2018 21st International Conference on Electrical Machines and Systems (ICEMS) October 7-10, 2018┃Jeju, Korea

Compensation for Multilevel Voltage Waveform
Generated by Dual Inverter System
Yoshiaki Oto
Environment and Energy Systems
Shizuoka University
Shizuoka, Japanohto.yoshiaki.15@shizuoka.ac.jp
Takahiro Yamada
Power Electronics R&I Department
DENSO CORPORATION
Aichi, Japan
takahiro_t_yamada@denso.co.jp

Toshihiko Noguchi
Environment and Energy Systems
Shizuoka University
Shizuoka, Japan
noguchi.toshihiko@shizuoka.ac.jp

Takanari Sasaya
Power Electronics R&I Department
DENSO CORPORATION
Aichi, Japantakanari_sasaya@denso.co.jp

Ryoya Kazaoka
Power Electronics R&I Department
DENSO CORPORATION
Aichi, Japanryoya_kazaoka@denso.co.jp

Abstract— A space vector modulation (SVM) technique of adual inverter system feeding an open-end-winding PM motor andimprovement technique of generated multi-level voltage
waveforms with the system are proposed in the paper. In the
proposed system, one of the inverters has a battery power source
and the other has a capacitor across the DC-bus. The SVM mustbe achieved both to generate multilevel voltage waveforms to themotor and to control the capacitor voltage constantly at the sametime by using redundant switching states of the system. In order
to control the capacitor voltage, it is necessary to select the
optimal switching state with SVM considering the instantaneous
motor power factor. In addition, it is also necessary to eliminate
error voltage vectors contained in outputted multilevel voltage
waveform. The error voltage vectors are generated during thedead time when the switching devices in the same phase of bothinverters are synchronously turned on or turned off. Therefore,
the special dead time technique is need for the SVM of the dual
inverter system. The paper demonstrates proposed SVM
techniques through computer simulation and experimental tests.
Keywords—Dual inverter system, space vector modulation,
open-end-winding motor, capacitor voltage control, dead time

I. INTRODUCTION
In recent years, mileage improvement and autopilot
technologies are focused on to reduce carbon dioxide emissionof hybrid vehicles. Many of the current hybrid vehicles are
based on the combination of a bidirectional chopper and a twolevel inverter, and drive a high-voltage permanent magnet (PM)motor. Therefore, the line-to-line voltage of the motor is athree-level waveform with high dv/dt, which may cause
deterioration of the total harmonic distortion (THD),
conduction noise, and radiation noise. The current system also
has a drawback from the viewpoint of the failsafe because themotor cannot be operated if either the chopper or the inverter isfailed. In order to solve the problems above, a dual inverter
system which drives open-end-winding motor with two
inverters is researched. In the conventional dual inverter
system, the both inverters have a battery power source acrossthe DC-bus and the battery voltages are same value [1]. On theother hand, one of the battery power source across the DC-bus
is replaced with capacitors and the capacitor voltage isThree-Phase
Three-Wire Motor

Chopper

InverterFig. 1. Conventional motor drive by single inverter system.
Open-EndWinding Motor
150 V
Battery

75 V
Capacitor

150 V

INV1 (u1, v1, w1)

75 V(u2, v2, w2)’INV2

Fig. 2. Open-end winding motor drive by dual inverter system.

controlled at a half value of the other hand battery voltage inthe proposed dual inverter system [2][3]. In the case, it isrequired both to control the capacitor voltage at commanded
value and to generate multilevel voltage waveform to the openend-winding motor terminals at the same time. Particularly, it isindispensable to take the instantaneous motor power factor into
account for the capacitor voltage control, i.e., charging ordischarging control of the capacitor. The proposed space vector
modulation (SVM) technique makes it possible to achieve bothto capacitor voltage control and multilevel voltage waveformgeneration at the same time [4]. However, the outputted
multilevel voltage waveforms with proposed system contain alot of unexpected error voltage pulses, which are generated
during the dead time when the both switching devices in thesame phase are synchronously turned on or turned off [5]. The
measure to improve the multilevel voltage waveforms is
proposed, however, this is incomplete because it doesn’t
consider the fluctuation of switching speed due to the motor
current norm [6]. In the paper, a novel strategy of the SVM forthe dual inverter system is proposed, which allows thecapacitor voltage control and the multilevel voltage waveformgeneration at the same time according to the instantaneous
motor power factor. Furthermore, the compensation forsynchronous switching of dual inverter system is also proposedin this paper, and the above SVM techniques are examinedthrough several experimental tests.

