Torque Boost Operation of
New Consequent-Pole Permanent Magnet Motor
Using Zero-Phase Circuit
Toshihiko Noguchi
Graduate School of Integrated
Science and Technology
Shizuoka University
Hamamatsu, Japan
noguchi.toshihiko@shizuoka.ac.jp

Kazuhiro Murakami
Graduate School of Integrated
Science and Technology
Shizuoka University
Hamamatsu, Japan
murakami.kazuhiro.14a@shizuoka.ac.jp

Akihisa Hattori
DENSO CORPORATION
Kariya, Japanakihisa.hattori.j6p@jp.denso.com

Yoichi Kaneko
DENSO CORPORATION
Kariya, Japan
yoichi.kaneko.j6y@jp.denso.com
Abstract—A novel consequent-pole permanent magnet (PM)motor is proposed in the paper, which has image pole pairs forevery pole pair of N and S. The three-phase synchronous
impedances of the motor are balanced owing to the rotor
configuration. In addition, it is possible to carry out field
weakening with less d-axis current, which leads to a highly
efficient operation in a high-speed range. However the motor
still has a drawback of low torque generation at low speeds due
to less PM volume. In order to solve the problem, the paper
discusses a torque boost operation by introducing a zero-phasewinding to the motor and a three-phase four-wire motor drive
circuit with an inverter. This paper describes a basic principleof the newly proposed consequent-pole PM motor and its
operation characteristics, and investigates the torque boost
approach using the proposed system.
Keywords—consequent-pole permanent magnet motor, field
weakening operation, zero-phase current, torque boost

I. INTRODUCTION
Research and development aiming at operation range
enlargement of the permanent magnet (PM) motors areintensively promoted in recent years. The PM motor can be
designed so as to generate a higher torque in a low-speed range
by increasing the electromotive force (e.m.f.) with highenergy-density PMs such as NdFeB and SmCo. In principle,
however, it is impossible to design the PM motor to achieveboth of the high-speed operation and the high-torquegeneration at low-speeds at the same time; hence field
weakening techniques are widely introduced to suppress thee.m.f. in the high-speed operation range.
Since the field weakening operation is generally carriedout by injecting a negative d-axis current to cancel the PM
magnetic flux and the e.m.f. generation, the copper loss due tothe d-axis current is unavoidable in the high-speed region,
which degrades efficiency of the PM motor. Therefore, it isstrongly required to develop a novel configuration of the PM
motor that can achieve efficient field weakening with less daxis current. In order to make it possible to reduce the d-axis
current, a novel geometry of the PM motor that can increase
the d-axis inductance is indispensable because more countermagnetic flux against the PM magnetic flux can be easily
generated with the less d-axis current.

In this paper, a novel consequent-pole PM motor is
proposed, which has a unique alignment of the PMs rather
different from a conventional consequent-pole PM motor.
The proposed PM motor has an image pole pair per one pairof N and S real PM poles on the rotor. There are two importantfeatures about the proposed motor, i.e., the three-phasesynchronous impedances are balanced, and the d-axis
inductance is increased. Therefore, torque ripple can beeffectively suppressed, and the field weakening operation isefficiently carried out with the less d-axis current. Both of theabove advantages make it possible to expand the wholeoperation range and to improve the operation efficiency.
However, it is rather difficult to avoid low-torquegeneration in the low-speed range because of lack of the PMvolume inherently caused by the consequent poleconfiguration. In order to solve this problem, a composite
magnetomotive force (m.m.f.) of the proposed consequentpole PM motor has been focused on to improve the torquegeneration characteristics in the low-speed range. In the paper,basic operation characteristics of the proposed consequentpole PM motor are discussed, compared with a standard
surface PM (SPM) motor and a conventional consequent pole
PM motor. In addition, an approach to boost the output torquein the low-speed range is presented, utilizing a zero-phasecurrent as well as normal three-phase currents, which can beachieved by taking advantage of the composite m.m.f. of the
proposed motor.
II.

