# Efficiency Improvement Strategy for Multiple Operating Points in Doubly Fed Magnetic Geared Motor
## 5 Role Exchange Analysis of Inner and Outer Windings  
The tendencies of the iron loss and efficiency presented in Sections 3 and 4 can be changed according to the frequency control sequence and the roles as the armature and field parts defined in Section 2. Namely, in this section, the roles of the inner and outer windings as the armature and field parts are switched with each other, that is, the inner winding (field part) current is fixed at the rated value and the outer winding (armature part) current is adjusted. Furthermore, with respect to the frequency control sequence, first, the outer winding frequency is increased, and then the inner winding frequency is changed. Hence, the inner and outer rated frequencies (\(f_{inner}\) and \(f_{outer}\)) are defined as 360 Hz and 180 Hz (Type I), 270 Hz and 270 Hz (Type II), and 180 Hz and 360 Hz (Type III), respectively, which are reversed as compared with the inner-armature case defined in Section 2.  
Figures 9 and 10 show the characteristic map of the iron loss and efficiency, and these are derived using the same method as shown in Figures 7 and 8 in described in Sections 3 and 4. As shown in Figure 9d, in the high-speed region, Type III with low frequency at the inner winding has smaller iron losses than those of Type I with high frequency at the inner winding. Hence, as shown in Figure 10d, in the high-speed region, the efficiencies of the Type III are higher than those of type I, and especially, in the high-speed and low-torque region, maximally, the Type III has 7.7% higher efficiency than that of Type I. The maximum efficiency map over the whole operating region is drawn by all efficiency maps of Types I, II, and III in Figure 10c, and the maximum efficiency is 92.5% in the high-speed and high-torque region. This value is 0.6% lower than 93.1% of the inner-armature cases presented in Section 4.  
Lastly, to compare the characteristics of the inner-armature case and the outer-armature case in detail, the iron loss map of the difference between the minimum iron loss maps of each case is presented in Figure 11a, and the efficiency map of the difference between the maximum efficiency maps of each case is drawn in Figure 11b. In the case of iron losses, the inner-armature case has higher  
Figure 9: Iron loss map in the constant torque region according to the winding frequency when the amplitude of the outer winding current is adjusted and the inner winding current is fixed at the rated current (424 Arms). (**a**) Type I (\(f_{inner}\) 360 Hz and \(f_{outer}\) 180 Hz); (**b**) Type II (\(f_{inner}\) 270 Hz and \(f_{outer}\) 270 Hz); (**c**) Type III (\(f_{inner}\) 180 Hz and \(f_{outer}\) 360 Hz); (**d**) Difference between Type III and Type I.  
values than those of the outer-armature case in the high-torque region. However, the efficiencies of the inner-armature case in most of the operating regions, except the high-torque region which is over 200 Nm, are higher than those of the outer-armature case. This is because the copper losses of the inner-armature case, shown in Figure 8b, are lower than those of the outer-armature case, shown in Figure 10b. Particularly, the inner-armature case has 5.7% higher maximum efficiency than the outer-armature case in the low-speed region.  
Figure 11: Loss and efficiency maps. (**a**) Iron loss difference between minimum iron loss maps of the inner-armature case and outer-armature case; (**b**) Efficiency difference between maximum efficiency maps of the inner-armature case and outer-armature case.  
Figure 10: Loss and efficiency maps in the constant torque region according to the winding frequency when the amplitude of the inner winding current is adjusted and the outer winding current is fixed at the rated current (168 Arms). (**a**) Minimum iron loss map; (**b**) Copper loss map; (**c**) Maximum efficiency map; (**d**) Efficiency difference between Type III and Type I.