## 4 The Efficiency of Hybrid Power Stage under Light-Load Conditions
### 125 kW Si IGBT Converter vs. 10 kW SiC Power Stage under Light-Load Conditions
#### 4.1.1 Conduction Losses of IGBT- and SiC-Based Light-Load Setup
According to the datasheet of Infineon's IMZ120R030M1H, the on-resistance at a junction temperature of 85 \({}^{\circ}\)C is approximately 35 m\(\Omega\). For an IGBT and dedicated antiparallel diode, the conduction losses are specified via:  
\[P_{\text{IGBT,con}}=V_{\text{T}}I_{\text{IGBT,avg}}+R_{\text{on,IGBT}}I_{\text {P,IGBT,rms}}^{2}, \tag{21}\]  
\[P_{\text{D,con}}=V_{\text{D}}I_{\text{D,avg}}+R_{\text{D}}{I_{\text{D,rms}}}^{2}, \tag{22}\]  
where \(V_{\text{T}}\) and \(V_{\text{D}}\) representing the forward voltage of IGBT and diode, respectively. \(R_{\text{on,IGBT}}\) and \(R_{\text{D}}\) denote the equivalent resistance of IGBT and antiparallel diode. Figure 8: Current stress of an IGBT-based three-phase six-switch inverter topology, incorporating the existing current ripple, for light- and no-load operation (\(I_{\text{N,pk}}<\Delta I_{\text{Lmax}}\)). Generally, modeling approaches to determine the required forward voltage drop and resistance refer to the nonlinear \(V/I\)-output characteristic of an IGBT. If the module with reverse conducting IGBTs is appropriately chosen, the nominal operating point of the converter lies typically within the approximatively linear region of the device (not exactly linear due to conductivity modulation of IGBT devices), which enormously simplifies the linearization process of such nonlinear curves. During light- and no-load condition, however, the IGBT module designed for 125 kW will operate in the nonlinear area (\(i_{\text{CE}}\) and \(i_{\text{D}}<100\) A) of both IGBT's and diode's \(V/I\)-output characteristics (shown in Figure 9a). For accurate results, \(V/I\) datasheet results are transferred into an \(I/P\) curve (cf., Figure 9b). The \(I/P\) curve is then used to generate a similar conduction loss characteristic according to Equation (21), which represents the original loss properties in the low power region as precisely as possible. The obtained values for \(V_{\text{T}}\) and \(R_{\text{on,IGBT}}\) can be verified by utilizing the-in-the \(V/I\) graph (retransferred linearized model). The same approach can be applied to extract linearized diode parameters of the forward-voltage \(V_{\text{D}}\) and the equivalent resistance \(R_{\text{D}}\). Results for IGBT and diode characteristics can be found in Table 3.  
A comparison of conduction losses of one IGBT, with dedicated antiparallel diode and the proposed SiC-MOSFET substitute are illustrated in Figure 10 and shown in Table 4. In these graphs, the losses are mapped to different phase angles \(\Phi=0^{\circ}\) (see Figure 10a), \(\Phi=45^{\circ}\) (shown in Figure 10b), (c) \(\Phi=90^{\circ}\) (depicted in Figure 10c) and \(\Phi=180^{\circ}\) (cf., Figure 10d). It should be noted that \(\Phi=0^{\circ}\) implies purely active power delivered from the grid to load and \(\Phi=180^{\circ}\) active power provided from the generator to the grid. It can be observed that for the chosen setup at hand, conduction loss reversal point varies between 5.5% \(P_{\circ}\) and 6.5% \(P_{\circ}\). It can thus be concluded that below 5.5% \(P_{\circ}\) the proposed WBG upgrade always comes with lower conduction losses. In this very specific case to conduction losses of the SiC MOSFET could be further reduced if (i) a SiC MOSFET with larger chip area would be chosen or (ii) the switching frequency of the SiC-MOSFETs would be increased beyond the switching  
Figure 6:0 (a) \(V/I\) and (b) \(I/P\) characteristic of a Si-IGBT to extract forward voltage and ON–resistance of an IGBT under light- and no-load condition for a 125 kW three-phase six-switch system.