This work was supported by the New Energy and Industrial Technology
Development Organization (NEDO) Grant-in-Aid for Scientific Researchfrom the National Government and Ministry of Economy, Trade and Industry,
Japan.

Copyright ⓒ KIEE Electrical Machinery and Energy Conversion Systems

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II. CONFIGURATION OF DUAL INVERTER SYSTEM
A. Circuit Configration of Proposed Dual Inverter System
Fig. 1 shows the conventional motor drive system with asingle two-level inverter which drives a three-phase PM motorwith a neutral point inside of the motor. Fig. 2 is a circuit
diagram of the proposed dual inverter system with two single
two-level inverters which drives an open-end-winding PM
motor. The left-hand side inverter is called INV 1 and the otheron the right-hand side is INV 2 whose DC-bus battery powersources are replaced with capacitors. Each leg of the bothinverters is complementary operated, and the combination of
the switching states is expressed as (u1, v1, w1) (u2, v2, w2)’,
where the switching states “1” and “0” mean that the upper arm
is turned on and off, respectively.
The dual inverter system can generate the multilevel
voltage waveforms by adding or subtracting one inverter output
voltage to/from the other inverter output voltage. The system
has a drawback of increasing the inverter counts and their DCbus battery power source counts, but does not require any
voltage boost power converter such as the bidirectional
chopper. The multilevel voltage waveform generation is
expected to improve the THD resulting in the copper loss andiron loss reductions, and expected to reduce the conduction
noise and the radiation noise owing to the reduction of dv/dt.
The dual inverter system has the redundancy in the switchingstates. In other words, a particular voltage vector can be applied
to the motor with different several switching states, whichallows operation of the motor with controlling the capacitor
voltage of INV 2. If capacitors are connected in parallel to thebatteries across both side inverter DC-buses respectively, thedual inverter system can continue to drive the motor even if oneof the batteries is in failure. Because the switching state
redundancy makes it possible to keep the capacitor voltage on
the failure side at constant value and to achieve continuous
operation of the motor as the dual inverter drive as shown in
Fig. 2. In addition, in the case of the failure in one switching
device of either inverter, the system can continue to operate themotor as a single inverter drive by shorting the three-phasewindings with normal condition arms of the fail inverter. In thisway, the proposed dual inverter system has advantages offailsafe.
B. DC-Bus Voltage Ratio and Switching State Redundancy
The dual inverter system discussed in the paper controls thecapacitor voltage of INV 2 at half of the INV 1 DC-bus battery
voltage. The reason is, in addition to generate the 9-level
voltage waveform, to utilize the switching state redundancy.
The single inverter can output 8 voltage vectors, i.e., 2 and
6 of them are zero-voltage vectors and non-zero voltage
vectors, respectively. The output voltage vectors of the dual
inverter system are sum of the output voltage vectors of the two
inverters. Fig. 3 shows the output voltage vectors from 0 to 60
deg. of the two dual inverter systems whose DC-bus voltage
ratios are 1:1 and 2:1, respectively. In the figure, the capacitor
charging, holding, and discharging modes are noted as “+,”“0,” and “-” after the switching states, respectively. As shownin Fig. 3, a particular voltage vector can be applied to the motorby using different several switching states, which means the(000)(001)’(-)(111)(001)’(-)(010)(011)’(-)(100)(101)’(-)(110)(000)’(0)(110)(111)’(0)(000)(000)’(0)(000)(111)’(0)(111)(000)’(0)(111)(111)’(0)(001)(001)’(+)(010)(010)’(+)(100)(100)’(+)(011)(011)’(+)(101)(101)’(+)(110)(110)’(+)(110)(001)’(-)(100)(001)’(-)(110)(011)’(-)(000)(011)’(-)(111)(011)’(-)(101)(001)’(-)(110)(010)’(-)(100)(000)’(0)(100)(111)’(0)(110)(000)’(0)(110)(111)’(0)(000)(001)’(-)(111)(001)’(-)(110)(110)’(+)(110)(001)’(-)(110)(011)’(-)(100)(101)’(+)(110)(010)’(-)(100)(001)’(-)(000)(000)’(0)(100)(011)’(-)(000)(111)’(0)(111)(000)’(0) (000)(011)’(-) (100)(000)’(0)(111)(111)’(0) (111)(011)’(-) (100)(111)’(0)(100)(100)’(+)(100)(011)’(-)(a) Dual inverter with(b) Dual inverter with
1:1 DC-bus voltage.
2:1 DC-bus voltage.
Fig. 3. Relationship between DC-bus voltage ratio and switching state
redundancy.
V60

