# A Review of Modular Multilevel Converters for Stationary Applications
## 5 Power Losses and WBG Technology  
Wideband gap (WBG) semiconductors, made on silicon carbide (SiC) and gallium nitride (GaN) provide advantages of increased energy efficiency, high power density, and cooling density thanks to improved electrical and thermal conductivities [132; 133]. WBG transistors are expected to occupy a wide range of power conversion applications which are dominated by the traditional Si-based power devices over the past decades. Figure 17[134; 135] accounts for the competitive advantages for WBG power modules over classical Si-based switches in the condition of high voltage, high frequency, and high-temperature operation. For low-voltage applications, GaN power modules, where all the electrodes are arranged on the top layer due to the lateral structure, are preferred as a result of significantly reduced on-state resistance with high switching frequency. In contrast, SiC switches are much more competitive for higher voltage applications because of the easily scalable voltage and current with a vertical conduction path [136]. Power loss calculation is critical for thermal management and cooling in terms of applications with high power density. Power losses for WBG and Si-based semiconductors consist of conduction and switching losses. The low on-state resistance of WBG power devices contributes to a reduced conduction loss compared with Si-based modules. Generally, a freewheeling diode is connected to the semiconductor to ensure current continuity, which contributes additional power losses during reverse recovery behavior. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**PWM** & **Category** &
\begin{tabular}{c} **Switching** \\ **Frequency** \\ \end{tabular} & **SM Count** & **Performance** & **Effort** \\ \hline PSC-PWM & HSF-PWM & \(f_{sw}>2000\) Hz & Small/Large & High & Complex \\ LSC-PWM & HSF-PWM & \(f_{sw}>2000\) Hz & Small/Large & Moderate & Moderate \\ SVM-PWM & LSF-PWM & \(<f_{sw}<\)2000 Hz & Small & High & Complex \\ SAM-PWM & LSF-PWM & \(100\) Hz & Small/Large & Moderate & Easy \\  & & \(<f_{sw}<\)2000 Hz & & & \\ NLM-PWM & LSF-PWM & \(f_{sw}=50\)/60 Hz & Large & Low & Easy \\ SHE-PWM & LSF-PWM & \(f_{sw}=50\)/60 Hz & Small & High & Complex \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Pulse width modulation techniques. Figure 17: Comparison between Si, silicon carbide (SiC) and gallium nitride (GaN) power modules. During the power losses calculation, the effect of temperature on the switching devices is neglected to simplify the loss model. The conduction loss for power switches is calculated within one fundamental period [137; 138] which is obtained by  
\[P_{comT}=\frac{1}{T}\int_{t_{0}}^{t_{0}+T}i_{T}(t)v_{T}(t)dt=\frac{1}{T}\int_{t _{0}}^{t_{0}+T}i_{T}(t)(V_{T0}+R_{T}i_{T}(t))dt \tag{33}\]  
\[P_{comD}=\frac{1}{T}\int_{t_{0}}^{t_{0}+T}i_{F}(t)v_{F}(t)dt=\frac{1}{T}\int_{t _{0}}^{t_{0}+T}i_{F}(t)(V_{D0}+R_{D}i_{F}(t))dt \tag{34}\]  
where \(P_{comT}\) and \(P_{comD}\) stand for the conduction loss of the transistors and diodes, \(i_{T}\) and \(i_{F}\) are the conduction current, \(V_{T0}\) and \(V_{D0}\) donate the saturation voltage, and \(R_{T}\) and \(R_{D}\) represent the slope resistance, respectively. Switching loss is related to the count of all the switching actions during each fundamental period, since energy is charged and discharged by the inherent capacitor during each transition of turning on and turning off period.