## 2 Materials and Methods
### Development of a Simulation Model of the Traction Drive Without a Control System
The ratio between the phase and linear voltages is as follows:\[\mathrm{U_{BA}}=\sqrt{3}\cdot\mathrm{U_{sm}}\cdot\sin\left(\theta_{\mathrm{r}}+ \frac{\pi}{6}\right);\ \mathrm{U_{CB}}=\sqrt{3}\cdot\mathrm{U_{sm}}\cdot\sin\left(\theta_{\mathrm{r}}- \frac{2\cdot\pi}{3}+\frac{\pi}{6}\right);\ \mathrm{U_{AC}}=\sqrt{3}\cdot\mathrm{U_{sm}}\cdot\sin\left(\theta_{\mathrm{r}}+ \frac{2\cdot\pi}{3}+\frac{\pi}{6}\right) \tag{13}\]  
Therefore, to account for the phase shift when transitioning from phase linear to voltages, the phase of each linear voltage in the system of Equation (13) should be reduced by an angle of \(\pi/6\). To match the amplitude levels when transitioning from phase linear to voltages, each amplitude of the linear voltage in the system of Equation (13) should be divided by \(\sqrt{3}\). Then, after fulfilling the above conditions for the system of Equation (13) and after substituting expression (12) into it instead of the amplitudes of the phase voltages, the system of reference phase voltages will be as follows:  
Figure 5:0  
That is, the simulation model of the traction drive with FOC and reactive power compensator must be supplemented with a block for implementing Equation (14). The comprehensive simulation model of the traction drive output section without FOC (Figure 6) is supplemented with the \"FOC\" unit, from which the following signals are derived:  
* \(\mathrm{u_{a\_PWM}}\), \(\mathrm{u_{b\_PWM}}\), \(\mathrm{u_{b\_PWM}}\) are the autonomous voltage inverter control signals. * \(\mathrm{teta_r}\) is the angle of coordinate plane rotation in the field-oriented control system. * \(\mathrm{w_{k}}\) is the angular velocity of coordinate plane rotation in the field-oriented control system. It should also be noted that \(\mathrm{w_{k}}\) signal in the \"FOC\" unit is determined in relative units. Therefore, in the \"Control unit for compensation of higher voltage harmonics\", this signal is multiplied by the nominal value of the electrical angular frequency--350 rad/s. The traction motor of the STA-1200 series has a nominal power output of 1200 kW. Consequently, conducting experimental research on a locomotive traction drive is energy-intensive and, therefore, costly. Moreover, integrating hardware components that implement the proposed technical solutions requires formal approvals from both the manufacturer and operating organizations. As a result, testing the proposed solutions on existing rolling stock presents significant challenges. The development of a prototype is further hindered by the following factors:  
1. Developing a full-scale model of a traction drive using a real traction motor, as previously noted, is highly energy-intensive and financially demanding. 2. Constructing a scaled-down model of a traction drive is also challenging due to the following consideration: in contrast to conventional industrial asynchronous motors, traction motors are designed to operate at frequencies exceeding their nominal values. To develop a scaled prototype, it would be necessary to manufacture a custom motor with appropriately scaled parameters. However, producing a prototype asynchronous motor is equally costly, as such a product would be considered non-standard and non-serial by the manufacturer. The use of a standard industrial asynchronous motor to develop a scaled-down prototype of the traction drive may yield inaccurate results when operating at frequencies above the motor's nominal range. Therefore, in this study, the authors have limited the scope of the investigation to simulation-based modeling only. In summary, the following key contributions should be highlighted based on the results presented in this section. In contrast to previous studies focused on harmonic voltage compensation in power systems with linear loads [40], this work introduces the following original contributions:It is proposed to perform harmonic compensation not in the system of line voltages but directly within the stator phase voltages of the inverter.