# Dual-Boost Inverter for PV Microinverter Application--An Assessment of Control Strategies
## 4 Control Strategies Comparison
### Steady-State Results  
Figures 12 and 13 present the simulation results for the DBI under steady-state behavior. These results were obtained in the nominal operation point, i.e., a solar irradiance of \(1000\) W/m\({}^{2}\). Figure 12 shows the behavior of the PV side for the linear control. The results of the PV side with the other control strategies are similar. For this reason, only the simulation results of the PV side with linear control are presented. The reference of the PV voltage and its measurement are observed in Figure 12a, where the three voltage levels around the maximum power point can be identified when the PV panel is operating under constant solar irradiance. Furthermore, the PV current and power are presented in Figure 12b and Figure 12c, respectively. In these figures, the maximum PV module's current and power can be identified. The output capacitor's voltages are composed by a DC-bias and an AC component, as shown in the first column of Figure 13. The AC component of the capacitor's voltages with the linear control, FCS-MPC, and flatness-based strategies is purely sinusoidal, in which the maximum amplitude is around 77 V, and their phases are shifted \(180^{\circ}\). The DC voltage component is 112.7 V, as expected. On the other hand, the DC component is 58 V with the sliding mode control, which is double the input voltage; this is an effect of the sliding mode strategy. The second column of Figure 13 shows the behavior of the inductor's current in each boost converter. The current waveforms are composed by a non-pure sinusoidal, where the maximum and minimum values are the same for both boost converters. Additionally, the phases are shifted \(180^{\circ}\); this is a similar effect to the one observed in the voltage. Moreover, the current through the inductors (\(i_{\text{L1}}\) and \(i_{\text{L2}}\)) in the four control selected reach a negative value, due to the circulating power. The current ripple chosen in the design was 5 A; this was achieved with the linear control, flatness-based control, and sliding mode control. However, the variable switching frequency inherent to FCS-MPC produces a higher current ripple. An alternative to solve this issue was proposed in [33], where the control of the switching period was introduced in the cost function. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Parameter** & **Value** \\ \hline
**PV Parameters** & & \\ \(V_{mpp}\) & PV voltage at MPP & 29 V \\ \(P_{pv}\) & PV power & 216 W \\ \(C_{pv}\) & Input capacitor & 25 mF \\ \hline
**Grid Parameters** & & \\ \(v_{\text{s}}\) & Grid voltage & 110 \(V_{\text{rms}}\) \\ \(f_{\text{s}}\) & Grid frequency & 60 Hz \\ \(L_{\text{s}}\) & Grid filter inductance & 10 mH \\ \hline
**Converter Parameters** & & \\ \(L_{1}\), \(L_{2}\) & Boost converters’ inductors & 55 \(\upmu\)H \\ \(C_{1}\), \(C_{2}\) & Boost converters’ capacitors & 5 \(\upmu\)F \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Simulation parameters of the DBI. The grid voltage and current are illustrated in the third column of Figure 13, where it is possible to identify that the current injected to the grid is sinusoidal and in phase with the grid voltage for the four control strategies. To analyze the power quality of the DBI with the four control strategies, the grid current spectrum and its total harmonic distortion (THD) were obtained, as shown in Figure 14. Furthermore, the IEEE standard 1547 is introduced in these figures to identify the limits of each harmonic. As can be observed, the THD of the grid current fulfills the standard (THD \(<\) 5%) for the four cases. In the linear control, the odd harmonics (the third, fifth, and seventh) are strongly marked. Nevertheless, the THD of the grid current is 3.85%, which is within the accepted range by the standard. On the other hand, the THD of FCS-model predictive control is 3.58%. This is a very good result, considering that the waveform of the grid current has appreciable oscillations.