In this paper, a new electro-thermal averaged model of PWM switching cell is presented. The main advantages of the proposed averaged model are that takes into account the nonlinear effects of semiconductor devices their electrical inertia and self-heating. It is useful in determining the device’s heat generation, junction temperature as well cooling performance of the connected heat sinks. The proposed electro-thermal model is general and can be applied to different DC/DC and DC/AC converters. The accuracy of the model in a simulation of the temperature dependence is verified through SABER simulation for the Buck converter and one-leg inverter.
In recent years, power semiconductor devices, especially IGBT and MOSFET, are widely used in a lot of industrial applications, such as power suppliers, motor drives, power systems, and consumer electronics. Due to the demand for high power density, the losses of power devices and the resulting thermal problems are more and more emphasized, because the high temperature would result in the failure of power devices and the surrounding components. They are the key factors that could influence the whole system's reliability and efficiency.]1-2[
To determine the losses in the semiconductor devices and to evaluate the cooling performance of the connected heat sinks, an accurate approach is to simulate a circuit by using a physically-based device model [3–5]. However, due to the complicated physical switching process, and the very fast transient period, this study requires very small simulation time steps (in the order of nanoseconds), which result in an unacceptably large CPU time and memory storage; for a multi-device power electronics systems and real-time simulation, the problem is even more intractable [. At the other end of the scale, it is common to use device datasheets, provided by manufacturers, to estimate losses . This method is simple but can be very inaccurate. It is clear that a method is needed which is fast and yet accurate at the system level. To reduce simulations time, we have proposed in [10-11] an average PWM-Switch model including semiconductor device non-linearity. The effects of the driving signals characteristics, the Dc loop inductance, the switching power losses, and the I-V characteristic are taken into account. Unfortunately, this model is an electrical model that neglects the effect of self-heating of semiconductor devices. In the present paper, we have developed a non-ideal averaged model of the PWM-switch which takes into account the evolution of the junction temperature. The developed model is useful for determining the device’s heat generation, junction temperature as well cooling performance of the connected heat sinks. The model provides accurate results without the need for an unreasonably small time step. The approach taken consists of two stages. First, the electrical averaged model is obtained by mathematical derivation from the known idealized switching characteristics of the active device switching characteristics. The electrical simulationof the averaged model gives the required electrical characteristics such as the effective voltage and current for power loss calculation. Then, the average power loss over each simulation time step has been mathematically calculated using the defined device characteristics in the look-up tables. After, by feeding this average power loss into a compact thermal network, the junction temperatures of devices are calculated. Because the device losses are functions of temperature, the computed device temperature is then used to change the parameters of the switch loss model for the next time step. This method is suitable for a long real-time thermal simulation for DC-DC and DC-AC power devices with arbitrary load operation. Throughout this paper, the simulation time step is set equal to the PWM switching period. This paper develops a complete average electrothermal model of the PWM switch. And experimental investigations have been performed in order to identify the different model parameters as a function of the load direct current and the applied junction temperature. The thermal parameters of each device are performed too. Finally, the accuracy of the advanced dynamic electrothermal averaged model has been studied in the case of DC/DC and DC/AC converters. The comparison between the obtained results with those obtained by the electrical averaged model and SABER simulation is performed.
II. DERIVING THE NON-IDEAL AVERAGED MODEL OF THE PWM-SWITCH
The average model of a converter is a simplified representation of the converter in quasi-cyclic operation that pictures the energy transformation without using explicitly any switching function . The studied PWM-switch structure is given in Figure (1.a), it has two basic switching cells (P-cell and N-cell). Each cell consists of one controlled switch and one diode. The four classical DC/DC converters (Buck, Boost, Buck-Boost, Cuk) can be easily decomposed into a P-cell and N-cell base circuit. In addition, the parallel combination of the N-cell and P-cell provides a bi-directional current flow switching cell. Therefore, bi-directional DC/DC converters and all inverters can be constructed.
The voltage source Ve can be an input or output DC voltage source according to the converter structure. The stray DC loop inductance is represented by an inductor Lst.
Depending on the sign of the load current IL, only two devices (one switch and one diode) operate.
The proposed averaged model of the PWM-switch is presented in Figure1.b. This model contains a controlled voltage source (V1) and a controlled current source (I1). The PWM-switch is the only nonlinear element that is supposed to be responsible for the non-linear behavior of the converter.
The permutation of the two sources’ positions is possible. In the proposed configuration, the current through the voltage source and voltage across the current source can be deduced.
Considering Ts as the switching period of the controlled switches and (d) the duty ratio which is the ratio of the on-time value (Ton) of the upper controlled switch (T1) and the switching period Ts.