V60in

#3
#2

Vz

#4
V0in

V30

#1
V0

m=0
m=0.5
m=1.0
Fig. 4. Voltage vectors used in SVM and definition of modulation index.

both systems have the switching state redundancy. However,
only one of the capacitor charging mode or the discharging
mode is available among the redundant switching states in thecase of the 1:1 DC-bus voltage ratio; hence, it is impossible toswitch over the charging mode and the discharging mode
redundantly. On the other hand, there is both of the charging
mode and the discharging mode in the redundant switchingstates of the dual inverter system with the 2:1 DC-bus voltage
ratio. This makes it possible to control the capacitor voltage
and simultaneously to generate multilevel voltage waveform,
which is the reason why the 2:1 DC-bus voltage ratio has been
employed for the proposed dual inverter system. However, thelongest voltage vectors that configure the most outer hexagon
do not have the redundancy even if the 2:1 voltage ratio is
employed, so the longest voltage vectors are not utilized in the
SVM discussed in the paper.
III. SELECTION OF VOLTAGE VECTORS IN SVM AND DEFINITION
OF MODULATION INDEX
Fig. 4 illustrates the voltage vectors from 0 to 60 deg. ofdual inverter system employed 2:1 DC-bus voltage ratio, where
the symbol “m” denotes a modulation index. The modulationindex is defined as m = 1.0 when the circular locus of thevoltage vector generated by the SVM is inscribed in the outerhexagon and m = 0.5 when the locus is inscribed in the inner
hexagon. As shown in Fig. 3., the system can generate a longer
voltage vector than m = 1.0 by using the longest voltage
vectors which configure the most outer hexagon, however, thelongest vectors do not have a switching redundancy, i.e., itcannot operate capacitor voltage with SVM. Therefore themodulation index m = 1.0 is defined as above, where thecapacitor voltage control is achieved with SVM.
The SVM is carried out by synthesizing three discrete
inverter voltage vectors at appropriate ratio to output a

1296

SVM 1 Period
V60in(000)(001)’(-)(111)(001)’(-)

V30

V60

(100)(101)’(-)(110)(010)’(+)(110)(000)’(0)(110)(111)’(0)(110)(110)’(+)

V60in(000)(001)’(-)(111)(001)’(-)

V60

V30

V60in

(110)(000)’(0)(100)(101)’(-)(110)(111)’(0)(110)(010)’(+)(000)(001)’(-)(111)(001)’(-)(110)(110)’(+)

Charge(110)(110)’(+)

Hold

Discharge

ChargeDischarge

Discharge

Hold

The Reference of Capacitor Voltage
The Voltage of Capacitor

Fig. 5. Simultaneous control of multilevel voltage waveform generation and capacitor voltage with SVM.

