## 5 Simulation Results
The catenary section currents of \(i_{lx}\) and \(i_{ly}\) at unitary load power factor are presented in Figure 10c. It is important to note that the results presented in Figure 10 are very similar when using the deadbeat predictive control or the PI controllers. The three-phase currents before compensation, \(i_{A}\), \(i_{B}\), and \(i_{C}\), and the catenary section currents, \(i_{lx}\), and \(i_{Ly}\), have no relation with the SRPC system operation. The three-phase currents after compensation, \(i_{A2}\), \(i_{B2}\), and \(i_{C2}\), are resulting after injecting the compensation currents of \(i_{rx}\), and \(i_{ry}\). The compensation currents are calculated according to the catenary section currents of \(i_{lx}\), and \(i_{ly}\), as in (10). In addition to that, and as has mentioned before, the circulating currents do not contribute to the compensation currents injected by the SRPC system. Therefore, the three-phase currents after compensation should have almost similar waveforms regardless of the controller used. Figure 9: Model used in simulation. Figure 11A presents the results when using the deadbeat predictive current control methodology for circulating current suppression. Figure 11A(a) presents the SRPC compensation currents. Phase \(x\) compensation current, \(i_{rx}\), has a higher value than in phase \(y\), \(i_{ry}\), because catenary section \(y\) has a higher load value, as referred in Table 1. Figure 11A(b,c) shows the MMC arm currents. Note that subtracting the lower arm current, \(i_{rol}\), from the upper arm current, \(i_{rou}\), gives the MMC compensation current, \(i_{ro}\). Figure 11A(d) shows the circulating currents in the MMC legs, \(i_{cro}\). The circulating currents were calculated according to Equation (13) and they have an average value of 5 A. This small current component is important to accomplish the balance between the MMC SM voltages. Figure 11B(a) presents the simulation results when using well-tuned conventional PI controllers, as shown in Figure 6b. The compensation currents injected into the power grid presented in Figure 11A(a) and Figure 11B(a) are similar, and have no relation with the MMC circulating currents. However, the upper and the lower arm currents presented in Figure 11B(b,c) are quite different from the ones presented in Figure 11A(b,c). In this case, arm currents have higher harmonic contents and higher RMS value due to the circulating currents between the MMC legs, which have an RMS value of 9.8 A, as shown in Figure 11B(d). As a result, the circulating current component distorts the MMC arm currents. Figure 11: Currents when using the predictive current controller (**A**) and when using the conventional PI controllers (**B**): (**a**) SRPC compensation currents; (**b**) Upper and lower arm currents of section \(x\) converter; (**c**) Upper and lower arm currents of section \(y\) converter; (**d**) MMC circulating currents. Figure 10: Simulation results: (**a**) Three-phase grid currents before compensation; (**b**) Three-phase grid currents after compensation; (**c**) Catenary section (\(x\) and \(y\)) currents. The frequency spectrum of SRPC compensation currents when using the deadbeat predictive current control methodology for circulating current suppression is presented in Figure 12A(a,b), where only fundamental current components of 50 Hz are present. In that case, the circulating currents frequency spectrum presented in Figure 12A(c,d) mainly shows DC components, which are important for the SM voltage balancing control, besides regulating the main DC-link voltage. On the other hand, Figure 12B(a,b) shows the frequency spectrum of SRPC compensation currents when using well-tuned conventional PI controllers. The circulating currents do not contribute to the total compensation currents. Therefore, the frequency spectrum of SRPC compensation currents presented in Figure 12A(a,b) is similar to the one presented in Figure 12B(a,b).