Pulse Switching Shock Suppression Methodof PWM Inverter
for Pole-Changing Induction Motor
H. Kato1, H. Watanabe1, J. Itoh1, and M. Kobayashi2
1

Nagaoka University of Technology, Japan2
Toyota Motor Corporation, Japan

Abstract-- This paper proposes a pulse switching shock
suppression method for a PWM inverter, which consists of
two original approaches: (i) a switching method between a
synchronous and an asynchronous carrier-based PWM
during pole-changing and (ii) a pulse pattern switching
method of the synchronous PWM, for a pole-changing
induction motor. Continuous changes in harmoniccomponents are confirmed by the proposed method, which
suppresses the switching shocks in the analysis andexperiment.
Index Terms--Pulse switching shock suppression method,PWM inverter, Induction motor, synchronous PWM

I. INTRODUCTION
In recent years, high-efficiency motors with a wide
operating range have been required as drive motors forelectric vehicles (EVs) [1][2]. The EV is used in both lowspeed-high-torque regions (e.g., starting and hill climbing)and high-speed-low-torque regions (e.g., high-speed
cruising). The motor should always be highly efficient inthese areas to reduce the size of the cooling system. Whena motor of the same volume is considered, a high-pole
motor is applied for low-speed, high-torque regions to
reduce the impact of the copper loss, which is the dominantfactor of the total loss. This motor reduces the phasecurrent due to being less susceptible to magnetic saturationof the back yoke. On the other hand, a low-pole motor,
which driven by low frequency compared with the highpole motor, is applied for high-speed-low-torque regions
where the iron loss is the dominant factor of the total loss.
Due to increased iron loss depending on the appliedfrequency, the low-pole motor is expected to be more
efficient than the high-pole motor at high speeds. These area trade-off relationship in motor design. Thus, a switching
method for the induction motor (IM) to switch the numberof poles according to the operating area has been proposed(Pole-changing IM) [3]. The pole-changing IM switches
electrical poles while maintaining a constant rotation
speed during operation. In other words, each pole has adifferent fundamental frequency. The motor efficiency is
expected to be improved by driving the motor as a highpole motor in low-speed, high-torque regions and as a lowpole motor in high-speed, low-torque regions [4].

Inverters installed in EV drive motors use asynchronous PWM to reduce switching loss and noise [5].
The synchronous PWM produces a waveform of theinverter line voltage at every 90 degrees of the electricangles, which reduces the harmonics current of the motor
without increasing the switching frequency. The
synchronous PWM assumes that the modulated wave issinusoidal due to its symmetry. However, as mentioned
above, the voltage command during pole-changing
includes different fundamental frequencies of the two pole
numbers. Synchronous PWM cannot be applied due to theasymmetry of this voltage command. As a result, a voltage
error, which causes acoustic noise and vibration, occurs
when switching from synchronous PWM to asynchronous
carrier-based PWM during pole-changing.
On the other hand, the synchronous PWM is used
except during pole-changing. The following methods havebeen proposed for deriving synchronous PWM: a method
using carriers with frequencies 3+6n times (n: zero andnatural numbers) the frequency of the fundamental
waveform, and a minimization method of the current RMS
value or iron loss [6]-[8]. In these methods, the switchingangles shift steeply when the number of pulses or voltage
command value changes because the transition pattern of
spatial vectors is not taken into account. This generates
noise and vibration.
This paper proposes a modulation method of inverters
specialized for pole-changing IM to solve the changing
pulse pattern problems. The proposed method consists of
two original approaches: (i) a switching method between a
synchronous and an asynchronous carrier-based PWM
during the pole-changing, and (ii) a pulse pattern switching
method of the synchronous PWM. The frequency
characteristics are maintained before and after by injecting
the harmonic components into the voltage command of
asynchronous carrier-based PWM in (i). The pulse patterns
are proposed in which the switching angles vary
continuously even when the voltage or the number ofpulses is changed by fixing the transition pattern of thespace vector, focusing on the switching sequence of threephase in (ii). The validity of the proposed method isdemonstrated by the experiment.

