## 1 Introduction
The analysis indicates that improving the energy efficiency of the traction drive requires targeted measures to mitigate higher-order harmonics in the stator phase current spectra of the traction motor. In electrical systems, this is typically achieved through the implementation of various reactive power compensators. The power stage of such compensators is commonly realized in the form of active filters [16; 17]. According to [PERSON]'s theorem [18], filtering can be performed either in the frequency domain or in the time domain. In the context of active filter control systems used in reactive power compensators, adaptive filtering techniques are employed to implement frequency-domain filtering. These techniques include the least mean squares (LMSs) adaptive method [19; 20; 21], predictive filtering based on forecasting of the controlled variable [22; 23], as well as Kalman filtering [24; 25] and Wiener filtering [26; 27]. The methods generally offer higher filtering accuracy compared to time-domain approaches; however, they also present several critical limitations. The first limitation is associated with low convergence rates, leading to prolonged transient behavior during filter adaptation [28]. This issue is particularly relevant in traction drive systems, where unstable operating modes frequently occur due to varying service conditions of the rolling stock. The second limitation also arises from operational characteristics. Traction drives typically utilize either Field-Oriented Control (FOC) [29] or direct torque control (DTC) [30; 31]. In both cases, the stator phase voltage frequency is proportional to the rotor speed of the asynchronous motor, which continuously varies during operation. This variability complicates the synthesis of accurate stator current reference signals required for implementing adaptive filtering algorithms. Time-domain filtering methods offer faster convergence and facilitate easier synthesis of reference signals for stator phase currents. When using time-domain filtering, control systems for active power filters can be developed based on strategies such as the instantaneous reactive power compensation scheme (p-q control) [31; 32; 33; 34] and the instantaneous active and reactive current control scheme (I\({}_{\text{d}}\)-I\({}_{\text{q}}\) control) [35; 36; 37]. A common feature of the control strategies is the calculation and extraction--via appropriate filters--of the reactive power to be compensated. Based on this quantity, control signals for the active power filter are synthesized. In harmonic compensation scenarios, where the source of distortion is non-linear loading, low-pass filters are typically employed. To attenuate higher-frequency voltage harmonics, filters with higher cut-off frequencies are used. The studies cited in this context frequently utilize Butterworth filters of the fourth or fifth order. In addition to the commonly used Butterworth approximation, other filter approximations exist, including the Chebyshev [38], Cauer (elliptic) [38], and Bessel [39] types. These approximations serve as the basis for synthesizing Chebyshev Type I and Type II filters, Cauer (elliptic) filters, and Bessel filters. Each of these filter types exhibits different ripple characteristics within both the passband and the stopband, as well as different transition bandwidths between these regions. These factors directly influence filtering quality and, consequently, the performance of the reactive power compensator. A key limitation observed in the reviewed studies on time-domain reactive power compensation methods is the use of filters with fixed cut-off frequencies. Given that the supply voltage frequency in traction drive systems is subject to continuous variation, employing filters with static cut-off frequencies is inappropriate in such applications, as this introduces filtering errors. This, in turn, reduces the effectiveness of reactive power compensation.