A pole changing vernier machine with consequent pole rotor

Abstract

This paper presents a consequent pole changing vernier machine (CPCVM) for variable speed application such as electric vehicles. The proposed topology works as a 48-pole vernier machine with a consequent pole rotor in the low speed region. In this mode, the machine provides high torque and high efficiency. Also, the machine uses less amount of magnet volume than a surface permanent magnet machine. However, in high speed region, the poles of the machine are changed and the machine switches to permanent magnet synchronous machine (PMSM) mode that provides high efficiency in the high speed region. Therefore, the machine combines the advantages of a consequent pole vernier machine and a conventional PMSM in a single topology. The variable speed range of the machine is extended by pole changing operation. The merits of the proposed topology are investigated by finite element analysis and the feasibility of the machine is confirmed for variable speed operation.

Keywords

Consequent pole pole changing vernier machine variable speed

1. Introduction

Conventionally permanent magnet synchronous machines (PMSMs) are used for variable speed applications such as electric vehicles because of their high torque density and high efficiency [1]. Generally, such machines use neodymium iron boron (NdFeB) magnets, which are expensive enough to constitute a significant part of total cost of the machine. Moreover, the airgap flux density is non-adjustable which limits the constant power wide speed range of the machine.

Permanent magnet vernier machine (PMVM) was first presented in [2] and its design and operation principle were explained in detail in [3]. The PMVM provides high torque density and high efficiency at low speed due to its so-called magnetic gearing effect. Due to these advantages, it has been extensively studied and many topologies have been presented [4–6]. However, vernier machines generally have large rotor permanent magnet (PM) pole pair numbers, therefore they are used for low speed direct drive applications. Also, the high operating frequency of vernier machines causes higher core losses than conventional PM machines. The core losses become increasingly serious at higher speeds. Therefore, the advantages of vernier machines are limited to low speeds.

To overcome the high cost of conventional PMSMs using NdFeB magnets, PM-less and PM-efficient machines are nowadays researched. PM machines with low cost ferrite magnets have been presented in the literature [7]. Consequent pole PM machines have been introduced [8–10] and it has been shown that they can save around 33% of PM material while achieving performance almost equivalent to a surface-type PMSM [11] in such machines. Therefore, the consequent-pole structure has been recognized as a promising solution to reduce machine cost while retaining with sufficient torque density.

Consequent pole vernier machines have also been presented in the literature to benefit from both the consequent pole structure and the magnetic gearing effect for reduced cost and increased torque density. A PMVM with consequent pole rotor was presented in [12], which discusses the advantages of the consequent pole structure such as reduced amount of PM, reduced fringing flux, and cogging torque. A consequent pole vernier machine with toroidal winding was proposed in [13], which shows a 20 % higher back EMF and magnet usage of 60% compared with a conventional vernier machine. Double consequent pole vernier machines with magnets on both the stator and rotor have also been analyzed [14,15] and it has been shown that they produce higher torque than vernier machines with PMs only on the rotor. However, vernier machines have rarely been analyzed for high speed operation due to their high core losses and therefore low efficiency at higher speeds.

To overcome the problem of constant flux at high speed, negative direct axis (d-axis) current is generally used for flux weakening in conventional PMSMs. However, using negative d-axis current, there is a risk of permanent demagnetization of the magnets; also, the continuous excitation results in copper loss and degrades the efficiency of the machine [9]. Variable flux machines that can adjust the airgap flux by applying a pulsed current have been presented [16]. The magnetization of the magnets is varied and the airgap flux is tuned. Pole changing machines, which not only provides flexible airgap flux density but also provide a wide speed range and high efficiency, have been presented in literature [17–19]. A pole changing machine that could operate in either 6 pole mode or 4 pole mode was first introduced in [20]. A pole changing machine with three different types of torques was presented in [21]; it offered reduced iron loss and high efficiency due to the change of poles at high speed. However, pole changing machines have a drawback; the winding has different connections for different pole numbers and the connection of the windings need to be changed every time the machine needs to operate with an alternate pole configuration for wide speed range operation.

