## 1 Introduction and Related Work  
Induction motors are widely preferred in railway propulsion system applications due to their mechanical robustness, good control properties, high overload capacities, and affordability [1, 2]. However, maintaining optimum temperatures in the critical parts of these traction motors is the key to maximizing their efficiencies and also to maintaining a safe operational margin. The maximization of motor utilization in terms of generating maximum torque and power can lead to a high current load, causing more heat load in the windings. This thermal overloading phenomenon increases the possibility of motor failure if the temperature exceeds the insulation-withstanding capacity. Furthermore, dynamically changing the ambient operating conditions and load demand in a traction drive system can cause the motors' performance to vary nonlinearly due to parasitic effects from the core saturation. Hence, temperature monitoring at the critical parts of the motor is essential to prevent any thermal stress while optimizing the motor's performance. In a drive system control environment, real-time temperature estimation is fed back to the controller to compensate for electrical signals such as voltage and current [3]. Thermal analyses using computational fluid dynamics (CFD) or the heat-equation-based finite element analysis (FEA) method are quite accurate in estimating temperatures [4] and are performed during the design phase. Nonetheless, these studies demand rigorous modeling effort and are computationally expensive. This makes the applicability of these tools unsuitable for real-time monitoring upfront. Installing contact-based sensors such as thermistors or thermocouples is the simplest means for temperature measurement. While the installation of sensors in the stationary parts of the motor such as stator winding, end-wining, core, etc., are straightforward, for the rotating parts, in addition to the sensors, the use of slip rings or other telemetry means such as Wi-Fi, Bluetooth, or infrared communication is necessary for data transmission. Regardless, the deployment of sensors requires integration efforts and additional costs. It also adds complexity due to their inaccessibility for replacement in the case of failures or detuning. As an alternative, model-based measurement techniques for temperature estimation have been in focus during the past decade [5; 6]. With these approaches, the targeted temperatures are estimated from the measurement of temperature-dependent electrical parameters in both offline and online manners. The accuracy of the estimation is dependent on the level of modeling effort in capturing the nonlinear, electro-thermal motor dynamics. This includes magnetic/core saturation, cross-saturation effects, hysteresis, eddy current effects, temperature-dependent material properties variation, etc. These methods are also invasive and create a disturbance during normal operation [7]. An alternative direct-temperature estimation technique is using the lumped-parameter thermal network model [8]. An LPTN model is a simplification of the motor physical model that can be represented in a thermal equivalent circuit diagram. The LPTN model comprises several nodes that represent each part of the motor and thermal parameters that represent the heat conduction, radiation, and convection phenomena between different parts, i.e., the nodes. The heat transfer values are represented as resistances and the thermal masses as capacitances in the LPTN. Thermal parameter values are calculated using heat transfer theory-based analytical equations and motor geometry and material information data. The other essential input to the LPTN models for calculating the temperature are the electro-mechanical power conversion losses, such as winding losses, core losses, and mechanical and windage losses. Equation (1) represents the differential equation that represents the heat balance for each node in a thermal equivalent circuit diagram.