# Analysis and Design of A PMQR-Type Repetitive Control Scheme for Grid-Connected H6 Inverters
## 4 Simulation Results and Analysis
### Simulation Results  
Simulations were carried out with Simulink in MATLAB software. The sampling time was set as \((1\times 10^{-6})\) s. The rated output power was 3 kW, and the average output current was about 14 A. In the SRF, the proportional controller was used to provide higher control gain. The repetitive control  
Figure 14: Nyquist plot of \(H\left(z\right)\) with different values of \(k_{r}\).  
was mainly responsible for compensating the harmonics. In order to confirm the superiority of the proposed PMQR-type RC scheme, the simulations of a variety of classical control scheme were carried out for comparison. All simulations were tested on the single-phase grid-tied H6-type inverter with SOGI-based PLL. The parameters are listed in Table 1, and the given current reference amplitude \(I_{ref}\) was set at 20 A.  
The inverter should pour current into the grid with unity power factor during steady state. The value of THD can reflect the harmonic suppression capability of each current controller. Figure 17 displays the steady-state waveforms of grid voltage \(v_{g}\) and output current \(i_{g}\) for the H6 inverter. The simulated cases were all well achieved such that the phase of output current was synchronized with grid voltage. The current tracking error waveforms in the steady state are illustrated in Figure 18. As can be seen, there existed a distinct periodic steady-state error in the inverter output current, which will decrease the capability of tracking the reference input signal. The amplitude of the output current error was about 0.5 A under PI control. The current steady-state error was the minimum in the case of the PMQR-type RC scheme, which demonstrates that the proposed controller had a better zero error tracking performance.  
Figure 17: Steady-state grid voltage \(v_{g}\) and output current \(i_{g}\) waveforms under different controllers. (**a**) With PI controller. (**b**) With PR controller. (**c**) With repetitive controller. (**d**) With PMQR-type RC controller.  
Figure 18: The current tracking error in the steady-state with different controllers. (**a**) With PI controller. (**b**) With PR controller. (**c**) With repetitive controller. (**d**) With PMQR-type RC controller.  
The performance of controllers mainly depends on the system parameters, such as the system frequency. The THD value of grid-tied current was selected as the performance criteria to observe the different controllers under the system frequency variation. Figure 22 shows the THD variation of the different controllers as the system frequency changes from 48 Hz-52 Hz. It can be found that the PI and PR control strategies were both insensitive to frequency variation. However, the ability of suppressing harmonics for RC and PMQR-type RC was significantly reduced at the frequency, except fundamental frequency, because the repetitive control was highly dependent on frequency. From another perspective, the performance was still excellent despite sensitivity to frequency changes.  
Due to the slow dynamic response of the traditional RC, a fast transient response should be achieved in the improved control scheme. When the given grid current reference \(I_{ref}\) steps from 20 A to 15 A at 0.24 s, the system dynamic response comparisons with the traditional PI control and the  
Figure 21: Most prominent harmonic components of output current.  
Figure 22: THD magnitude of current controller during variation in frequency.  
proposed PMQR-type repetitive control were as illustrated in Figure 23. It can be seen that the dynamic performance of the PMQR-type RC was almost the same as the PI control scheme. Just as mentioned in Section 3.3, fast dynamic response of the proportional controller will not be affected by slow RC, which indicates that the dynamic performance was mainly determined by the proportional controller, and the RC just like the MQR controller was only used to improve steady-state harmonics compensation.