This paper presents a consequent pole changing vernier machine (CPCVM) for variable speed application. The machine operates as a PMVM at low speed and as a PMSM at high speed through a pole changing operation. At low speed, it displays the advantages of a vernier machine such as high torque density and high efficiency. At high speed, the machine operates as a PM machine, therefore the disadvantages of a vernier machine at high speed are avoided. Moreover, the consequent pole structure reduces the cost of the machine by reducing the magnet volume and produces performance almost equivalent to that of a surface permanent magnet (SPM) machine.

2. Configuration, magnetization characteristics and operating principle

2.1. Configuration of CPCVM

The structure of general SPM machine is shown in Fig. 1(a).

Fig. 1.

Topology (a) General SPM machine (b) SPMPCVM (c) Proposed CPCVM.

The general SPM machine has surface type constant permanent magnets (PMs) on the rotor, whereas the stator has semi-closed slots with armature winding. However, the constant airgap flux of PMs becomes a hurdle for wide speed range operation of the SPM machine. This is due to the constraints of the direct current (DC) link voltage and inverter power rating. Therefore, a flux weakening operation is conventionally performed to increase the variable speed range of the PMSM. However, a continuous negative direct-axis current is required in the flux weakening operation to suppress the PM flux, which increases the inverter rating, causes extra copper loss and therefore decreases the efficiency of the machine.

In order to avoid above problems, a surface permanent magnet pole changing vernier machine (SPMPCVM) is presented as shown in Fig. 1(b). In SPMPCVM, half of the magnets are constant, and half of the magnets are low coercive force (LCF). LCF magnets have low coercive force and therefore, they can be easily magnetized and demagnetized. For variable speed operation, the magnetization direction of LCF magnets is changed, which decreases the back EMF and phase voltages of the machine. Hence, speed of the machine can be increased. However, large amount of constant and LCF magnets are used, which increases the cost of the machine. Hence, in order to decrease the cost of the machine, a consequent pole changing vernier machine (CPCVM) has been investigated for an electric vehicles (EV) application. The number of LCF magnets is reduced to half and hence changing the magnetization state of LCF magnets is rather easier in CPCVM compared to SPMPCVM.

The configuration of proposed CPCVM is shown in Fig. 1(c). It has an outer rotor and inner stator. The outer rotor has consequent pole PMs. It has 12 pole pairs of constant magnets and 12 pole pairs of LCF magnets. The stator has 36 slots and 12 pole pairs of concentrated armature winding. The stator is of open slot type. The height of the constant magnet is less than that of the LCF magnet because the coercive force of constant magnet is much greater than the LCF magnet. Therefore, the operating point of the LCF magnet is affected by the constant magnet. To prevent the accidental demagnetization of the LCF magnets and operate both type of magnets on identical operating flux densities, the height of the LCF magnets have been kept greater than that of the constant magnets. The machine can switch between 24 pole pairs and 12 pole pairs by changing the direction of magnetization of the LCF magnets using armature winding. When the constant magnets and LCF magnets have same direction, the machine works with 24 pole pairs. When the constant magnets and LCF magnets have alternate directions, the machine works with 12 pole pairs.

2.2. Magnetization characteristics and operating principle of CPCVM

The constant flux of the PMs causes high induced voltages as the speed increases in conventional PMSMs used for variable speed applications. However, to drive the motor, the induced voltage should not exceed the supply voltage. Therefore, with increasing speed, the flux of the PMs need to be weakened to limit the induced voltages.

The constant magnets used in conventional PMSMs have large coercive force. The constant magnets used in the analysis of this paper is NdFeB with Hc of −906670 A/m. Decreasing the magnetomotive force (MMF) of such PMs, which in turn will decrease the induced back EMF at high speed, requires a large external magnetic field. However, the external magnetic field generated by d-axis current (I _d) is bounded by the inverter rating. Therefore, varying the MMF of constant magnets is a difficult job and is not used to increase the variable-speed constant-power range of the machine. LCF magnets however, have a small coercive force compared to constant magnets. Therefore, they are easy to magnetize and demagnetize, and the speed range of the machine can be extended using LCF magnets. The LCF magnets used in the analysis of this paper is Alnico with Hc of −110500 A/m.