V ref = Vfnd. ( t ) + w1 ⋅ V hrm. ( t )(1)where Vfnd.(t) is the fundamental component of the phasevoltage command, Vhrm.(t) is the harmonic components
included by the synchronous PWM, and w1 is theweighting coefficient. Vref is modulated with w1=1 whenswitching from the synchronous PWM to theasynchronous carrier-based PWM. Then, the harmoniccomponents can be continuously reduced by changing w1
from 1 to 0. After switching the number of poles, the sameprocedure is used to switch to synchronous PWM.
B. Pulse Pattern Switching Method
First, the determining method of the switching phasewhen the voltage command changes is explained. Then,the reduction of the switching shock method when thenumber of pulse changes is explained.
Fig. 3 shows the partitioned regions of the basic vector
and space vector coordinates of the three-phase inverter,
and Table 1 shows the transition patterns of the space
vectors in the 7-pulse PWM. In the synchronous PWM, thebasic unit of the transition pattern of the space vectors is
0–π/9 rad due to the symmetry of the waveform. In the caseof the N-pulse PWM, the number of switching m at 0–π/9
rad is (N+1)/2. The switching is determined under thefollowing conditions,0Fig. 1.

Phase voltage command during pole-changing.

Ed c/2Phase voltage

A. Modulation Method During Pole-Changing
Fig. 1 shows the phase voltage command during thepole-changing. In the pole-changing IM, the synchronous
PWM cannot be used because the voltage command duringpole-changing is an asymmetrical waveform. Thus,
switching from the synchronous PWM to theasynchronous carrier-based PWM is necessary when thenumber of poles is changed. However, switching between
the synchronous PWM and the asynchronous PWM withand without low-order harmonics causes a shock due to thesteep change in harmonic components.
Fig. 2 shows the harmonic components of the phasevoltage included in the synchronous PWM. Fig. 2(b) is
derived by subtracting the fundamental component fromthe synchronous PWM waveform in Fig. 2(a). To keep theharmonic components unchanged when switching
between the synchronous PWM and the asynchronous
carrier-based PWM, the voltage command in theasynchronous carrier-based PWM should include theharmonic components shown in Fig. 2(b). The phasevoltage command Vref in the asynchronous carrier-based
PWM is shown in

Phase voltage

The proposed method consists of two approaches. First,
the modulation method for pole number switching is
explained, followed by the method for determining thepulse pattern.

Phase voltage

II. PROPOSED SWITCHING SHOCK REDUCTION METHOD

0-Ed c/2

Ed c/20-Ed c/2(a) Syn. PWM(b) Harmonic components
Fig. 2. Phase voltage command during pole-changing.

V3(010)V2(110)
Sector 2
V0(000)V7(111)V1(100)V4(011)

Sector 3
Sector 4

Sector 1
Sector 6

Sector 5
V5(001)

V6(101)(a) Space vector of(b) Dividing region of
three phase inverter
space vector
Fig. 3. Transition modes of space vector.

Table 1. Transition mode and switching phase
at 0 to 30 deg.
Mode 1Mode 2Mode 3Mode 4Mode 5Mode 6
Mode 7
vuo
Edc
2
Edc O
2
vvo
Edc
2
Edc O
2
vwo
Edc
2
Edc O
2 α0

Transition mode
V0→V1→V0→V1
V0→V1→V2→V1
V1→V0→V1→V2
V1→V2→V1→V2
V1→V2→V7→V2
V7→V2→V1→V2
V7→V2→V7→V2

Switching phase
U→U→U
U→V→V
U→U→V
V→V→V
V→W→W
W→V→V
W→W→W

π
9

θ

π
9

θ

π
9

α1

Fig. 4.

α2

α3

θ

α4

Phase voltage waveforms at Mode2.

Table 2. Combination of space vector pattern.
Case 1Case 2
Case 3
Case 4
Case 5
Case 6
Case 75-pulse PWM
V0→V1→V0
V0→V1→V0
V0→V1→V0
V0→V1→V0
V7→V2→V1
V7→V2→V1
V7→V2→V1

7-pulse PWM
V0→V1→V0→V1
V1→V0→V1→V0
V0→V1→V2→V1
V1→V2→V7→V2
V7→V2→V1→V2
V0→V1→V0→V1
V1→V2→V7→V2

Vector transition
Continuous
Continuous
Discontinuous
Discontinuous
Continuous
Discontinuous
Discontinuous

・One switch per vector transition.
・No switching at 0 rad.
・Vector at 0 rad can be output in both Sectors 1 and 6.
・Switching at π/9 rad.
・Vectors before and after π/9 rad are nonzero.
From the above, there are transition patterns of the vectors
shown in Table 1 with the 7-pulse PWM.
Fig. 4 shows the switching patterns in the case of “Mode2” of Table 1. In this method, the transition pattern of thespace vectors is fixed by defining the phase to be switchedfrom α1 to αm in advance when deriving the pulse pattern.
The equation for converting U, V, and W-phase switching
αi to U-phase switching βj is expressed as (2),β j = αiβ j = π / 3 + αi β j = π / 3 − α i( U-phase switching )( V-phase switching )( W-phase switching )

