*Scenario 1*

In this scenario, all the PV panels connected to the sub-module of the MMC receive equal irradiance. At the Standard Test Condition (STC), the irradiance is 1000 W/m2, cell temperature is 25 °C, and airmass is 1.5. The operation of the MMC under STC, where all the sub-module receive equal irradiance of 1000 W/m<sup>2</sup> is shown in Appendix B.

All the sub-module capacitor voltages (*vcxy* [*V*] for x = u, l and y = a, b, c, respectively) are maintained at the desired MPP voltage references, as shown in Appendix B Figure A1a. Active power (*P* [*kW*]) is injected to the grid by maintaining zero reactive power (*Q* [*KVAr*]). During the entire operation of the MMC the *dc* and *ac* circulating currents are zero, as shown in Appendix B Figure A1b.

The frequency spectrum of the phase currents injected to the grid for scenario 1 is analyzed in this paper and are shown in Figure 6a–c. The THD for each phases are 1.01%, 1.1%, and 1.04% for phase "a", "b", and "c" currents, respectively. The THD of currents in each phase do not vary significantly. The control of the MMC makes sure that the distortion in all the three phases are minimized by maintaining the desired *ac* voltage reference. The THD is well below the 5% limit as required by IEEE 519 [21] for the scenario 1.

**Figure 5.** The sorting and tracking algorithm used in the arm power control of the MMC for PV application [13].

 **Figure 6.** Frequency spectrum of the output phase currents in % with respect to the 50 Hz fundamental current (100%).

The positive, negative and zero sequence components of the three phase currents are shown in Figure 7. The negative sequence component under steady state is less that 1 A. The amount of unbalance in the currents is 0.3% for scenario 1.

**Figure 7.** The positive sequence current (*is*(+)), negative sequence current (*is*(−)), and zero sequence current (*is*(0)) for the currents injected to the grid.

#### **4. Uneven Irradiance and Its Consequence**

The distribution of irradiance pattern within an arm of the MMC is highly dependent on weather conditions and shading. In [13], the irradiance across the sub-modules in an arm of the MMC are assumed to be identical, and the MPPT is allowed only at arm-level. Such a restriction decreased the harvested power when the irradiance is uneven across the sub-modules in an arm of the MMC. Therefore, the sub-module level MPPT is investigated in this section as scenario 2.
