Iron Loss Reduction Method of V/f Control
for Switched Reluctance Motor
Hirotaka Kato1, Hiroki Watanabe1, and Jun-ichi Itoh1
1

Nagaoka University of Technology, Japan

Abstract-- This paper proposes an iron loss reduction
method in a V/f control for a switched reluctance motor(SRM). The proposed method applies the three-level
modulation method to reduce harmonic iron loss. In addition,a reactive power compensation control of the proposed
strategy eliminates fundamental iron loss caused by areactive power. The proposed method reduces 69.0% of theharmonic iron loss and 4.7% of the fundamental iron loss inthe experiment.
Keywords— Iron loss, Switched reluctance motor, V/fcontrol

I. INTRODUCTION
A switched reluctance motor (SRM) is composed ofonly an iron core and windings without a permanent
magnet using a rare earth, which is inexpensive tomanufacture. The SRM has attracted attention as avariable-speed motor for industrial applications due to therobust salient pole structure of its rotor [1][2]. The
variable-speed drive without a position sensor is expected
for the SRM to take advantage of the high-temperature andhigh-speed durability and cost-effectiveness.
Many studies have been conducted on the rotor position
sensorless drive methods with the estimated position using
the position dependency of inductance [3-6]. In thesemethods, the instantaneous value of the inductance is first
calculated from the voltage and current. Then, thecalculated inductance is converted into the rotor position
information with a look-up table or an approximation
formula of the relationship between inductance and rotor
position. However, these methods require complicatedcontrols such as harmonic voltage superposition [3][4] oradditional analog circuits [5][6] to detect the instantaneous
inductance accurately. The authors have proposed a V/fcontrol for the SRM in order to overcome the above
disadvantages [7]. The V/f control does not require therotor position information because it is based on therotating coordinate system with respect to the inverter
output voltage. Therefore, the V/f control does not havethe accuracy problems of the inductance detection and therotor position conversion essentially.
The reduction of both the copper loss and iron losses isimportant to achieve the high-efficiency drive of the SRM.
The maximum torque/ampere control is proposed

assuming that the controller for the SRM is based on amathematical model, such as field-oriented control (FOC)and the V/f control [8]. Although this method minimizes
the copper loss by minimizing the RMS current, the ironloss increases with the speed of the motor. The iron loss inhigh-speed operation can be a significant problem in the
SRM since it is expected to be applied for high-speed
rotation applications [9-11]. The iron loss is divided into
the harmonic iron loss caused by the switching operationof the inverter and the fundamental iron loss caused byfundamental voltage [11]. Different approaches are
required to reduce both fundamental iron loss andharmonic iron loss.
Ref. [12] has reduced the iron loss by optimizing the
conduction timing for the hysteresis current control.
However, this method requires a trial-and-error approachto optimize the control parameters, which make theimplementation complicated. Therefore, it is not easy to
implement the SRM control based on the mathematicalmodel. In addition, the iron loss reduction method is
proposed for the FOC of the synchronous reluctance motor,
which adjusts the excitation current depending on thetorque [13]. However, this method also cannot be appliedwith the V/f control because the V/f control does not havea torque controller.
This paper proposes an iron loss reduction method in
the V/f control for the SRM. The fundamental iron loss andthe harmonic iron loss are reduced by the proposed method.
The proposed method consists of two approaches,(i)applying the three-level modulation method: theharmonic ripple in the flux density is reduced by applying
the three-level modulation to the asymmetrical half-bridge
converter, (ii)reactive power compensation control: thefundamental amplitude of the flux density is reduced bycompensating the reactive power command based on the
maximum torque/ampere control. This paper describes
first (i) and then (ii).

II. IRON LOSS REDUCTION METHOD
OF V/F CONTROL FOR SRM
Fig.1 shows the control diagram of the V/f control for
the SRM. The V/f control consists of (A)zero-phasecurrent control, (B)V/f control and damping control, and(C)high-efficiency control [7]. This paper reduces the ironloss by adding the following two parts to the V/f control,(i)the three-level modulation method and (ii)reactive
power compensation control.

