## 1 Introduction  
The railway sector remains one of the most energy-intensive branches of the economy. The largest share of energy consumption in rail transport is attributed to train traction, specifically to the operation of the traction drive systems of rolling stock. Therefore, improving the technical and operational performance of rolling stock by reducing energy consumption is a strategic priority for railways in every country worldwide [1, 2]. The traction drive of railway rolling stock is the single largest consumer of energy within the railway infrastructure. Consequently, enhancing its energy performance con stitutes the highest-priority direction in addressing the challenge of reducing energy consumption in the railway transport sector [3,4]. Addressing this challenge is further complicated by the operational characteristics of rolling stock. During service, the dynamic properties of the rolling stock are subject to continuous variation [5, 6, 7]. This results in continuous fluctuations in load, which in turn lead to persistent transient processes and, consequently, to a reduction in the energy efficiency of the traction drive system of the rolling stock. Asynchronous motors [8], synchronous motors [9,10], and series-excited direct current motors [11] are used as traction machines in the traction drive systems of rolling stock. Among these, asynchronous (induction) motors are the most widely applied in traction systems for railway transport. The traction drive system with asynchronous motors can be conventionally divided into two main components: the input stage and the output stage. The output stage, which includes the traction motors and output power converters, accounts for the largest share of energy consumption within the traction system. Therefore, this study focuses exclusively on the output stage of the traction drive for subsequent analysis and modeling. The output power converter in the traction drive system is implemented as a standalone inverter. Its operation is typically controlled using a pulse-width modulation (PWM) algorithm. This control approach introduces higher-order current harmonics into the output stage of the traction drive. Although increasing the PWM switching frequency reduces the amplitude of these harmonics, it simultaneously leads to greater switching losses in the inverter's power transistors [12]. Moreover, the switching frequency of traction inverters is typically limited to 1 kHz [12], which is significantly lower than that of general-purpose drives. As a result, power losses in the traction drive system of rolling stock increased substantially. An analysis of operational factors and the structure of traction drive components reveals the following:  
1. Non-linear current-voltage characteristics of the inverter's power transistors are primary sources of higher-order current harmonics. 2. Variations in the dynamic behavior of the train lead to instability in the loading conditions of the traction drive. This results in continuous transient processes within the system, which in turn affect the harmonic content of the stator phase currents in the traction motor. The presence of higher-order harmonics in the stator phase voltages of an asynchronous motor leads to increased power losses within the machine. This effect can be attributed to the following factors:  
* An increase in the temperature of the motor windings [13], which results in a rise in their ohmic resistance. * An increase in magnetic (core) losses in the motor steel laminations [14], which are frequency-dependent and grow with the order of the harmonic components. In addition, the presence of higher-order harmonics in the stator phase voltages causes torque ripple generation [15], which leads to power losses in the mechanical part of the drive. It should also be noted that the temperature rise in the motor windings--induced by the higher-order harmonic components of the phase currents--can result in insulation overheating. This reduces the motor's reliability and may ultimately lead to fault conditions or failure.