## 4 Magnetic Field Analysis under MTPA and Field Weakening Control Strategy  
Figure 4 shows the vector control system used in this section to analyze the core loss under different working conditions [24; 25; 26; 27; 28]. During the operation of the motor, affected by different armature currents, the changes in the magnetic flux density at various internal positions are quite different, and detailed analysis of the magnetic field at different positions under various operating conditions is required. For this motor, its operating characteristic curve and drive control mode under different working conditions are shown in Figure 5. The motor ran at low speed with constant torque and at high speed with constant power. In constant torque operation (0-3200 rpm), the winding current was 579.4 A, the current angle was 28.33\({}^{\circ}\), the terminal voltage was gradually increased to 440 V, the motor achieved \begin{table}
\begin{tabular}{c c c} \hline \hline
**Working Point** & **Without Considering Magnetic Saturation** & **Considering Magnetic Saturation** \\ \hline
1660 Nm/1000 rpm & 4.08\% & 4.39\% \\
1660 Nm/3200 rpm & 3.7\% & 4.42\% \\
1110 Nm/3200 rpm & 5.29\% & 5.51\% \\
588 Nm/6000 rpm & 6.9\% & 7.55\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The total harmonic distortion rate of the phase current of the motor with and without considering the magnetic saturation effect. Figure 4: Vector control system of PMSM. maximum torque current ratio operation, and the output rated torque was 1134 Nm; in field weakening control Area (3200-6000 rpm), the direct-axis current Id kept increasing, the quadrature-axis current Iq kept decreasing, the current angle gradually increased, the terminal voltage remained unchanged at 440 V, and the motor output rated power was 370 kW. The torque, power, current, and internal power factor angle (\(\psi\)) of the motor operating points (1000, 2000, 3200, 4000, 5000, and 6000 rpm) under different working conditions are shown in Table 3.  
It can be seen from Table 3 that in the field weakening control zone, as the speed increased, due to the decrease of the quadrature axis current \(I\)q, the phase current \(I\)s synthesized by Id and Iq gradually decreased, and the speed continued to increase; although the alternating current The shaft current \(I\)q continued to decrease, the effect of the increase in the direct-axis current \(I\)d was more obvious, and the phase current \(I\)s began to rise again. Figure 6 shows the distribution of magnetic field lines and air gap radial flux density when the motor was under no-load and field weakening control (3200 rpm, 6000 rpm) output rated power. When there was no load, there is no stator current, only the permanent magnet of the rotor provides the magnetomotive force, and the air-gap flux density waveform was close to a rectangular wave; in the field weakening control, the d-axis current gradually increases with the increase of the speed to weaken the magnetic field. Compared with the magnetic field at 3200 rpm, the magnetic field was significantly weakened at 6000 rpm. The air gap radial flux density changes of the motor with no load and load are shown in Figures 7 and 8. Figure 7 shows the air gap flux density under the armature reaction when the rotor permanent magnet magnetic field was not considered. Figure 8 shows the air gap flux density when the rotor permanent magnet magnetic field and the armature reaction magnetic field were combined. d-axis current Id increased, the d-axis current demagnetized. Obviously, the air gap flux density gradually decreased. Under different working conditions, the control mode of the motor is different, and the flux density waveform in the stator core also changes under the action of the armature reaction.