## 3 Simulation Results
### Simulation Results in a Circuit with FOC at Rated Motor Shaft Rotation Frequency
* Static drive torque \(\mathrm{T_{c}}=10\),324 N\(\cdot\)m.
* Angular rotation frequency of the motor shaft in a stable mode \(\omega_{\mathrm{r}}=174.6\) rad/s, which corresponds to the nominal frequency of the supply voltage \(\mathrm{f_{nom}}=27.9\) Hz. * Since in FOC \(\psi_{\mu}=\mathrm{const}\), \(\omega_{\mathrm{r}}=0.5\cdot\omega_{\mathrm{mom}}\), then in accordance with Equation (1), the supply voltage of the inverter \(\mathrm{U_{d}}=0.5\cdot\sqrt{2}\cdot\mathrm{U_{nom}}=1322.5\) V.
* Acceleration of the motor shaft rotation is chosen equal to \(\mathrm{a_{\omega}}=0.333\) rad/s\({}^{2}\). * Delay time of switching on the speed controller is chosen equal to \(0.7\) s.  
The analysis of the results presented in Table 4 showed that the drive circuit with FOC in the presence of a compensator with elliptic filter with adapted cut-off frequency has the highest efficiency value, as well as the lowest values of the torque ripple factor and convergence time in stable mode. However, the Bessel filter has a minimum convergence time during motor acceleration. The presence of filters with adapted cut-off frequency in the compensator compared to a fixed frequency leads to:  
* Increase in drive efficiency. * Reduction in torque ripple factor both in stable mode (Table 4) and during motor acceleration. * Reduction in THD. * Reduction in convergence time both for stable mode and for motor acceleration. \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Parameter** & & & & & & & & & & & & \\ \hline Average torque value \(\mathrm{T_{av}}\), N-m & 10,320 & 10,320 & 10,320 & 10,320 & 10,320 & 10,320 & 10,320 & 10,320 & 10,320 & 10,320 \\ Torque ripple value \(\mathrm{\Delta T_{av}}\), N-m & 20.31 & 15.51 & 21.21 & 15.77 & 21.19 & 15.79 & 17.57 & 20.21 & 19.85 & 14.59 \\ Torque ripple factor \(\mathrm{k_{p}}\), \% & 0.32 & 0.3 & 0.158 & 0.15 & 0.158 & 0.151 & 0.158 & 0.157 & 0.158 & 0.145 \\ Motor shaft rotation frequency & 548 & 548 & 548 & 548 & 548 & 548 & 548 & 548 & 548 & 548 \\ Useful power \(\mathrm{P_{2}}\), kW & 592.2 & 592.2 & 592.2 & 592.2 & 592.2 & 592.2 & 592.2 & 592.2 & 592.2 & 592.2 \\ Consumed current \(\mathrm{I_{d}}\), A & 485.83 & 484.95 & 485.44 & 484.9 & 485.23 & 484.52 & 484.68 & 484.41 & 484.79 & 484.14 \\ Consumed power \(\mathrm{P_{1}}\), kW & 667.2 & 666.0 & 666.7 & 665.9 & 666.4 & 665.39 & 665.62 & 665.77 & 664.87 \\ THD, \% & 1.65 & 1.46 & 1.63 & 1.45 & 1.5 & 1.44 & 1.42 & 1.41 & 1.39 & 1.36 \\ Efficiency \(\mathrm{P_{1}}\), \% & 88.76 & 88.92 & 88.83 & 88.93 & 88.87 & 89.0 & 88.97 & 89.02 & 88.95 & 89.05 \\ Convergence time for stable mode \(\mathrm{t_{conv\_st}}\), s & 0.304 & 0.214 & 0.296 & 0.211 & 0.252 & 0.212 & 0.246 & 0.222 & 0.239 & 0.197 \\ Convergence time for motor acceleration \(\mathrm{t_{conv\_dc}}\), s & 2.2 & 0.545 & 2.2 & 0.528 & 2.2 & 0.534 & 2.2 & 0.317 & 2.2 & 0.428 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Calculation results of the parameters of the traction drive output section with FOC in the presence of a compensator (when the motor supply frequency in stable mode is less than the nominal frequency). Simulation Results in a Circuit with FOC at a Steady Motor Shift Rotation Frequency, Which Is Greater than the Nominal  
The operation of the traction drive system with FOC was studied at the nominal shaft rotation frequency of the motor for five scenarios: with a Butterworth filter in the reactive power compensator, with a direct Chebyshev filter in the reactive power compensator, with an inverse Chebyshev filter in the reactive power compensator, with a Bessel filter in the reactive power compensator, with an elliptic filter in the reactive power compensator. For the circuits with compensators, the studies were conducted at a fixed and adapted filter cut-off frequency to the motor shaft rotation frequency. The simulation was carried out for the following conditions:  
* PWM frequency \(\mathrm{f_{PWM}}\) = 20-f\({}_{\mathrm{nom}}\) = 1116 Hz.