## 5 Simulation Results
The circulating currents in this case have the multiples of the second-order frequency component (100 Hz), as shown in Figure 12B(c,d). Figure 13A(a-d) shows the frequency spectrum of the MMC arm currents when using the deadbeat predictive current control methodology for circulating current suppression. There are no second-order components (100 Hz and other even-order harmonics, such as 4 th, 6 th, and 8 th) in the MMC arm currents, which proves the effectiveness of the deadbeat predictive control methodology for circulating current suppression. This methodology mainly eliminates the even-order harmonics of the circulating currents, but it does not eliminate the DC component of the circulating currents, which is important to achieve the SM voltage balancing control. On the other hand, and due to the fact that circulating current harmonics exist when using the conventional PI controllers, the frequency spectrum of the MMC upper and lower arm currents, in this case, shows the orders of the even-order harmonics. This is shown in Figure 13B(a-d). Figure 12: Spectrum of currents when using the predictive current controller (**A**) and when using the conventional PI controllers (**B**): (**a**) Compensation current of section \(x\) converter; (**b**) Compensation current of section \(y\) converter; (**c**) Circulating current of section \(x\) converter; (**d**) Circulating current of section \(y\) converter. Figure 14A shows the MMC DC-voltages when using the deadbeat predictive current control methodology: the DC-link voltages are presented in Figure 14A(a), the SM voltages of section \(x\) converter (\(v_{SMx,up}\): for the upper arm SM voltages, \(v_{SMx,low}\): for the lower arm SM voltages) and section \(y\) converter (\(v_{SMy,up}\): for the upper arm SM voltages, \(v_{SMy,low}\): for the lower arm SM voltages) are presented in Figure 14A(b,c), respectively. Figure 14B shows the MMC DC-voltages when using the PI controllers and when there are circulating currents in the MMC arms: the DC-link capacitor voltages in Figure 14B(a), the SM voltages of section \(x\) converter (\(v_{SMx,up}\): for the upper arm SM voltages, \(v_{SMx,low}\): for the lower arm SM voltages), and the SM voltages of section \(y\) converter (\(v_{SMy,up}\): for the upper arm SM voltages) in Figure 14B(b,c), respectively. These waveforms confirm the effectiveness of the voltage balancing control algorithm presented in Figures 6 and 7. Besides the operation in steady-state, simulation results showing the SRPC system performance in transient conditions were also obtained. A variable load power was adopted to study the dynamic response of the SRPC system when using the deadbeat predictive current controller. For this purpose, Table 3 presents the load section power values during the simulation. The results do not show the instants between 0 and 0.4 s, since the SRPC converter does not reach the steady-state operation before the 0.4 s. Between the instants 0.4 s and 0.6 s, load section \(x\) and section \(y\) have  
Figure 14: DC-voltages when using the predictive current controller (**A**) and when using the conventional PI controllers (**B**): (**a**) DC-link capacitors voltage; (**b**) SM voltages of section \(x\) converter; (**c**) SM voltages of section \(y\) converter. Figure 13: Spectrum of currents when using the predictive current controller (**A**) and when using the conventional PI controllers (**B**): (**a**) Upper arm current of section \(x\) converter; (**b**) Lower arm current of section \(x\) converter; (**c**) Upper arm current of section \(y\) converter; (**d**) lower arm current of section \(y\) converter. and 2.62 MW, respectively. However, double these power values is applied between 0.6 s to 0.8 s. After 0.8 s, both load sections have the same power of 5.24 MW. Figure 15 shows the SRPC simulation results in transient conditions. The three-phase currents before compensation are shown in Figure 15a. As shown in this case, the three-phase currents are imbalanced and have NSC of currents.