*4.1. Simulation Results*

The first simulation result presented the injected grid current *is* with reference *i*∗*s* and both capacitor voltages for each power cell under steady-state operation. In Figure 7, it is possible to appreciate the good regulation and synchronization in respect to the grid voltage *vs* performed by the grid current control and the synchronization control loop. Furthermore, in Figure 8, the voltage balancing control is demonstrated, where the upper *vdcu*,*<sup>k</sup>* and lower *vdcl*,*<sup>k</sup>* voltage capacitors for each *k*-th power cell are well balanced.

**Figure 7.** Steady-state operation of the grid current PMR control.

**Figure 8.** Steady-state operation of capacitor voltages for each power cell.

The second simulation results present a dynamic operation under two different scenarios. An irradiation step from 1 kW/m<sup>2</sup> to 0.8 kW/m<sup>2</sup> was applied to the lower cell, maintaining 1 kW/m<sup>2</sup> of irradiation in the PV string connected to the upper cell. After the irradiation step took place, a temperature step changes was performed from 25 ◦C to 18 ◦C to the upper cell, generating an increase in the power. The irradiation and temperature changes were introduced in a simplified PV model provided by PLECS. Figure 9 shows the dynamic operation of the DC-link voltage *vdck* and the

power at DC-side *Pck* = *vdck* · *ipvk* for each k-th cell. It is possible to appreciate how the irradiation step at *t* = 3.5 s only affected to the lower module, producing a voltage perturbation and a power reduction in *Pc*2. Since the reference voltage is provided by the P&O algorithm, the stepped voltage was required to maintain the maximum power operation. In the second scenario, the temperature decreased at *t* =8s and the DC voltage as well as the power in the upper module increased. The three-level voltage *vck* of each converter cell, and the overall five-level voltage *vc* are depicted in Figure 10 under unbalance operation. Additionally, it is possible to appreciate how the power reduction in the lower arm affects the modulation indexes *mck*, creating signals with different magnitudes.

**Figure 9.** Dynamic operation of DC-link and power on the DC-side under unbalanced power per string.

**Figure 10.** Steady-state converter output voltage performance under unbalanced power per string.
