Reduction Method of Torque Ripple, DC Current
Ripple, and Radial Force Ripple with Control
Flexibility of Five-Phase SRM
Takahiro Kumagai
Dept. of Science of Technology Innovation
Nagaoka University of Technology
Nagaoka, Japan
kumagai_t1125@ stn.nagaokaut.ac.jp

Jun-ichi Itoh
Dept. of Science of Technology Innovation
Nagaoka University of Technology
Nagaoka, Japan
itoh@vos.nagaokaut.ac.jp

Abstract—This paper proposes a torque ripple, DC current
ripple, and radial force ripple reduction method with five-phaseswitched reluctance motor (SRM). The proposed method makesthese three ripples simultaneously zero, which is so-called“triple zero” in this paper, by improving control flexibility with
five-phase. In particular, the triple zero is achieved with thesame efficiency as the general driving method of SRM by
utilizing the control flexibility effectively. A three-phase 18S/12P
type SRM and a five-phase 20S/16P type SRM are used in finiteelement analysis and experiment in order to validate theproposed method. As a result, the main components of thetorque ripple, the DC current ripple, and the vibration are
reduced by 92.8%, 95.5%, and –18.0bB respectively. In addition,in comparison with the single pulse-wide current drive, thecurrent RMS in three-phase SRM is increased by 27.8% as asacrifice of the triple zero, while the current RMS in five-phase
SRM is increased by only 2.4%.
Keywords—switched reluctance motor, instantaneous current
control, torque ripple, acoustic noise, vibration, DC current ripple,
five-phase

I. INTRODUCTION
Recently, high-efficiency motors and high-power-density
motors have been studied actively due to the expansion ofelectric vehicles (EVs) and hybrid electric vehicles (HEVs)[1-3]. In particular, switched reluctance motor (SRM) has
attracted much attention as alternative motor for permanent
magnet synchronous motor (PMSM) and induction motor(IM) thanks to its rare-earth-element free and low
manufacturing cost [4][5]. However, large torque ripple, DC
current ripple, and radial force ripple are major problems in
the practical use of SRM. These ripples lead to acoustic noise,
vibration, and deterioration of the battery lifespan. In addition,
SRM has a problem of low efficiency compared with PMSM.
In order to solve these problems, current control strategies
have been studied actively with the development of the powerelectronics technology in recent year [6-17].
Single pulse-wide current drive, which controls the current
to a simple rectangular, is used as a general driving method[6]. In order to improve the efficiency, the excitation timingof single pulse-wide current drive is optimized inconsideration of inductance and torque characteristics [7][8].
Meanwhile, in order to reduce the torque ripple, the two-phase
This work is financially supported by JSPS KAKENHI Grant Number
19K21968.

Keisuke Kusaka
Dept. of Electrical, Electronics, andInformation Engineering
Nagaoka University of Technology
Nagaoka, Japan
kusaka@vos.nagaokaut.ac.jp

excitation is applied during the switching phase interval[9][10]. On the other hand, in order to reduce the DC current
ripple, the specific current waveform is introduced in order tomake the magnetic energy oscillation between load and power
supply theoretically constant [11][12]. In order to reduce theradial force ripple, the optimized harmonic is superimposed tothe command current in order to eliminate the radial force sumof the neighboring stator poles [13][14]. In addition, thecurrent control strategies for simultaneously reducing multiple
ripples have been studied [15-18]. However, in three-phase
SRM, the control flexibility during positive torque region is
not enough to reduce multiple ripples simultaneously. In orderto reduce multiple ripples simultaneously, it is necessary topositively use the negative torque region, which significantly
increases the copper loss. As a result, the efficiency is
extremely deteriorated with respect to the single pulse-widecurrent drive [15][16]. In order to solve this problem, there isa method of optimizing the rotor configuration forsimultaneously reducing the torque ripple and the DC current
ripple; however, the radial force ripple is not considered [17].
Meanwhile, there is a multi-objective optimization method inorder to reduce each ripple according to its weight; however,
it is impossible to reduce multiple ripples simultaneously [18].
This paper proposes a torque ripple, DC current ripple, andradial force ripple reduction method with five-phase SRM.
The proposed method makes these three ripples
simultaneously zero, which is so-called “triple zero” in thispaper, by improving control flexibility with five-phase. The
new contribution of the proposed method, the triple zero isachieved with the same efficiency as the general driving
method of SRM by utilizing the control flexibility effectively.
This paper is organized as follows; first the configurationof the five-phase SRM and its control flexibilities are
explained. Next, the derivation method of the ideal current
waveform to achieve the zero torque ripple, zero DC current
ripple, and zero radial force ripple simultaneously is explained.
Finally, the finite-element analysis and experimental results
are shown to validate the proposed method.
II. TRIPLE ZERO WITH FIVE-PHASE SRM
A. Structure and Specification
Fig.1 depicts the motor diagrams, whereas Table.1 shows
the motor parameters of the three-phase SRM and the five-phase SRM. For comparative verification, the five-phase
SRM is designed to have the same specification and same size
as our three-phase 18S/12P SRM. Note that the polecombination of the five-phase SRM is 20S/16P, which is theclosest to that of the three-phase SRM. In addition, the numberof turns of the five-phase SRM is adjusted to equalize thewinding space factors of the three-phase SRM and the fivephase SRM.

