#### 5.1. Experimental Results

Figure 12a shows the waveform of eight capacitor voltages of SMs for the full sorting method. The voltage ripple is the smallest and the switching frequency is the greatest because it is a method that updates the switching sequence of SMs by sorting the capacitor voltages at every cycle. As shown in

Figure 12b, the full sorting method has very low circulating currents. The switching frequency is affected by the control cycles and the number of SMs. Therefore, the full sorting method has a switching frequency of about 6.6 kHz in this 1 GW MMC-HVDC system, with a control period of 10 usec and 432 SMs.

Figure 13a shows the waveform of capacitor voltages for the reduced switching frequency (RSF)-type sorting method, in which the switches are turned on/off according to the previous state of SMs. When charging, the SM which the voltage is the lowest and the previous state has turned off is turned on. On the contrary, when discharging, the SM which the voltage is the highest and the previous state has turned on is turned off. Therefore, it is the capacitor voltage balancing method that has the smallest switching frequency, while having the greatest ripple. As shown in

Figure 13b, the magnitude of the circulating current is large. In this 1 GW MMC-HVDC system, the RSF method has a switching frequency of about 55 Hz.

Figure 14a shows the waveform of capacitor voltages for the cell tolerance band (CTB) method, which balances the SM capacitor voltages band between 2.1 kV and 2.5 kV by limiting the minimum and maximum value of the capacitor voltages.

Figure 14b shows the waveform of circulating currents for the CTB method with a band between 2.1 kV and 2.5 kV. In this 1 GW MMC-HVDC system, the CTB method has a switching frequency of about 103 Hz when the capacitor voltages are within a maximum of 2.5 kV to a minimum of 2.0 kV.

Figure 15a shows the waveform of capacitor voltages for the average tolerance band (ATB) method, which calculates the average value of the SM capacitor voltages and generates a 4% band based on the average value of capacitor voltages.

Figure 15b shows the waveform of circulating currents for ATB with a 4% band. In this 1 GW MMC-HVDC system, the ATB method has a switching frequency of about 150 Hz when the tolerance band of the average value of the capacitor voltages is set to 4%. As can be seen from the two tolerance band schemes, the tolerance band methods are a balancing technique that can trade off the DC-link voltage ripple and the switching frequency by varying the band. Therefore, it is a good balancing method for MMC-HVDC class or higher using many SMs.

Figure 16a shows the waveform of the SM capacitor voltages for the 3% band ATB method, and

Figure 16b shows the waveform of the SM capacitor voltage waveforms for the 3% band proposed method. The line in the middle is the average value of the total SM capacitor voltages, and the circled area is where the sorting occurs when the average value exceeds the 3% tolerance band. If sorting occurs, it means that the previous states of the SMs are initialized due to the rearrangement of the SM capacitor voltages. In other words, if the average value of capacitor voltages quickly exceeds the tolerance band, sorting will reset the previous states of the SMs, increasing the numbers of switching of the SMs. As shown in

Figure 16, compared to the ATB method, the proposed method has a relatively slow cycle to occur the sorting. This means that the SM capacitor voltages of the proposed method are balanced more evenly throughout than in the ATB method.

Figure 17 shows the capacitor voltage balancing waveforms of the ATB method and proposed method for the MMC-HVDC of 240 MW. Of the total 108 SMs (including 8% redundancy), only eight capacitor voltages of SMs were displayed.

Figure 17a–c show ATB methods with 4%, 6%, and 8% tolerance bands, respectively.

Figure 17d–f are proposed methods with 4%, 6%, and 8% tolerance bands, respectively. Because the proposed method sorts the capacitor voltages at every cycle, the average value of capacitor voltages takes longer to cross the band. In addition, the switching frequency of the proposed method is smaller than the switching frequency of the ATB method because the SMs maintain the previous switching state even when the average value of capacitor voltages is out of the band.

Figure 18 shows the circulating current waveforms of the ATB and proposed methods for the MMC-HVDC of 240 MW. This is the sum of the upper and lower arm currents for the R-phase, S-phase, and T-phase divided by two, respectively.

Figure 18a–c show ATB methods with 4%, 6%, and 8% tolerance bands, respectively.

Figure 18d–f are proposed methods with 4%, 6%, and 8% tolerance bands, respectively. As shown in the

Figure 18, the proposed method has less ripple of circulating currents than the ATB method. Since the circulating currents are closely related to the quality of the DC-link voltage, it can be seen that the quality of the DC-link voltage can be improved.

Figure 19 shows the capacitor voltage balancing waveforms of the ATB method and proposed method for the MMC-HVDC of 1 GW. Of the total 432 SMs (including 8% redundancy), only eight capacitor voltages of SMs were displayed.

Figure 19a–c show ATB methods with 4%, 6%, and 8% tolerance bands, respectively.

Figure 19d–f are proposed methods with 4%, 6%, and 8% tolerance bands, respectively. Similar to the waveforms of 240 MW specification, because the proposed method sorts the capacitor voltages at every cycle, the average value of the capacitor voltages takes longer to cross the band. In addition, the switching frequency of the proposed method is smaller than the switching frequency of the ATB method because the SMs maintain the previous switching state even when the average value of capacitor voltages is out of the band.

Figure 20 shows the circulating current waveforms of the ATB and proposed methods for the MMC-HVDC of 1 GW. This is the sum of the upper and lower arm currents for the R-phase, S-phase, and T-phase divided by two, respectively.

Figure 20a–c show ATB methods with 4%, 6%, and 8% tolerance bands, respectively.

Figure 20d–f are proposed methods with 4%, 6%, and 8% tolerance bands, respectively. Similar to waveforms of 240MW specification, as shown in the

Figure 20, the proposed method has less ripple of circulating currents than the ATB method. Since the circulating currents are closely related to the quality of the DC-link voltage, it can be seen that the quality of the DC-link voltage can be improved.

#### 5.2. Experimental Conclusions

The proposed method is based on tolerance band methods. In this paper, band generation of the proposed method applies the average value of capacitor voltages like the ATB method and compared with the conventional method, and analyzes its characteristics. The band generation method may be a band using the indicated average value of capacitor voltages, or a band with a specific value may be used. The experimental results show application of 4%, 6%, and 8% of the tolerance bands for ATB, and application of 4%, 6%, and 8% of the tolerance bands for the proposed method. If the average of capacitor voltages is out of the allowable band, the conventional method sorts the SMs and regulates the on/off index of SMs again. On the other hand, the proposed method achieves better balancing because the sorting algorithm is continuously performed even if the average of the capacitor voltages is not out of the allowable band. Therefore, capacitor voltage balancing is performed evenly compared with the conventional method, so that the magnitude of the circulating current and the DC-link ripple can be reduced, and the switching frequency is reduced because the speed to reach the band is relatively slow.

As shown in

Figure 21, the proposed method proved to be able to perform better than the conventional method by comparing with the ATB method. Although other specific band generation methods can be applied, the proposed method is applied to band generation using the average value of capacitor voltages, which is one of the tolerance band methods. As shown in

Figure 21a, in case of 240 MW-class MMC-HVDC, the proposed method reduces the switching frequency by about 13%, compared to ATB at 4%, 6%, and 8%, of the tolerance band. Likewise, as shown in

Figure 21a, in case of 1 GW-class MMC-HVDC, the proposed method reduces the switching frequency by about 20%, compared to ATB at 4%, 6%, and 8%, of the tolerance band. As a result, the proposed method has about 20% better performance than the ATB method, and the larger the number of SMs, the better the effect.