(A) Zero-phase current control
i0*
v0*
PI
v*
0 g*
vd
(B) V/f control

wm*

w*

Pf

f/V conv.

HPF
K1
Damping control

Fig.2 shows the operating principles of the two-level
and three-level modulation methods. Fig.3 shows the
waveform of each modulation method. The two-level
modulation method, as shown in Fig.2(b), is generally
adopted to drive the SRM with the voltage command[8][14]. The iron loss is formulated with the Improved
Generalized Steinmetz Equation (iGSE) [15] as
1 T dB(t ) −( B ) dt
 PV = 0 ki
T
dt


k
 ki =
 −1 2( 2 ) 0 cos  2 − dProposal (ii)Fig. 1.

swx2

w1* 1
s

x: u, v, w

1*

ig
id
3f/gd0
i0

iu
iv
iw

V/f control method based on gd axis.

(1)

Ed c

vx*

x: u, v, w

-Ed c
1

carrier

Edc

V (t ) = Edc(2)(a)Driving circuit

swx1

-Ed c
1

0
1
0
1

swx2
(c)three-level modulation

Fig. 2. Operating principals
Between two-level and three-level modulation.

Phase Flux
Phase
current density voltage

where Pv is the iron loss per unit volume, T is the one
period of the electric angle, k, ,  is the Steinmetz
coefficient, B is the flux density of the stator core, B is
the peak-to-peak of B, V(t) is the output voltage of theinverter, Edc is the DC voltage of the inverter, N is thenumber of turns of the slot winding, and A is the effective
cross-section. According to (1), the iron loss is generated
when the inverter output voltage V(t) is ±Edc and becomeszero when V(t) is zero [16]. The flux density oscillates, as
shown in Fig.3(a) because the applied voltage is only Edc
or -Edc when the two-level modulation method is used. On
the other hand, the three-level modulation method shownin Fig.2(c) outputs not only ±Edc but also zero by fixing theswitching state of either the upper or lower arm to ON or
OFF during the half of the electric period. The iron loss is
not generated during the zero-voltage period because dB/dt
shown in (2) becomes zero. In particular, the iron loss ofthe three-level modulation is reduced significantly inoperation with a low modulation index because the zerovoltage period becomes longer as the modulation index
decreases.

carrier

Edc
-Edc

Avg.
B

dB(t)
dt

6.09ARMS(a)two-level modulation
Edc
0
-Edc

Avg.
B

0

Ed c

vx*

swx2

Phase Flux
Phase
current density voltage

V (t ) = − Edc01

swx1, swx2(b)two-level modulation

Phase-x

where

V (t ) = 0

swx1

PWM 3

(C) High
Efficiency
control

swx1

 Edc
 NA
dB(t ) 
= 0
dt
 E
− dc
 NA

3

Proposal (i)vd*

A. Reduction Method of Harmonic iron lossvu*
v*
3f/gd0 v *
vw

dB(t)
dt

6.05ARMS(b)three-level modulation
Fig. 3. Comparison of waveform
between two-level and three-level modulation.

0B. Reduction Method of Fundamental iron loss
Fig.4 shows the control diagram of the reactive powercompensation control. This control module is based on the
maximum torque/ampere control using reactive power
feedback. The maximum torque/ampere control is
explained first, followed by the reactive powercompensation control. The condition of the maximum
torque/ampere ratio of the SRM is expressed by thefollowing equation [8].

i0 = 2iq
id = 0(3)

where id, iq, i0 is the dq0-axis current, 2 means thecoefficient in the park transformation. Note that the zerophase current is larger than the AC current amplitude
because the negative current does not flow due to theasymmetrical half-bridge converter. Therefore, it isnecessary to satisfy not only id=0 but also i0=iq for thecondition of the maximum torque/ampere ratio.
First, the i0=iq control is explained. iq is equal to theamplitude of the AC current Iac when id=0. Thus, i0 is
controlled to 2 Iac so that the negative current does not
flow. The command value of the zero-phase current
control is expressed as (4).

i0* = 2iq = 2I ac = 2 iγ 2 + iδ 2

(4)where ig and id are the g and d-axis currents, respectively.
As shown in Fig.4, the value calculated by (4) is used as
the reference value for zero-phase current control for thei0=iq control.
Next, the id=0 control is explained. The id=0 control isachieved indirectly in the gd coordinate by the feedback of
the reactive power of the SRM. In the dq-axis coordinate,
the reactive power Qdq injected into the SRM is expressed
as in (5).



