Design and analysis of a double consequent pole changing vernier machine

Abstract

This paper proposes a double consequent pole changing vernier machine (DCPCVM) which adopts double consequent pole and flux modulation configuration. The proposed machine combines a vernier machine and a permanent magnet synchronous machine (PMSM) in a single topology. Therefore, the advantages of both machines can be realized in a single topology. The proposed machine provides high torque at low speed while operating in vernier mode whereas it operates in PMSM mode at high speed to avoid the disadvantages of vernier machines at high speeds such as high core losses. Parametric analysis of the proposed machine is performed to show the effect of the main variables on the electromagnetic characteristics of the machine. A finite element method (FEM) analysis is conducted, and meaningful conclusions are drawn.

Keywords

DCPCVM pole changing vernier machine PMSM parametric analysis

1. Introduction

Permanent magnet vernier machines (PMVMs) provide high torque density and high efficiency at low speed owing to their so-called “magnetic gearing effect” [1]. Owing to their high torque density, they have been extensively studied in the last two decades and many novel topologies have been presented [2–4]. However, a vernier machine uses a permanent magnet(PM) with a multipole structure which produces leakage flux and its power factor is known to be low [5]. Moreover, the reactance of the machine is high, which further decreases the power factor [6]. Consequently, a high-capacity inverter is required to operate the machine. Vernier machines have a high operating frequency, which leads to high core losses. The core losses become increasingly serious at higher speeds, resulting in low efficiency during operation at a wide speed range. Hence, vernier machines are usually preferred at low speed.

Some studies have been conducted to operate vernier machines in applications with a wide speed range. Field winding has been incorporated along with PMs in a vernier machine for operation in a wide speed range [7,8]. However, the extra field winding in the stator limits the fill factor of the armature winding and also increases the weight of the machine. Furthermore, a dual-consequent-pole vernier memory machine has been proposed for operation in a wide speed range, which uses a combination of low coercive force (LCF) and NdFeB PMs [9]. The proposed structure is complicated with PMs between the slot openings. Furthermore, magnetizing winding is used for the magnetization and demagnetization of LCF PMs; therefore, the weight of the machine is high. Furthermore, the power factor of the machine is low. Recently, a pole changing vernier machine with consequent pole rotor has been presented in [10]. The number of LCF PMs is low compared with that in surface permanent magnet pole changing vernier machine (SPMPCVM). However, the back electromotive force (EMF) and torque are also low.

This paper presents a high-performance DCPCVM which operates in two modes, i.e., that is vernier mode and PMSM mode. The proposed machine has a PM on both the stator and rotor [11], which enhances the back EMF and torque compared with those of existing pole changing vernier machines [10]. The rest of this paper is organized as follows. Section 2 presents the machine topology and the pole changing method. Section 3 presents the parametric analysis of the proposed machine. The effects of different variables on the performance of the machine in the two modes are explained in this section. Section 4 presents the finite element analysis of the proposed model. Section 5 concludes the paper.

2. Machine topology, working principle, and pole changing method

2.1. Topology and working principle

A general surface permanent magnet vernier machine (SPMVM) is shown in Fig. 1(a). As it has a limitation of low power factor and lower efficiency at high speed, the SPMPCVM has been proposed by applying pole changing to overcome this limitation [10]. The topology of an SPMPCVM with flux modulation is shown in Fig. 1(b).

An SPMPCVM uses constant (high coercive force) PMs and LCF PMs in a 1:1 ratio. Owing to their low coercive force, LCF PMs can be easily magnetized and demagnetized. For variable-speed operation, the number of poles of the machine was reduced by changing the magnetization direction of the LCF PMs. This reduced the back EMF and phase voltages of the machine. Consequently, the speed range of the machine was extended. However, large numbers of constant and LCF PMs were used, which increased the cost of the machine. Furthermore, changing the direction of LCF PMs required complex control. To overcome these issues, a consequent pole changing vernier machine (CPCVM) was adopted [10]. The number of LCF PMs is reduced to half; hence, changing the magnetization state of LCF PMs is easier in CPCVM compared with that in SPMPCVM as shown in Fig. 1(c). However, the CPCVM reduces the back EMF by approximately 30% compared with that of SPMPCVM as the number of PMs decreases. This negatively affects the performance of the machine. Therefore, a constant PM is added to the stator to increase the back EMF.