commanded voltage vector. The commanded voltage vector
can be synthesized by using three voltage vectors surrounding
the commanded voltage vector in a triangle shape. For
example, in the case that the commanded voltage vector is in
the #1 triangle sector, the three voltage vectors V0, V0in, andV30 surrounding the corresponding triangle sector are used for
the SVM to synthesize the commanded voltage vector, which
contributes to reduce the dv/dt. The triangle sectors from #1 to#3 do not use zero-voltage vectors Vz for the SVM, resulting in
9-level voltage waveforms across each motor winding, but Vz
must be used in the sector #4.
IV. CAPACITOR VOLTAGE CONTROL AND IMPACT OF
INSTANTANEOUS MOTOR POWER FACTOR
A. Capacitor Voltage Control of INV2
The DC-bus voltage sources of INV 2 are replaced withcapacitors in the proposed dual inverter system of the paper.
The capacitor voltage must be controlled at constant value by
charging and discharging it, and simultaneously multilevel
voltage waveform generation must also be achieved.
The dual inverter system has redundant switching states andcan output a particular voltage vector with different several
redundant switching states as described previously. The
capacitor charging mode or the discharging mode changes
according to polarity of the current flowing into the capacitor.
As illustrated in Fig. 5, the multilevel voltage waveformgeneration with the SVM and the capacitor voltage control cansimultaneously be carried out by selecting an appropriate
switching state among the redundant states.
B. Impact of Instantaneous Motor Power Factor
Fig. 6 shows the relationship between the phase of motor
line current vector and the polarities of the motor line currents,
where the polarity signs “+” means a motor current direction
from INV 1 to INV 2, while “-“ means the opposite direction.
The capacitor charging mode or the discharging mode isdetermined by the motor line current directions in every
switching state. The PM motor connected to dual inverter
system is, however, inherently an inductive load; thus, themotor line currents lag behind the voltage vector generated
with SVM. Each line current direction changes according to theinstantaneous motor power factor, which is affected by the
motor operating conditions and the motor parameters. Thisimplies that the instantaneous motor power factor must be
taken into account to control the capacitor voltage. Let’s

Current
Polarity C
U−
V＋
W−

Current
Polarity B
U＋V＋
V60 W −
V30

V60in

Current
Polarity D
U−
V＋
W＋

Current
Polarity A
U＋
V−
W−

V
Vz

Current
Polarity E
U−
V−
W＋

Current
Polarity F
U＋
V−
W＋

Fig. 6. Relationship between current vector phase angle and motor line
currents polarity.
Current Polarity

The redundant switching states generating V30（1，1，0） （0，1，0）’
V＋

B

U＋

W－

F

U＋

Discharging

W－

Charging
V－A（1，0，0） （1，0，1）’

V＋
U＋

U＋

W－

W － Discharging
V－

U＋

U＋

W＋

W ＋ Discharging

Charging

V－
Charging

V－

Fig. 7. Relationship between redundant switching states and capacitor voltage
control modes.

assume the case that the commanded voltage vector is in thehatched sector as illustrated in Fig. 6. The three voltage vectors
V60, V60in, and V30 are used to synthesize the command
voltage vector. The maximum lagging phase angle between thevoltage vector and the current vector is 90 deg., which meansthat the current polarity is in one of “B,” “A,” and “F.” Two of
the redundant switching states to generate V30 voltage vector
are shown in Fig. 7, for example, where the relationshipbetween the motor line current polarity and the capacitor
charging or the discharging mode. A switching state(110)(010)’ is the capacitor charging mode in the case of thecurrent vector direction “B,” but the switching state is capacitor

1297

i d*

ωm*
＋
－

PI

T*

1/Ψ

iq* ＋ －
＋

PI
PI

vd*

dq
↓
αβ

vq*

－

tan−1

tan−1

swu1

vα*

swv1

vβ*

sww1

θ v*
θi*

S
V
M

Vcap

ωm

iu
INV1

iv

iw

PM

Motor
swu2
swv2
INV2
sww2

1
s

id
iq

αβ
↓
dq

iα

uvw
↓
αβ

iβ

Power Factor Angle Motor Rotation Speed(r/min)Fig. 8. Control block diagram of dual inverter system for open-end winding PM motor drive.
2500
TABLE . COMPUTER SIMULATION CONDITIONS.
1 _re f2000
Switching frequency
10 kHz1
1500
1000
Voltage of battery (INV1)
300 V
500
Voltage of capacitor (INV2)
150±5 V
050
Capacitance of capacitor (INV2)
1329.4 μF
4030Motor speed command value
1150, 2300 r/min
20
Dead time
100 μs
0Number of poles
8
180
170
160
Number of flux linkage
0.174 Wb
150
140
2
130
Momentofinertia0.00173
kgm
Motor
120
110
parameters
Damping coefficient
0.005 N/rad/s
100
300
200
Phase resistance1Ω
dv/dt = 100 V
1000Phase inductance
5 mH

