**4. Experimental Results**

To verify the behavior of the proposed converter, we conducted an experimental text. The test circuit is shown in Figure 12. The PV module LUXEN LNSA-160P has specifications at standard test conditions (STCs) of 160 W, 18.30 V, and 8.75 A at the maximum power point. The source *v<sup>o</sup>* fixes the voltage to a desired value. Additionally, since the voltage source *v<sup>o</sup>* does not accept input currents, a load *R* was added to dissipate the power generated by the PV module. Finally, a switching frequency of 50 kHz was used for the proposed converter.

**Figure 12.** Experimental prototype of step-up/down quadratic converter. (**a**) Circuit diagram. (**b**) Experimental setup.

The resulting waveforms of currents and voltages from the operation of the proposed converter are shown in Figures 13–15. This test was performed with a clamped output voltage of *v<sup>o</sup>* = 56 V, an incident solar radiation of 912 W/m<sup>2</sup> , and a PV module temperature of 67 ◦C. Figure 13 shows the voltage at the terminals of each switching devices, where it can be observed that active switches operate synchronously, whereas passive switches (diodes) have a complementary operation. In all cases, well-defined transitions are observed.

**Figure 13.** Switching device voltages. (**a**) Active switch *S*<sup>1</sup> (**Top**) and diode *S*<sup>2</sup> (**Bottom**). (**b**) Active switch *S*<sup>3</sup> (**Top**) and diode *S*<sup>4</sup> (**Bottom**).

Figure 14 shows the waveforms of the current of the PV module and the inductor currents. Here, it can be observed that both inductor currents increase linearly when the active switches are turned on, and the current decreases when the switches are turned off. The measured average current in each element is *Ipv* = 7.622 A, *IL*<sup>1</sup> = 10.8 A ,and *IL*<sup>2</sup> = 4.53 A, whose values are consistent with those obtained from Expressions (27) and (28).

**Figure 14.** Inductor and PV module currents. (**a**) PV module (**Top**) and inductor *L*<sup>1</sup> (**Bottom**). (**b**) PV module (**Top**) and inductor *L*<sup>2</sup> (**Bottom**).

Finally, the waveforms of the voltages in the switching converter capacitor *C<sup>i</sup>* (input port) and capacitor *C*<sup>1</sup> are shown in Figure 15. In this condition, the voltage at the terminals of the PV module is *Vpv* = 13 V, which is lower than the open-circuit voltage *Voc* = 19.18 V, whereas the voltage in the capacitor *C*<sup>1</sup> is *VC*<sup>1</sup> = 37 V.

**Figure 15.** Capacitor voltages: capacitor *C<sup>i</sup>* (**Top**) and capacitor *C*<sup>1</sup> (**Bottom**).

The experimental voltage conversion ratio (*M* = *Vo*/*VCi*) of the proposed converter is shown in Figure 16. In the test, the output voltage was maintained constant (test 1: *V<sup>o</sup>* = 56 V, and test 2: *V<sup>o</sup>* = 48 V), whereas the duty ratio was changed step-by-step from 0.5 to 0.9. At the start of the test, the conversion ratio was constant since the voltage at terminals of the PV module is equal to its open-circuit voltage (*Vpv* = 19.9 V). When the duty ratio increases, the converter forces the reduction in the PV module voltage, increasing the conversion ratio of the converter. The maximum conversion ratio at *D* = 0.9 is *M* = 25.64 for *V<sup>o</sup>* = 56 V, and *M* = 21.87 for *V<sup>o</sup>* = 48 V.

**Figure 16.** Experimental voltage conversion ratio using *v<sup>o</sup>* = 56 V (solid line) and *v<sup>o</sup>* = 48 V (dashed line).

Figure 17 shows the main voltages and currents of the converter when the duty cycle is varied from 0.6 to 0.9. In Figure 17a, the PV module voltage is reduced when the duty ratio increases; therefore, the PV module voltage can be controlled through the duty ratio, as can the power delivered by the PV module. It can be observed in Figure 17b that the PV module current increases until it reaches a constant current region. Here, a further increase in the duty ratio implies that voltages *Vpv* and *VC*<sup>1</sup> tend to zero, whereas the current *Ipv* tends to the short-circuit current, which is consistent with the operation of the PV module.

**Figure 17.** Currents and voltages in the converter. (**a**) Voltage at the terminal of the PV module: capacitor *C*<sup>1</sup> and capacitor *C*2. (**b**) Current generated by the PV module: inductor *L*<sup>1</sup> and inductor *L*2.

Figure 18 shows the power–voltage (P–V) and current–voltage (I–V) curves of the PV module, which were built with the measured input current and voltage of the converter. In Figure 18a, it can be observed that an increase in the duty ratio increases the current *Ipv*, whereas the voltage *Vpv* decreases. This behavior continues until the PV module enters the constant current region. Figure 18b presents the behavior of the power delivered in the PV module when the duty ratio is varied. In this test, ia maximum power of 95.61 W is obtained at *D* = 0.68, where *Ipv* = 7.054 A and *Vpv* = 13.55 V.

**Figure 18.** Experimental results in the converter's input port. (**a**) I–V curve. (**b**) P–V curve.

Then, the proposed converter was tested in a scenario to determine the maximum power of the PV module. In this test, the duty cycle of the converter was determined by a perturb and observe (P&O) MPPT algorithm. Figure 19 shows the principal measurements that confirm the operation of the converter in a day with partially cloudy conditions. Global solar irradiance shows a significant variability due to clouds, which is strongly correlated with the current and power developed. The voltage at the terminals of the PV module varies according to the perturbations introduced by the P&O algorithm. In the test, the efficiency was over 80%. Notably, efficiency can be increased by adopting high-quality components such as SiC semiconductors [38] and techniques such as synchronous rectification, amongst others; however, in this work, experimental evaluation was performed to

support the theoretical results of the conversion ratio, operation, and its potential use in PV applications.

**Figure 19.** Time responses of the switching converter with an MPPT perturb and observe algorithm. (**Top**) to (**bottom**): Measured global solar irradiance, generated current of the PV module, voltage at the terminals, power developed by the PV module, and efficiency (partially cloudy day).

Finally, the large-signal model of the converter(35) was implemented in MATLAB/Simulink (MathWorks Inc., R2021a, Natick, MA, USA), where transient responses were obtained when steps in the duty ratio were applied. Simulations and experimental results are shown in Figure 20 for capacitor voltages. In this test, the duty ratio was changed from 0.64 to 0.71 and back. As can be observed, the simulated responses predicted the dynamic response of the converter prototype, confirming the validity of the developed models.

**Figure 20.** Simulation and experimental results of the transient responses of the converter under duty ratio steps. (**a**) Voltage in capacitor *C<sup>i</sup>* (time: 5 ms/div). (**b**) Voltage in capacitor *C*<sup>1</sup> (time: 5 ms/div).
