## 3 Global Loss Model of PMSM
### Harmonic Motor Loss
}^{\infty}I_{s\_mn}^{2}\cdot R_{s\_mn}\right] \tag{38}\]  
From Equation (26), it can be seen that the harmonic iron loss is affected by the frequency of magnetic field and amplitude of magnetic flux density. As the magnetic flux density is different between stator tooth and yoke, the harmonic iron loss can be presented as:  
\[P_{Fe\_mn}=P_{Fe\_l\_mn}+P_{Fe\_y\_mn}=dP_{Fe\_l\_mn}\cdot V_{t}+dP_{Fe\_y\_mn} \cdot V_{y} \tag{39}\]  
where \(V_{t}\) and \(V_{y}\) is the total volume of stator tooth and stator yoke, respectively. \(dP_{Fe\_t\_mn}\) is the iron loss density of the \(n\)-th fundamental signal and the \(m\)-th carrier signal in the stator tooth, which is shown as:  
\[dP_{Fe\_t\_mn}=dP_{Fe\_h\_t\_mn}+dP_{Fe\_d\_t\_mn}=k_{h}B_{m\_t\_mn}^{2} \cdot V_{t}+dP_{Fe\_y\_mn}^{2}\cdot V_{y} \tag{40}\]  
where \(f_{mn}\) is the frequency of the \(n\)-th fundamental signal and the \(m\)-th carrier signal, and \(B_{m\_t\_mn}\) is the amplitude of harmonic magnetic flux density in the stator tooth:  
\[B_{m\_t\_mn}=\frac{\Phi_{mn}}{\frac{\alpha_{i}\cdot Q\cdot S_{t}}{2n_{p}}} \tag{41}\]  
where \(\alpha_{i}\) is the pole arc factor, \(Q\) is the number of slot, \(S_{t}\) is the physical area of a stator tooth. As the harmonic fluxes can be obtained from harmonic flux linkage as:  
\[\Phi_{mn}=\frac{\Psi_{mn}}{N_{1}\cdot K_{dp\_mn}} \tag{42}\]  
where \(N_{1}\) is the number of turns per phase, and \(K_{dp\_mn}\) is the harmonic winding factor. Therefore, from Equations (40)-(42), the harmonic iron loss in the stator tooth can be expressed as:  
\[P_{Fe\_t\_mn}=\left[k_{h}\left(\frac{\Psi_{mn}}{N_{1}\cdot K_{dp\_mn}\frac{ \alpha_{i}QS_{t}}{2n_{p}}}\right)^{2}f_{mn}+\frac{\pi^{2}\sigma k_{d}^{2}}{6} \left(\frac{\Psi_{mn}}{N_{1}\cdot K_{dp\_mn}\frac{\alpha_{i}QS_{t}}{2n_{p}}} \right)^{2}f_{mn}{}^{2}\right]\cdot V_{t} \tag{43}\]  
Similar to the calculation of magnetic flux density in the stator tooth, the magnetic flux density in the stator yoke can be:  
\[B_{m\_y\_mn}=\frac{\Psi_{mn}}{\frac{1}{2}N_{1}\cdot K_{dp\_mn}\cdot S_{y}} \tag{44}\]  
where \(S_{y}\) is the physical areas of a stator tooth. From Equations (39) and (44), the harmonic iron loss in the stator yoke can be calculated as:  
\[P_{Fe\_y\_mn}=\left[k_{h}\left(\frac{\Psi_{mn}}{\frac{1}{2}N_{1}\cdot K_{dp\_ mn}\cdot S_{y}}\right)^{2}f_{mn}+\frac{\pi^{2}\cdot\sigma\cdot k_{d}^{2}}{6} \left(\frac{\Psi_{mn}}{\frac{1}{2}N_{1}\cdot K_{dp\_mn}\cdot S_{y}}\right)^{2 }f_{mn}{}^{2}\right]\cdot V_{y} \tag{45}\]  
Therefore, the harmonic iron loss can be expressed as:\[ \begin{array}{ll}P_{Fe\_mn}&=P_{Fe\_t\_mn}+P_{Fe\_y\_mn}\\ &=\Bigg{[}k_{h}\Bigg{(}\frac{L_{\text{\tiny{mg}}}I_{\text{\tiny{gs,mn}}}}{N_{1} \cdot K_{dp\_mn}\frac{\alpha_{s}Q_{\text{\tiny{g}}}}{2\pi p}}\Bigg{)}^{2}f_{mn} +\frac{\pi^{2}\sigma k_{\text{\tiny{g}}}^{2}}{6}\Bigg{(}\frac{L_{\text{\tiny{mg}}}I _{\text{\tiny{gs,mn}}}}{N_{1}\cdot K_{dp\_mn}\frac{\alpha_{s}Q_{\text{\tiny{g}}} }{2\pi p}}\Bigg{)}^{2}f_{mn}{}^{2}\Bigg{]}\cdot V_{\text{f}}\\ &+\Bigg{[}k_{h}\bigg{(}\frac{L_{\text{\tiny{mg}}}I_{\text{\tiny{gs,mn}}}}{2N_{1} \cdot K_{dp\_mn}\cdot S_{\text{\tiny{g}}}}\bigg{)}^{2}f_{mn}+\frac{\pi^{2} \sigma k_{\text{\tiny{g}}}^{2}}{6}\bigg{(}\frac{L_{\text{\tiny{mg}}}I_{\text{ \tiny{gs,mn}}}}{2N_{1}\cdot K_{dp\_mn}\cdot S_{\text{\tiny{g}}}}\bigg{)}^{2}f_{ mn}{}^{2}\Bigg{]}\cdot V_{\text{y}}\end{array}