CONFIGURATION AND OPERATING PRINCIPLE

Figure 1 shows a cross section of the proposed consequentpole PM motor. The motor employs equivalent eight-poles(four real PM poles and four image poles) and 12-slot
concentrated winding structure, which contributes to the down
sizing of the motor. The real PM pole pairs are mounted on
the rotor and the image pole pairs are formed between the real
PM pole pairs. This configuration is rather different fromconventional consequent pole PM motors, and this uniqueconfiguration gives the following advantages. Focusing on
the U-phase winding , for example, two teeth of the twelve arealways facing with the real PM pole pairs, while the other twoteeth are always on the image pole pairs, i.e., iron core parts.
This feature is same in the V-phase and the W-phase, which

978-1-7281-3398-0/19/$31.00 ©2019 IEEE

U2

V2

Three-phasewindings

Three-phasewindings

W1

(S)

W2

N

V1

(S)

N

N

S

Rotor

S
N
N

PM

StatorImage‐pole

Rotor

N

S

PM

(a) Consequent pole motor.
(b) SPM motor.
Fig. 2. Comparison motor model.

S

StatorTABLE I. MOTOR SPECIFICATIONS.
Consequent
Proposedpole PM
SPM motor
PM motor
motor

Image‐pole

Rotor

N

Stator

U1

(N)

(S)

S

(S)

(S)

N

(S)

(N)
U3

N

N

S

Three-phasewindings

U4

PM

Stator diameter

80 mm

←

←

Rotor diameter

42.85 mm←←

Facing an image pole

U1

Facing a magnet

U2

Stack length

37 mm

←

←

Facing an image poleU3

Air gap length

1.045 mm←←

Facing a magnet

U4
Number of poles8(PM:4,
Image
pole:4)8(PM:4,
Image
pole:4)8

Number of slots

12

←

←

(b) Winding structure of proposed motor.
Fig. 1. Proposed motor model.

Number of turns

16

←

←

cannot be expected in the conventional consequent pole PM
motors. Therefore, the magnetic circuit of the rotor iron coreis necessarily imbalance, but the impedance of the stator
windings can be balanced if the two windings on the real PMpole sides and the other two windings on the image pole sides
are connected in series. The three-phase balanced windings
do not affect on the motor current control in spite of theimbalance rotor magnetic circuit and give the freedom ofmagnetic circuit design of the image pole pair parts on therotor.

PM volume7.672 cc

7.672 cc15.344 cc

Armature
winding
connection

4-seriesstar
connection←←

PM type

NMX-43SH←←

The proposed motor has a high inductance value because
it has lower magnetic flux due to the half amount of the PM
and the higher amount of the rotor iron than standard SPM
motors. The e.m.f. of the motor is expressed as (1)Voltage (V)(a) Proposed motor.

W1

W2

W3

W4 V4

V3

V2

V1

8
6
4

( Ψa + Ld id ) + ( Lqiq ).

-8

A. Comparison of No-Load Electromotive Force
Comparison of the operation characteristics has been madeamong the proposed motor, a conventional consequent pole
PM motor, and a standard surface PM (SPM) motor, using anelectromagnetic analysis software JMAG-Designer 18.0TM.
The proposed motor model is indicated in Fig. 1, and the othermotor models are in Fig. 2, of which detailed specifications
are listed in TABLE I. The motor volume of all the three

Proposed motor
Consequent pole motor
SPM motor

0

60

120

180

240

300

360

Electrical angle (deg)(a) Back e.m.f. waveform.
8
7

(1)

III. OPERATION CHARACTERISTICS OF PROPOSED MOTOR

-2
-6

6

Voltage (V)V0 = ω

2

0-4

Therefore, the electromagnetic torque of the motor islower in a low-speed range, but the efficient high-speed
operation can be expected because it requires reduced
negative d-axis current owing to the lower magnetic flux ofthe field PM and the higher inductance value of the stator
windings.
22

Proposed motor
Consequent pole motor
SPM motor

5
4
3
2
1
0

0 1 2 3 4 5 6 7 8 9 10 11 12

Order(b) FFT result.
Fig. 3. Comparison of back e.m.f. and FFT analysis results.