Qdq = vq id − vd iq = 2w Ldc (id 2 + iq 2 ) + Laci0id

2



(5)

where vd and vq are the d-axis and q-axis currents,
respectively. The reactive power Qdq under the conditionof id=0 is expressed in (6).

Qdq = 2w Ldc iq 2 = 2w Ldc I ac 2 = 2w Ldc (ig 2 + id 2 )(6)i0=iq control
sqrt

ig
id

w

*
1

2Ldc
Table

Qgd*

i0*

2

P

Qdq_cmp Qgd

vd*

LPF
Limit
[0, Vdc ]vd*
id=0 control

Fig. 4.

Control diagram of high-efficiency control.

On the other hand, in the coordinate gd-axis, the reactive
power Qgd is expressed as in (7).

Qγδ = vδiγ

(7)

On the other hand, the deviation between (6) and (7) isregulated to zero by adjusting the vd with the P controller
for id=0 control. Note that the low pass filter (LPF) in thesecond stage of the P controller shown in Fig.2 reduces theloop gain at high frequency to achieve id=0 only the steadystate [17-20]. In addition, a limit is provided to prevent
overcompensation.
Finally, the reactive power compensation control is
explained. Although the maximum torque/ampere control
can minimize the copper loss, the iron loss is notconsidered. This paper minimizes the sum of the copper
loss and the iron loss. According to (1), the iron loss
increases depending on B. B decreases as vd decreases,
which can be achieved by reducing the modulation index
in the V/f control. In the reactive power compensation
control, the reactive power command Qgd is modified by
the additional term Qdqref_cmp as*
Qγδ
= Qdqref_cmp + 2w Ldc ( iγ2 + iδ2 )(8)Negative Qdqref_com reduces vd and results in the reductionof iron loss [21].
Table 1 shows the parameter of the SRM in theexperiment. Fig.5 shows the experimentally measured loss
with respect to Qdqref_cmp. Fig.6 shows Qdqref_cmp thatminimizes the total loss at different speeds from theexperimental results. The loss breakdown method in Fig.5
is explained below. In this paper, the total loss is defined
as a sum of the mechanical loss, the copper loss, and theiron loss. The mechanical loss is estimated from the output
torque when the test motor is driven by the load motor. The
copper loss is calculated from the winding resistanceconsidering the temperature dependency and the RMS
current measured by a power meter. The iron loss isdetermined by subtracting the mechanical power,
mechanical loss, and copper loss from the motor input
power. As mentioned above, Qdqref_cmp is set to a negativevalue to make vd lower than that in the maximum
torque/ampere control. Compared to the condition of
maximum torque/ampere ratio, negative Qdqref_cmp reduces
the iron loss while increasing the copper loss. Since theiron loss is frequency dependent, Qdqref_cmp that minimizes
the total loss is speed dependent. The optimum Qdqref_cmp isreferred from the table so that Qdqref_cmp is adjusted
according to the speed when implementing the V/f control.

Table 1.

Motor parameters
2.2kW
4800rpm, 7200rpm
4.38Nm300V
Stator:18, Rotor:12
62.3×10-4kgm2
0.45W
7.82mH
5.19mH
7.7A(i0M ax, iqMax)

Qdqref_cmp=-0.067

50

Conv.: 33.0W

Min.:
31.7W

40

Wc+Wi

30

Wi

20
Wc

10
0
-0.2

-0.1
0
0.1
0.2
0.3
0.4
Compensation reactive power value Qdqref_cmp [p.u.]

100

Wc+Wi
Conv.: 66.6W

Min.:
80
62.3W
60

Wi

40
Wc

0
-0.2

Compensation-reactive-power
Qdqref_cmp [p.u.]

-0.1
0
0.1
0.2
0.3
0.4
compensation reactive power value Qdqref_cmp [p.u.](b)wn=1.5p.u.
Relationship between Qdq_cmp and the total loss
(Torque=0.1p.u.)

