## 2 High-Frequency Current Harmonics Analysis of HPMSM  
In order to analyze the high-frequency current harmonics of HPMSM, it is necessary to establish its mathematical model. The mathematical model of PMSM is studied in [31]. Because the circuit topology is the same, this model is also applicable to HPMSM. The voltage equation for the three-phase winding of HPMSM in the three-phase coordinate system can be written as  
\[u_{A}=Ri_{A}+\frac{d\psi_{A}}{dt}, \tag{1}\]  
\[u_{B}=Ri_{B}+\frac{d\psi_{B}}{dt}, \tag{2}\]  
\[u_{C}=Ri_{C}+\frac{d\psi_{C}}{dt}. \tag{3}\]  
where \(u_{A}\), \(u_{B}\), \(u_{C}\) represent three-phase voltages respectively; \(i_{A}\), \(i_{B}\), \(i_{C}\) represent three-phase currents; \(\psi_{A}\), \(\psi_{B}\), \(\psi_{C}\) represent three-phase flux linkages. \(R\) is the stator winding resistance. The HPMSM is a complex nonlinear system, and, for its high-performance control, vector control methods are proposed, which require the reconstruction of the motor mathematical model in the \(d\)-\(q\) coordinate system. By using Clark transformation and Park transformation, the following current expression in \(d\)-\(q\) coordinate system is obtained as  
\[ \begin{bmatrix}i_{d}\\ i_{q}\end{bmatrix} =\frac{2}{3} \begin{bmatrix}\cos\theta_{e}&\cos(\theta_{e}- \frac{2\pi}{3})&\cos(\theta_{e}+\frac{2\pi}{3})\\ -\sin\theta_{e}&-\sin(\theta_{e}-\frac{2\pi}{3})&-\sin(\theta_{e}+\frac{2\pi}{ 3})\end{bmatrix}\begin{bmatrix}i_{A}\\ i_{B}\\ i_{C}\end{bmatrix} . \tag{4}\]  
where \(i_{d}\), \(i_{q}\) are the stator currents in \(d\)-\(q\) axis; \(\theta_{e}\) is the electrical angle of the rotor. The flux linkage equation in \(d\)-\(q\) coordinate system can be expressed as  
\[ \begin{cases}\psi_{d}=L_{d}i_{d}+\psi_{f}\\ \psi_{q}=L_{q}i_{q}\end{cases} , \tag{5}\]  
where \(\psi_{d}\), \(\psi_{q}\) are the flux linkages in \(d\)-\(q\) axis; \(L_{d}\), \(L_{q}\) are the winding inductances in \(d\)-\(q\) axis; \(\psi_{f}\) is the flux linkage generated by the permanent magnet. The voltage equation in \(d\)-\(q\) coordinate system is  
\[ \begin{cases}u_{d}=Ri_{d}+L_{d}\frac{di_{d}}{dt}-\omega_{e}L_{q}i_{q}\\ u_{q}=Ri_{q}+L_{q}\frac{di_{q}}{dt}+\omega_{e}(L_{d}i_{d}+\psi_{f})\end{cases} , \tag{6}\]  
where \(u_{d}\), \(u_{q}\) are the \(d\)-axis and \(q\)-axis stator voltages; \(\omega_{e}\) is the electrical angular speed of the rotor. For the purpose of achieving efficient control of the HPMSM, a drive control method based on the SVPWM technology is used. The SVPWM drive voltage signal contains a large number of PWM harmonics and their sideband components in steady-state operation, and the odd and even times sideband harmonics of the carrier wave have different variation patterns, respectively. The harmonic frequency contained in the three-phase stator currents can be expressed as [9]  
\[nf_{s}\pm f_{b}, \tag{7}\]  
where \(f_{s}\), \(f_{b}\) are the switching frequency and fundamental frequency, respectively; \(n\), \(k\) are the harmonic orders of the switching frequency and the fundamental frequency, respectively. When \(n\) is odd, \(k\) is a positive even number that is not an integer multiple of 3. When \(n\) is even, \(k\) is a positive odd number that is not an integer multiple of 3. Set \(f_{s}\) to 10 kHz and \(f_{b}\) to 500 Hz; the three-phase current harmonics are plotted in Figure 1. The Harmonics with high content are marked in red, and the other harmonics are represented by blue bars. As shown in the figure, the main current harmonics appear in the vicinity of the switching frequency, which is consistent with (7). The current harmonic content is further studied in [9], where the amplitude of the first and second harmonic sidebands have been obtained as  
\[\left\{ \begin{aligned} I_{s,\omega_{s}\pm 2\omega_{b}}& =\frac{U_{dc}\sqrt{M_{2}^{2}+N_{1}^{2}+2M_{2}N_{1}\text{cos}(2\varphi _{0})}}{8\pi(f_{s}\pm 3f_{b})}\\ I_{s,\omega_{s}\pm 4\omega_{b}}&=\frac{U_{dc}\sqrt{M_{1}^{ 2}+N_{2}^{2}+2M_{1}N_{2}\text{cos}(2\varphi_{0})}}{8\pi(f_{s}\pm 3f_{b})} \end{aligned} \right., \tag{8}\]  
\[\left\{