The d-axis inductance of the proposed motor is the highest
among the three motors, and is larger by approximately 45 %than the SPM motor, which means that the reluctance of themagnetic circuit in the proposed motor is the least. The SPM
motor has the minimum inductance values in both of the daxis and the q-axis. However, the conventional consequentpole PM motor has the highest q-axis inductance. As
described above, any types of the consequent pole PM motors
have more iron in the rotor cores and higher inductance values,
compared with the standard SPM motor of which rotor isentirely surrounded by the PMs. As can be expected, theproposed motor is capable to realize the field weakening withless d-axis current owing to the higher d-axis inductance.
C. Harmonics Comparison of Mgnetic Flux
Harmonic components of the magnetic flux has been
compared among the three motors. Only the d-axis current of
20 A is given to the motor, where the electromagnetic analysis
has been conducted under an assumption of the ideal iron rotor
using the PMs replaced with air. Figure 5 shows the magnetic
flux linkages of the U-phase and their FFT analysis results ofthe three motors. Because the permeance variation is hardly
caused in the SPM motor, only the fundamental component isseen in the FFT result. On the other hand, the conventional
consequent pole PM motor has a significant permeancevariation due to the real PM poles and the image poles on therotor, resulting in the even-order harmonic components of themagnetic flux linkage. However, the proposed motor is notaffected by the permeance variation because one U-phasewinding is facing with the real PM pole while the other Uphase winding is on the image pole side; hence the even-orderharmonic components are not seen in the magnetic flux
linkage to the U-phase winding.
D. Comparison of N-T Characteristics
N-T characteristics of the three motors are indicated in Fig.
6, where the maximum output power is delivered to the loads.
The test conditions are 12-V DC bus voltage, the maximum

d-axis inductance (μH)
q-axis inductance (μH)

B. Comparison of Inductance
Figure 4 shows variations of the d-axis and the q-axis
inductances of the three models, where the current phase angle
β is changed under the constant stator current amplitude. As
the β increases, the d-axis inductance as well as the q-axis
inductance is increased because the amounts of the magnetic
fluxes to the both axes are reduced.

550
500
450
400
350
300
250
200
150
100
50
0

550
500
450
400
350
300
250
200
150
100
50
0

Proposed motor
Consequent pole motor
SPM motor

0

15

30

45

60

75

90

Current phase β (deg)(a) d-axis inductance.

Proposed motor
Consequent pole motor
SPM motor

0

15

30

45

60

75

90

Current phase β (deg)(b) q-axis inductance.
Fig. 4. Comparison of .inductance.
0.012

Proposed motor
Consequent pole motor
SPM motor

0.008

Magnet Flux (Wb)

Figure 3 shows the no-load e.m.f. waveforms of the Uphase and their FFT analysis results when the three motors areoperated at 600 r/min. The e.m.f. amplitude of the proposed
motor is almost half of that of the SPM motor because the PMvolume is 50 % of the SPM motor's. Therefore, the proposed
motor can extend the high-speed operation range. The
proposed motor has a lower e.m.f. constant and more
fundamental component in the e.m.f. waveform, comparedwith the conventional consequent pole PM motor: thus the
motor is suitable for the high-speed operation with field
weakening control.

0.004
0.000
-0.004-0.008-0.012

0

60

120

180

240

300

360

Electrical angle (deg)(a) U-phase flux linkage waveform.

0.010

Proposed motor
Consequent pole motor
SPM motor

0.008

Magnet Flux (Wb)motors is identical, whereas only the rotor geometries of thethree are different from each other. The proposed motor andthe conventional consequent pole motor have equivalent eightpoles on the rotor (four real PM poles and four image poles
composed with iron core), but the standard SPM motor has
eight real PM poles; hence the PM volume is double of theconsequent pole PM motors.