The topology of the proposed DCPCVM is shown in Fig. 1(d). The rotor has consequent pole PMs and the stator has consequent pole constant PMs. The coercive force of a constant PM is much larger than that of an LCF PM. Therefore, the operating point of the LCF PM is affected by the presence of a constant PM. To prevent accidental demagnetization of the resulting LCF PMs and to operate the two types of PMs at the same operating flux density, the height of the LCF PMs must be maintained greater than the height of the constant PMs [12]. To obtain smooth torque using the vernier effect and enable pole changing, the numbers of rotor poles and stator poles in the proposed model are set using Eq. (1). $\begin{eqnarray}\displaystyle Zr=Zs-P & & \displaystyle\end{eqnarray}$ (1) where Zr is number of rotor pole pairs, Zs is the number of stator slots, and P is the number of armature pole pairs. In the proposed model, Zr, Zs, and P were chosen as 24, 36, and 12 respectively. The main parameters of the proposed DCPCVM are shown in Table 1.

Fig. 1.

Topologies of (a) SPMVM (b) SPMPCVM (c) CPCVM (d) the proposed DCPCVM.

Table 1

Main parameters of the proposed DCPCVM

Item	Unit	Value
Rotor outer diameter	mm	300
Stator outer diameter	mm	248
Airgap length	mm	1
Rated current	A	3.5
Stack length	mm	40
Coercive force of constant PM	kA/m	850
Coercive force of LCF PM	kA/m	110

2.2. Pole changing method

Magnetization and demagnetization analysis is performed for a pole changing operation of a machine operating as a vernier machine at low speed and a PMSM at high speed. A negative d-axis current is applied to perform demagnetization and a positive d-axis current is applied to perform magnetization of the LCF PMs in the rotor. Figure 2 shows the hysteresis model of an LCF PM.

Fig. 2.

Hysteresis model of LCF PM.

For vernier mode operation, the LCF PMs should be in a fully magnetized state (point A in Fig. 2) and their direction is shown in Fig. 3(a). Then, by applying a negative current pulse to the armature windings, the LCF PMs can be reverse-magnetized for PMSM mode operation and their direction is shown in Fig. 3(b). The operating point is then located at point B along the line AB (Fig. 2). To change the operation from PMSM mode to vernier mode, a positive current pulse is applied to the armature windings so that the operating point is located at point A along the line BA.

Fig. 3.

Direction of PMs in (a) vernier mode (b) PMSM mode.

Hence, the pole pairs of the rotor can be changed between 24 pole pairs, which is the vernier mode, and 12 pole pairs, which is the PMSM mode, by changing the magnetization direction of the LCF PMs as illustrated. Moreover, the back EMF of the machine can be controlled by demagnetizing and magnetizing the LCF PMs.

3. Parametric analysis

As the proposed topology operates in two modes through the pole changing technique, the characteristics of the two modes should be considered in its design. A higher back EMF is preferred at low-speed operation whereas a lower back EMF is required at high-speed operation in electric vehicle applications. This is because a higher torque is required during low-speed operation whereas, to increase the speed of the machine, the back EMF should be low. Therefore, parametric analysis is performed to show the effect of the main variables on the electromagnetic performance of the proposed machine.

3.1. Design variables and their limitations

The design variables for parametric analysis are shown in Fig. 4. Table 2 shows the definition of each variable. The height and width of the PMs affect the flux modulation of a vernier machine. Hence, the back EMF and torque of the machine will be severely affected by these variables. Moreover, the height and width of the LCF PMs affect the demagnetization characteristics of the machine, which in turn affect the wide-speed-range operation of the machine. The coercive force of a constant PM is much larger than that of an LCF PM. The height of the LCF PMs must be maintained greater than the height of the constant PMs for two reasons. First, it prevents accidental demagnetization of the LCF PMs owing to the presence of constant magnets. Second, it operates both types of PMs at the same operating flux density, which induces balance back EMF in the stator windings.

