## 2 Fatigue Characteristics of High-Power IGBT Model
### Effect of FWD Actions on Device Aging  
It is not enough to consider IGBT only in the fatigue model. In the device, current can flow in two directions, as shown in Figure 5, where C and E are the external terminals of the device. In Figure 5a, current flows through IGBT. In Figure 5b, current flows through FWD. In AFT, the DUT is heated by the test current flowing through it. However, conventional AFT only offers the test current in one direction, i.e., the direction shown in Figure 5a [13; 14; 15], considering that IGBT is more fragile. In conventional AFT (hence SAFT, single-directional AFT), the aging of IGBT is equal to the aging of DUT. However, the current through FWD also generates heat, hence FWD actions also cause DUT to age. SAFT should be improved to bidirectional AFT (BAFT) where the test current flows through both the IGBT and FWD. The data that is obtained by BAFT accurately shows the aging effects caused by IGBTs and FWD. Such an effect is shown more clearly in junction temperature variation, as shown in the simulation of the TC operation below.  
Figure 6 shows TC topology, where Q\({}_{11}\)-Q\({}_{32}\) are IGBTs, D\({}_{11}\)-D\({}_{32}\) are FWDs, QB, RB and DB constitute the brake energy consumption branch. Q\({}_{11}\)-Q\({}_{32}\) and D\({}_{11}\)-D\({}_{32}\) are usually packaged in six modules onto the heat sink. QB and DB is not used frequency, therefore only the fatigue of Q\({}_{11}\)-Q\({}_{32}\) and D\({}_{11}\)-D\({}_{32}\) are considered here.  
Figure 5: IGBT and FWD current flow differences. (**a**) IGBT current flow; (**b**) FWD current flow.  
Figure 6: TC (traction converter) circuit topology.  
The internal temperature of the IGBTs and FWDs under the given operating conditions was obtained in an electro-thermal simulation of the TC model. In the simulation, the EMU went through two operating cycles. The simulation results are shown in Figure 7. The horizontal axis in Figure 7 is time, and the vertical axis is junction temperature. The switching device used is 1500 A/3300V, the switching frequency is 57 Hz\(\sim\)1000 Hz and the ambient temperature is 25 \({}^{\circ}\)C.  
In Figure 7, the maximum variation of FWD junction temperature (\(\Delta T_{\rm j2}\)) is 56.3 \({}^{\circ}\)C, and that of IGBT (\(\Delta T_{\rm j1}\)) is 39.7 \({}^{\circ}\)C. Junction temperature variation severely affects device lifetime [20; 21]. According to the experimental data of LESIT [22] and CIPS08 [23], the junction temperature change and the average junction temperature are the key factors affecting the aging process. Table 2 shows the maximum values of \(\Delta T_{\rm j2}\) and\(\Delta T_{\rm j1}\) under different load conditions [24]. \(\Delta T_{\rm j2}\) and \(\Delta T_{\rm j1}\) are affected by various factors, such as power loss of IGBT and FWD, heat dissipation condition and thermal resistance. In Table 2, \(\Delta T_{\rm j2}\) and \(\Delta T_{\rm j1}\) increase as the vehicle load increases (which appears in the form of load current, i.e., the fatigue current), which means that there is certain one-to-one correspondence between \(\Delta T_{\rm j1}\), \(\Delta T_{\rm j2}\) and the load current.  
In Figure 7, it should be noted that \(\Delta T_{\rm j1}\) is higher in the traction phase than \(\Delta T_{\rm j2}\) and lower in the braking phase. What is more, \(\Delta T_{\rm j2}\) grows much faster than \(\Delta T_{\rm j1}\) in the high-speed braking phase. This stems from the fact that more TC power output is required in the high-speed braking phase than in the traction phase, and such braking power mainly flows through the FWD instead of the IGBT [6]. Therefore, the role of FWD should not be ignored during the fatigue of the switching device.  
As stated above, the IGBT ages faster with the FWD actions, i.e., the fatigue process is accelerated. If the aging state of the DUT is still represented by the aging state of the IGBT (as is the case in the existing references [2; 3; 4]), this acceleration effect of the FWD action must be considered.