# Circulating Current Reduction in MMC-HVDC System Using Average Model
## 6 Analytical and Simulation Results  
A two terminal symmetrical monopole MMC-HVDC shown in Figure 1 is simulated in PSCAD/EMTDC software. A master-slave approach is used, in which one power converter regulates the DC voltage and the other converter regulates the active power, whereas reactive power can be controlled independently at both sides of the AC side terminals. A vector current control is applied to the MMC here; the outer power controller and inner current controllers are similar to VSC (voltage source converter) traditional two-level configurations [46]. However, unlike the VSC two-level configuration, the circulating current is generated inside the MMC due to inner voltage differences among the phase units without influencing AC side voltages and currents [47]. The active and reactive powers are selected as control objectives similar to the VSC two-level configuration. Furthermore, the DC line is modelled using cascaded \(\pi\)-sections developed in [48]. A reference DC bus voltage of 640 kV with a power of 1000 MVA from terminal \(T_{2}\) to terminal \(T_{1}\) was considered. Both MMCs operate at s 0.96 power factor and generate 40 MVAr to meet the required  
Figure 4: Flowchart of proposed direct modulation. reactive power demand at the AC side of the HVDC system. The real and reactive current components \(i_{ud}\) and \(i_{uq}\) shown in Figure 2a adjusts the real and reactive power demand of the HVDC system. Figure 5 shows simulation results of the MMC-HVDC system. Figure 5a-d shows the real powers (P\({}_{1}\), P\({}_{2}\)), reactive powers (Q\({}_{1}\), Q\({}_{2}\)), the DC bus voltage maintained at 640 kV, and the current in the HVDC line using direct and proposed direct modulation techniques. Figure 5: \(Cont.\)  
The system level control (active and reactive power) of MMC-HVDC at terminal \(T_{2}\) and \(T_{1}\) based on Equations (30) and (31) is shown in Figure 5a,b. At 0.08 s, the active power around both terminals are controlled to maintain their reference values (P = 960 MW). The AC side reactive power is controlled at 40 MVAr at 0.1 s. From t = 0 to t =0.05 s, there is a small over-shoot in AC reactive power, but it quickly reaches a stable value at around 0.08 s.  
At the rectifier side terminals \(T_{2}\) and \(T_{1}\), DC voltage is controlled at the reference value of 640 kV. Due to changes in active power at t = 0 s to t = 0.08 s, small transients are generated in DC voltages, which finally reaches the reference value at 0.08 s due to the DC voltage controller as shown in Figure 5c. The current in the upper and lower DC line is shown in Figure 5d. Due to small oscillations in DC power, there are small transients in the DC current, which finally reaches steady state at the reference value of around 1 kA at 0.14 s.  
Figure 5: Results of (**a**) P\({}_{1}\), P\({}_{2}\) at T1 and T2; (**b**) Q\({}_{1}\), Q\({}_{2}\) at T1 and T2; (**c**) DC bus voltage at T1 and T2; and (**d**) current in the DC line. Figure 6a,b shows the three-phase line-to-line voltage and the three-phase current, representing the AC system connected to the MMC-HVDC system. The MMC grid side three-phase line-to-line output voltage and output current waveforms are shown in Figure 6c,d. The direct modulation and proposed direct modulation methods are tested on the MMC-HVDC system as shown in Figure 1a. Figure 7a,b shows the voltage reference signals used to generate firing signals for SMs in each arm of MMC. The direct modulation and proposed method is implemented by vector current control method based on Equations (44)-(47). The upper and lower arm current waveforms using direct modulation and the proposed direct modulation can be observed in Figure 7c-f. These simulation results are based on the analytical Equations, derived in (11), (12), (39), (40), (48) and (49). Due to the flow of the circulating current, the upper and lower arm current peak values are distorted during the direct modulation approach.