The general hysteresis curve of the LCF magnets is shown in Fig. 2.

Fig. 2.

Hysteresis curve of LCF magnets.

Contrary to constant magnets, LCF magnets have a non-linear curve. Initially the working point of the LCF magnet in the machine is at point A. Using negative d-axis armature current, the operating point of the magnet can be moved to point B and further to point C, at which point the LCF magnet is completely demagnetized. If further negative d-axis current is applied, the operating point can be moved to point D; at this point the magnet is magnetized in the opposite direction. If the negative d-axis current is removed, the operating point moves to point E, and magnetic flux in the reverse direction will be generated. Similarly, a positive d-axis current can be applied to change the direction of magnetization of LCF magnets that were previously reversed. In that way, the direction of magnetization of LCF magnets can be changed using armature current.

The proposed CPCVM has two modes, vernier mode and PMSM mode. At low speed, the machine works in vernier mode and at high speed, the machine works in PMSM mode. The basic relationship of a vernier machine is shown in (1) $\begin{eqnarray}Z_{r}=Z_{s}\pm P\end{eqnarray}$ (1) where Z _r is the number of rotor pole pairs, Z _s in the number of slots, and P is the number of armature pole pairs. In the proposed CPCVM, Z _r, Z _s and P are 24, 36, and 12 respectively.

In vernier mode, the direction of magnetization of the constant magnets and LCF magnets is the same as shown in Fig. 3(a).

Fig. 3.

(a) Direction of magnetization in vernier mode (b) Airgap flux density in vernier mode.

In this mode, the machine works with 24 pole pairs. All the magnets have the same direction, and the iron poles behave as the opposite pole for each magnet. Therefore, the number of magnets is reduced compared to a conventional SPM machine. The airgap flux density in vernier mode is shown in Fig. 3(b), which shows 24 pole pairs and agrees with the aforementioned discussion. In vernier mode, the machine provides high torque density and high efficiency at low speed to provide the benefits of a consequent pole vernier machine. At high speed, the direction of magnetization of the LCF magnets is changed using d-axis armature current as shown in Fig. 4(a).

Fig. 4.

(a) Direction of magnetization in PMSM mode (b) Airgap flux density in PMSM mode.

After reversing the direction of magnetization of the LCF magnets, the airgap flux density is shown in Fig. 4(b), which shows 12 pole pairs in the airgap. In this mode, the 12 pole pairs of armature winding and 12 pole pairs of rotor pole pairs work together, and the machine operates as a conventional PMSM machine. It is worth mentioning here that the armature winding does not have different winding connections for different modes. The armature winding has the same pole pairs in both modes. In PMSM mode, the frequency of the armature current is halved, and therefore the efficiency of the machine is improved and its speed range is extended. The different excitation sources (constant magnets and LCF magnets), affect each other, and the operating point of the LCF magnets is decided by the constant magnets. If the height of the constant magnets is equal to that of the LCF magnets, the constant magnets can demagnetize the LCF magnets even in a no load condition. Therefore, the height of the constant magnets is less than that of the LCF magnets. Also, the number of LCF magnets is halved compared to an SPM machine, therefore the magnetization and demagnetization of the LCF magnets in the proposed CPCVM is relatively easy.

3. Finite element analysis

3.1. Operating flux density of constant and LCF magnets

The operating flux densities of constant and LCF magnets should be similar in order to induce balanced and symmetrical back EMF in the armature winding. In vernier mode, the operating flux density of the constant magnets is shown in Fig. 5(a) where the average flux density over a period of 1 electrical cycle is 0.49 T. In the same mode, the operating flux density of LCF magnets is shown in Fig. 5(b), where the average flux density over a period of 1 electrical cycle is 0.52 T. Hence, the operating flux densities of two types of magnets is similar for proper operation of the machine.

