# Novel Thermal Management Strategy for Improved Inverter Reliability in Electric Vehicles
## 3 Proposed Thermal Management Strategy
### Power Loss and Highest Virtual Junction Temperature Estimation  
In general, two possible approaches can be considered to estimate the highest \(T_{vj}\) among all switches:  
1. If reliable estimation of semiconductor \(T_{vj}\) through temperature measurement sensors (thermistor, NTC or PTC) soldered on the Direct Bonded Copper (DBC) substrate of the power module is possible [36], the highest of all the estimated temperatures is provided to the TCT algorithm for its regulation. (As temperature sensors are placed at a given distance to the semiconductor die, it provides a lower temperature than \(T_{vj}\). To obtain accurate results, such a measurement point can be treated as a node within a simplified Foster thermal network to compensate the temperature underestimation (which is not straightforward) or, for simplicity, a security margin can be considered instead [36].) 2. If the previous is not possible, temperature should be estimated by using accurate thermal and power loss models in conjunction with an external temperature sensor (measuring heatsink or coolant temperature) [36]. This approach has been proven successful in [27; 30], as estimated and measured temperatures matched very well. In such works, power losses of all semiconductors were estimated online. This work follows the latter approach for the temperature estimation. However, as stated in the introduction of the document, low computational burden is a key feature demanded by the automotive industry. Thus, it is proposed to calculate the highest single semiconductor average power losses (worst case) per electrical period offline for all the torque/speed map of the machine and store these results in a 4-D LUT (Figure 1), considering \(T_{vj}\), \(F_{sw}\), \(T_{em}\) and \(\omega_{m}\) as inputs. (Although at high speedsthe junction temperatures are balanced, unbalances occur at very low speeds that need to be considered for obtaining accurate estimations.) For the offline power loss estimation, an accurate electric drive model has been implemented in Matlab/Simulink incorporating a per-device power loss model. In this work, a novel automotive grade SiC power module FS03 MR12A6 MA1B [37] of Infineon Technologies has been used to validate the proposal. This module offers state-of-the-art Trench SiC MOSFET technology with very low switching and conduction losses, which is necessary to reach high efficiency in traction inverters. It is packaged in a stray-inductance optimized module, which is also necessary for reaching high switching speeds as the ones considered for this application (\(f_{sw}=25\) kHz). Figure 2 shows the most significant power loss related parameters considered from the datasheet. Regarding MOSFETs, the average conduction (\(P_{cond\_MOS}\)) and switching (\(P_{sw\_MOS}\)) losses during a modulation period \(T_{sw}\) are calculated as:  
Figure 2: MOSFET and body diode curves for the offline determination of power losses of the FS03 MR12A6 MA1B Silicon Carbide (SiC) power module. Source: _“Target Datasheet of FS03 MR12A6 MA1B: Version 1.1”_. \[P_{cond,MOS}=\frac{1}{T_{sw}}\int_{0}^{T_{sw}}V_{DS}(i_{D},T_{vj,MOS})i_{D}(t)dt, \tag{9}\]  
\[P_{sw,MOS}=\frac{1}{T_{sw}}\left[\frac{V_{DC}}{V_{DC(test)}}\right]^{K_{V}}[E_ {ON}(i_{D},T_{vj,MOS})+E_{OFF}(i_{D},T_{vj,MOS})], \tag{10}\]  
where \(V_{DS}(i_{D},T_{vj,MOS})\) is the drain-to-source voltage drop (Figure 2a), \(i_{D}(t)\) is the drain current, \(T_{vj,MOS}\) is the virtual junction temperature of the MOSFET, \(E_{ON}(i_{D},T_{vj,MOS})\) and \(E_{OFF}(i_{D},T_{vj,MOS})\) are the energy losses produced during turn-on and turn-off (Figure 2b), \(V_{DC}\) is the DC-link voltage value, and \(V_{DC(test)}\) is the blocking voltage from which \(E_{ON}(i_{D},T_{vj,MOS})\) and \(E_{OFF}(i_{D},T_{vj,MOS})\) were calculated by the manufacturer [38]. For the sake of simplicity, the compensation factor \(K_{V}\simeq 1\).