In Figure (1.b), the current source (I1) and the voltage source (V1) are given by
In this paper we have developed an advanced PWM-Switch electrothermal averaged model. Contrarily to the classical averaged model, the proposed model takes into account the device non-linearity (on state voltage and switching characteristics), the circuit stray inductance, the driving signals nonlinearity (dead times), and the junction temperature evolution. The device’s non-linearity can be evaluated from the manufacturer data sheets or by experimental tests on the studied devices. The obtained average model corresponds directly to the original converter circuit. Only the switches are replaced by their average models.
Taking into account the device’s switching parameters and their variations according to the temperature, the proposed averaged model, allows an accurate estimation of the total dissipated power in the semiconductor devices.
The proposed electro-thermal model gives a good trade-off between accuracy, efficiency, and CPU-cost. It can be implemented in any circuit-oriented simulation tool.
 Zhen Hu,Wenfeng Zhang, Juai Wu, “An Improved Electro-Thermal Model to Estimate the Junction Temperature of IGBT Module” Electronics 2019, 8(10), 1066, 20 September 2019
 Kati Sidwall, Paul Forsyth, “A Review of Recent Best Practices in the Development of Real-Time Power System Simulators from a Simulator Manufacturer’s Perspective”
 Ceccarelli, Lorenzo; Bahman, Amir Sajjad; Iannuzzo, Francesco; Blaabjerg, Frede, “A Fast Electro-Thermal Co-Simulation Modeling Approach for SiC Power MOSFETs” Proceedings of the 2017 IEEE Applied Power Electronics Conference and Exposition (APEC)
 F. Blaabjerg, K. Ma and D. Zhou, “Power electronics and reliability in renewable energy systems”, IEEE International Symposium on Industrial Electronics (ISIE), July 2012, pp. 19-30.
 Nicolae-Cristian Sintamarean, FredeBlaabjerg, \"Real Field Mission Profile Oriented Designof a SiC-Based PV-Inverter Application\"IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 50, NO. 6, NOVEMBER/DECEMBER 2014
 Kojima T, Yamada Y, Ciappa M, Chiavarini M, Fichtner W. A novel electro-thermal simulation approach of power IGBT modules for automotive traction applications. Proceedings of 2004 International Symposium on Power Semiconductor Devices & ICs, Kitakyushu, 2004.
 Mantooth HA, Hefner AR. Electro thermal simulation of an IGBT PWM inverter. IEEE Transaction on Power Electronics 1997; 12(3):474–484.
 Hefner R, Blackburn DL. Thermal component models for electro-thermal network simulation. IEEE Transactions on Components Package Manufacture Technology 1994; 17:413.
 Laprade A, Randal RH. Numerical method for evaluating IGBT losses. Application Note 7520 Rev. A1.
 A.AMMOUS et al, An advanced PWM-Switch Model including semiconductor device nonlinearities, IEEE Transactions on Power Electronics. Vol. 18, No.5, September 2003, pp.1230-1237
 S.ABID et al, Advanced Averaged Model of PWM-Switch operating in CCM and DCM conduction modes, IREE. Vol. 2, No.4, August 2007, pp.544-556
 Edwin Van Dijk et all, PWM-Switch Modeling of DC-DC Converters, IEEE Transactions on Power Electronics, Vol. 10, No. 6, November 1995, pp. 659-664.
 Fang Z. Peng et all, “Power Electronics’ Circuit Topology – the Basic Switching Cells” Proceedings of 2005 PESEC
 A. Ammous et all, “ Choosing a thermal model for electrothermal simulation of power semiconductor Devices” IEEE Tran. On Power Electronics, Vol 14, No 2, Mars 1999.
 A.AMMOUS et all, Developing an equivalent thermal model for discrete semiconductor packages, Elsevier International Journal of thermal sciences 2003 pp533-539
 FredeBlaabjerg and John K.Pedersen, Optimized Design of a Complete Three-Phase PWM-VS Inverter, IEEE Transactions On Power Electronics, Vol 12, No 3, MAY 1997
 J. Baliga, “Modern Power Devices”, New York: John Wiley and sons, 1987
 H. Mantooth, J. Duliere, \"A unified diode model for circuit simulation,\" IEEETrans. on Power Electronics, vol. 12, no. 5, Sept. 1997.
 A.R. Hefner, “A Dynamic Electro-Thermal Model for the IGBT,” IEEE Trans. On Industry Applications. vol. 30, p. 394, 1994.
 Jose Miguel Ortiz-Rodriguez, “Electro-Thermal Modeling of a Power Electronic Module,” University of Puerto Rico Maya Guez Campus, Master of Science Thesis, 2004.
 Gary E. Dashney, “Basic semiconductor thermal measurement,” Motorola Semiconductor products sector, Phoenix, Arizona, Application note AN1570.