## 5 Experimental Verification  
For the purpose of verifying the analysis of the effect of grid harmonics and proposed closed-loop control strategy, the experiment platform of this QIS AC-DC converter has been built. Figure 15 clearly shows its photograph. The corresponding experimental parameters are the same as Tables 1 and 2. We inject 10% of the 3 rd, 5% of the 5 th and 7 th harmonics to output voltage of AC source supply, with the aim to realize the simulation of the distorted single-phase grid voltage. All of these experimental results are measured by Memory Hicorder MR6000 from HIOKI (Ueda, Japan). Figure 14: Curves of amplitude-frequency characteristics of control error transfer function of compound controller. Figure 13: Nyquist curve of \(H\) (z). First, the influence of grid harmonics on grid current of this converter driven by ITPS control under open-loop situations is verified, as displayed in Figure 16. From Figure 16a,c, when given grid current amplitudes are 3A and 5A, respectively, obvious distortions of grid currents can be seen. From Figure 16b,d, under two different current amplitudes, 3 rd, 5 th, and 7 th current harmonics obviously exist and THDs of grid currents are 8.22% and 5.27%, respectively. This verifies that the grid harmonics do cause the same order harmonics in the grid currents. In consequence, the validity of previous theoretical analysis is verified. In the following, the steady-state control performance of the compound closed-loop control strategy that we put forward is verified. Grid voltage and given grid current amplitude are the same as that under open-loop situations. Figure 17 shows relevant experiment results in detail. According to Figure 17a,c, under two given different grid current amplitudes, the actual grid currents are both sine waves, whose amplitudes are precisely 3A and 5A. It verifies that the closed-loop control strategy put forward realizes the function that control of grid current fundamental component is without steady-state error. Figure 16: Experimental waveforms of QIS AC-DC converter driven by ITPS. (**a,b**) Im is 3A, (**c,d**) Im is 5A. Figure 15: Photograph of experimental platform of QIS AC-DC converter. From Figure 17b,d, THDs of grid currents are 2.35% and 2.14%, respectively, and the 3 rd, 5 th, and 7 th harmonic contents are all reduced below 1% under these two situations. Therefore, the proposed closed-loop control strategy effectively eliminates the grid current odd harmonics. For the purpose of verifying the control error convergence rate of OMRC that we put forward, Figure 18 shows the respective experiment results when proposed OMRC controller and another standard RC are suddenly enabled. From Figure 18, before the two controllers are enabled, there is a periodic ripple in \(i_{Er}\) and the grid current is distorted. After either OMRC or RC is enabled, \(i_{Er}\) reduces to zero gradually. The difference is that after OMRC is enabled, \(i_{Er}\) reduces to zero within 1/2 grid period; however, after the standard RC is enabled, \(i_{Er}\) reduces to zero within one grid period. Hence, it verifies the convergence speed of the OMRC is twice that of the standard RC. Next, the dynamic performance of the proposed compound controller is verified in Figure 19. In Figure 19a, when the reference grid current steps up from 3A to 5A, the actual grid current amplitude can be adjusted to the given value within 2 ms. After around 60 ms (three grid periods), an undistorted sinusoidal grid current is obtained. Figure 19b shows the situation that the reference grid current steps down from 5A to 3A. Its dynamic process is similar to Figure 19a. Therefore, Figure 19 certifies that the proposed controller realizes good dynamic performance. Figure 17: Experimental waveforms of proposed closed-loop controller. (**a**,**b**) Im is 3A, (**c**,**d**) Im is 5A. Figure 18: Experimental dynamic waveforms of two controllers. (**a**) OMRC, (**b**) standard RC. Finally, the ability of the proposed strategy to reject the step disturbance of AC or DC sources is verified.