system in the environment of uncertain grid impedance and distorted grid. Furthermore, when the grid is subject to large impedance variation, high resonance frequency of the LCL filter is preferable since it extends much the stability margin under unexpected weak grid condition. Figure 15:8 Simulation result for integral-resonant state feedback controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 10 uF under distorted grid voltages and \(L_{g}\) = 7 mH in Case 2. Figure 15:9 Simulation result for integral-resonant state feedback controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 10 uF under distorted grid voltages without grid impedance in Case 2.