Fig. 5.
0

8

×10

-2

U-phase current [A]20500us/div

6420(a)two-level modulation method

-2

8
-4
-6
-8

-10

0

0.25

0.5

0.75
1
Speed wn [p.u.]

1.25

1.5

Fig. 6. Relationship between wn and Qdqref_cmp
when the total loss minimum (Torque=0.1p.u.)
III. EXPERIMENTAL RESULTS
Fig. 7 and Fig.8 show the comparison of the current andthe loss with the two-level modulation and the three-level
modulation. The harmonic ripple caused by the switchingis suppressed by the three-level modulation in Fig.7(b)compared with the two-level modulation in Fig.7(a). As
a result, the application of the three-level modulation
reduces the iron loss by 52.8%, whereas the reduction of
the copper loss is relatively small as shown in Fig.8. Inother words, a reduction of the harmonic iron loss isachieved.

U-phase current [A]Copper loss Wc, Iron loss Wi,
Total loss Wc+Wi [W](a)wn=0.5p.u.
Qdqref_cmp=-0.095

500us/div

6420(b)three-level modulation method
Fig.7. Current waveform with each modulation
method when each modulation method is applied.

Loss [W]

Copper loss Wc, Iron loss Wi,
Total loss Wc+Wi [W]Rated power
Base speed(1p.u.), Max. speed
Max. torque(1p.u.)
DC voltage
Poles
Inertia
Resistance
DC inductanceAC inductance
Rated current(1p.u.)

Fig.9 shows the loss comparison results when (A): thetwo-level modulation and the maximum torque/ampere
control, (B): the three-level modulation and the maximum
torque/ampere control, and (C): the three-level modulationand the reactive power compensation control, are applied.
Fig. 10 compares the breakdown results of the measured
loss at 0.25p.u. and 1.5p.u. speed among (A), (B), and (C).
Fig.11 shows the current waveform when (B) or (C) is
applied. According to Fig.9 and Fig.10, the loss is reduced
by up to 69.0% by changing the modulation method andby up to 4.7% by applying the reactive powercompensation control. The effect of the iron loss reduction
at 0.25p.u. speed is better than that at 1.5p.u. speed, as
shown in the comparison between (A) and (B). This isbecause the modulation index at 0.25p.u. speed is lower
than that at 1.5p.u. speed, which generates longer periodsof zero-voltage, as aforementioned in section II.A. On theother hand, the effect of the iron loss reduction at 1.5p.u.
speed is better than that at 0.25p.u. speed, as shown in thecomparison between (B) and (C). This is because the ratioof the fundamental iron loss in the total loss increased as
the fundamental frequency increased. In addition, acomparison of Fig.11(a) and (b) reveals that the RMS
currents are almost the same, which is due to the small

160

with max. torque/ampere control

120

Reduced by 52.8%
Reduced by 1.8%80

Iron loss
Copper loss
Mechanical loss
0
two-level modulation three-level modulation

40

Fig. 8. Loss comparison
between two-level and three-level modulation(wn=1.5p.u., Torque=0.1p.u.).

Fig. 9.(b)

40

(C)

0

0.25

Fig. 9.

Loss comparison between 3 methods(Torque=0.1p.u.).

0.5

0.75
1
Speed wn [p.u.]

100

1.5

Iron loss
Copper loss
Mechanical loss

80

20
(A)

(B)

(C)

(a) wn=0.25p.u.
Iron loss
Copper loss
Mechanical loss
Reduced by 39.0%
Reduced by 4.7%
from (B)

160

Loss [W]

120
80
40
0

4
2
0

(A)

Fig. 10.

(B)(C)(b) wn=1.5p.u.
Comparison by Loss separation(Torque=0.1p.u.).

RMS: 3.16A
4ms/div

0.6
0.4
0.2
0
-0.2
-0.4
8

idAvg. =-0.01p.u. iqAvg. =0.31p.u. i0Avg. =0.32p.u.

