# Novel Thermal Management Strategy for Improved Inverter Reliability in Electric Vehicles
## 4 Validation of the Proposed Thermal Management Algorithm
### Low Speed and High Torque Operation Results  
EV drives usually operate at low speeds with high torque, for example starting uphill, or also when driving in urban driving conditions with a dense traffic, intersections and traffic lights. These operation conditions are critical, as at very low speeds power losses are concentrated in a few power semiconductors, which implies high junction temperatures. Thus, a high torque step demand (from 100 Nm to 300 Nm) has been simulated while driving at \(\omega_{m}=1\) rpm (Figure 5a).  
When no TCT algorithm is applied, the high power losses on the semiconductors produced by the high torque step (Figure 5b, from t = 0.4 s) result on a high junction temperature (Figure 5c). As a consequence, the power converter overheats, significantly reducing its life-cycle if such operation conditions are constantly repeated. However, such temperature can be constrained by using the proposed thermal management algorithm (Figure 6). Figure 6b shows that power losses are reduced when the TCT algorithm reduces the switching frequency from 25 kHz to approximately 10 kHz, maintaining the temperature around the maximum allowed one, which in this work has been set at 120 \({}^{\circ}\)C (Figure 6c). Note that the switching frequency regulation dynamics can be set by adjusting such a parameter. In this context, Figure 7 exemplifies the temperature response of the system obtained for  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Units** \\ \hline Power semiconductor maximum drain-source voltage & \(V_{DSS}\) & 1200 & V \\ \hline Power semiconductor nominal drain current & \(I_{D,nom}\) & 400 & A \\ \hline Nominal switching frequency & \(F_{sw}^{*}\) & 25 & kHz \\ \hline Nominal battery (DC-link) voltage & \(V_{DC}\) & 300 & V \\ \hline Cooling fluid temperature & \(T_{fluid}\) & 105 & \({}^{\circ}\)C \\ \hline \hline \end{tabular}
\end{table}
Table 1: Most relevant parameters of the simulated power electronics system.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Units** \\ \hline Maximum power & \(P_{max}\) & 75 & kW \\ \hline Nominal power & \(P_{nom}\) & 50 & kW \\ \hline Maximum mechanical speed & \(\omega_{max}\) & 1500 & rpm \\ \hline Stator maximum current & \(I_{max}\) & 400 & \(A_{rms}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Most relevant parameters of the automotive Interior Permanent Magnet Synchronous Machine (IPMSM).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Units** \\ \hline Maximum junction temperature constraint & \(T_{j,max}\) & 120 & \({}^{\circ}\)C \\ \hline TCT tunable parameter & \(\alpha\) & 1 & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: Regulation parameters of the Temperature Constraint Tracking (TCT) controller.  
various values of \(\alpha\). The higher the value of \(\alpha\), the faster the settling time and the lower the overshoot. However, a trade-off between temperature settling time and current regulation robustness must be considered. In this particular application, the TCT regulation parameter \(\alpha\) has been set to 1.  
It is important to remark that a small temperature overshoot (Figure 6c) has been produced due to the high torque step. However, as torque reference is always ramped in EVs to ensure driving comfort  
Figure 5: Simulation results obtained at very low speed and under a high torque step without using the proposed TCT algorithm.  
Figure 6: Simulation results obtained at very low speed and under a high torque step when using the TCT algorithm.  
and vehicle's mechanical integrity, the TCT algorithm has enough time to react and ensure that the power semiconductor junction temperature does not exceed a given temperature constraint.