_re f

discharging mode in the case of the current vector direction“A” or “F.” In general, the relationship between the switchingstate and the capacitor charging or discharging mode cannot
uniquely be determined if the phase angle of motor line current
vector changes due to the instantaneous motor power factor.
Therefore, it is indispensable for the SVM to select an optimal
switching state among the redundant switching states thatmakes it possible to control the capacitor voltage at constantvalue according to the instantaneous motor power factor.
V. COMPUTER SIMULATION RESULTS
Some computer simulations have been conducted to
examine the basic operation of the dual inverter system feeding
the open-end winding PM motor, where the DC-bus powersource of INV 2 is replaced with capacitors. The control block
diagram is indicated in Fig. 8. The motor is controlled with afield-oriented control (vector control) algorithm, so has a speed
control loop and a current control loops in the controller. The
phase angle between the voltage vector and the motor line
current vector is calculated on the synchronously rotating (d-q)
reference frame, which is utilized to select the most optimal
switching state among the redundant switching states, as wellas the feedback value of the capacitor voltage of INV 2.
TABLE
and Fig. 9 show the simulation conditions andthe simulation results, respectively. The motor speed, theinstantaneous motor power factor, the capacitor voltage, andthe voltage across the U-phase winding terminals are shown
from the top to the bottom of Fig. 9. As can be seen in the
figure, even though the dynamic variation of the instantaneous
motor power factor is caused by a transient acceleration of the
motor speed, the capacitor voltage is properly kept constant at

U-Phase Voltage
Vu (V)

Capacitor Voltage
Vcap (V)_dv/dt = 200 V

-100
-200
-300

0

10

20

30

Time (ms)

40

50

60 0

10

20

30

40

50

60

Time (ms)(a) m = 0.4 (1150 r/min)(b) m = 0.8 (2300 r/min)Fig. 9. Simulation results.

150±5 V. At the same time, the 5-level voltage waveform isobserved at low modulation index (m = 0.4, 1150 r/min) while
the 9-level voltage waveform is observed at high modulationindex (m = 0.8, 2300 r/min.)VI. EXPERIMENTAL SETUP AND TEST RESULTS
Experimental tests have been conducted with anexperimental setup of the dual inverter system as shown in Fig.
10. The open-end winding PM motor is controlled by a fieldoriented control (vector control) algorithm, and its speed isregulated at 840 r/min (m = 0.4) and 1680 r/min (m = 0.8) by aload servo motor directly connected to the test motor. The rated
output power of the test motor is 1 kW, and is fed by the two 5kVA inverters in which one of the inverter has only thecapacitor across the DC-bus. Experimental test conditions andthe test results are shown in TABLE
and Fig. 11,
respectively. As shown in the test results, the multilevel voltage
waveform is outputted across the open-end winding of the test
motor, but contains a lot of unexpected error pulses in the
waveform, which detrimentally deteriorates the THD of thevoltage waveform. In particular, the dv/dt deteriorates in caseof capacitor charging mode at low modulation index andcapacitor discharging mode at high modulation index.
However, the three-phase line currents are balanced, and thecapacitor voltage is properly controlled to be around 150 V
within the operated hysteresis band. Therefore, the proposed
approach works well, but must be improved to generated
multilevel voltage waveforms.

1298

Motor Current(A)
Capacitor Voltage
Vcap (V)TABLE Ⅱ. EXPERIMENT TEST CONDITIONS.
Switching frequency
10 kHzVoltage of battery (INV1)
300 V
Voltage of capacitor (INV2)
150±5 V
Capacitance of capacitor (INV2)
1329.4 μF
d-axis current command value
0A
q-axis current command value
1A
Motor speed
840, 1680 r/min
Dead time
4 μs
Number of poles
8
Rated power
1000 W
Rated speed
2000 r/min
Rated torque4.78 Nm
Motor
Rated current
3.7 A
parameters
Armature resistance
1.1 Ω
Number of flux linkage
0.174 Wb
d-axis inductance
11.0 mH
q-axis inductance
25.0 mH

U-Phase Voltage
Vu (V)

Fig. 10. Experimental setup of dual inverter system.