d (ix , m ) 
iDCx ( m )  1  ix ( m )

Edc 
dt

(ix ,  m )di ( ) (ix ,  m )    ix ( m ) ix ( m ) x m

Edc 
 m
d m
ix

(1)
Where  is the rotation speed, Edc is the input voltage, ix isthe motor current,  is the flux linkage, and the subscript x
indicates the phase in SRM. The flux linkage  can beapproximated with Fourier series with parameters as a

Fig. 1.

Examples of general forms of SRMs.

TABLE I.

MOTOR PARAMETERS OF SRMS.

Rated power Pm
Rated speed nRated torque Tn
Input voltage
Number of poles
Number of turns
Winding resistanceThree-phase 18S/12P
Five-phase 20S/16P
SRM
SRM
5.5 kW
12000 r/min
9.3 Nm
48V
Stator 18, Rotor 12
Stator 20, Rotor 16
12 turns
11 turns
0.012W
0.018W

Unaligned

AlignedTorque T

Inductance L

StatorRotor(CW)

ActualIdeal

Ideal
In 3-phase SRM

In 5-phase SRM

AActualNegative torque(dL/dm<0)

Sequence

C. Derivation of Ideal current waveform for Triple Zero
The ideal current waveform to achieve the zero torqueripple, zero DC current ripple, and zero radial force ripple
simultaneously is derived based on the optimization methodof the current waveform which consists of dc and someharmonic components [13-16]. In this method, first, torqueand radial force expression are approximated with Fourier
series with parameters as a function of motor current inconsideration of magnetic saturation, next, the motor current
is derived to minimize the variation of the torque or radial
force sum with the proper approximation by numericalanalysis. In order to reduce the DC current ripple as well as
torque ripple and radial force ripple, DC current has to be
expressed as a function of the motor current. If the winding
resistance is ignored, DC current iDC is expressed as in (1).

(a) Three-phase 18S/12P SRM (b) Five-phase 20S/16P SRM

Sequence

B. Control flexibilities of SRMs
Fig.2 shows the inductance distribution and torquecharacteristic, and the conduction regions which are necessary
to achieve the zero torque ripple, zero DC current ripple, andzero radial force ripple simultaneously in three-phase SRM
and five-phase SRM. The reluctance torque is generated by
the variation of magnetic resistance, i.e. inductance, according
to the change of rotor position. In the single pulse-wide current
drive; first, the current is raised to the reference level in thesmall inductance period [M, J], then, the current is controlled
to the constant in the positive torque (dL/dm>0) period [J,K], finally, the current is decayed to the zero before thenegative torque (dL/dm<0) start angle N. This is because alarge torque is obtained efficiently by raising the current withthe limited input voltage of the inverter. On the other hand, inorder to achieve the triple zero, three control flexibility isrequired, i.e. it is necessary to always energize three phases
simultaneously. In three-phase SRM, it means continuous
energization during one cycle; thus, the use of the negative
torque (dL/dm<0) period [N, M] is required. As a result, thedriving method for triple zero in three-phase SRM is far off
from the single pulse-wide current drive, and the current RMS
is extremely increased, which is not practical use. Meanwhile,in five-phase SRM, the energization of three phases isachieved by energizing only the 3/5 period of one cycle; thus,
the use of the negative torque period is not required. As aresult, the triple zero is achieved with the same efficiency as
the single pulse-wide current drive in five-phase SRM.