Fig. 5.

Operating flux density (a) Constant magnet (b) LCF magnet.

3.2. Back EMF and phase voltages

When the number of poles is changed, the machine also switches from vernier mode to PMSM mode; which changes the magnitude of the back EMF. The comparison of back EMF in vernier mode and PMSM mode at base speed of 300 rpm is shown in Figs 6(a) and 6(b), respectively.

Fig. 6.

Back EMF (a) Vernier mode (b) PMSM mode.

In vernier mode, the machine has higher back EMF because of the magnetic gearing effect of vernier machines; however, in PMSM mode, the back EMF is less and also, there are harmonic components present in the back EMF in PMSM mode compared to vernier mode.

The high space harmonics are present both in vernier mode and PMSM mode and they cause eddy current loss of PMs. The high space harmonics can be minimized by optimizing the machine parameters and using the semi-closed slot structure. Also, the NdFeB magnets can be divided into multiple divisions, which will also decrease the eddy current. However, this method will increase the manufacturing cost of the machine. Further, distributed winding can also be used to minimize the higher-order space harmonics. The high space harmonics can be minimized by properly optimizing the machine, which will be performed in a future analysis of this research.

The comparison of phase voltages of CPCVM in both modes is shown in Figs 7(a) and 7(b), respectively.

Fig. 7.

Phase voltages (a) Vernier mode (b) PMSM mode.

Vernier mode has higher phase voltages compared to PMSM mode. This is since in PMSM mode, the frequency of the machine is halved, which decreases the reactance of the machine, hence the phase voltages of the machine are decreased. Therefore, speed of the machine can be further increases until the inverter limit is reached.

3.3. Torque and flux density distribution

The comparison of torque in vernier mode and PMSM mode is shown in Figs 8(a) and 8(b), respectively.

Fig. 8.

Torque (a) Vernier mode (b) PMSM mode.

Due to higher back EMF, vernier mode has higher torque than PMSM mode. However, one of the drawbacks associated with the proposed CPCVM is the high torque ripple. The torque ripple of the machine in vernier mode is 23%. However, the machine has not been optimized and the torque ripple of the machine can be minimized by properly optimizing the machine. The different parameters of the machine such as stator tooth width, magnet shape and angle can be optimized to reduce the torque ripple in proposed CPCVM, which will be performed in a future analysis of the machine. Moreover, the torque ripple of the machine further increases in PMSM mode. This is due to following reasons: 1st, the cogging torque of the machine is increased in PMSM mode. The comparison of cogging torque in vernier mode and PMSM mode is shown in Figs 9(a) and 9(b), respectively.

Fig. 9.

Cogging torque (a) Vernier mode (b) PMSM mode.

The cogging torque depends on the LCM (slots, rotor pole pairs), where LCM stands for least common multiple. Larger the LCM value is, the smaller the cogging torque. In PMSM mode, since the number of rotor pole pairs is decreased, therefore LCM is decreased and consequently, cogging torque is increased, which dramatically increases the torque ripple in PMSM mode. 2nd, a normal PMSM machine uses semi-closed structure of the stator slots to decrease the cogging torque and hence obtain low torque ripple. In the proposed machine open slots have been used. This is to utilize the vernier effect in the proposed machine. Torque ripple of the machine is high in PMSM mode due to open slot structure. The torque ripple of the machine in PMSM mode is 55.5%.

The distribution of the flux density in vernier mode and PMSM mode is shown in Figs 10(a) and 10(b), respectively. It can be observed that the machine works under the saturation limits in both vernier mode and PMSM mode.

Fig. 10.

Flux density distribution (a) Vernier mode (b) PMSM mode.

3.4. Variable speed characteristics of CPCVM

In order to explore the variable speed characteristics of the CPCVM, FEA was performed and the machine was run at different rotational speeds. The comparison of torque vs speed curve in vernier mode and PMSM mode is shown in Fig. 11.

