## 5 Simulation Results
The imbalance ratio (ratio of the NSC of currents) is the smallest between 0.8 s and 1.0 s since both load sections have the same power of 5.24 MW. Figure 15b shows the three-phase currents after compensating reactive power and shifting the active power between sections. The currents are balanced and the SRPC system can follow the dynamic changes of the loads. Figure 15c shows the catenary load section currents of \(i_{Lx}\) and \(i_{Ly}\). Between 0.4 s and 0.8 s, the load section \(y\) has always the double of the load value of the load section \(x\). However, after 0.8 s, both load sections have the same loading parameters. Figure 16 shows the MMC currents when using the predictive current controller under load dynamic changes. The compensation currents value of \(i_{rx}\), and \(i_{ry}\) changes dynamically according to the loading conditions of the load sections, as shown in Figure 16a. It is worthy to mention that, from 0.6 s to 0.8 s, the compensation currents synthesized by the SRPC system are higher than in the case between 0.4 s and 0.6 s. This is because the power difference between the load sections is higher from 0.6 s to 0.8 s. Figure 16b,c shows the upper and the lower arm currents of the section \(x\) and section \(y\) converter, respectively. Note that subtracting the lower arm current from the upper arm current gives the MMC compensation current. The arm currents have mainly the fundamental frequency component of 50 Hz and a DC current component (the circulating current), which is important to achieve the voltage balance control of the MMC. Figure 16d shows the circulating currents, \(i_{cirx}\), and \(i_{city}\), where these currents do not contribute to the compensation currents injected by the SRPC. The higher the  
Figure 8:0 Simulation results under load transients: (**a**) Three-phase grid currents before compensation; (**b**) Three-phase grid currents after compensation; (**c**) Catenary section (\(x\) and \(y\)) currents. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Time** & **0.4 s to 0.6 s** & **0.6 s to 0.8 s** & **0.8 s to 1.0 s** \\ \hline Section \(x\) power & 1.75 MW & 3.5 MW & 5.24 MW \\ Section \(y\) power & 2.62 MW & 5.24 MW & 5.24 MW \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Section power values during the simulation. load power difference between the load sections, the higher the circulating current component in the MMC. At high load power difference, the MMC should inject a higher amount of power to compensate the reactive power and shift the active power difference between the sections. This entails to higher circulating current to balance the MMC DC-links (the MMC main DC-link and the SM DC-links) since a higher energy is provided by the converter. A high value of the circulating currents increases the amplitude of the DC-voltages ripple, hence, the DC-link voltages waveform of Figure 14A(a) have lower voltage ripples when using the deadbeat predictive current control methodology. On the contrary, Figure 14B(a) shows higher voltage ripples of the DC-link voltages when using the conventional PI controllers. On the other hand, the circulating currents may lead to an easier tuning of the SM voltages balancing control and the main DC-link voltage control. As a result, the overflow/over-suppression of the MMC circulating currents is a trade-off between several factors, such as, higher/lower MMC power losses, higher/lower MMC equipment power ratings, robust/fragile DC-voltages control and higher/lower DC-voltage ripples. Therefore, attention must be considered since the over-suppression of the MMC circulating current may affect the response of the SM voltage balancing control. The advantages of the deadbeat predictive current control methodology for circulating current suppression can be summarized as follows:  
1. Removing the AC components of the MMC circulating current, then, the circulating current amplitude is reduced while keeping balanced SM voltages.