## 4 Performance Assessment under Distorted Weak Grid Condition
### Simulation Results  
To evaluate the current control performance of the direct current control and the integral-resonant full-state feedback current control under distorted weak grid condition, the simulation results are presented by using the control structure in Figures 2 and 3, and LCL filter parameters given in Table 1, in which different values of capacitor are used to produce different resonance frequencies of the LCL filter. Figure 17 shows the current control performance of the direct grid current controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 4.5 \(\upmu\)F under distorted grid voltages without grid impedance in Case 1. Figure 17a shows three-phase distorted grid voltages which contain the 5 th, 7 th, 11 th, and 13 th harmonics with the magnitude of 5% of the fundamental component. Figure 17b,c show grid-side three-phase current waveforms and the fast fourier transform (FFT) result for \(a\)-phase current with the harmonic limits specified by the grid interconnection regulation IEEE Std. 1547 [36]. As is clearly shown, the current harmonic distortion caused by distorted grid is well suppressed and the total harmonic distortion (THD) value of current is 3.59%, which represents that this controller effectively deals with the resonance of the LCL filter and low-order harmonic disturbance in grid voltages. Figure 16: Experimental test setup. Figure 15: Configuration of system. To demonstrate the influence of the grid impedance change in the direct grid current control scheme, Figure 18 shows the simulation result when \(L_{g}\) is suddenly increased to 7 mH in Case 1 at 0.5 s under the same distorted grid condition. With this value of \(L_{g}\), the poles of the PR controllers in 11 th and 13 th orders for harmonic suppression are located outside of the unit circle. As a result, grid phase-currents are gradually oscillating, and eventually, the entire system becomes unstable. Figure 19 shows the simulation result for the direct grid current controller with \(L_{1}=1.7\) mH, \(L_{2}=1.0\) mH, and \(C_{f}=10\) uF under distorted grid voltages without the grid impedance in Case 2. Decrease of the resonance frequency improves the harmonic suppression of the LCL filter. Thus, the grid current quality in Figure 19 is much improved as compared with Figure 17, producing only the THD of 2.54%. However, reducing the resonance frequency makes the inverter resonant controller to be more vulnerable to uncertain grid impedance. Figure 17: Simulation results for direct grid current controller with \(L_{1}=1.7\) mH, \(L_{2}=1.0\) mH, and \(C_{f}=4.5\) uF under distorted grid voltages without grid impedance in Case 1: (**a**) Distorted grid voltages; (**b**) Grid-side three-phase currents; (**c**) FFT result for \(a\)-phase grid-side current. Figure 20 shows the simulation result of grid-side three-phase currents when \(L_{g}\) has a step change from 0 to 2 mH in Case 2 at 0.5 s with the same conditions and control parameters as Figure 19. Currents become unstable as soon as uncertain grid impedance is applied. Figures 19 and 20 show a strong agreement with the stability analysis in Figure 7. Obviously, with the LCL filter designed at lower frequency band, the direct current controller including the PR compensators is more vulnerable to uncertain grid impedance. Figure 19: Simulation result for direct grid current 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. Figure 20: Simulation result for direct grid current controller with \(L_{1}\) = 1.7 mH, \(L_{2}\) = 1.0 mH, and \(C_{f}\) = 10 uF under distorted grid voltages and \(L_{g}\) = 2 mH in Case 2. To test the current control performance of the direct grid current controller with the LCL filter designed at the resonance frequency below the critical frequency, Figure 21 uses the test condition of \(L_{1}=1.7\) mH, \(L_{2}=1.0\) mH, and \(C_{f}=30\) uF under ideal grid voltages without the grid impedance in Case 3.