## 1 Introduction
In [13], the non-parametric Gaussian process regression (GPR) technique is used to predict missing data points. GPR is  
Figure 1: Four-wheel electric drive vehicles. used to predict Ids on several Vds and Vgs. The kernel function is applied to extract the information for accurate prediction. The exponential kernel function is used to create a model, but this method is complicated. The lookup table method has been applied in a simulation to approximate switching as well as on-state losses of the IGBT transistors [14,15]. This method gives an automatic, compact, and accurate model of semiconductors for the PEs inverter's analysis by the use of the average computational time of the CPUs. Thermal simulation of IGBT modules has been designed to calculate the system's responses. It is essential to optimize the system, i.e., reducing design cost, increasing reliability, risks or faults occur, time to be powered off when overheating, and calculating maximum switching frequency, which would depend on the junction temperature [16]. The power losses, as well as thermal optimization, have been in general controlled by modifying electrical parameters. The power losses have been estimated by means of electrical loading on the devices and then transformed into a thermal model to generate the junction temperature of the semiconductor devices, as discussed in [17]. The junction temperature is an important parameter for reliability prediction [18]. The passive filters have been reported to be essential to obtain fewer ripples and high-efficiency responses from the converter, and system cost, weight, and size are greatly impacted. Hence the optimum design is mandatory with a variation of the switching frequency [19]. Analytical-based model is an effective method for controllability analysis, stability analysis, and control system design [20, 21, 22]. This research aims to design an accurate and fast electro-thermal high-fidelity simulation model for the inverter, which would precisely reflect the functional behavior of the Si MOSFET-based existing inverter. Therefore, the manufacturer-based data are applied through the interpolation method, depending on the voltage, current, and junction temperature. This model calculates the instantaneous power loss at every switching interval, regardless of how fast your switching frequency is. The transfer function of the thermal model of MOSFET is designed as a virtual sensor to convert power loss into junction temperature. These features make the model unique from literature. The heatsink model is created to calculate the inverter case temperature. The complete electro-thermal model runs such as a real inverter, and the efficiency depends on temperature, voltage, and current. The WBG devices can easily be integrated into the inverter model to operate at higher switching frequencies and analyze the power loss and temperatures of the inverter at a higher frequency for the case of GaN and SiC. Moreover, the model allows the pre-establishment and the post-analysis of the system by varying control design, circuit parameters and operating switching frequency, etc. Figure 2: Material characteristics of Si and WBG (SiC and GaN). This paper has been arranged into seven sections. Section 2 comprises the passive filter design to minimize the ripples at the AC and DC sides of a multi-purpose inverter. Section 3 illustrates the inverter modeling and control, inverter and motor design parameters, analytical model of the inverter and IM, and control strategy for IM. Moreover, space vector (SV) pulse width modulation (PWM)-based IFOC control is designed using steady-state feedback analysis and implementation on the simulation model. In Section 4, an electro-thermal model of an inverter is created. The high-fidelity MATLAB/Simulink simulation is developed for the three-phase inverters, and the power losses are calculated through a datasheet-based lookup table technique. The designed state-space thermal model has been incorporated as a virtual sensor to convert power losses to the temperature.