## 2 Derivation of 45 kW-Class MG-PMSM Basic Design Model  
### Structure of the Conventional Tran Vehicle and Design Target Specification of MG-PMSM  
As shown in Figure 3, a 3-phase induction motor and single-stage vertical-typed reduction gear with a gear ratio of 6.29 were adopted as a driving system of the conventional tram [17]. In this research, the 45 kW-class MG-PMSM model smaller than the combined volume of the conventional traction motor and mechanical reduction gear should be derived. Table 1 shows the restrictions on the required design size of the 45 kW class MG-PMSM, and as shown in Figure 4, it was derived by considering the space available for installation through the space analysis of the existing tram bogie [18]. As shown in Table 1, The design restrictions of the MG-PMSM are a maximum of 520 mm based on the outer diameter of the stator core and 400 mm in the axial length direction. Figure 5 shows a required torque-speed curve of the low-speed part (wheel side) on the 45 kW-class driving system for the Korean tram. As shown in Figure 5, the resulting model should generate 2000 Nm/717 Nm of torque at rated and maximum speed (214 rpm/599 rpm). Figure 4: Application concept of MG-PMSM to low-floor tram driving system. Figure 3: Structure of bogie and conventional driving system for the low-floor tram. Derivation of MG-PMSM Design Model with Distributed Winding and Limits of Application for Tram Vehicle  
In this research, a new MG-PMSM design process is presented. This design technique is based on the existing PMSM design process as a method to design pole pieces in consideration of double airgap structure. Figure 6 shows the design process of the MG-PMSM for tram vehicle traction as presented in this research. As shown in Figure 6, the basic model of the MG-PMSM can be derived using the magnetic load-electric load distribution method and the equivalent circuit method applied in the design of a general PMSM. In MG-PMSM, regardless of the MG-PMSM structure, the number of pole pieces in the outer rotor is derived from the combination of the respective pole pairs of the stators and the inner rotor magnet. In addition, it is derived from the combination of the rotational speed of the inner and outer rotors and the number of poles of pole pieces and permanent magnets [19]. In general, the stator winding method of a traction motor has a distributed winding and a concentrated winding, and the characteristics and size of the motor vary according to the winding method. A traction motor with a distributed winding has excellent control characteristics but has a disadvantage of increasing the volume due to the large end-turns [20; 21]. Since the MG-PMSM must be installed in the bogie space where the conventional mechanical reduction gear system is installed, minimizing the size of the MG-PMSM is the main design goal in this study. In this research, first, to derive the detailed model of the 45 kW-class MG-PMSM with distributed winding for the tram, the basic design model candidates according to the design parameter change in MG-PMSM are derived, and the torque and efficiency characteristics are compared. Table 2 shows a comparison of the design results of 45 kW-class MG-PMSM basic design model candidates. As shown in Table 2, the design combination of Model 4 satisfies the rated torque and efficiency requirements. Therefore, the detailed design was carried out with a basic model with a 42 slots/9 pole pieces/14 magnet poles combination. Figure 7 shows the \begin{table}
\begin{tabular}{c c} \hline \hline
**Contents** & **Design Criteria** \\ \hline MG-PMSM installation space & Max. Dia. 620 mm/Depth 450 mm \\ \hline Required size of MG-PMSM & Max. Dia. 520 mm/Depth 400 mm \\ \multicolumn{2}{c}{(Based on the stator out dia.)} \\ \hline Required torque & 2 kNm@214 rpm/0.71 Nm@599 rpm \\ \multicolumn{2}{c}{Efficiency} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: MG-PMSM design criteria through installation space analysis.