All of one cycle

3/5 of one cycle

M

N

U

J

Rotor position m

K

A

Fig. 2.
The inductance distribution and torque characteristic, and the
conduction regions which are necessary to achieve the zero torque ripple,
zero DC current ripple, and zero radial force ripple in three-phase SRM
and five-phase SRM.

function of current in consideration of magnetic saturation. In
addition, the differential term of (1) can be formulated bydifferentiating i(m) or (i,m) given as mathematicalexpressions. The DC current ripple iDCRip. is obtained bysubtracting T* which is the average input power from thesum of the DC current iDCx of all phase, and is expressed as in(2).
C or EiDCRip. ( m )   iDCx ( m )  T 
Edc
x A
*

(2)

Where e is electric position, in and n are the amplitude
and phase of n-order harmonic current, and N is the highest
order of the current harmonic. On the other hand, in the fivephase SRM, the current value have to be zero at both the turnon angle o and the end of conduction angle z. In this paper,z is set to the aligned angle A with reference to the single
pulse-wide current drive [6-8]. On the other hand, o is set toA-3/5*2/Nr in order to achieve the energization of threephases. Therefore, in the five-phase SRM, the ideal current
waveform is expressed as in (4).

N
 Nr 5 2
2 2   2 2 in sin n 2 3  e  5 N   5 N  e  Ni(e )   n 1

r 
r
r


0
otherwise(4)III. FINITE-ELEMENT ANALYSIS AND EXPERIMENT RESULTIn this section, first, the ideal current waveform is derived
based on the method explained in Section II, next, the derived
current is applied in FEM analysis and experiment. Note thatthe ideal current waveform is optimized with Generalized
Reduced Gradient (GRG) method to make each ripple rate 5%
or less and minimize the motor current RMS. The reason forchoosing 5% is that a few percent of the ripple occurs due tothe approximation error [13-16].
Fig.3 shows the ideal current waveform to achieve thetriple zero in three-phase SRM and five-phase SRM. In thethree-phase SRM, negative torque is generated, and iscompensated by larger torque than the torque reference fromthe other phase, resulting to large current. Meanwhile, in thefive-phase SRM, no negative torque is generated, and thetorque makes constant by sharing by each phase without thewasted current.
A. Finite-Element Analysis
Fig.4 shows the FEM analysis results of the current
waveforms, the torque, the DC current, the radial force, andthe current RMS with the single pulse-wide current drive(SPCD) and the ideal current waveform drive (ICWD) in thethree-phase SRM and the five-phase SRM. In both of thethree-phase SRM and the five-phase SRM, these ripples are
reduced by around 90% with ICWD compared with SPCD. In
addition, the current RMS in three-phase SRM is increased by
24.2% as a sacrifice of the triple zero, while the current RMS
in five-phase SRM is increased by only 1.7%. Therefore, in
FEM analysis, it is confirmed that the triple zero is achieved

iE

iA

iB

Current i[A]

100

50
50

0

0

TSUM

Torque T[Nm]

6
4

TSUM

6

4

TU

TW
TV
Negative

2

TC TD TE TA TB
2

0

0
0
-2

10

20

Machnical angle m[deg]Fig. 3.

030(a) Three-phase 18S/12P SRM

-2

150

150

100

SPCD
:55.9ARMS

50

ICWD:56.8ARMS

100
50

SPCD
:85.3ARMS

0
7
6
5
4
3
2
1
0
400

SPCD:Rip.44.7%

ICWD:Rip.7.8%

SPCD:Rip.238N

0
7
6
5
4
3
2
1
0
400

300

300

200

200

100

ICWD:Rip.13.3N

SPCD:Rip.51.7ARMS

100
50
0

10

20

-100

30

0

-50

75

ICWD:Rip.3.0ARMS-100
Machnical angle m[deg]75
increased by
105.9A
24.2%
60
85.3A
45

50

30

25

15

0

SPCD:Rip.140N

0
SPCD:Rip.42.7ARMS 150

0100

SPCD: ICWD:Rip.5.3%
single-pulse wide current drive
ICWD:ideal current waveform
drive (proposal)

100

50

125

SPCD:Rip.52.1%

ICWD:Rip.19.3N

0
100

-150

9 13.5 18 22.5(b) Five-phase 20S/16P SRM

ICWD:105.9ARMS

-50

4.5

Machnical angle m[deg]Ideal current waveforms and calculated torque.

200
Current [A]

(3)

n 1

iD

100

Torque [Nm]i(e )  i0   in sin(ne  n )

iC

150

Radial force [N]

N

150

iU

iW

iV

DC current [A]In this paper, the ideal current waveform to achieve thetriple zero is derived by optimizing the current amplitude andphase of each order of the harmonic current. In the three-phase
SRM, the ideal current waveform is expressed as in (3) [1316].

