**4. Results**

Once the operation principle has been presented and the design equations given, simulation studies in PSIM, and experimental tests were performed with the parameters shown in Table 1. Simulations were performed considering the schematic in Figure 1; a PV system with a MF link including 3 primary ports and 2 secondary ports with a turn ratio of 1:7. A variable DC load is applied to each secondary port in order to extract 300 W from each PV array to ge<sup>t</sup> a total output power of 900 W, also, each CZSI module has a switching frequency ok 20 kHz with an input voltage of 50 V.

After the validation through simulations, a prototype has been built. The experimental prototype consists in two input CZSI modules energized by a PV array of two 250W PV panel in order to ge<sup>t</sup> a total power of 500 W and 50 V input voltage at MPP. Turn ration in the multiport transformer and *Dz* reference parameters were retained from simulation studies.

#### *4.1. Simulation Results*

In first instance, the system's performance was evaluated under balanced conditions using a PV array of 2 panels in series obtaining 50 V, 6.6 A, 300 W with an irradiance of 1 kW/m<sup>2</sup> applied to each CZSI module, and a variable load is applied to each secondary port in order to extract the maximum power around 900 W. In Figure 6 the voltage *voczsi* on modules 1, 2 and 3 are presented, and it can be see that they have a *vozp* value of 80 V. In the secondary side, the voltages *vsec*1 and *vsec*2 shows the same waveform with the voltage gain due to MF link's turn ratio, an thus the voltage in all of the ports remains balanced. From Equation (1), the voltage in conduction mode can be estimated in 80 V for the *VPV* in the simulation, and from Equation (2), its RMS value of 62.3 V can be found.


**Table 1.** Simulation and experimental parameters.

**Figure 6.** Simulation results: CZSI modules output voltages *voczsi*1 , *voczsi*2 , *voczsi*3 and secondary ports voltages *vsec*1 and *vsec*2 under balanced conditions.

Since the study is in balanced power conditions, the same current *ioczsi* is expected on the three CZSI modules and RMS value can be estimated from Equations (3) and (6) to be around 5.6 A and 4.8 A respectively. Figure 7 validates that under balanced conditions the current on primary modules are equal. It can be observed that during shoot-through times, there is a non-zero current on CZSI modules output and in conduction mode. On the other hand, the current on the secondary ports, does not present non-zero current in shoot-through times and thus the effect of parasitic elements on MF link are decoupled from primary side.

**Figure 7.** Simulation results: CZSI modules output current *ioczsi*1 , *ioczsi*2 , *ioczsi*3 and secondary ports currents *isec*1and *isec*2under balanced conditions.

Figure 8 presents the average power on primary and secondary ports. First, the average output power on CZSI modules are shown in the first graphic and all of them are overlapped as expected for balanced conditions. In the same fashion, the average power in secondary side is balanced in both secondary outputs, and finally it can be observed that the sum of the average power of the three CZSI modules, matches with the sum of the average power on the secondary ports, and the difference between both is attributed to parasitic resistance in the MF link.

Once the operation under balanced conditions are validated, power imbalance studies were carried out. In order to appreciate the power imbalance, different irradiance were applied to each CZSI module: 900 W/m<sup>2</sup> for module 1, 500 W/m<sup>2</sup> in module 2, and 300 W/m<sup>2</sup> to module 3. Variable loads were kept on each secondary output in order to obtain the maximum power extraction. Also a fixed 0.37 *Dz* in all modules was set to put the system in MPP; since the higher *Dz* is imposed to all

coupled modules, a master-slave configuration is used, selecting the module with higher irradiance as the master.

**Figure 8.** CZSI simulation results: Average power in primary ports and average power in secondary ports under balanced power operation.

Voltages in primary and secondary ports in steady state are shown in Figure 9. Voltage in primary ports are the output of CZSI modules and all three of them presents the same *voczsi* value of 80 V during conduction state, and zero voltage in shoot-through states despite the imbalance applied. Similarly, the voltage on the secondary side has the same waveform with the gain of the MF link in the magnitude, passing from 80 V peak on primary side to 560 V peak on the secondary side. This validates that voltage balance is kept in primary and secondary ports despite power imbalance.

**Figure 9.** Simulation results: CZSI modules output voltages *voczsi*1 , *voczsi*2 , *voczsi*3 and secondary ports voltages *vsec*1 and *vsec*2 under unbalanced conditions.

Figure 10 shows the steady state current on primary and secondary ports and it can be observed that currents *ioczsi*1 , *ioczsi*2 and *ioczsi*3 are different in function of the power supplied by the corresponding PV array. The non-zero current can be see during shoot-through state produced by parasitic elements in MF link. Considering, all primary ports have the same voltage, and each one has different current values, it validates that each port is managing different power levels. Despite the imbalance in CZSI modules, the second graphic shows that the current on secondary ports are equal without non-zero current during shoot-through states, which validates a balanced and decoupled power on secondary ports.

