## 3 Simulation Results
### Simulation Results in a Circuit with FOC at Rated Motor Shaft Rotation Frequency  
The performance of the traction drive system with FOC was investigated at the nominal rotor speed of the motor under five different 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 investigations were carried out at a fixed and adapted filter cut-off frequency to the motor shaft rotation speed. The simulation was carried out for the following conditions:  
* Inverter supply voltage \(\mathrm{U_{d}}=\surd\cdot\mathrm{U_{nom}}=2645\) V.
* PWM frequency \(\mathrm{f_{PWM}}=20\cdot\mathrm{f_{nom}}=1116\) Hz. * Static drive torque \(\mathrm{T_{c}}=10\),\(324\) N\(\cdot\)m.
* Angular frequency of the motor supply voltage in steady mode \(\mathrm{\omega_{r}}=348.7\) rad/s, which corresponds to the nominal frequency of the supply voltage \(\mathrm{f_{nom}}=55.8\) Hz. * Acceleration of the motor shaft rotation is chosen to be equal to \(\mathrm{\omega_{\omega}}=0.333\) rad/s\({}^{2}\). * The delay time of the speed controller is chosen to be equal to 0.7 s.  
From the time diagrams of the torque in stable mode, we obtained maximum (\(\mathrm{T_{max}}\)) and minimum (\(\mathrm{T_{min}}\)) torque values (Appendix A). Based on these values, we calculated the average values (\(\mathrm{T_{av}}\)), the ripple values (\(\mathrm{\Delta T_{av}}\)), and the ripple factor (\(\mathrm{k_{p}}\)) of the torque. The average torque value was calculated by the formula:  
\[\mathrm{T_{av}}=\frac{\mathrm{T_{max}}+\mathrm{T_{min}}}{2} \tag{15}\]  
The magnitude of the torque ripple was calculated as follows:  
\[\mathrm{\Delta T_{av}}=\mathrm{T_{max}}-\mathrm{T_{min}} \tag{16}\]The torque ripple factor was calculated as follows:  
\[\mathrm{k_{p}}=\frac{\mathrm{\Delta T_{av}}}{2\cdot\mathrm{T_{av}}} \tag{17}\]  
Since the drive has symmetrical windings and symmetrical inverter arms \(\mathrm{I_{sa}}=\mathrm{I_{sb}}=\mathrm{I_{sc}}=\mathrm{I_{s}}\), for all five cases in stable mode, the amplitude-frequency spectrum was calculated for the stator in phase a, on the basis of which the THD was calculated for the first 40 harmonics using the formula [28]:  
\[\mathrm{TDH}=\frac{\sqrt{\sum_{i=2}^{40}\mathrm{I_{s(i)}^{2}}}}{\mathrm{I_{s1 }}}\cdot 100\% \tag{18}\]  
where \(\mathrm{I_{s(i)}}\) is the higher harmonics of the stator phase current. For all five cases in the stable mode, the values of the consumed current \(\mathrm{I_{d}}\) were determined on the simulation model. Based on the obtained values of the consumed current \(\mathrm{I_{d}}\) the values of the consumed power \(\mathrm{P_{1}}\) were calculated (Appendix C). As a result of the simulation, the values of the motor shaft rotation frequency were also obtained for all cases \(\mathrm{n_{r}}\). The calculated useful motor shaft power was determined as follows:  
\[\mathrm{P_{2}}=\mathrm{T_{av}}\cdot\omega_{r}=\mathrm{T_{av}}\cdot\frac{2 \cdot\pi\cdot n_{r}}{60} \tag{19}\]  
The efficiency of the output section of the drive is calculated as follows:  
\[\mathrm{\eta}=\frac{\mathrm{P_{2}}}{\mathrm{P_{1}}}\cdot 100\% \tag{20}\]  
The convergence time was calculated based on the following considerations. It would be an optimal solution to determine the convergence time under the condition of coincidence of the forms of the stator phase currents with the desired forms of these quantities. The desired forms can be the forms of the stator currents obtained when the induction motor is powered from a sinusoidal voltage system. In the simulation model, such a system of phase currents can be easily obtained by replacing a three-phase inverter with a three-phase system of supply voltages.