IEEE PEDS 2017, Honolulu, USA
12 – 15 December 2017

Space Vector Modulation of Dual Inverterwith Battery and Capacitor across DC Buses
Yoshiaki Ohto, Toshihiko Noguchi, and Takanari Sasaya†
Shizuoka University and Denso Corporation†
ohto.yoshiaki.15@shizuoka.ac.jp, noguchi.toshihiko@shizuoka.ac.jp

Abstract-A space vector modulation (SVM) technique of a dual
inverter system feeding a three-phase motor with open-endwindings is proposed in the paper, where one of the inverters
has a battery power source and the other has a capacitor acrossthe DC bus. The SVM must be achieved both to operate themotor with field-oriented control and to control the capacitor
voltage at a half value of the battery by using redundantswitching states at the same time. The control of the capacitor
voltage is carried out by alternating a charging or a discharging
mode in each switching state, taking relative phase angle
between the motor voltage vector and the motor line current
vector into account. In other words, it is necessary to select an
optimal switching state among various redundant states whichmakes the capacitor voltage follow its command properly,
considering the instantaneous motor power factor. The paper
demonstrates an experimental setup and test results as well as
computer simulation results.

Three-Phase
Three-Wire Motor

Chopper

InverterFig. 1. Conventional motor drive with single inverter.
Open-EndWinding Motor
75 V

150 V
Battery

Capacitor
75 V

150 V

INV1 (u1, v1, w1)(u2, v2, w2) INV2

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

I.

INTRODUCTION

In recent years, mileage improvement and autopilot
technologies are focused on, aiming at further reduction ofcarbon dioxide emission of hybrid vehicles. Many of thecurrent hybrid vehicles are based on the combination of abidirectional chopper and a two-level inverter, and drive ahigh-voltage permanent magnet (PM) motor. Therefore, theline-to-line voltage of the motor is a three-level waveformwith high dv/dt, which may cause deterioration of the total
harmonic distortion (THD), conduction noise, and radiationnoise. The current system has a drawback from the viewpointof the failsafe because the motor can no longer be operated if
a failure should happen in either the chopper or the inverter.
In order to solve the problem above, a dual inverter system is
discussed in the paper, which drives the motor with open-end
windings [1]-[4].
The dual inverter technique makes it possible to generate
multilevel voltage waveforms across the motor winding
terminals, and has an advantage of the failsafe by replacing
one of the inverter DC bus with a capacitor. In the case, it isrequired to generate the multilevel voltage waveforms
simultaneously with controlling the capacitor voltage at aconstant value [5] [6]. Particularly, it is dispensable to takethe instantaneous motor power factor into account for thecapacitor voltage control, i.e., charging or discharging controlof the capacitor. In the paper, a novel strategy of the space
vector modulation (SVM) for the dual inverter system togenerate the multilevel voltage waveforms across the open-

end windings of the PM motor, which allows regulating thecapacitor voltage according to the instantaneous motor power
factor. The proposed technique is examined through several
computer simulations and experimental tests [7]. In addition,
it is pointed out in the paper that the dead time detrimentallyaffects generation of the multilevel voltage waveforms.
II.

CONFIGURATION OF DUAL INVERTER SYSTEM

A. Circuit Configuration of Dual Inverter System
Fig. 1 shows the conventional system composed of a single
two-level inverter driving a three-phase PM motor with aneutral point inside of the motor. Fig. 2 is a circuit diagramof a dual inverter system, which drives an open-end winding
PM motor. One inverter on the left hand side is called INV 1
and the other on the right hand side is INV 2 whose DC-bus
power sources are replaced with capacitors. Each leg of theboth inverters 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.
It is possible in the dual inverter system to generate themultilevel voltage waveforms by adding or subtracting one
inverter voltage to/from the other inverter voltage. The
system has a drawback of increase of the inverter counts andtheir DC-bus power sources, but does not require any voltage
boost power converter such as the bidirectional chopper. The
multilevel voltage wane form generation is expected to1,172
978-1-5090-2364-6/17/$31.00 ©2017 IEEE

INV1

INV2

INV1

V60

INV2

V60in

#3

V30

#2
#4
Vz

(a) Single inverter. (b) Dual inverter with(c) Dual inverter with
1:1 DC-bus voltage.
2:1 DC-bus voltage.
Fig. 3. Output voltage vectors of three systems.

#1
V0

V0in
m=0

m=0.5

m=1.0

Fig. 5. Voltage vectors used in SVM and modulation index.