4

π

π /2

0

vuo cos θ dθ

(2)

(3)

Expanding with βj yields (4),a1 = sign {vuo (0)}2 Edc  m −1
i +1
m
 2  ( −1) sin β i − ( −1)  (4)π  i =1
For simplicity, (5) is obtained by standardizing thesquare wave voltage by its maximum amplitude 2Edc/π.
Ke =a1
2 Edc / π

 m −1i +1m
= sign {vuo (0)} ⋅  2 ( −1) sin β i − ( −1)  i =1

αi = w2αi_N-pulse + (1 − w2 ) αi_N-1-pulse ,i :1, 2,3,L( N + 1) / 2(6)

The number of pulses is N-1 when w2=0 and N when w2=1
in (9). The harmonic components can be changed
continuously by changing w2 from 1 to 0.
III. SIMULATION RESULTThe fundamental wave amplitude a1 of the U-phasevoltage vuo is expressed bya1 =pulse pattern that is “Continuous” in “Vector transition” inTable 2 is selected. Note that the pulse pattern is optimized
based on the transition pattern of the space vectors
determined above. Finally, the switching angles whileswitching the number of pulses is determined by (6) using
the weight coefficients w2,(5)

Ke is a constraint on the phase voltage command. After that,the pulse pattern is optimized by using the current RMS
value of the U-V line currents as an evaluation function, as
in the method described in Ref. [6]. The method in Ref. [6]optimizes the switching angles of the U-phase at 0–π/4 rad.
On the other hand, the proposed method optimizes theswitching angles of the U, V, and W-phase at 0–π/9 rad,which fixes the transition pattern of the space vectors.
The reducing the switching shock method when thenumber of pulses is changed is described. This method
focuses on the transition pattern of space vectors before
and after the number of pulses is changed.
Table 2 shows the transition pattern of the space vectors
before and after switching between 5 and 7-pulse
synchronous PWM. The change in the transition pattern of
the space vectors before and after switching must be
minimized to reduce the gaps in the switching angles. In
the 5 and 7-pulse, an additional vector must be selectedthat is adjacent to the first or last vector of the 5-pulse. The

Fig. 5 shows the simulation results and harmonic
analysis results when switching between the synchronous
PWM and the asynchronous carrier-based PWM for polechanging. The proposed method suppresses the steep
change of harmonics immediately after switching that
occurs in the conventional method. Besides, the proposed
method maintains the same fundamental component
during pole-changing.
Fig. 6 shows the pulse pattern optimization results andthe current RMS values when the voltage commandchanges. In the conventional method, the switching angles
obtained by optimization have gaps because there are local
solutions of the switching angles for each transition patternof the space vectors. The switching angles do not havegaps by fixing the transition pattern of space vectors in the
proposed method. In addition, the increase of the current
RMS values due to the application of the proposed method
is suppressed to 0.09% at maximum.
Fig. 7 shows the simulation results and harmonic
analysis results when the number of pulses changes. Whenthe number of pulses is changed, the proposed method
suppresses the steep change of harmonic components that
occurs in the conventional method. The fundamental
amplitude is kept constant when the number of pulses ischanged by changing the switching angles linearly with theweighting coefficient.
IV. EXPERIMENTAL RESULT
Fig. 8 shows the experimental results and harmonic
analysis results when switching between the synchronous
PWM and the asynchronous carrier-based PWM for polechanging. Pole-changing IM with a rated speed of
1800rpm and a rated torque of 11.67Nm. The motor
operates 4-pole and 8-pole. The number of poles ischanged at no-load, rated speed. The proposed method
suppresses the steep change of harmonics immediately
after switching that occurs in the conventional method,
similar to the simulation results. Low-order harmoniccomponents do not occur during pole switching because
the carrier frequency of the asynchronous carrier-based
PWM is set to 20kHz, which is far enough away from thefundamental frequency.