Figure 11 shows the power in primary ports as well as the average power in secondary ports. It can be see that each module has a different average power in primary side, in contrast to the secondary side that has exactly the same average power in both secondary ports.

**Figure 10.** Simulation results: CZSI modules output current *ioczsi*1 , *ioczsi*2 , *ioczsi*3 and secondary ports currents *isec*1 and *isec*2 under unbalanced conditions.

**Figure 11.** CZSI simulation results: Average power in primary ports and average power in secondary ports under unbalanced power operation.

When comparing the sum of the average power on primary and secondary side it is basically the same, but similar to balanced conditions, a small difference can be observed due to leakage inductance which produces the non-zero current present in primary side but not in secondary side. Finally a summary of the results obtained in the simulation studies is presented in Table 2.


**Table 2.** Simulation results.

## *4.2. Experimental Results*

Once the CZSI modules and MF link were validated through simulations, an experimental prototype has been tested in multiport configuration. The prototype is shown in Figure 12 and consists in 2 input CZSI modules, a magnetic link and two secondary cells with a diode full-wave rectifier on the output. The MF link consist on a multiport transformer with 15 turns on each primary port and 106 turns on each secondary port, built in a N27 E-80 ferrite core. Each CZSI module is energized by a PV panel array consisting on two 30 V, 8,33 A, 250 W panels connected in series achieving 60V at its MPP. Tests were carried out applying a 940 Ω resistive load to the output in order to demand 470 W at MPP. The CZSI modules were operated with a fixed *Dz* as marked in Table 1, but due to ambient conditions, only 60% of the array power was produced. Despite the last, tests validates the behavior of the system with a PV system supply.

**Figure 12.** Experimental prototype.

In Figure 13 the performance of the prototype under balanced conditions is shown. The currents *ioczsi*1 and *ioczsi*2 are on channels 1 and 3 respectively, it can be see that they are overlapped with very small variations with a peak value of 7.5 A and 7.3 A on conduction mode, giving an approximate RMS value of 5 A; it can be noticed that the values are consistent with the simulation presented in Figure 7 with a peak value around 7.5 A and descending to 4.5 A. A high-frequency component oscillation due to a resonance between the leakage inductance of the MF link and the parasitic capacitance of the MOSFET can be appreciated during shoot-through times. In channels 2 and 4, voltages *voczsi*2 and *voczsi*2 are shown and are also equal with a *vozp* near to 75 V for a more-less 60 V RMS on both modules. The *voczsi* values obtained are similar to the ones presented in Figure 6 and the behavior is consistent showing a small spike during conduction state. The similar values of both CZSI values confirm that both PV systems are in a balanced state. In balanced state, both modules extracted 300 W from each PV array for a 600 W output power.

**Figure 13.** System test under balanced conditions. Ch1 (10 mV/div=5 A/div): *ioczsi*1 , Ch3 (5 A/div): *ioczsi*2 , Ch2 (100 V/div): *voczsi*1 and Ch4 (100 V/div): *voczsi*2 .

Once the performance of the prototype was validated in balanced conditions, a test under power imbalance was performed using the same two PV panels arrays of the balanced test. The resistive load and *Dz* duty cycle was also kept the same as before. Additionally, partial shade was applied to the PV panel array in module 2 in order to introduce the power imbalance.

In Figure 14, current *ioczsi* in module 1 and 2 can be observed on channel 1 and 3 respectively. It can be noted that the same high frequency oscillation due to resonance between MOSFET's parasitic capacitance and the leakage inductance of the MF link in Figure 13 is also present under unbalanced conditions. Different current levels can be clearly appreciated, with 7.2 A peak on *ioczsi*1 and 6 A peak on *ioczsi*2 . Despite both cells have different current levels, *voczsi* stays on the same level as in balanced condition with 75 V *vozp*. A non-zero current in *ioczsi* during shoot-through times can be observed and is related to the parasitic elements of the transformer.

**Figure 14.** Multiport power imbalance test. Ch1 (10 mV/div=5 A/div): *ioczsi*1 , Ch3 (5 A/div): *ioczsi*2 , Ch2 (100 V/div): *voczsi*1 and Ch4 (100 V/div): *voczsi*2 .

In Figure 15 power in primary and secondary ports are presented. The first and second waveforms were taken after the diode full-wave rectifier and correspond to power in secondary ports 1 and 2 respectively; it can be see that they are equal in magnitude. The third and fourth waveform are the power in CZSI module 1 and 2 respectively, observe that they have different power levels and the sum matches the sum of power in the secondary side. The last validates that a balanced output can be generated despite power imbalances in the MF link inputs.

**Figure 15.** Multiport power imbalance test. Ch1 (500 W/div): output power in secondary port 1 *psec*1 , Ch2 (500 W/div): output power in secondary port 2 *psec*2 , Ch3 (500 W/div): output power in CZSI module 1 *poczsi*1, and output power in CZSI module 2 Ch4 (500 W/div): *poczsi*1.
