# Hybrid Modulation Strategy to Eliminate Current Distortion for PV Grid-Tied H6 Inverter
## 5 Simulation Study  
The simulation model is developed on the MATLAB/Simulink platform, using the Simulink S-Function module for realizing the control algorithm. The corresponding simulation parameters for the model are shown in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variables** & **Value** & **Variables** & **Value** \\ \hline Rated Power & 4.67 kVA & \(T_{s}\) & 52 μs \\ Capacitor & 1000 μsF & \(f_{s}\) & 19.2 kHz \\ \(E\) & 400 V & \(L\) & 10 mH \\ \(V_{ac}\) & 220 V & \(f\) & 50 Hz \\ \(\Delta i_{LN}\) & 15\% Peak Current & \(I_{LN}\) & 21.22 A \\ \(K_{P}\) & 19.23 & \(K_{I}\) & 1923.1 \\ \(K_{R}\) & 19.23 & R & 0.2 \(\Omega\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for simulation. Figure 10: The block diagram of control with the new HMM. Figure 11 displays the inductor current, grid voltage and common-mode voltage of H6 inverter for two kinds of modulation modes in the scenario when the inductor current leads the grid voltage by 30\({}^{\circ}\). As shown in Figure 11a, there is an uncontrollable region for modulation mode I and the current is seriously distorted in this region. It can be seen that the time duration of current distortion is larger than the time for which voltage and current have opposite polarity of \(\Delta\varphi\), which is due to the system changing-over between a non-controlled region and a controlled area for which the current controller needs time to adjust. The results using the presented HMM techniques, are shown in Figure 11b. Clearly, adopting the new HMM for the H6 inverter system results in a controllable current with a more stable waveform characteristic. Figures 12 and 13 show a similar comparison between the use of MMI and the new HMM, applied to the H5 and HERIC converter topologies. Again, it can be seen the new hybrid modulation mode eliminates the current distortion. Figure 11: Grid voltage and inductor current of H6. \(\theta\) = 30\({}^{\circ}\), 5 times attenuation of voltage. (**a**) Modulation I. (**b**) Hybrid modulation mode (HMM). Figure 12: The grid voltage and inductor current of H5. \(\theta\) = 30\({}^{\circ}\), 5 times attenuation of voltage. (**a**) Modulation I. (**b**) Hybrid modulation mode (HMM). Figure 14 plots the common-mode voltage for the H6 converter using both modulation techniques. Note that for MMI as shown in Figure 14a the common-mode voltage is not a constant value in the region of opposite current and voltage polarity. However, when using the HMM the common-mode voltage becomes a constant value with no common-mode leakage current as displayed in Figure 14b. Based on the system parameters from Table 1 earlier, the open loop and closed loop transfer function of the system under the PI, PR, and PIR controllers can be easily obtained. Both the open and closed loop bode plots for three controllers are shown in Figures 15 and 16 respectively. It should be noted that the closed loop bode plots in Figure 15 are obtained from the systems which have already been controlled. As can be seen from Figure 14, the gain at the resonant frequency under the PR controller is 300 dB. The drawback of PR control is that the gain at the low-frequency stage is lower than the PI control. However, zero steady-state error cannot be achieved while adopting PI control alone due to the gain of PI control at the grid frequency (the resonant frequency of the PR controller) being limited. At the high frequency stage, both the gain of PI and PR controllers drops at a rate of 40 dB per decade reducing the influence of the external noise on the system. Figure 14: Common-mode voltage. (**a**) Common-mode voltage of modulation mode I, \(\theta=30^{\circ}\). (**b**) Common-mode voltage of HMM, \(\theta=30^{\circ}\). Figure 13: Grid voltage and inductor current of HEIRC. \(\theta=30^{\circ}\), 5 times attenuation of the voltage. (**a**) Modulation I. (**b**) Hybrid modulation mode (HMM).