## 4 Thermal Model of Power Semiconductors  
Over recent years, system design requirements and reliability issues related to the thermal analysis of power electronic converters have been placed at the top of the priority list. Thus, an accurate approach for determining and simulating the thermal behavior of power semiconductors utilized within a power converter seems to be crucial; and the key to achieving optimal performance and increasing the lifespan of the converter is to determine the junction temperature. Due to the large time constant and delayed response of the heatsink (or cooling system) relative to the temperature, direct measurement of the junction temperature from these available points is subject to a great deal of error. Nevertheless, a method for proper temperature estimation should be provided. This method mainly involves thermal modeling of both semiconductor devices and cooling systems by assuming the thermal resistances and capacitances; then, applying the power losses as the input to this model and the output would be equal to the junction temperature. Therefore, the first step for estimating the temperature is adopting a method of power loss estimation in a power module. Types of power semiconductors' losses are mainly divided into two categories: conduction and switching losses. The IGBT switch is not ideal and has an internal resistance, which is why a voltage will be caused by conducting the current. The conduction losses can be calculated by multiplying the instantaneous-collector current (\(I_{c}\)) by the on-state collector-emitter voltage (\(V_{cc}\)) as follows [47]:  
\[P_{con}=I_{c}\times V_{cc}\left(I_{c},\ T_{j}\right) \tag{20}\]  
The voltage \(V_{cc}\) at the same time depends on both the collector current and the junction temperature (\(T_{j}\)); thus, at each step, the temperature of the previous step should be determined for calculation. The voltage, current, and junction temperature relationships are presented as a line graph in the product's datasheet. Given that this graph is only provided for a limited number of temperatures (e.g., 25 \({}^{\circ}\)C and 125 \({}^{\circ}\)C), linear interpolation and extrapolation should be employed for the rest of the temperatures between and outside the given two temperatures. The whole process will be implemented by the lookup table method as a measurement-based method. The conduction losses of the diode can be extracted by substituting the diode forward voltage (\(V_{j}\)) and the current in a forward-biased state (\(I_{j}\)) with the aforementioned parameters. The switching losses in an IGBT can be defined as the losses due to the charging and discharging of the internal capacitance while fast turning off and on. The switching losses can be determined by multiplying the switching frequency (\(f_{sw}\)) by the energy losses in each commutation, where this energy loss is a function of the supply voltage (\(V_{cc}\)) and the collector current (\(I_{c}\)) as follows [47]:  
\[P_{sw}=\left(E_{on}\left(V_{cc},\ I_{c},\ T_{j}\right)+E_{off}\left(V_{cc},\ I_{c},\ T_{j}\right)\right)\times f_{sw} \tag{21}\]  
Figure 6: Circuit diagram of the Cuk converter. Meanwhile, this type of loss is also directly dependent on the junction temperature, and by raising the temperature, it will increase. For this reason, similar to the conductive losses, the lookup table method is also required for calculating switching losses, but with the difference that the interpolation should also be used for the supply voltage and junction temperatures. It is evident that by increasing the switching frequency, the switching losses will also rise. The mentioned procedure should be repeated for the diode's losses by using reverse recovery energy loss (\(E_{tr}\)) instead of the summation of on-off energy losses [47]. Power losses play the role of a heat source for the thermal modeling of an IGBT module. If the power loss inside the module is so high, an extreme junction temperature will be produced which can cause severe damage to the component.