The ratio of the height of the constant PMs to that of the LCF PMs is maintained at 1:5 throughout the parametric analysis to avoid demagnetization of LCF PMs as discussed earlier. Moreover, the widths of both types of PMs on the rotor are maintained to be equal. The maximum height of the stator PMs (variable Z) is restricted to 5 mm during parametric analysis to enable the design. Furthermore, the area of the PM per stator slot is defined by a variable S. In the parametric analysis, S can be defined as X_1, X_2 and Y_1, Y_2 as shown in Eq. (2) because the total PM area is equally limited. $\begin{eqnarray}\displaystyle S=\{2626.4-12(X\_1Y\_1+X\_2Y\_2)\}/18 & & \displaystyle\end{eqnarray}$ (2) where 2626.4 mm² indicates the fixed value of the total PM area, 12 is half the number of rotor PMs and 18 is the number of PMs per stator slot.

Fig. 4.

Design variables.

Table 2

Definitions of the design variables

Variable	Definition	Variable	Definition
X_1	Height of rotor constant PM	X_2	Height of rotor LCF PM
Y_1	Width of rotor constant PM	Y_2	Width of rotor LCF PM
Z	Height of stator PM	S	Area of PM per stator slot

3.2. Parametric analysis and discussion

The effect of each variable on the torque of the machine was initially analyzed using FEM software JMAG.

The effect of variables X_1 and Y_1 on the torque in vernier mode is shown in Fig. 5(a). It can be observed that a large height of rotor PMs (both constant and LCF) is not preferable whereas a large width of the PMs is more preferable. Hence, a small height and large width tend to produce higher torque in vernier mode. The effect of variables Z and S on the torque in vernier mode is shown in Fig. 5(b). A very large area tends to increase the flux leakage and thus reduce the torque in vernier mode whereas a large height tends to decrease the modulation effect.

The difference between the back EMFs in vernier mode and PMSM mode should be as high as possible. A higher difference will increase the speed of the machine accordingly. The effect of variables X_1 and Y_1 on the back EMF difference between the two modes is shown in Fig. 5(c). Notably, a large height of the PM tends to increase the back EMF in PMSM mode whereas a small height of PMs tends to increase the back EMF in vernier mode owing to higher modulation effect. Therefore, the machine should be designed to have a small height of PMs whereas the width of the PMs should be sufficiently large. A similar phenomenon can be observed with the effect of variables Z and S as shown in Fig. 5(d). The stator PMs also need to have small heights and large widths.

To change the poles of the machine, the direction of the LCF PMs needs to be reversed. Hence, the reverse-magnetization ratio is an important electromagnet characteristic in the design of the proposed machine. The reverse-magnetization ratio is a measure of how much the direction of magnetic flux changes at the same current when the machine needs to switch from one mode to the other. A higher magnetization ratio shows that it is easier to convert poles at a specified current. The reverse-magnetization ratio is measured at a negative d-axis pulsed current of 20 A. The effect of variables X_1 and Y_1 on the reverse-demagnetization ratio is shown in Fig. 5(e). Notably, larger heights decrease the reverse-magnetization ratio; hence, it is difficult to change the direction of LCF PMs. The same effect can be observed with the height of stator PMs as shown in Fig. 5(f).

Fig. 5.

Effect of the design variables on the performance (a)(b) Torque (c)(d) Back EMF (e)(f) Reverse- magnetization ratio.

From the above results of parametric analysis, it is concluded that, for the design of the proposed machine, the height and width of the LCF PMs and constant PMs are very important. The width of the PMs should be sufficiently large; however, it should not be too large, as it will increase the saturation in the rotor teeth causing high torque ripple and lower overload capabilities. The height of the PMs should be small, which will provide higher torque and higher reverse-demagnetization ratio, which are advantageous for the higher power and lower inverter rating required for pole changing operation, respectively.

