# A Review of Modular Multilevel Converters for Stationary Applications
## 5 Power Losses and WBG Technology
The switching loss is calculated by using a look-up table technique, and the calculation model is expressed by [137; 138]  
\[P_{onT}=\frac{1}{T}\sum_{i=1}^{N_{i}}\left\{\frac{v_{T}(t)}{v_{T\_ref}}E_{on}( i_{T}(t))\right\}=\frac{1}{T}\sum_{i=1}^{N_{i}}\left\{\frac{v_{T}(t)}{v_{T\_ref}}i _{T\_ref}^{i}E_{on}(i_{T\_ref})\right\} \tag{35}\]  
\[P_{offT}=\frac{1}{T}\sum_{i=1}^{N_{i}}\left\{\frac{v_{T}(t)}{v_{T\_ref}}E_{off} (i_{T}(t))\right\}=\frac{1}{T}\sum_{i=1}^{N_{i}}\left\{\frac{v_{T}(t)}{v_{T\_ ref}}i_{T\_ref}^{i}E_{off}(i_{T\_ref})\right\} \tag{36}\]  
\[P_{recD}=\frac{1}{T}\sum_{i=1}^{N_{i}}\left\{\frac{v_{D}(t)}{v_{D\_ref}}E_{rec} (i_{D}(t))\right\}=\frac{1}{T}\sum_{i=1}^{N_{i}}\left\{\frac{v_{D}(t)}{v_{D\_ ref}}i_{F}(i_{F\_ref})E_{rec}(i_{F\_ref})\right\} \tag{37}\]  
where \(P_{outT}\) and \(P_{offT}\) donate the turn-on and turn-off switching loss of the transistors and diodes, \(P_{recD}\) donates the diode reverse recovery loss, \(E_{on}\) and \(E_{off}\) stand for the turn-on and turn-off energies of power switches, and \(E_{rec}\) is the diode reverse recovery energy. The switching energies are proportional to the ratios of the occurring blocking voltage (\(v_{T}\) and \(v_{D}\)) to the reference blocking voltage (\(v_{T\_ref}\) and \(v_{D\_ref}\)) and the switching current (\(i_{T}\) and \(i_{F}\)) to the reference current (\(i_{T\_ref}\) and \(i_{F\_ref}\)). Therefore, the total power losses \(P_{tot}\) can be calculated by the sum of the conduction and switching losses of transistors and diode, as  
\[P_{tot}=P_{com}+P_{sw}=P_{comT}+P_{comD}+P_{outT}+P_{offT}+P_{recD} \tag{38}\]  
The MMC efficiency is given by  
\[\eta=\left(1-\frac{P_{tot}}{P_{MMC}}\right)\times 100\% \tag{39}\]  
where \(\eta\) is the MMC efficiency and \(P_{MMC}\) is the MMC power. In order to assess the thermal performance of conventional Si-based semiconductors and WBG switching modules modulated by different modulation techniques for the MMC, the power losses calculation model is carried out with the simulation model in MATLAB by using the simulation parameters in Table 3. The comparative evaluation indexes include power losses and MMC efficiency. In addition, the total harmonic distortion (THD) of the output voltage is also investigated regarding different modulation methods. The modulation methods applied in the comparative study include PSC-PWM, PD-PWM, and SAM-PWM. PD-PWM is selected as a representative of LSC-PWM. SVM-PWM and SHE-PWM are excluded owing to their implementation complexity and calculation burden. In addition, the reason for not selecting NLM-PWM is that it is not suitable in application with a relatively small number of submodules, which leads to serious harmonic distortion. The switching frequency for both PSC-PWM and PD-PWM is set to 20 kHz, and the sampling rate for SAM-PWM is 2000 Hz. The semiconductor characteristics are extracted from the device datasheets CAS120M12 BM2 and 2 MBI150U2A-060. The simulation results are demonstrated graphically as in Figure 17:0 Figure 18 illustrates the comparative performance based on semiconductor power losses, MMC efficiency, and output voltage THD by using different modulation methods. From Figure 18a,b, it is noticed that SiC modules, compared to Si devices, yield lower power losses and higher power efficiency for all the three modulation techniques. It is also indicated that the PSC-PWM has higher power losses following with the PD-PWM and SAM-PWM for both Si and SiC switches in Figure 18a, which leads to a reduced MMC efficiency, as shown in Figure 18b. In spite of lower performance in power losses and efficiency, Figure 18c manifests that PSC-PWM is prominent in providing good voltage quality with lower THD compared to the other two methods. Furthermore, to investigate the influence of switching frequency on Si and SiC semiconductors concerning power losses and MMC efficiency, the switching frequency is set from 20 to 100 kHz. PSC-PWM is selected as the modulation scenario in this comparative study.