6

4
2
0

RMS: 3.17A
4ms/div

0.6
0.4
0.2
0
-0.2
-0.4
8

idAvg. =0.00p.u. iqAvg. =0.32p.u. i0Avg. =0.32p.u.

6

4
2
0

RMS: 3.18A
500us/div

dq, zero-axis
current [p.u.](c)When (B) is applied ( wn=1.5p.u.)

Reduced by 2.3%
from (B)40

06Reduced by 69.0%

60

dq, zero-axis
current [p.u.]

Loss [W]1.25

U-phase current [A]80

idAvg. =0.00p.u. iqAvg. =0.31p.u. i0Avg. =0.32p.u.

(b) When (C) is applied ( wn=0.25p.u.)dq, zero-axis
current [p.u.]

(B)

0.6
0.4
0.2
0
-0.2
-0.4
8

(a) When (B) is applied ( wn=0.25p.)

U-phase current [A]Loss [W](A)two-level modulation & max. torque/ampere control(B)three-level modulation & max. torque/ampere control(C)three-level modulation & reactive power compensation control
160(A)
Fig. 9.(a)120U-phase current [A]This paper proposed the iron loss reduction method of
the V/f control for the SRM. The harmonic iron loss is
reduced by changing the modulation method from the twolevel modulation to the three-level modulation. In addition,
the fundamental iron loss is reduced by applying thereactive power compensation control. From theexperimental results, it was confirmed that the harmoniciron loss is reduced by 69.0% at maximum with the threelevel modulation, and the fundamental iron loss is reduced
by 4.7% with the reactive power compensation control.

dq, zero-axis
current [p.u.]

IV. CONCLUSIONS

U-phase current [A]Qdqref_cmp shown in Fig.6. On the other hand, the RMS
current in Fig.11(d) is higher than that in Fig.11(c) because
the Qdqref_cmp is set to the small value in order to minimize
the total losses. It is concluded that the proposed method
reduces both the harmonic iron loss and the fundamental
iron loss, which are clarified by the comparison between(A) and (B) and by the comparison between (B) and (C),respectively.

0.6
0.4
0.2
0
-0.2
-0.4
8

idAvg. =-0.09p.u. iqAvg. =0.32p.u. i0Avg. =0.34p.u.

6

4
2
0

RMS: 3.46A
500us/div(d)When (C) is applied ( wn=1.5p.u.)
Fig. 11. Current waveform with (B) and (C)(Torque=0.1p.u.).

