## 3 Equivalent Circuit Model of the N-TWSRIM
According to [PERSON]'s equations, the equations in the layer can be expressed as shown in Equations (4) and (5). Figure 6: Multilayer model of the N-TWSRIM. \[\left\{ \begin{array}{c}\
abla\times\dot{H}=\dot{J}\\ \
abla\times\dot{E}=-\partial\dot{B}/\partial t\\ \\ \dot{J}=\sigma\dot{E}\\ B_{x}=\mu_{i}H_{x}\end{array} \right. \tag{5}\]  
The equation can be expressed as shown in Equation (6). \[\left\{ \begin{array}{c}\frac{d^{2}B_{y}}{dy^{2}}=\left(a^{2}+j\omega_{i}\mu_ {i}\sigma_{i}\right)\!B_{y}\\ E_{z}=-\frac{\omega_{i}}{\dot{a}}B_{y}\\ H_{x}=\frac{1}{j\mu_{i}}\frac{dB_{y}}{dy}\end{array} \right. \tag{6}\]  
By solving Equation (6), Equation (7) becomes available. \[\left\{ \begin{array}{c}B_{y}=Acosh(\gamma_{i}y)+Bsinh(\gamma_{i}y)\\ H_{x}=\frac{\gamma_{i}}{j\mu_{i}a}[Asihh(\gamma_{i}y)+Bcosh(\gamma_{i}y)] \end{array} \right. \tag{7}\]  
where \(\gamma_{i}=\left(a^{2}+j\omega_{i}\mu_{i}\sigma_{i}\right)^{1/2}\). Equation (8) gives the boundary conditions for each layer and Equation (9) gives the transfer matrix for the electromagnetic field. \[\left\{ \begin{array}{c}y=0,\quad B_{y}=B_{yi-1},\quad H_{x}=H_{xi-1}\\ y=b_{i},\quad B_{y}=B_{yi},\quad H_{x}=H_{xi}\end{array} \right. \tag{8}\]  
where \(y=0\) is the junction of the \(i-1\) layer and \(i\) layer, \(b_{i}\) is the \(i\) layer thickness, \(H_{xi}\) is the tangential magnetic field intensity of the \(i\) layer, and \(B_{yi}\) is the radial magnetic flux density of the \(i\) layer. \[\left[ \begin{array}{c}B_{yi}\\ H_{xi}\end{array} \right]=\left[ \begin{array}{cc}\cos\mathrm{h}(\gamma_{i}b_{ i})&\frac{1}{\beta_{i}}\sin\mathrm{h}(\gamma_{i}b_{i})\\ \beta_{i}\mathrm{sinh}(\gamma_{i}b_{i})&\cos\mathrm{h}(\gamma_{i}b_{i})\end{array}  \right]\left[ \begin{array}{c}B_{yi-1}\\ H_{xi-1}\end{array} \right] \tag{9}\]  
where \(\beta_{i}=\gamma_{i}/(j\mu_{i})\). The overall boundary conditions are given as  
\[\left\{ \begin{array}{c}H_{x1}=\beta_{1}B_{y1}\\ H_{xi}=J_{0}\end{array} \right. \tag{10}\]  
The difference between composite multilayer theory and traditional multilayer theory is the difference in the calculation method of the \(N-1\) layer (copper layer), in which composite multilayer theory uses the propagation constant to calculate the copper layer parameters. Figure 7 shows a block diagram of the calculation process for the N-TWSRIM multilayer composite model. The explanation of the relevant steps is as follows. 1. \(N\) is an arbitrary value of the number of layers, and, generally speaking, the larger \(N\) is, the thinner each layer is and the more accurate the results are, but the greater the calculation time is. 2. Set the stator current \(I_{1}\) and \(\mu_{1}\sim\mu_{N-2}\) values based on actual motor parameters. 3. The magnetic field components \(H_{xi}\), \(H_{yi}\) and \(B_{yi}(i=1\sim N)\) are calculated by the transfer matrix (7) and boundary condition (8). Thus, the resultant \(H_{i}=\sqrt{H_{xi}^{2}+H_{yi}^{2}}\) is derived. To consider the nonlinearity of the rotor, the \(B\)-\(H\) curve is represented [21]. \[\mu=K_{t}H^{(1-n)/n}\] (11)For the N-TWSRIM rotor steel \(K_{t}\cong 0.85,\ t\cong 12\). By applying \(H_{i}\) into Equation (11), the new permeability \(\mu_{ii}\) is obtained. 4. According to the \(\mu_{ii}\) transfer matrix, magnetic field intensity \(H_{xn}\) is calculated. A loop ensures that \(H_{\rm xn}\ =J_{0}\). 5. When the cycle meets the conditions, the steel layer impedance \(Z_{\rm steel}\) can be obtained according to Equation (12). \[Z_{\rm steel}=\frac{4m_{1}\big{(}K_{dp}W\big{)}^{2}}{\pi D_{2}}Z_{N-2}L_{e}K_{e}\] (12) \[Z_{N-2}=\frac{s\omega_{1}}{a}\frac{B_{yN-2}}{H_{xN-2}}\] (13) where \(D_{2}\) is the diameter of the rotor, \(Z_{N-2}\) is the wave impedance, \(Z_{N-2}=\big{(}\frac{s\omega_{1}}{a}\big{)}\big{(}B_{yN-2}/H_{xN-2}\big{)}\), and \(s\) is the slip. \(H_{xN-2}\) is the tangential magnetic field intensity of the \(N-2\) layer and \(B_{yN-2}\) is the radial magnetic flux density of the \({\rm i}=1\ \sim N-2\) layer. 6.