Fig. 11.

Torque speed curves.

Fig. 12.

Efficiency maps (a) Vernier mode (b) PMSM mode.

Under the same operating conditions, the variable speed range of the CPCVM in PMSM mode is much higher than vernier mode. This is due to the pole changing operation which halves the number of poles and thereby the frequency of the machine. Therefore, the proposed CPCVM has good flux regulation capability and is suitable for variable speed applications such as electric vehicles.

The efficiency maps of the CPCVM in vernier mode and PMSM mode are shown in Figs 12(a) and 12(b) respectively. In vernier mode, more than 70% efficiency is achieved between 500 rpm and 1000 rpm, however, this range is significantly extended in PMSM mode. In PMSM mode, more than 70% efficiency is achieved between 1000 rpm and 1650 rpm. Therefore, the maximum efficiency range of the CPCVM is extended when the machine switches from vernier mode to PMSM mode at high speed. However, the vernier mode has higher efficiency at very low speed operation, such as 50 rpm that is 59.2% compared to PMSM mode, having 55% efficiency. Hence, the machine is operated in vernier mode at low speed and in PMSM mode at high speed.

4. Conclusion

This paper presents a consequent pole changing vernier machine that works in both vernier mode and PMSM mode. The characteristics of the proposed machine are as follows.

The poles of the machine can be changed, to provide the advantages of a consequent pole vernier machine in vernier mode (at low speed) and the merits of a conventional PMSM machine, such as high efficiency in PMSM mode (at high speed).

The consequent pole structure decreases the cost of the machine by reducing the magnet volume.

Concentrated winding is used, which reduces the end winding length and therefore copper losses are reduced.

The machine can operate in vernier mode and PMSM mode without requiring a change in winding connections contrary to a conventional pole changing machine.

The machine’s constant power speed range is extended by the pole changing operation.

Due to the consequent pole structure, the number of low coercive force (LCF) magnets is reduced compared to a SPM pole changing machine. Therefore, pole changing operation is relatively easier than in a SPM pole changing machine.

The electromagnetic characteristics of the machine at variable speed are analyzed and it is shown that the proposed machine is suitable for variable speed applications, such as electric vehicles.

Footnotes

Acknowledgements

This work was supported in part by the Human Resources Program in Energy Technology of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea, and in part by the BK21PLUS Program through the National Research Foundation of Korea within the Ministry of Education.

References

Zhu

Z.Q.

and Howe

, Electrical machines and drives for electric, hybrid, and fuel cell vehicles, Proceedings of the IEEE 95(4) (2007), 746–765, doi:10.1109/JPROC.2006.892482.

Ishizaki

Tanaka

Takasaki

and Nishikata

, Theory and optimum design of PM Vernier motor, in: 1995 Seventh International Conference on Electrical Machines and Drives (Conf. Publ. No. 412), Durham, 1995, pp. 208–212.

Toba

and Lipo

T.A.

, Generic torque-maximizing design methodology of surface permanent-magnet vernier machine, IEEE Transactions on Industry Applications 36(6) (2000), 1539–1546, doi:10.1109/28.887204.

and Lipo

T.A.

, High-power-factor vernier permanent-magnet machines, IEEE Transactions on Industry Applications 50(6) (2014), 3664–3674, doi:10.1109/TIA.2014.2315443.

Zhao

Lipo

T.A.

and Kwon

B.I.

, A novel dual-stator axial-flux spoke-type permanent magnet vernier machine for direct-drive applications, IEEE Transactions on Magnetics 50(11) (2014), 1–4, doi:10.1109/TMAG.2014.2329861.

Zhao

Zheng

Wang

Liu

Zhao

and Fang

, Design and analysis of a linear permanent- magnet vernier machine with improved force density, IEEE Transactions on Industrial Electronics 63(4) (2016), 2072–2082, doi:10.1109/TIE.2015.2499165.