Fig. 9 shows the experimental results and harmonic
analysis results when the number of pulses changes. The
proposed method, suppresses the steep change ofharmonics immediately after switching that occurs in theconventional method similar to the simulation results.

into the voltage command of asynchronous carrier-based
PWM before and after pole-changing in (i). In addition, theswitching shock, when the pulse pattern changes, wassuppressed with the maximum increase in current RMS
value of 0.09% by limiting the transition pattern of thespace vectors in the synchronous PWM in (ii). Bothmethods achieved zero shift in switching angles caused byswitching the pulse patterns. The suppression of theswitching shock with the proposed method wasdemonstrated in the analysis and experiment.

V. CONCLUSIONSThis paper proposed a new modulation method tosuppress a switching shock in a pole-changing induction
motor. The switching shock was suppressed by injecting
the harmonic components that synchronous PWM includes

Vref [V]Edc /20500ms/div

Frequency [Hz]-Edc /2
4.8k

0dB

3.6k

-5dB

2.4k

-10dB
Steep change

1.2k

-15dB
V8fnd.: 240Hz
500ms/div

V4fnd.: 120Hz-20dB
w1 [-]

04-pole4+8-pole
Asyn. 20kHz

0500ms/div-Edc /2
4.8k
Frequency [Hz]Vref [V]Edc /2

0dB

3.6k

-5dB

2.4k

-10dB
Seamless

1.2k
V4fnd.: 120Hz01
08-poleSyn. 13-pulse

4-poleSyn. 7-pulse-15dB
V8fnd.: 240Hz
500ms/div

4+8-pole
Asyn. 20kHz

Syn. 13-pulse-20dB

500ms/div
8-poleSyn. 7-pulse

Fig. 5. Simulation results and harmonic analysis results
when switching between the synchronous PWM and the asynchronous carrier-based PWM for pole-changing.

Mode3

α1 α2 α3

0.4
Mode1
0.2
0

8

0.8
0.6

α1 α2 α3

Mode1

0.4
0.2
0

30
60
90
U-phase switching angle [deg.]

30
60
90
U-phase switching angle [deg.]

Current RMS value [A]

0.8
0.6

1

Mode4
Mode2
Voltage command Ke [-]Voltage command Ke [-]1

Conventional Method
Proposed Method
6

4

2

0

Max.: Increased
by 0.09% (Ke=0.96)
0.2 0.4 0.6 0.8
Voltage command Ke [-]

1

0dB

3.6k

-5dB

2.4k

-10dB
-15dB

1.2k

Steep change

0

V8fnd.: 240Hz
500ms/div

Frequency [Hz]

4.8k

-20dB
w2 [-]

Frequency [Hz](a) Conventional method(b) Proposed method(c) Current RMS value
Fig. 6. Pulse pattern optimization results and the current RMS values when the voltage command changes.

Syn. 5-pulse

Syn. 7-pulse

4.8k

0dB

3.6k

-5dB

2.4k

-10dB

1.2k

Seamless010Syn. 5-pulse-15dB
V8fnd.: 240Hz
500ms/div
500ms/div
Syn. 7-pulse

Fig. 7. Simulation results and harmonic analysis results when the number of pulses changes.

-20dB

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4.8k

0dB

3.6k

-5dB

2.4k

-10dB
Steep change

1.2k

V4fnd.: 120Hz-20dB

w1 [-]

0-15dB
V8fnd.: 240Hz
500ms/div

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Asyn. 20kHz

Syn. 13-pulse

4.8k

0dB

3.6k

-5dB

2.4k

-10dB
Seamless

1.2k
0
1
0

8-pole4-poleSyn. 7-pulse-15dB
V8fnd.: 240Hz
500ms/div

V4fnd.: 120Hz

4+8-pole
Asyn. 20kHz

Syn. 13-pulse-20dB

500ms/div
8-poleSyn. 7-pulse

0dB

3.6k

-5dB

2.4k

-10dB
-15dB

1.2k

Steep change

0

V8fnd.: 240Hz
500ms/div

Frequency [Hz]

4.8k

-20dB
w2 [-]

Frequency [Hz]Fig. 8. Experimental results and harmonic analysis results
when switching between the synchronous PWM and the asynchronous carrier-based PWM for pole-changing.

Syn. 5-pulse

Syn. 7-pulse

4.8k

0dB

3.6k

-5dB

2.4k

-10dB

1.2k

Seamless010Syn. 5-pulse-15dB
V8fnd.: 240Hz
500ms/div
500ms/div
Syn. 7-pulse

Fig. 9. Experimental results and harmonic analysis results when the number of pulses changes.

-20dB