REFERENCES[1] T. Kosaka, A. Kume, H. Wakayama, and N. Matsui:“Development of high torque density and efficiency
switched reluctance motor with 0.1mm short airgap”, inProceedings of the IEEE European Conference on PowerElectronics and Applications 2007, pp. 1–9 (2007)[2] H. Yamai, Y. Sawada, and K. Ohyama: “Applying Switched
Reluctance Moor to Oil Hydraulic Pump Use”, IEEJ Journal
Industry Applications, vol. 123, no. 2, pp. 96-104 (2014)[3] K. -W. Hu, Y.-Y. Chen, and C.-M. Liaw: “A reversible
position sensorless controlled switched-reluctance motor
drive with adaptive and intuitive commutation tunings”,
IEEE Transactions on Power Electronics, Vol.30, No.7,
pp.3781-3793 (2015)[4] K. Ha, R.Y. Kim, and R. Krishnan: “Position estimation inswitched reluctance motor drive using the first switchingharmonics through Fourier series”, IEEE Transactions on
Industrial Electronics, Vol.58, No.12, pp.5352–5360 (2011)[5] G.G. Lopez, P.C. Kjaer, and T.J.E. Miller: “A new
sensorless method for switched reluctance motor drives”,
IEEE Transactions on Industry Applications, Vol.34, No.4,
pp.832–840 (1998)[6] S. Sumita, K. Deguchi, and Y. Iwaji: “Position Sensorless
Control Method for SRM Using Analog Circuit of Type-1
Control System”, IEEJ Transactions on Industry
Applications, Vol.137, No. 8, pp.612-621 (2017)[7] T. Kumagai, J. Itoh, M. Kato, "V/f Control for Switched
Reluctance Motor," 2022 IEEE Energy Conversion
Congress and Exposition (ECCE), Detroit, MI, USA, 2022,
pp. 1-6 (2022)[8] N. Nakao, K. Akatsu: “Vector Control Specialized for
Switched Reluctance Motor Drives”, IEEJ Transactions ofIndustry Applications, Vol.134, No.12, pp.1006-1015(2014)[9] V. Raulin, A. Radun, I. Husain: “Modeling of Losses in
Switched Reluctance Machines”, IEEE Transactions on
Industry Applications, Vol. 40, No. 6, pp.1560-1569 (2004)[10] H. Hayashi, K. Nakamura, A. Chiba, T. Fukao, K.
Tungpimolrut, D. G. Dorrell: “Efficiency Improvements of
Switched Reluctance Motors with High-Quality Iron Steeland Enhanced Conductor Slot Fill”, IEEE Transactions on
Energy Conversion, Vol.24, No.4, pp. 819-825 (2009)[11] Q. Yu, B. Bilgin, A. Emadi, “Loss and Efficiency Analysis
of Switched Reluctance Machines Using a New Calculation
Method”, IEEE Transactions on Industrial Electronics, Vol.
62, No. 5, pp3072-3080 (2015)[12] Y. Nakazawa, K. Ohyama, H. Fujii, H. Uehara, Y.
Hyakutake: “Efficiency Improvement of Switched
Reluctance Motor by Single-Pulse Control with Variable
Excitation Period”, Vol. 135, No.3, pp284-290 (2014)[13] R. Hiyoshi, T. Noguchi: “Maximum Efficiency Operationof Synchronous Reluctance Motor Using Mathematical
Models of Magnetic Saturation and Iron-Core Loss
Characteristics”, 2013 IEEJ Annual Meeting, No. 4-114(2013)[14] R. Shi, H. A. Toliyat: “Vector control of five-phasesynchronous reluctance motor with space vector pulse widthmodulation (SVPWM) for minimum switching losses”,
APEC. Seventeenth Annual IEEE Applied PowerElectronics Conference and Exposition, Vol.1, pp. 57-63(2002)[15] J. Muhlethaler, J. Biela, J. W. Kolar, A. Exklebe: “Improved
Core-Loss Calculation for Magnetic Components Employedin Power Electronic Systems”, IEEE Transactions on PowerElectronics, Vol. 27, No. 2, pp. 964-973 (2012)[16] T. Kumagai, T. Itoh, K. Nishikawa, J. Itoh, K. Yamane, M.
Nawa: “Reduction of Iron Loss in Stator Core using an
Optimum Pulse Pattern for High-Speed IPMSM”, IEEJ
Transactions on Industry Applications, Vol. 141, No. 4, pp.
313-323 (2021)[17] J. Itoh, N. Nomura, and H. Ohsawa, “A comparison between
V/f control and position-sensorless vector control for thepermanent magnet synchronous motor”, Proceedings of thePower Conversion Conference-Osaka 2002, Vol.3,
pp.1310-1315 (2002)[18] J. Itoh, T. Toi, M. Kato: "Maximum Torque per Ampere
Control Using Hill Climbing Method Without Motor
Parameters Based on V/f Control", 18th European
Conference on Power Electronics and Applications(EPE'16), No. DS3d-Topic 4-0283, (2016)[19] J. Itoh, T. Toi, K. Nishizawa: "Stabilization Method Using
Equivalent Resistance Gain Based on V/f Control for
IPMSM with Long Electrical Time Constant", The 2018
International Power Electronics Conference, No. 23E1-5, pp.
2229-2236 (2018)[20] J. Itoh, T. Toi, K. Nishizawa: "Stabilization Method for
IPMSM with Long Electrical Time Constant Using
Equivalent Resistance Gain Based on V/f Control", IEEJ
Transactions on Industry Applications, Vol. 8, No. 4, pp.
592-599 (2019)[21] J. Itoh, Y.Nakajima, G.T.Chiang: "Maximum Torque per
Ampere and Maximum Efficiency Control Methods basedon V/f Control for IPM Synchronous Motors", IEEJ Journalof Industry Applications, Vol. 3, No. 2, pp. 112-120 (2013)