## 6 Validation Using Circuital Simulations
Such a value exhibits an error of 2.5% with respect to  
Figure 14: PV system circuit implemented in PSIM. the theoretical value calculated from (26), which is mainly caused by the changes on the switching frequency introduced by the SMC. Moreover, the figure confirms that both the NEC and classical boost converters provide the same voltage and current ripples at the PV panel side, verifying the correct design of the classical boost converter and NEC converter input capacitor. The ripple magnitudes of the inductor current reported in this simulation have errors equal to 2.98% with respect to the theoretical values calculated from (23) and (24), which are also caused by the changes on the switching frequency. The simulation results of Figure 15 confirm the advantage of the NEC topology over the classical boost option: the current delivered to the DC bus by the NEC boost converter (which corresponds to \(i_{2}\)) is continuous, while the current delivered by the classical boost topology (which corresponds to diode current) is discontinuous. In order to provide a numerical comparison, the RMS and DC values of those output currents are calculated: for the NEC boost converter, they are \(i_{\text{\tiny{2,DC}}}=1.76\) A and \(i_{\text{\tiny{2,RMS}}}=1.78\) A, while for the classical boost converter they are \(i_{\text{\tiny{4,DC}}}=1.76\) A and \(i_{\text{\tiny{4,RMS}}}=2.90\) A. Then, the AC components of the output currents are \(i_{\text{\tiny{2,AC}}}=0.26\) A for the NEC topology and \(i_{\text{\tiny{4,AC}}}=2.30\) A for the boost converter, calculated from \(i_{\text{\tiny{RMS}}}^{2}=i_{\text{\tiny{DC}}}^{2}+i_{\text{\tiny{AC}}}^{2}\). Therefore, the proposed PV system based on the NEC boost converter introduces nine times less (1/9) undesired current harmonics than a PV system based on the classical boost converter, thus providing a much better power quality to the DC bus or grid-connected inverter. This reduction in the AC current component has a difference of 8% with respect to the values calculated from (39) and (40), which is caused by the change on the duty cycle from \(d=0.5\) (used in the comparison of Section 2.2) to \(d=0.6177\) (set by the MPPT algorithm at 1000 W/m\({}^{2}\)). The simulation results also report a switching frequency equal to 98.5 kHz at \(S=1000\) W/m\({}^{2}\), which confirms the fulfillment of the practical restriction imposed in Table 2 for the switching frequency (\(F_{sw}\leq 100\) kHz). Finally, Table 2 reports that the current of \(L_{2}\) in the NEC boost converter must fulfill \(\delta i_{2}\leq 0.39\) A at \(S=250\) W/m\({}^{2}\) to ensure a continuous output current for 75% of the irradiance space (as described in Figure 12). This is verified by Figure 15, which shows (in the bottom waveforms) the behavior of both inductors' currents in the NEC boost converter at \(S=250\) W/m\({}^{2}\), confirming the desired condition. In conclusion, the simulation results reported in Figure 15 confirm the correct design of \(C_{pp}\), \(L_{1}\), and \(L_{2}\) for the NEC boost converter. Figure 15: Steady-state operation of the PV system and comparison with the classical boost topology. The stable operation of the proposed PV system is also confirmed by the simulation results of Figure 16, which verify that the ripple condition for \(v_{cb}\), given in Table 2, is fulfilled with an error of 4.5% with respect to the theoretical value calculated from (25), thus confirming the correct design of \(C_{cb}\). In addition, Figure 16 also reports the same steady-state value given in (19) and (20) for \(v_{cb}\) and \(v_{pe}\), respectively, and the relation given in (21) for the inductor currents; therefore, the stable operation of the NEC boost converter is confirmed. Finally, this simulation also reports the waveform of the switching function \(\Psi\), thus validating the correctness of the control law defined in Equation (51). In conclusion, the simulation results reported in both Figures 15 and 16 confirm the correct design of both the NEC boost converter and switching circuit.