*Temperature rise in the SixPack IGBT module can be predicted within a few seconds.*

*When it comes to the simulation of entire drive systems, the thermal cycling is becoming more and more a designers issue. The lifetime of semiconductor components is strongly depending on thermal cycling. Therefore a detailed analysis is required of the maximum junction temperature in the IGBT and MOSFET.*

*By Peter van Duijsen; Simulation Research, and Pavol Bauer, TU Delft, The Netherlands*

Thermal simulations are usually carried out in FEM or in specialized products such as CFD packages. To determine thermal cycling, the maximum junction temperature should be simulated. This requires a coupled thermal-circuit/system simulation using FEM and a circuit/system simulation. However closed loop coupled System-FEM simulations take too much time. Therefore thermal models are developed that can be used in a circuit/system simulation to predict the temperature rise on the semiconductor junction. First the loss prediction models are introduced and used in a simple single-phase inverter. Second, a Reduced Order Model is approximated in FEM and coupled to a three-phase inverter simulation. Third, a thermal model for a SixPack IGBT module build from different layers is coupled to an inverter simulation and briefly discussed.

### Thermal cycling and loss predicting models

An analysis of thermal cycling is required to predict the lifetime of a component. Also important is that the thermal cycling of the semiconductor can simultaneously be simulated with the electric and thermal circuit, from which the temperature dependent losses are determined. Converter efficiency, cooling requirements and heat sink dimensions are in this way calculated. In Caspoc the dynamic non-linear semiconductor models standard have a thermal connection to a thermal model. Using this thermal node, the temperature rise on the junction of the semiconductor can be calculated and the temperature depending parameters of the semiconductor change their value during the simulation. If only the thermal cycling is of interest, the detailed semiconductor models, with their long simulation times, are not always required. In Caspoc loss-prediction models can be used that replace the detailed non-linear dynamic models. Using these loss-predicting models, the thermal cycling and the temperature dependent losses are approximated on basis of parameters and characteristics in data sheets provided by the semiconductor manufactures. The losses in the switches are approximated based on the temperature, gate driver data, computed currents and voltages of the ideal switches. The data sheet provides the parameters and/or characteristics for the conduction and switching losses.

The loss predicting models replace the detailed semiconductor models in a power electronics simulation when the overall system simulation is of importance. The detailed waveforms are now approximated by ideal waveforms, since an ideal semiconductor switch replaces the detailed dynamic model of the switching semiconductor. The advantage is the increased simulation speed. Figure 1 shows the application of a single-phase inverter with inductive load.

The IGBT modules, PWM controlled including deadtime, are connected to a simple thermal network represented by a Cauer model [5] of the fourth order. The losses are temperature depending and are calculated on base of the worst case data sheet parameters for the conduction, switching and reverse recovery losses. The conduction losses are calculated from the on state voltage and on resistance of the IGBT and diode. These parameters are temperature depending. The switching inductor current is shown in detail in this simulation, as is the PWM pattern of the voltage across the inductive load. Switching turn-on and turn-off details like reverse recovery are omitted in this simulation, since ideal models are used. The advantage is the improved simulation speed. Figure 2 shows the junction temperature of one of the IGBT junctions.

Since the simulation is performed for only the first 10ms, the heat sink remains at nearly the same temperature (blue line in figure 2). However the junction temperature is rising fast towards 150 degrees Celsius (red line in figure 2). From this simulation it becomes obvious that a simulation is preferred over a measurement to identify the junction temperature, simply because a measurement of junction temperature of a closed IGBT module during such a short transient is very difficult, if possible at all. A shortcoming in this simulation is that the thermal model is not a good approximation of the applied heat sink. A more realistic heat sink model is required, but this would require many equivalent thermal components building up the 3D geometrical structure of the heat sink.

### More detailed thermal model

In a one-dimensional model heat flow is only possible in one direction. In reality the heat flow is a 3-dimensional process.

