## 5 Cooling Calculations and Cooling System Design  
In power stage design, some criteria are considered to select the heatsink. Figure 7 shows the thermal resistances of the system with the heatsink. Such thermal resistances and the parameters are described in Table 7. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Name** & **Unit** \\ \hline \(\Theta_{\mathrm{JC}}\) & Thermal resistance between the junction and IGBT case & \({}^{\circ}\)C/W \\ \hline \(\Theta_{\mathrm{CS}}\) & Case to heatsink thermal resistance & \({}^{\circ}\)C/W \\ \hline \(\Theta_{\mathrm{SA}}\) & Thermal resistance between the heatsink and medium & \({}^{\circ}\)C/W \\ \hline T\({}_{\mathrm{j}}\) & Junction temperature & \({}^{\circ}\)C \\ \hline T\({}_{\mathrm{A}}\) & Ambient Temperature & \({}^{\circ}\)C \\ \hline P & Lost power & \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters and their meanings. Figure 7: Thermal resistance of the system with cooler. The total thermal resistance is calculated with Equation (23) using the catalog values of \(\Theta_{\rm JC}\) (R\({}_{\rm JC}\)) and \(\Theta_{\rm CS}\) (R\({}_{\rm CS}\)) in the heatsink catalog to determine the heat emitted by the IGBT modules used. \[\Theta_{\rm JC}+\Theta_{\rm CS}+\Theta_{\rm SA}=\frac{\rm T_{j}-T_{A}}{\rm P} \tag{23}\]  
The total junction thermal resistance can be expressed by Equation (24), as computed in Equations (25) and (26). \[\rm Q_{\rm aTotal}=Diode(K/W)+IGBT(K/W)+Module\ (K/W) \tag{24}\]  
\[\rm Q_{\rm aTotal}=(0.086\cdot 6)+(0.049\cdot 6)+(0.03\cdot 3) \tag{25}\]  
\[\rm Q_{\rm aTotal}=0.9\ K/W \tag{26}\]  
Equation (27) can be used to calculate the lost power. The parameter values are substituted in Equation (28), and the result can be seen in Equation (29). \[\rm P_{dissipation}=(T_{j}-T_{a})/Q_{\rm aTotal} \tag{27}\]  
\[\rm P_{dissipation}=[(150-80)\ ^{\circ}C]/0.9=(423-353)\ K/0.9 \tag{28}\]  
\[\rm P_{dissipation}=77.8\ W \tag{29}\]  
Effect of mounting distances of KBTs on heat dissipation; when the IGBT modules are positioned as shown in Figure 8, the thermal resistance between the IGBT case and the heatsink decreases, thus ensuring that the amount of heat dissipated to the heatsink is equal and the temperature value is lower than the value when they are positioned side by side [16]. It is also recommended for liquid-cooled systems to implement a similar spacing between IGBTs as in air-cooled systems. The liquid cooling system should be designed by maintaining the distance between the IGBTs [16]. When the SKM300 GB126D module case was used in this thesis, such points were considered in thermal design. The analysis was performed in the Fluent program using the following parameters: ambient and heatsink parameter (T\({}_{a}\)): 40 \({}^{\circ}\)C, number of elements installed per heat-sink: 6, number of parallel devices on the same heat-sink: 1, additional power supply: 0 W on this heat-sink, cooling methods forced air cooling, correction factor: 1, flow rate: 80 m\({}^{3}\)/h or L/min, and R\({}_{\rm th}\) (s \(-\) a): 0.11 K/W. If the number of switches on the heatsink and the number of components connected in parallel are more than one, the total power is calculated by Equation (30). \[P_{TOTAL}=n_{s}\cdot n_{p}\ (P_{d(6\cdot TOTALnom)}+P_{i(TOTALnom)}) \tag{30}\]  
\(\rm n_{s}\) = number of switches on the heatsink;  
Figure 7:0 Placement of IGBT modules in the heatsink. n\({}_{\text{p}}\) = number of components connected in parallel in the switch. In the thermal analysis example shown in Figure 9, it was determined that the IGBTs had a temperature of 90 \({}^{\circ}\)C with a distance of 20 mm between them. As illustrated in Figure 10, the temperature rises to 96 \({}^{\circ}\)C when there is no space between the IGBTs [16]. Since the combined layout will cause higher temperatures in case of high current flow through the IGBTs, the design in Figure 9 is adopted as the optimum design. A greater distance between IGBTs is better for maintaining low temperatures.