0.006
0.004
0.002
0.000

0

1

2

3

4

5

6

7

8

9 10 11 12

Order(b) FFT result.
Fig. 5. Comparison of U-phase flux linkage.

4.0

current amplitude of 20 A, and the maximum m.m.f. of 1280
AT.
The SPM motor can deliver the higher torque in the lowspeed range owing to the high e.m.f., compared with the othermotors. On the other hand, the proposed motor can expand
the higher-speed range because the motor has a lowcoefficient of the e.m.f. and the counter e.m.f. is high enoughto cancel the PMs' e.m.f. Therefore, the higher-speed range
can effectively be expanded by means of the field weakening.
The conventional consequent pole PM motor has almost same
N-T characteristic as the SPM motor, and is hard to expand
the high-speed operation range. This is due to the even-orderharmonic components in the e.m.f. when the field weakening
is applied to the motor.

Torque (Nm)

3.0
2.5
2.0
1.5
1.0
0.5
0.0

N

S

IV. COMPOSITE MAGNETOMOTIVE FORCEOF PROPOSED MOTORNSThe conventional standard SPM motor has the space
m.m.f. distribution of the PMs that synchronizes a rotating
magnetic field generated by the stator three-phase windings,
In other words, the m.m.f. of the rotor has only the positive
sequence component with less harmonic components.
However, the proposed motor has not only the eight-polecomponent but also the four-pole component of the rotor
m.m.f. Figure 7 illustrates a composite m.m.f. of the proposed
motor. As can be seen in the figure, it is possible todecompose the proposed consequent poles (four real PM poles
and four image poles) to a set of the two full PM m.m.f.
distributions, i.e., one is a four-pole m.m.f. distribution, andthe other is an eight-pole m.m.f. distribution.
If the proposed motor has two sets of the three-phase stator
windings, i.e., the four-pole windings and the eight-polewindings, it is possible to generate higher torque by feedingthese windings with two inverters. One inverter must be
operated synchronously with the eight-pole m.m.f. component,
and the other inverter must drive the motor synchronouslywith the four-pole m.m.f. component. In the case, thecombined operation of the two inverters is indispensable, andsix-wire connection to the two inverters is necessary, which isa drawback of the motor drive utilizing the composite m.m.f.
Therefore, the novel motor drive technique is investigatedin the paper, where the proposed motor with the composite
m.m.f. can be driven by a single inverter. Figure 8 shows across section of the proposed consequent pole PM motor withdouble stator windings, i.e., one set of the windings is a normal
three-phase windings, and the other is a special single-phasewinding. The three-phase windings synchronize with the

0

1000

2000

3000

4000

5000

Speed (r/min)Fig. 6. Comparison of N-T characteristics.

As described above, it has been found that the proposed
motor has the largest high-speed operation range with the least
negative d-axis current; thus the field weakening operation
can efficiently be achieved among the three motors.

As described in the previous section, the proposed
consequent pole PM motor can expand the high-speed
operation range with the less field weakening current, i.e., thenegative d-axis current. It is difficult, however, to obtain thehigher torque in the low speed range because the e.m.f.
coefficient is almost half of that of the standard SPM motor.
As mentioned previously, the PM amount of the SPM motor
is exactly twice of the proposed motor, so it is necessary toconsider enhancement of the torque generation without
sacrificing the wide-speed operation range of the proposed
motor.

Proposed motor
Consequent pole motor
SPM motor

3.5

N

N

S

S

N

S

N

S

N

Proposed motor
pole
N
S

S

8-poleN4-poleFig. 7. Illustration of proposed motor magnet arrangement.

zero-phaseU2 winding
Three-phase
W1 windings

V2
W2

S

V1

N

(N)

(S)

(S)

(N)

U3
N

U1

S

StatorImage‐pole

Rotor

PM

U4

Fig. 8. Proposed motor with double stator winding model.