Cai

Guan

and Xu

, Low-cost ferrite PM-assisted synchronous reluctance machine for electric vehicles, IEEE Transactions on Industrial Electronics 61(10) (2014), 5741–5748, doi:10.1109/TIE.2014.2304702.

Chung

S.U.

Moon

S.H.

Kim

D.J.

and Kim

J.M.

, Development of a 20-Pole–24-Slot SPMSM with consequent pole rotor for in-wheel direct drive, IEEE Transactions on Industrial Electronics 63(1) (2016), 302–309, doi:10.1109/TIE.2015.2472375.

Yang

Lin

Fang

Huang

and Zhu

Z.Q.

, A novel stator-consequent-pole memory machine, in: 2016 IEEE Energy Conversion Congress and Exposition (ECCE), Milwaukee, WI, 2016, pp. 1–8.

10.

Onsal

Demir

and Aydin

, A new nine-phase permanent magnet synchronous motor with consequent pole rotor for high-power traction applications, IEEE Transactions on Magnetics 53(11) (2017) 11.1–6, doi:10.1109/TMAG.2017.2709788.

11.

Chung

S.U.

Kim

J.W.

Chun

Y.D.

Woo

B.C.

and Hong

D.K.

, Fractional slot concentrated winding PMSM with consequent pole rotor for a low-speed direct drive: reduction of rare earth permanent magnet, IEEE Transactions on Energy Conversion 30(1) (2015), 103–109, doi:10.1109/TEC.2014.2352365.

12.

Chung

S.U.

Kim

J.W.

Woo

B.C.

Hong

D.K.

Lee

J.Y.

and Koo

D.H.

, A novel design of modular three-phase permanent magnet vernier machine with consequent pole rotor, IEEE Transactions on Magnetics 47(10) (2011), 4215–4218, doi:10.1109/TMAG.2011.2157324.

13.

and Xu

, Consequent-pole toroidal-winding outer-rotor vernier permanent-magnet machines, IEEE Transactions on Industry Applications 51(6) (2015), 4470–4481, doi:10.1109/TIA.2015.2458953.

14.

Zhao

Sun

and Liu

, Design and analysis of new vernier permanent-magnet machine with improved torque capability, IEEE Transactions on Applied Superconductivity 26(4) (2016), 1–5, doi:10.1109/TASC.2016.2518927.

15.

Jang

D.K.

and Chang

J.H.

, Design of a vernier machine with PM on both sides of rotor and stator, IEEE Transactions on Magnetics 50(2) (2014), 877–880, doi:10.1109/TMAG.2013.2284509.

16.

Maekawa

, Study of the magnetization method suitable for fractional-slot concentrated-winding variable magnetomotive-force memory motor, IEEE Transactions on Power Electronics 29(9) (2014), 4877–4887, doi:10.1109/TPEL.2013.2288635.

17.

Wang

Lin

Yang

Zhang

and Wang

, Cogging torque optimization of flux memory pole-changing permanent magnet machine, IEEE Transactions on Applied Superconductivity 26(4) (2016), 1–5, doi:10.1109/TASC.2016.2535361.

18.

Chau

K.T.

and Liu

, Pole-changing flux-weakening DC-excited dual-memory machines for electric vehicles, IEEE Transactions on Energy Conversion 31(1) (2016), 27–36, doi:10.1109/TEC.2015.2479458.

19.

Wang

Lin

Yang

Zhang

and Lu

, Design and analysis of a variable-flux pole-changing permanent magnet memory machine, IEEE Transactions on Magnetics 51(11) (2015), 1–4, doi:10.1109/TMAG.2015.2448118.

20.

Ostovic

, Pole-changing permanent-magnet machines, IEEE Transactions on Industry Applications 38(6) (2002), 1493–1499, doi:10.1109/TIA.2002.805568.

21.

Sakai

Yuzawa

and Hashimoto

, Permanent magnet motors capable of pole changing and three-torque-production mode using magnetization, IEEJ Journal of Industry Applications 2(6) (2013), 269–275.