## 2 Description the PV System Based on the NEC Boost Converter
### Comparison with the Classical Boost Converter  
PV systems with a first stage based on the classical boost converter, similar to the one reported in [12], have the structure depicted in Figure 4. Such a circuit provides continuous input current; hence, the same input capacitor \(C_{pv}\) used in the NEC boost PV system can be adopted in this classical boost alternative to provide a fair comparison. The switched model of this classical boost PV system is given in Equations (31) and (32), where the strong difference with the PV system based on the NEC boost converter is evident due to the difference with the switched Equations (9)-(12). Design procedures and controllers previously developed for the classical boost converter are not applicable to the  
Figure 4: PV system based on the classical boost converter. PV system based on the NEC boost converter; thus, new design and control analyses must be developed. \[\frac{di_{L_{b}}}{dt} = \frac{v_{pv}-v_{b}\cdot(1-u)}{L_{b}} \tag{31}\] \[\frac{dv_{pv}}{dt} = \frac{i_{pv}-i_{L_{b}}}{C_{pv}} \tag{32}\]  
A fair comparison between PV systems based on both the NEC and classical boost converters also requires providing the same PV voltage ripple--in the case of the classical boost converter, given in (33)--while the current ripple \(\delta i_{L_{b}}\) in the classical boost inductor is given in (34). \[\delta v_{pv}=\frac{\delta i_{L_{b}}\cdot T_{sw}}{8\cdot C_{pv}} \tag{33}\] \[\delta i_{L_{b}}=\frac{v_{pv}\cdot d\cdot T_{sw}}{2\cdot L_{b}} \tag{34}\]  
For the sake of simplicity, the comparison between the NEC and classical boost PV systems considers both NEC inductors equal (\(L_{1}=L_{2}\)), and the duty cycle is selected as \(d=0.5\) for both DC/DC converters. Then, analyzing Equations (26) and (33) shows that the same PV voltage ripple is achieved when \(\delta i_{L_{b}}=(\delta i_{1}+\delta i_{2})=2\cdot\delta i_{1}\) since \(\delta i_{1}=\delta i_{2}\) because \(L_{1}=L_{2}\). From Equations (23) and (34), it is obtained that \(L_{b}=L_{1}/2\) achieves the same PV voltage ripple. However, the average current of the classical boost inductor, obtained from considering the differential Equation (32) equal to zero, is \(i_{L_{b}}=i_{pv}\). Therefore, in the classical boost PV system, the inductor must support the complete PV current, while in the NEC boost PV system both inductors share the PV current, as observed in (18); in fact, for \(d=0.5\), both NEC inductors support half of the PV current (\(i_{1}=i_{2}=i_{pv}/2\)). In conclusion, the classical boost inductor has half of the inductance value but supports double the current in comparison with the NEC boost inductors. Then, a suitable way to contrast the inductance requirement of both PV systems is to compare the energy stored in the inductors: the energy stored in an inductor is \(E_{L}=\frac{1}{2}\cdot L\cdot l^{2}\), where \(l\) is the current of the inductor. Applying the previous analysis to the classical boost PV system results in \(E_{b}=\frac{1}{2}\cdot L_{b}\cdot\hat{r}_{pv}^{2}=\frac{1}{4}\cdot L_{1}\cdot \hat{r}_{pv}^{2}\); for the NEC boost PV system, the energy stored in each inductor is \(E_{1}=\frac{1}{2}\cdot L_{1}\cdot\left(\frac{i_{pv}}{2}\right)^{2}=\frac{1}{ 8}\cdot L_{1}\cdot\hat{r}_{pv}^{2}\), resulting in a total energy stored in both inductors \(E_{L,NEC}=\frac{1}{4}\cdot L_{1}\cdot\hat{r}_{pv}^{2}\), which is the same energy stored in the inductor of the classical boost converter. Therefore, both PV systems require similar inductance storage. Figure 4 shows that the classical boost PV system provides a discontinuous conduction current to the second stage, which corresponds to the diode current \(i_{d}\). Figure 2 shows that the NEC boost PV system instead provides a continuous current to the second stage. The quantification of this difference can be performed using three measurements: the DC current expected by the second stage \(i_{dc}\), the RMS current provided by the first stage, and the resulting AC current.