*3.4. Calculation of Armature Winding Parameters*

By using *λ*∗ *<sup>d</sup>*(*θ*) and *λ*<sup>∗</sup> *<sup>q</sup>* (*θ*), the armature winding parameters can be easily obtained. *Lmd* and *L*mq can be expressed as:

$$L\_{\rm md} = \frac{2m\mu\_0 D\_i(l+2\delta)k\_{\rm dm}}{\delta k\_\delta \pi} \left(\frac{\mathcal{N}\mathcal{K}\_{\rm N1}}{p}\right)^2 \lambda\_{d1}^\*(\theta) \tag{25}$$

$$L\_{mq} = \frac{2m\mu\_0 D\_i(l+2\delta)k\_{qm}}{\delta k\_\delta \pi} \left(\frac{NK\_{N1}}{p}\right)^2 \lambda\_{q1}^\*(\theta) \tag{26}$$

where *Di* is the inner diameter of the squirrel-cage rotor and *l* is the length of a single side core. *λ*∗ *<sup>d</sup>*1(*θ*) and *λ*<sup>∗</sup> *<sup>q</sup>*1(*θ*) are the fundamental components of *λ*<sup>∗</sup> *<sup>d</sup>*(*θ*) and *λ*<sup>∗</sup> *<sup>q</sup>* (*θ*).

The steady-state salient ratio *ρ* can be expressed as:

$$\rho = \frac{L\_{\rm Ia} + L\_{\rm sq}}{L\_{\rm Ia} + L\_{\rm sd}} \tag{27}$$

According to Equations (11) and (12), under no-load excitation, the composite magnetic density of armature winding cutting can be expressed as:

$$B\_{\rm dc}(\theta) = \frac{N\_f I\_f}{2} k\_m \lambda\_{\rm dc}^\*(\theta) \Lambda\_B \tag{28}$$

Therefore, the fundamental component of mutual inductance between excitation winding and armature winding can be expressed as:

$$M\_{\rm af} = \frac{\mu\_0 D\_i (l + 2\delta) \lambda\_1^\*}{\delta k\_\delta} \frac{\mathcal{N} \mathcal{K}\_{N1}}{p} \mathcal{N}\_f \tag{29}$$

From the calculations of the above parameters, it can be clearly seen that by using *λ*∗ *dc*(*θ*), *λ*<sup>∗</sup> *<sup>d</sup>*(*θ*), and *λ*<sup>∗</sup> *<sup>q</sup>* (*θ*), the design flow becomes more efficient. As for the calculation of leaked inductance, it is the same as that of a conventional machine. Furthermore, because the winding in the conductor rotor core is a squirrel cage type, the end ring parameters need to be considered [32].

#### *3.5. Magnetic Circuit Calculation*

To consider the influence of different position saturation on the calculation of the inductance parameters, the magnetic circuit of the HTR-ASD needs to be calculated. Considering that the surfaces of each part of the HTR-ASD are equimagnetic potential surfaces, the calculation can be simplified using Carter's coefficient. Figure 10 shows the calculation model of the homopolar-type rotor obtained by Carter's factor.

**Figure 10.** The key parameters and magnetic equivalent circuit of the HTR-ASD.

Figure 11a shows the key parameters of the machine and Figure 11b shows the MEC of the calculation. *δ*<sup>1</sup> can be written as:

$$
\delta\theta\_1 = \delta\_{\text{min}} k\_{\delta\text{HTR}} k\_{\delta S\text{CR}} \tag{30}
$$

where *kδHTR* and *kδSCR* are the Carter coefficients of the homopolar-type rotor and the squirrel-cage rotor.

**Figure 11.** The key parameters and magnetic equivalent circuit of the HTR-ASD. (**a**) The key parameters of the machine. (**b**) The MEC of the calculation.

Therefore, the reluctances can be expressed as:

$$\begin{cases} \begin{aligned} r\_{S1} &= \frac{\ln(R\_S/(R\_C+\delta\_2))}{2\mu\_s \pi l\_1} \\ r\_{S2} &= \frac{l\_2}{2\mu\_S \pi \left(R\_S - R\_C - \delta\_2 - h\_f\right)^2} \\ r\_{\delta 2} &= \frac{\ln(1+\delta\_2/R\_C)}{2\mu\_0 \pi l\_1} \\ r\_{\delta 1} &= \frac{\ln\left(1+\delta\_1'/R\_H'\right)}{2\mu\_0 \pi l\_1} \\ r\_{C1} &= \frac{\ln\left(1+\delta\_1'/R\_H'\right)}{2\mu\_C \pi l\_1} \\ r\_{H1} &= \frac{\ln\left(R\_H'/R\_{H2}\right)}{2\mu\_H \pi l\_1} \\ r\_{H2} &= \frac{l\_2}{2\mu\_H \pi R\_{H2}'} \end{aligned} \tag{31}$$

The use of a MEC can simplify the calculation of a 3D magnetic circuit and speed up the calculation and analysis processes. At the same time, the air gap magnetic density can be determined by *λ*∗ *dc*(*θ*) after calculating the no-load magnetic circuit.

*3.6. Summary of the Analysis and Design Method of the HTR-ASD*

The above analysis can be summarized as follows:

