## 2 Modeling the Electric Drive Transmission System  
### Equivalent Magnetic Network Model of DTP-PMSM  
The equivalent magnetic network model, or permeance network model, decomposes an electromagnetic system into multiple magnetic flux tubes according to magnetic paths. Each flux tube is characterized by one or more magnetic permeabilities. These permeabilities, along with the magnetic flux they convey and the magnetic potential at their endpoints, form the fundamental unit of the network. The mathematical model is grounded in the core principles of electromagnetism and [PERSON]'s magnetic circuit law. Figure 1 depicts the partial equivalent magnetic network model of the non-phase shift DTP-PMSM. This model includes the stator's primary magnetic flux path, represented by permeances for the stator yoke (\(G_{sb}\)), stator teeth (\(G_{st}\)), and inter-tooth regions (\(G_{stst}\)). \(F_{sb}\) and \(F_{st}\) represent the nodal magnetomotive potentials of the stator yoke and teeth, respectively, with \(i_{s}\) as the magnetic potential source from the stator winding. The rotor's permeances and nodal magnetomotive potentials are similarly defined. The formula for calculating the stator's main magnetic permeability is provided in [12]. The rotor's main magnetic permeability parameters can be expressed as follows [12; 19; 20]:  
\[G_{r,j}=\frac{4\mu_{0}h_{m}L}{\pi(r_{od}-h_{m})} \tag{1}\]  
\[G_{b,j}=\frac{4\mu_{fe}(r_{od}-r_{id}-2h_{m})L}{\pi(r_{od}+r_{id}-2h_{m})} \tag{2}\]  
In the equation, \(\mu_{fe}\) and \(\mu_{0}\) denote the magnetic permeability of the motor core iron and air, \(r_{od}\) and \(r_{id}\) represent the rotor outer and inner diameters, \(h_{m}\) specifies the magnetization thickness of the permanent magnet, and \(L\) defines the machine's axial length. A permanent magnet can be modeled and represented as a magnetomotive force (MMF) source in series with a magnetic permeance component, as derived from Equation (3) [21]. Given that the magnetic permeability of air is significantly lower than  
Figure 1: Simplified equivalent magnetic network model of motor components: (a) stator; (b) rotor. that of electrical steel, this study deliberately disregards flux leakage paths in the magnet's flux barriers. \[\left\{ \begin{array}{l}F_{m,j}=H_{c}h_{m}\\ G_{m,j}=\frac{h_{0}h_{m}h_{m}L_{m}}{h_{m}}\end{array} \right. \tag{3}\]  
where \(F_{m}\) denotes the equivalent magnetomotive force source, \(G_{m}\) represents the equivalent magnetic permeance, \(H_{c}\) is the coercive force of the permanent magnet, \(h_{m}\) defines the magnetizing direction length, \(b_{m}\) indicates the permanent magnet width, \(L_{m}\) specifies the axial length, \(\mu_{0}\) is the permeability of free space, and \(\mu_{r}\) signifies the recoil permeability of the permanent magnet. The air-gap permeance is influenced by the relative positioning of the stator and rotor. In the non-phase shift DTP-PMSM, the rotor maintains complete circumferential symmetry. This design assumes that magnetic flux moves vertically between the stator tooth tips and the rotor surface, allowing both to be considered magnetic equipotential surfaces. The rotor is discretized into \(N_{r}\) equivalent rotor teeth, while the stator comprises \(N_{s}\) teeth. Figure 2 depicts the relative position of stator tooth (\(i\)) and equivalent rotor tooth (\(j\)) during rotation. The air-gap permeance \(G_{gap}\)(\(i\),\(j\)) is determined by the overlapping area between stator tooth \(i\) and rotor tooth \(j\), and is expressed as follows [12; 19; 20],  
\[G_{gap}(i,j)=\left\{ \begin{array}{ll}\frac{\mu_{0}S_{f\mu}L}{g}&|\theta|\leq \theta_{1}\\ \frac{\mu_{0}S_{f\mu}L}{g}\frac{1/2+1/2\cos(\pi\theta/\theta_{2})}{1/2+1/2 \cos(\pi\theta_{1}/\theta_{2})}&\theta_{1}\leq|\theta|\leq\theta_{2}\\ 0&|\theta|\geq\theta_{2}\end{array} \right. \tag{4}\]  
where \(S_{f\mu_{0}}\) is the width of stator tooth surface; \(g\) is the length of air gap.