# Dual-Boost Inverter for PV Microinverter Application--An Assessment of Control Strategies
## 4 Control Strategies Comparison
### Comparison  
The main parameters considered in the comparison are the number of cascaded control loops, total number of measured variables, and two performance metrics [34]: the total harmonic distortion (THD) and averaged switching frequency. For the linear control, the control targets are the input capacitor's voltage \(v_{\text{pv}}\), the output capacitor's voltages (\(v_{\text{c1}}\), \(v_{\text{c2}}\)), and the inductor's currents (\(i_{\text{t1},\,i_{\text{t2}}}\)). In the case of FCS-MPC, the main control goals are the current through the inductor and voltage in the output capacitor for each boost converter. Therefore, a cascaded control loop scheme was used, where the first control loop regulates the voltage of the input capacitor \(C_{\text{pv}}\), followed by the FCS-MPC stage. The flatness-based control scheme consists of two cascaded loops. The targets of its first control loop are similar to the control scheme of the linear control, i.e., input capacitor's voltage. The second loop control regulates the energy stored in the output capacitors \(C_{\text{1}}\), \(C_{\text{2}}\) and inductors \(L_{\text{1}}\), \(L_{\text{2}}\) of the DBI. These three control strategy are based on the individual switching strategy. In a different way, the control based on the sliding mode approach considers the output current of the DBI, as the main control purpose. To achieve this objective, a cascaded control scheme with three loops was employed. The target of the first loop, like the previous schemes, is the voltage of the input capacitor. The output current of the DBI is the control objective of the second control loop. To continue, the inner control loop determines the switching surface based on the difference of the current in the inductors regulation. Considering the description of the control schemes mentioned before, five control loops in total are required to regulate the DBI with linear control. For FCS-MPC and flatness-based control, two and three control loops in total are necessary, respectively, while the sliding-mode-based control presents three control loops. On the other hand, the linear control, FCS-MPC, and flatness-based control strategies are based on the individual switching strategy. For this reason, the measured variables used in these control schemes are seven, which are the input current and voltage (\(i_{\text{pv}}\), \(v_{\text{pv}}\)), the inductor's current (\(i_{\text{L1}}\), \(i_{\text{t2}}\)), and the output capacitor's voltage (\(v_{\text{c1}}\), \(v_{\text{c2}}\)). Since the sliding mode control is based on a current regulation, fewer sensors are required. Hence, the output voltage is not directly controlled and does not need to be measured. Therefore, five variables are measured. The averaged switching frequency (\(\overline{f}_{\text{sw}}\)) is another point to analyze, because this parameter is directly associated with the inductor's current ripple. In the linear, flatness-based, and sliding mode controls, the average switching frequency obtained was around 80 kHz and the current ripple was around 5A. However, in FCS-MPC, the averaged switching frequency was 80 kHz, while the current ripple in the positive peak was 9.94 A. It is important to indicate that the current ripple does not correspond to the design, since the switching frequency in FCS-MPC is variable, and it is difficult to establish the current ripple for all ranges. To evaluate the power quality obtained with each control strategy, the total harmonic distortion and spectrum of the grid current were analyzed. The spectrum of the grid current obtained with the four control methods complies with the IEEE standard 1547, as can be observed in Table 4. However, the highest THD among the four controls was obtained with the linear control strategy, because the output current of the DBI with the linear control contains more oscillations than with other control strategies.