## 6 Simulation Results
### Current Evaluations  
Two nonlinear loads were supplied through the MMC in this study. Figure 14 illustrates the MMC output currents which supply the loads. According to this figure, three similar nonlinear currents belonging to the three proposed controllers were produced by the MMC.  
Figure 15 demonstrates the MMC circulating currents of phase \"a\" under load change. As predicted, the circulating current due to the third proposed control strategy was significantly smaller than the other responses, as depicted in Figure 15c.  
As seen in Figure 15a, the circulating current of the first controller was more than 4 times the third controller's circulating current. On the other hand, this value deceased to more than double the third controller's circulating current for the second controller, as shown in Figure 15b. Since the third proposed controller consists of the various harmonic components of circulating currents, this controller provides a better response for circulating currents compared with the other control strategies. The effects of decreasing circulating currents can be observed in Figures 16 and 17.  
Figure 16 shows the upper arm currents of phase \"a\" for the three proposed control strategies. As shown in Figure 16c, when the third proposed control strategy was applied to the MMC, the MMC upper arms generated less current in comparison with those under other strategies. The same scenario occurred for the MMC lower arms.  
Based on Figure 17c, the MMC lower arm current showed smaller values in both steady and dynamic operating conditions. Both the MMC upper and lower arm currents generated under the first and second proposed control strategies had approximately the same results, with high values for circulating currents.  
This point verifies that the control of all harmonic components of circulating currents will improve the circulating current responses under varying loads. On the other hand, when the circulating currents are increased, the upper and lower currents experience an increment in their values. This means that the arm losses will be noticeably increased, which is regarded as a drawback for the control strategy. This drawback is acceptably eliminated by the third proposed control strategy, as can be seen from Figures 16c and 17c.  
Figure 13: The output voltages of phase “a” for the (**a**) first controller, (**b**) second controller, and (**c**) third controller.  
Figure 14: The output currents of phase “a” for the (**a**) first controller, (**b**) second controller, and (**c**) third controller.  
Figure 15: _Cont._  
Figure 16: The upper arm currents of phase \"a\" for the (**a**) first controller, (**b**) second controller, and (**c**) third controller.  
Figure 17: _Cont._  
Figure 15: The circulating currents of phase \"a\" for the (**a**) first controller, (**b**) second controller, and (**c**) third controller.  
To provide a complete comparison of the steady-state and dynamic performance of the three proposed control strategies, Table 2 is presented. According to this table, the smallest errors in the upper and lower capacitor voltages belong to the third proposed control strategy. In addition, the magnitude of the circulating current can be minimized by applying the third control strategy to the MMC, as demonstrated in Table 2.