200

Current RMS [A]Where the range of the summation in three-phase SRM isfrom A-phase to C-phase, while that in five-phase SRM isfrom A-phase to E-phase. The DC current ripple RMS can bederived by computing the root mean square of (2). In order toreduce the DC current ripple as well as torque ripple and radial
force ripple, the current is derived to minimize the (2) bynumerical analysis.

SPCD

ICWD

0

0

4.5

9 13.5 18 22.5

ICWD:Rip.2.9ARMS
Machnical angle m[deg]increased by 1.7%
56.8A
55.9A

SPCD

ICWD

(a) Three-phase 18S/12P SRM (b) Five-phase 20S/16P SRM
Fig. 4.
FEM results of waveforms of the current, the torque, DC
current, radial force, current RMS in cases of single pulse-wide current
and ideal current at T*=4.91Nm, =2400r/min.

140
120
100
80
60
40
20
0

30
Amplitude of
torque ripple [%]Real current

Current [A]Reference

0

5

10
15
20
Mechanical angle m[deg]

25

SPCD
ICWD

25
Reduced by
82.0%

20
15
10

Reduced by
91.8%

5
0

30

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
Frequency [order](a) Single pulse-wide current drive (SPCD)(a) Torque ripple
Amplitude of
DC current ripple [A]

140
120
100
80
60
40
20
0

Current [A]Real current
Reference

0

5

10
15
20
Mechanical angle m[deg]

25

30

35
30
25
20
15
10
5
0

1st frequency is 573Hz

Reduced by
91.2%

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th
Frequency [order]

100

Current RMS [A]105.9A

80
85.3A

60

(b) DC current ripple
125
Vaibration [dB]Fig. 5. Measured currents of the three-phase SRM in cases of single
pulse-wide current and ideal current at T*=3Nm, =2866r/min. in theexperiment.

SPCD
ICWD
Reduced by
88.1%

Reduced by
79.9%(b) Ideal current waveform drive (ICWD)

increased by 27.8%

1st frequency is 69Hz

115

SPCD
ICWD

Reduced by-8.3dB

Reduced by-10.9dB105
95
85

1st frequency is
573Hz

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th40

Frequency [order]

20(c) Vibration acceleration

0

Fig. 7. Experimental results of the torque ripple, DC current ripple, andvibration of three-phase SRM in cases of single pulse-wide current andideal current at T*=3Nm. Note that  is 345r/min in the torque ripple
measurement, while  is 2866r/min in the others due to the limitation of
cutoff frequency of the torque meter and avoidance of torsional resonanceof test bench

SPCD

ICWD

Fig. 6. Comparison of motot current RMS of the three-phase SRM incases of single pulse-wide current and ideal current.

with the same efficiency as the general driving method byutilizing the control flexibility.
B. Experiment Result
The effectiveness of the proposed method is confirmed byexperiment with the three-phase SRM and the five-phase
SRM. In order to realize high-speed current control and reduce
the ripples caused by the hysteresis error, current-hysterisis
controller is constructed by analog circuit. Due to thelimitation of cutoff frequency of the torque meter andavoidance of torsional resonance of test bench, the torqueripple is measured at low speed. Note that fundamental motor
current frequency f1 is NrN/60. In addition, the main
components of the ripples of three-phase SRMs are 3f1, 6f1,
9f1, and so on. Meanwhile, those of five-phase SRMs are 5f1,
10f1, 15f1, and so on. Therefore, the ripple frequency of the
five-SRM is higher than that of the three-phase SRM. This
results in the experiment at lower speed with five-phase SRM.
Fig.5 shows the measured currents of the three-phase SRM
with the single pulse-wide current drive (SPWD) and ideal
current waveform drive (ICWD) in the experiment. In SPWD,
the motor current is a trapezoidal as shown in Fig.5 (a). On theother hand, in ICWD, the motor current follows the ideal
current reference accurately as shown in Fig.5 (b).

