## 5 Simulation Analysis  
For the purpose of verifying the effectiveness of the proposed harmonic suppression strategy for HPMSM based on the LC filter and ANF, the simulations based on MATLAB/Simulink R2020b are carried out. The simulation model of the proposed scheme is shown in Figure 14. To ensure the reliability of the simulation, the same parameters are used in the simulation and experiment, as detailed in Table 1. The parameters of the PI controller are selected as follows: \(K_{p\omega}\) is 0.5, \(K_{i\omega}\) is 20; \(K_{pd}\), \(K_{pq}\) are 0.1, and \(K_{id}\), \(K_{iq}\) are 200. In the simulation, the load torque is 0.5 N m, and the rotor speed is 8000 rpm, which is equivalent to 20,000 rpm for a 2-pair pole motor.  
Figure 15 gives the three-phase current waveforms and the FFT analysis using different schemes, where Figure 15a is without the harmonic suppression method; Figure 15b adopts the harmonic suppression method based on the LC filter; Figure 15c adopts the traditional active damping method based on proportional feedback of capacitance current, and Figure 15d adopts the harmonic suppression method based on the LC filter and ANF. It should be noted that in order to make it easier for readers to distinguish the content of each harmonic, the FFT waveforms have different scales.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Symbol** & **Value** \\ \hline Power rating & \(P_{n}\) & 730 W \\ Pole pairs & \(\mathrm{P}_{n}\) & 5 \\ Permanent magnetic linkage & \(\psi_{f}\) & 0.0509 Wb \\ Rated speed & \(\omega_{n}\) & 10,000 rpm \\ Rotor diameter & \(\mathrm{D}_{r}\) & 28 mm \\ Stator resistance & \(R_{b}\) & 1.41 \(\Omega\) \\ \(D\)-axis stator inductance & \(L_{\rm d}\) & 0.8 mH \\ \(Q\)-axis stator inductance & \(L_{\rm q}\) & 0.8 mH \\ Rotor inertia & \(\int\) & 0.0005 kg\(\cdot\)m\({}^{2}\) \\ ANF step size & \(\mu\) & 0.02 \\ Filter inductance & \(L_{\rm l}\) & 0.3 mH \\ Filter capacitance & \(C\) & 4.7 \(\mu\)F \\ Switching frequency & \(f_{\rm s}\) & 10 kHz \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of HPMSM Control System.  
Figure 13: \(Q\)-axis ANF structure.  
Figure 14: The simulation model of proposed scheme.  
Figure 15: Simulation results of three-phase current waveforms and FFT analysis at 8000 rpm with 0.5 N-m load: (**a**) without LC filter; (**b**) with LC filter; (**c**) with LC filter and traditional active damping method; (**d**) with LC filter and ANF.  
By simulation, it can be seen that the phase current in Figure 15a is obviously distorted due to the existence of harmonic current. The current harmonics of HPMSM are considerably large, with a total harmonic content of 13.8%. The harmonics are mainly distributed around the integer multiples of the switching frequency, and the distribution law satisfies (7). When the LC filter is introduced, the high-frequency jitter of the current is suppressed; however, the sinusoidality of the waveform decreases. From FFT analysis, it is clear that the use of the LC filter effectively suppresses the high-frequency harmonics, but it brings the system resonance peak as shown by the red column in Figure 15b. The amplitude of the resonance peak reaches 22%. Consequently, the total harmonic content of the system increases instead. From Figure 15c,d, it can be seen that, with the use of the active damping method, the current waveform becomes smooth, and the sinusoidality improves dramatically. The resonant peak is suppressed extremely well, and the resonance peak has completely disappeared. At the same time, it can be concluded that the damping capacity of the two schemes are almost the same, and they both make the three-phase current harmonic content of the HPMSM drops to about 4%, which is 10% lower than the case without filtering. In contrast, the ANF is more advantageous because it does not require additional sensors. Therefore, the simulation results prove the effectiveness of the proposed scheme.