2.0
1.5
1.0
0.5
0.0
-0.5
-1.0
-1.5
-2.0
180
170
160
150
140
130
120
110
100
300

Iu
Iv
Iw

Iu
Iv
Iw

dv/dt = 375 V

dv/dt = 360 V

200
100
0
-100
-200
-300

0

10

20

30

Time (ms)

40

50 0

10

20

30

40

50

Time (ms)(a) m = 0.4 (840 r/min)(b) m = 0.8 (1680 r/min)Fig. 11. Experimental test results.

immediately after the first dead time of INV2 is finished at thestart of state #3. In state #3, the lower arm of INV1 turns onwith the diode which is during the second dead time, and thelower arm of INV2 also turns on which is after the first deadtime. After the second dead time of INV1 is finished, the lower
arms of the both inverters turn on in state #4. In this way, it cansynchronously turn on or turn off the switching devices in thesame phase of the both inverters without error voltages.

A. Dead Time Technique of Dual Inverter System
Particular switching sequences are included on the dual
inverter system with the 2:1 DC-bus voltage ratio, where theswitching devices in the same phase of both inverters aresynchronously turned on or turned off. For example, let’s
assume the transition from a switching state “A” to “B” asshown in Fig. 12, where the upper arms of the both inverters
are turned on in “A,” while both lower arms are turned on in“B.” Because the switching state during the dead time isdetermined by the line current direction, the error voltage
vector is generated because the switching state of INV1 andINV2 during the dead time are “0” and “1,” respectively. Fig.
13 shows an example of the unexpected error voltages inserted
during each dead time. In the case of the commended voltage
vector in the hatched sector, the three voltage vectors V60,
V60in, and V30 are used for the SVM. The proper switchingsequence is V60in → V30 → V60 → V60 in → ···, however,
the irregular voltage vectors such as V120in, V0, and Vz are
generated during every dead time of synchronous switching.

B. Proposed Compensation for Synchronous Switching ofDual Inverter System
However, there is a difference of the switching speed
between switching devices in the same phase of INV1 andINV2; hence, it is difficult to insert the second dead time
precisely at the end of the first dead time. Fig. 14 shows thedifference of switching timings between INV1 and INV2
obtained through the experimental test, which means thedifference is changed by the line current norm. In the figure,the positive line current indicates a direction from INV 1 to
INV 2 and the negative does the opposite. Let’s assume thesynchronous turning off as shown in TABLE Ⅲ, where theturning off time of the switching device of INV1 is expressed
as toff1, the turning on time of INV2 as ton2, and the reverse
recovery time of the diode of INV2 as trr2. When thesynchronous switching is done and the state changes from #2 to#3, the lower arm of INV1 gets turning on with diode after theupper arm turns off with the IGBT, while the lower arm of
INV2 gets turning on with the IGBT after the upper arm turns
off with the diode. In this case, the switching time of INV1 isalmost equal to toff1 because the turning on time of the diodecan be ignored for such a high speed, while the switching timeof INV2 is the sum of the reverse recovery time of diode andthe turning on time of IGBT, i.e., trr2 + ton2. As a result, theswitching time of INV1 is longer than INV2 because thereverse recovery time of INV2 is shorter in case the line current
norm is small, i.e., toff1 > trr2 + ton2.

TABLE Ⅲ shows the dead time technique of dual inverter
system to eliminate unexpected irregular voltage vectors during
the dead time in case of the line current direction from INV1 to
INV2. The upper arms of the both inverters are turned on instate #1. The first dead time is inserted in INV2 where the line
current follows into INV2 in state #2, when the upper arm of
INV1 keeps turning on, and the upper arm of INV2 also keeps
turning on with the diode. The second dead time starts to beinserted in INV1 where the line current follows out

The test results employed the conventional dead time
technique and the dead time technique with proposedcompensation are shown in Fig. 15 and Fig. 16, respectively. It
is observed that the dv/dt is reduced by 16.7 % at low
modulation index (m = 0.4) and deteriorated by 2.7 % at highmodulation index (m = 0.7) with conventional dead time
technique, on the other hand the dv/dt is reduced by 30.6 % at
low modulation index (m = 0.4) and deteriorated by 4.0 % athigh modulation index (m = 0.7) with proposed dead timeVII. IMPACT OF DEAD TIME

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1

Difference of Switching Timing INV1 - INV2 (ns)

INV1

INV2
1

i

Switching State A
0

0

INV1
0

INV2
1

i

Dead-Time
0

1

INV1

0

Switching State B
1

1

Fig. 12. Impact of dead time in synchronous switching.