Fig.6 shows the comparison results of motor current RMSof the three-phase SRM in cases of single pulse-wide current
and ideal current. The current RMS of ICWD is increased by
27.8% compared with SPWD as a sacrifice of the triple zero.
In other word, the copper loss is increased by 63.3%, which is
not practical use.
Fig.7 shows the experimental results of the harmoniccomponents of the torque ripple, the DC current ripple, andthe vibration acceleration with SPCD and ICWD in the threephase SRM. The main components of the torque ripple, theDC current ripple, and the vibration are reduced by 82.0%,
79.9%, and -8.3bB respectively by ideal current waveform.
Therefore, in experiment, the effectiveness of the ideal current
waveform is confirmed in three-phase SRM.
Fig.8 shows the measured currents of the three-phase SRM
with the single pulse-wide current (SPWD) and ideal current
waveform drive (ICWD) in the experiment. In SPWD, themotor current is a trapezoidal as shown in Fig.7 (a). On theother hand, in ICWD, the motor current follows the ideal
current reference accurately as shown in Fig.7 (b).

100

Current [A]80

Amplitude of
torque ripple [%]Real current
Reference

60
40
20

0
0

4.5

9
13.5
18
Mechanical angle m[deg]

14
12
10
8
6
4
2
0

80
Reference

40
20
0
4.5

9
13.5
18
Mechanical angle m[deg]

35
30
25
20
15
10
5
0

Current RMS [A]

45

55.9A

Reduced by
98.3%

1st frequency is 320Hz(b) DC current ripple
140
Vaibration [dB]

56.8A

Reduced by
95.5%

Frequency [order](b) Ideal current waveform drive (ICWD)

60

SPCD
ICWD

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

22.5

Fig. 8. Measured currents of the three-phase SRM in cases of single
pulse-wide current and ideal current at T*=3Nm, =1200r/min. in theexperiment.

increased by 2.4%

Reduced by
97.0%

Frequency [order]

Amplitude of
DC current ripple [A]Current [A]Real current0

1st frequency is 51Hz(a) Torque ripple

120

60

Reduced by
92.8%

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

22.5(a) Single pulse-wide current drive (SPCD)
100

SPCD
ICWD

130

SPCD
ICWD

Reduced by-18.0dB
Reduced by-5.1dB

120

110
100

1st frequency is
320Hz

90
1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th30

Frequency [order](c) Vibration acceleration

15
0
SPCD

ICWD

Fig. 9. Comparison of motot ccurrent RMS value of the three-phase
SRM in cases of single pulse-wide current and ideal current.

Fig.9 shows the comparison results of motor current RMSof the five-phase SRM in cases of single pulse-wide current
and ideal current. The current RMS of ICWD is increased byonly 2.4% compared with SPWD. In other word, the copper
loss is increased by only 4.9%, which is low sacrifice as thetriple zero and practical use.
Fig.10 shows the experimental results of the harmoniccomponents of the torque ripple, the DC current ripple, andthe vibration acceleration with the single pulse-wide current
drive and the ideal current waveform in the five-phase SRM.
The main components of the torque ripple, the DC current
ripple, and the vibration are reduced by 92.8%, 95.5%, and –18.0bB respectively by ideal current waveform. Therefore, inexperiment, the effectiveness of the ideal current waveform isconfirmed in five-phase SRM. In addition, these ripple
reduction are achieved with the almost same copper loss as
SPCD as shown in Fig.9. Therefore, torque ripple, DC current
ripple, and vibration caused by radial force ripple, which aremajor problems in the practical use of SRM, are reduced withthe same efficiency as the general driving method of SRM by
utilizing the improved control flexibility with five-phase SRM
effectively.

Fig. 10. Experimental results of the torque ripple, DC current ripple, andvibration of three-phase SRM in cases of single pulse-wide current andideal current at T*=3Nm. Note that  is 191r/min in the torque ripple
measurement, while  is 1200r/min in the others due to the limitation of
cutoff frequency of the torque meter and avoidance of torsional resonanceof test bench.

IV. CONCLUSION
In this paper, the reduction methof of a torque ripple, DC
current ripple, and radial force ripple with five-phase switched
reluctance motor has been proposed. The proposed method
makes these three ripples simultaneously zero, which is socalled “triple zero” in this paper, by improving control
flexibility with five-phase. In particular, the triple zero isachieved with the same efficiency as the general driving
method of SRM by utilizing the control flexibility effectively.
A three-phase 18S/12P type SRM and a five-phase 20S/16P
type SRM are used in finite-element analysis and experimentin order to validate the proposed method. The main
components of the torque ripple, the DC current ripple, andthe vibration are reduced by 92.8%, 95.5%, and –18.0bB
respectively by proposed current drive method. In addition, incomparison with the single pulse-wide current drive, thecurrent RMS in three-phase SRM is increased by 27.8% as asacrifice of the triple zero, while the current RMS in fivephase SRM is increased by only 2.4%.

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