The identification of such a thermal model is based on the approximation of the FEM model into a Reduced Order Model (ROM). The reduced order state space model is approximated from the internal FEM model. This model includes all details regarding material and geometry of the thermal path and can be used to model the transient temperature rise as function of the injected losses.

In [2] a study is presented of the base-plate with components of an IGBT module with free wheeling diodes. The module is designed for a hybrid electrical vehicle and contains all the semiconductors required in the inverter. Since the components are closely packed together, thermal problems are expected in this assembly.

The thermal model in FEM includes all layers in the module of the IGBT components. There are various materials such as copper, solder, ceramic and silicon that build the IGBT and the free wheeling diode. For each component, IGBT and diode, a thermal node is defined in FEM. This thermal node is the connection to the circuit/system simulation. Using the ROM approximation method, a reduced order model is calculated from the full model in FEM. This model is included in the cicruit/system simulation as shown in figure 3.

A library block MOR30 covers the reduced order model, since in this case there are 30 thermal nodes that have to be connected. The inverter is modeled with parallel IGBT and diode branches. Each IGBT and diode has a thermal node that is exported from the IGBTmodule. Since there are two IGBT’s in parallel in this model there are also two gates per parallel IGBT set. The gates are controlled by a symmetrical PWM signal of 10kHz. The inverter has a V/f regulation and is modulating signal rises to a maximum of 50Hz. The left side of the MOR30 block shows the thermal nodes that are connected to the thermal nodes of the IGBT module. The right side of the Mor30 block only has temperature sensor outputs without any physical connection. They are used to view the temperatures in scope 2 in figure 3. Scope 3 in figure 3 shows the output waveforms of the inverter in the electrical load. Scope 4 shows the V/F characteristic and in scope 1 the angular speed and electric torque of the induction machine is displayed.

### SixPack IGBT module thermal model

The disadvantage of the ROM is that, since it is a state space approximation of the FEM model, it is a linear model. This means that only linear relations between power loss and temperature are modeled. Radiation or forced water-cooling is a non-linear relation between power and temperature where the mathematical relation includes the fourth power of the temperature. Another disadvantage is that a costly FEM analysis is required to get the reduced order model. A simple change in geometry of the cooling systems requires a complete new evaluation of the ROM. By examining the heat sink a reduced order model can also be build using discrete thermal models that are interconnected. This is shown in the simulation below. Here the thermal model of the SixPack IGBT module is combined with a thermal model of the base plate that is mounted onto a forced water cooling system. A simple change of water flow, water temperature or geometric size of the base-plate, directly result in a different temperature profile in the inverter. Combined with a detailed space vector modulation and electric load, the temperature rise in the SixPack IGBT module can be predicted within a few seconds.

**Conclusions**

To investigate the temperature rise on the semiconductor junctions, an overview is given on the methods for thermal modeling for power electronics simulations. First the loss predicting models are presented and simulations are presented where this model is connected to an equivalent thermal network. Second a reduced order method is shown, where a thermal ROM is derived that is coupled to the fast loss predicting models. Third a thermal model of a complete SixPack module is connected to the inverter simulation for fast and flexible simulation. In the third simulation the non-linear models of forced water-cooling and convection can be included in the simulation.

**References:**

[1] Caspoc user guide, www.Caspoc.com

[2] Dehbi A., Wondrak W., Rudnyi E.B., Killat U., van Duijsen P.J., Efficient Electrothermal Simulation of Power Electronics for Hybrid Electric Vehicles., Eurosime 2008, 21-23 April 2019, Freiburg, Germany, Proceedings of the EuroSime 2008, page 412-418.

[3] P.J. van Duijsen, P. Bauer, Thermal Simulation of Power Electronics, PCIM 04, Nurnberg, May 25-27, ISBN 3-922018-39-8, pp.881-886.

[4] Bauer P., Duijsen P.J. van, Challenges and Advances in Simulation, PESC 2005, Brazil.

[5] Lutz J., Halbleiterbauelemente, Springer 2006.