V60in

V30
V

V30
(100)(101)’

V120in(000)(101)’

V60(110)(111)’

V0(100)(111)’

V60in(111)(001)’

Vz(111)(111)’-1.5-1.0 -0.5
0.0
0.5
Motor Line Current (A)

1.0

1.5

2.0

dv/dt = 385 V

dv/dt = 300 V

-300

0

10

20

30

40

50 0

10

Time (ms)The irregular voltage vector
generated in dead-time. Dead time technique to eliminate error voltage vectors.
INV1
INV2
State
Phase Voltage
Up Un Up Un
#1
1
0
1
0
Vdc1-Vdc2
#2
1
0
0
0
Vdc1-Vdc2
#3
0
0
0
1
0
#4
0
1
0
1
0

technique. Therefore, the proposed approach works well at low
modulation index, but there is not remarkable improvement athigh modulation index. At high modulation index, there is not
only synchronous switching in the same phase of both inverters
in the SVM sequence, but complicated switching transientswhere the switching devices in several phases in one inverter
get turned on or turned off at the same time. For this reason, it
is difficult to improve the multilevel voltage waveform with theabove dead time technique at high modulation index.

30

40

50

Time (ms)

180
170
160
150
140
130
120
110
100
300
200

dv/dt = 390 V

dv/dt = 250 V

100
0
-100
-200
-300

0

10

20

30

40

50 0

Time (ms)

10

20

30

40

50

Time (ms)(a) m = 0.4 (840 r/min)(b) m = 0.8 (1680 r/min)Fig. 16. Experimental results with proposed dead time technique.

voltage waveforms through experimental tests. However, theoutput multilevel voltage waveforms still have error voltage
pulses, which will be investigated in detail in future works.
REFERENCES
[1]

[2]

VIII. CONCLUSION
This paper has described SVM techniques of the dual
inverter system for open-end winding PM motor drive, where
one of the inverters has only capacitors across the DC-bus. The
SVM is achieved to output voltage waveforms across the openend winding terminals and simultaneously regulate thecapacitor voltage at a half of the other battery voltage by
selecting an appropriate switching state among the redundantstates. In particular, it is indispensable for capacitor voltage
control with the proposed SVM to consider the instantaneous
motor power factor. This paper has also been described that thedead time causes unexpected irregular voltages in the generated
multilevel voltage waveforms and proposed compensation forthe conventional dead time technique. It has been verified thatthe dead time technique employed the proposed compensation
eliminates the irregular voltage vectors in the output multilevel20(a) m = 0.4 (840 r/min)(b) m = 0.8 (1680 r/min)Fig. 15. Experimental results with conventional dead time technique.

・・・

Fig. 13. Unexpected error voltages during dead time.
TABLE

-300
-2.0

0

Capacitor Voltage
Vcap (V)V60in(000)(001)’

-200

-100
-200

(V0)

(Vz)

0
-100

100

U-Phase Voltage
Vu (V)(V120in)

100

180
170
160
150
140
130
120
110
100
300
200

U-Phase Voltage
Vu (V)

V60

Current Polarity B
Discharging Mode

Synchronous Turning On
Synchronous Turning Off

200

Fig. 14. Difference of switching speed between INV1 and INV2.

INV2iCapacitor Voltage
Vcap (V)

0

300

[3]

[4]

[5]

[6]

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Y. Ohto, T. Noguchi, and T. Sasaya, “Space Vector Modulation of Dual
Inverter with Battery and Capacitor across DC Buses,” IEEE
International Conference on Power Electronics and Drive System, 2017,1172-1177.
A. Mizukoshi, and H. Haga, “Control Method of Open-Winding
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1300