Three-phase inverter
1
E
2 dc

1
E
2 dc

Proposed motor withdouble stator windings
Three-phase windingsia +(1⁄3)io

ib +(1⁄3)io

ic +(1⁄3)io

Zero-phasewindingio

Back e. m. f.

Fig. 9. Motor drive circuit using zero-phase winding.

eight-pole m.m.f. component, while the single-phase winding
generates additional torque with the four-pole m.m.f.
component. Figure 9 shows a circuit configuration of the
motor drive with a single inverter. As shown in the figure, thesingle-phase winding is connected to the neutral point of thethree-phase windings and the midpoint of the inverter DC bus.
Therefore, the current flowing into the single-phase winding
can independently be controlled at a different amplitude, adifferent frequency, and a different phase angle from those of
the three-phase windings, using the common mode (zerophase) current in the circuit. An alternating magnetic field isgenerated by the single-phase winding and the zero-phasecurrent, and is synchronized with the four-pole m.m.f. of therotor, which is easily carried out by superimposing the singlephase AC onto the three-phase currents. The drawback of the
proposed approach is a large torque ripple caused by thealternating magnetic field generated by single-phase winding
and the single-phase common mode current. However, it ispossible to generate additional torque with no extra threephase inverters.

TABLE II. MOTOR SPECIFICATIONS.
Proposed motorwith double stator windings
Stator diameter

80 mm

Rotor diameter

42.85 mmStack length

37 mm

Air gap length

1.045 mm

Number of poles8(PM:4,
Image pole:4)

Number of slots

12

Number of zero-phase turns

10

Number of three-phase turns

16

PM volume7.672 ccThree-phase winding
connection
Zero-phase winding
connection

V. OPERATION CHARACTERISTICS EXAMINEDTHROUGH SIMULATIONS

0.8
4-pole component

1.0

Flux density (T)Flux density (T)

1.5

0.5
0.0
-0.5
-1.0
-1.5

0

60

120

180

240

300

0.4
0.2
0.0

360

8-pole component

0.6

Mechanical angle (deg)

0 1 2 3 4 5 6 7 8 9 10 11 12

Order(a) Rotor surface flux density.
(b) FFT result.
Fig. 10. Rotor surface flux density and FFT analysis result.
5
3

4

2

Voltage (V)Voltage (V)5U-phaseV-phaseW-phase

4

1
0
-1
-2

2
1

-3
-4

240

220

200

180

160

140

0

0.05

120

0.04

100

0.03

80

0.02

60

0.01

40

-5
0.00

3

20

Frequency (Hz)Time (s)(a) Back e.m.f. waveform.
(b) FFT result.
Fig. 11. Back e.m.f. waveforms and FFT analysis result of proposed motor
three-phase windings.
5

5

4
4

3

Voltage (V)

2
1
0
-1
-2

3
2
1

-3
-4

240

220

200

Frequency (Hz)

180

160

140

0

120

0.05

100

0.04

80

0.03

Time (s)

60

0.02

40

0.01

20

-5
0.00

0

C. Torque Boost Operation
Therefore, three-phase sinusoidal currents to the threephase windings can generate smooth torque without the torqueripple in principle, and a single-phase rectangular current tothe single-phase winding can generate additional average
torque with torque ripple.
As described previously,
independent current control is possible in the three-phasewindings and the single-phase winding owing to the threephase four-wire motor drive circuit configuration with aninverter. The rectangular currents with 1/3 amplitude of thesingle-phase winding is superimposed to the three-phase

NMX-43SH

0

B. No-Load Electromotive ForceNo-load e.m.f. of the three-phase windings and the otherno-load e.m.f. of the single-phase winding are depicted in Fig.
11 and Fig. 12, respectively. These e.m.f. waveforms andtheir FFT analysis results are measured at the rotating speedof 600 r/min. As can be seen in these figures, the three-phasee.m.f. waveforms are almost sinusoidal because they do notcontain low-order harmonic components. On the other hand.
the e.m.f. waveform of the single-phase winding is close torectangular because it contains odd-order harmoniccomponents of which amplitudes are approximately inverse
proportional to the orders. The frequency of the three-phasee.m.f. is 40 Hz, which corresponds to the eighth-order (eightpoles) component, while the single-phase e.m.f. frequency is
20 Hz, which is fourth-order (four poles) component.