Figure 5(a) shows two points marked as A (X_1 = 1.6, Y_1 = 16) and B (X_1 = 1.7, Y_1 = 16) with high torque in vernier mode. However, to finalize the values of these variables, electromagnetic characteristics such as back EMF and reverse magnetization of LCF PMs also need to be considered. Figures 5(c) and (e) show that the back EMF and reverse-demagnetization ratio decrease as X_1 increases. Therefore, the values X_1 = 1.6 and Y_1 = 16 are used in the final design of the proposed machine. Furthermore, the value of X_2 should be five times that of X_1 to avoid the demagnetization of LCF PMs as discussed earlier. Hence, the value of X_2 is decided to be 8 mm. Similarly, the value of Y_2 should be the same as that of Y_1 (the widths of the LCF PMs and constant PMs are maintained to be equal). Hence, Y_2 is finalized as 16 mm.

Table 3

Design values of the parameters

Model	Design value of variable
	X_1	X_2	Y_1	Y_2	Z	S
Proposed DCPCVM	1.6 mm	8 mm	16 mm	16 mm	2 mm	42.4 mm²

Now, S can be determined according to Eq. (2). Parametric analysis in Figs 5(b), (d), and (f) shows that the large value of Z produces poor electromagnetic performance in terms of torque, back EMF, and reverse demagnetization. Therefore, Z was determined to be 2 mm. The finalized values of these design variables are shown in Table 3.

4. Finite element analysis

A comparison of the back EMFs of the CPCVM and the proposed DCPCVM is shown in Fig. 6(a). It can be observed that the proposed model provides slightly better back EMF than the CPCVM does. A comparison of the back EMFs of the machine when it operates in PMSM mode after pole changing is shown in Fig. 6(b). A lower back EMF is obtained in the proposed model compared with that in CPCVM when operating in PMSM mode.

Fig. 6.

Comparison of the results according to parametric analysis (a) Back EMF of vernier mode (b) Back EMF of PMSM mode (c) Torque of vernier mode (d) Torque of PMSM mode.

A comparison of the torques of the CPCVM and the proposed DCPCVM is shown in Fig. 6(c). It can be observed that the proposed model provides better torque than the CPCVM does when operating in vernier mode. A comparison of the torques of the machines when operating in PMSM mode after pole changing is shown in Fig. 6(d). It can be observed that the performance is improved according to the characteristics of each mode.

With the same amount of current for the two models, the LCF PMs in the proposed model are 100% reverse magnetized whereas the corresponding percentage is only 76.1% in the CPCVM. This can be observed in Fig. 7. Therefore, to achieve the same amount of reverse magnetization, the proposed model requires a smaller current. Hence, the proposed model reduces the burden of the inverter. The characteristics of the two models are compared and summarized in Table 4.

Fig. 7.

Movement of operating point.

Table 4

Comparison of the results of CPCVM and the proposed DCPCVM

Model	Back EMF (V)		Torque (Nm)		Reverse- magnetization ratio (%)
	Vernier mode	PMSM mode	Vernier mode	PMSM mode
CPCVM	68.1	45	17	15.5	76.1
Proposed DCPCVM	74.2	36.8	18.1	12.8	100

5. Conclusion

This paper proposed a DCPCVM operating in two modes. At low speeds, it operates as a vernier machine to provide high torque, and at high speeds, it operates as a PMSM to avoid the disadvantages of vernier machines at high speeds such as high core losses. Furthermore, the pole changing analysis was performed using FEM. Based on the final design through parametric analysis, the proposed DCPCVM showed an increase in the back EMF and torque values in vernier mode compared with those of the CPCVM. It can also be observed that the back EMF of the PMSM, which affects wide-speed-range operation, decreased significantly. Finally, when the same negative d-axis current is applied, the reverse-magnetization ratio confirms that the proposed DCPCVM is more suitable for the pole changing analysis. Therefore, the proposed DCPCVM showed improved performance compared with that of the CPCVM.

Footnotes

Acknowledgements

This work was supported in part by the BK21PLUS Program through the National Research Foundation of Korea within the Ministry of Education, and in part by the National Research Foundation of Korea grant funded by the Korea government (Ministry of Science) (No. NRF-2020R1A2B5B01002400).

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