4 series

PM type

Voltage (V)A. Magnetomotive Force of Proposed Motor
Operation characteristics have been examined throughcomputer simulations using an electromagnetic analysis
software JMAG-Designer 18.0TM. The motor model and its
specifications are shown in Fig. 8 and TABLE II, respectively.
Figure 10 is the rotor surface magnetic flux density
distribution and its FFT analysis result of the proposed motor.
It is confirmed that the motor has two sets of the real PM polepairs and that there are two parts with no magnetic flux density
corresponding to the iron core parts. In addition, both of the
four-pole component and the eight-pole component can be
confirmed in the FFT analysis of the magnetic flux density
distribution, which demonstrates the composite m.m.f. of therotor.

4 series(a) Back e.m.f. waveform.
(b) FFT result.
Fig. 12. Back e.m.f. waveforms and FFT analysis result of proposed motor
zero-phase winding.

currents. The simulation test conditions are 20-Arms
rectangular current, which generates 800 ArmsT m.m.f. in the
single-phase winding, while the 1280 ArmsT m.m.f. is given to
the three-phase windings, respectively. Figure 13 shows
torque waveforms and their FFT analysis results when the
proposed motor is driven by only the three-phase windings
and when the motor is driven by both of the three-phasewindings and the single-phase winding. Although theproposed method generates low-even-order harmonic torquecomponents, it can boost the average torque by 20 %. Theseeven-order harmonics in the torque waveform is caused by thealternating magnetic field generated by the single-phasewinding and the zero-phase current, but the extra average
torque is effectively added to the torque delivered by thenormal three-phase windings.

In addition to the above basic operation characteristics, thepaper has proposed torque boost operation. Focusing on thecomposite m.m.f. of the proposed motor, a four-pole and aneight-pole synchronous rotating magnetic fields are generated
in the motor at the same time. Therefore, it is possible to boost
the torque by utilizing both magnetic fields. In order toachieve the torque boost operation, a four-pole single windingis added to the normal three-phase windings in the motor. By
introducing a three-phase four-wire motor drive circuit
configuration with a single inverter, it has been confirmed thatthe average torque can be effectively increased by the single
phase winding.
In the future work, influence of the e.m.f. generated in the
additional single-phase winding must be investigated because
the potential variation at the neutral point of the three-phasewindings may affect the voltage margin of the inverter. It isalso required to investigate the mutual interference between
the three-phase windings and the single-phase winding and todesign the stator iron core that has an independent slot
configuration.

Three-phase
Three-phase+Zero-phase

Torque (Nm)

2.5
2.0
1.5
1.0
0.5
0.0

0

30

60

90

120

150

180

Mechanical angle (deg)(a) Torque waveforms.
2.5
2.0

Torque (Nm)VI. CONCLUSION
A novel consequent pole PM motor has been proposed,
and its operating characteristics have also been investigated in
the paper. The proposed motor has a unique rotor
configuration where the real PM pole pairs and the image polepairs are placed every other pole pair. The image pole pairs
are constituted on the iron core parts next to the real surface
PMs on the rotor. one of the most important features of the
proposed motor is high-speed operation capability with lessfield weakening current (negative d-axis current); thus
efficient expansion of the high-speed operation range ispossible without increasing copper loss.

3.0

Three-phase
Three-phase+Zero-phase

1.5
1.0
0.5
0.0

0 1 2 3 4 5 6 7 8 9 10 11 12

Order(b) FFT results.
Fig. 13. Torque waveforms and FFT analysis results between three-phaseand three-phase plus zero-phase.

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[3]
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[5]

[6]

[7]
[8]

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