dual inverter system are sum of the output voltage vectors of
the two inverters. Fig. 4 illustrates the output voltage vectors(110)(001) (-)
from 0 to 60 deg. of the two dual inverter systems whose DC(110)(000) (0)(110)(111) (0)(100)(001) (-)
bus voltage ratios are 1:1 and 2:1, respectively. In the figure,(110)(011) (-)(110)(011) (-) (000)(001) (-)(100)(101) (+)
the capacitor charging, holding, and discharging modes are(111)(001) (-)(000)(000) (0)(110)(010) (-)(110)(110) (+)(000)(111) (0)noted as “+,” “0,” and “” after the switching states,(100)(001)(-)(111)(000) (0)(000)(000) (0)(100)(011) (-)(111)(111) (0)(000)(111) (0)respectively.
(000)(011) (-) (100)(011) (-) (111)(000) (0)(001)(001) (+)(000)(011) (-) (100)(000) (0)(111)(011) (-)(010)(010) (+)
It is found from Fig. 4 that a particular voltage vector can(111)(111) (0) (111)(011) (-) (100)(111) (0)(101)(001) (-)(100)(100) (+)(100)(100)(+)(110)(010) (-)(011)(011) (+)
be applied to the motor by using different switching states,(100)(000) (0)(101)(101) (+)
which means the both systems have switching state(100)(111) (0)(110)(110) (+)(a) Dual inverter with(b) Dual inverter withredundancy. Only one, however, of the capacitor charging
1:1 DC-bus voltage.
2:1 DC-bus voltage.
mode or the discharging mode is available among theFig 4. Relationship between DC-bus voltage ratio of dual inverter system
redundant switching states in the case of the 1:1 DC-bus
and switching state redundancy.
voltage ratio; hence, it is impossible to switch over
improve the THD resulting in the copper loss and iron loss redundantly the charging mode and the discharging mode.
reductions, and to reduce the conduction noise and the On the other hand, the dual inverter system with the 2:1 DCradiation noise owing to the reduction of dv/dt. There is bus voltage ratio has both of the charging mode and theredundancy in the switching states of the dual inverter system. discharging mode in the redundant switching states to output
In other words, a particular voltage vector can be applied to a particular voltage vector. This makes it possible to achieve
the motor by selecting different switching modes, which the multilevel voltage waveform generation on the basis ofallows operation of the motor with controlling the capacitor the SVM and the capacitor voltage control at the same time,
voltage of INV2. Therefore, the dual inverter system can which is the reason why the 2:1 DC-bus voltage ratio has
continue to drive the motor even if one of the batteries is in been employed for the dual inverter system. However, thefailure because the switching state redundancy makes it longest voltage vectors that configure the most outer hexagon
possible to keep the capacitor voltage on the failure side at do not have the redundancy even if the 2:1 DC-bus voltage
constant value and to achieve continuous operation of the ratio is employed, so the longest voltage vectors are notmotor. In addition, even in the case of the failure in one utilized in the SVM discussed in the paper.
switching device of either inverter, the system can continue tooperate the motor as a single inverter drive by shorting theIII.
SELECTION OF VOLTAGE VECTORS IN SVM
three-phase windings with normal condition arms of the failFig. 5 illustrates the voltage vectors whose phase angle isinverter.
from
0 to 60 deg., for example, where m denotes a
B. DC-Bus Voltages and Switching State Redundancy
modulationindex. The modulation index m = 1.0 when the
The dual inverter system discussed in the paper controls thecircularlocus
of the voltage vector generated by the SVM is
INV 2 capacitor voltage at half of the INV 1 DC-bus battery
inscribed
intheouter hexagon, and m = 0.5 when the locus isvoltage. The reason is to utilize the switching state
inscribed
in
the
inner
hexagon.
redundancy and simultaneous control of the capacitor voltage
The
SVM
is
carriedout by synthesizing some discreteand the SVM.
invertervoltage
vectors
at appropriate ratio to output a
Fig. 3 shows output voltage vectors that the single inverter,
commandedvoltage
vectorwith an arbitrary phase angle andthe dual inverter system with 1:1 DC-bus voltage ratio, andanarbitrarynorm.
Thecommandedvoltage vector can be
the dual inverter system with 2:1 DC-bus voltage ratio,synthesized
by
using
three
voltage
vectors
surrounding therespectively. As can be seen in Fig. 3 (a), the single inverter
commandedvoltage
vectorinatriangleshape.
In the case of
can output 8 voltage vectors, i.e., 2 and 6 of them are zerothecommandedvoltage
vectorinthe#1
triangle
sector, forvoltage vectors and non-zero voltage vectors, respectively.
example,thethreevoltage
vectorsV0,
V0in,
and V30
As Figs. 3 (b) and (c) show, the output voltage vectors of the(000)(001) (-)(111)(001) (-)(010)(011) (-)(100)(101) (-)(110)(000) (0)(110)(111) (0)(110)(001) (-)

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SVM 1 period
V60in

V30

V60

(000)(001) (-)

V60in

V60

V30

V60in

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

Charge(110)(110) (+)

Hold

Discharge

ChargeDischarge

Discharge

Hold

The Reference of Voltage of Capacitor
The Voltage of Capacitor

Fig. 6. Simultaneous control of multilevel voltage waveform generation with SVM and Capacitor voltage.

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
INSTANTANEOUS MOTOR POWER FACTOR

A. Capacitor Voltage Control of INV 2
The DC-bus voltage sources of INV 2 are replaced with thecapacitors in the dual inverter system of the paper. The
voltage across the capacitor must be controlled to keep a
constant value by charging and discharging it, and multilevel
voltage waveform generation must also be achieved at thesame time.
The dual inverter system has redundant switching states,
and can output a particular voltage vector with different
redundant switching states as described previously. Polarityof the current flowing into the capacitor changes according to
the capacitor charging mode or the discharging mode
specified by every switching state. As illustrated in Fig. 6,
the multilevel voltage waveform generation with the SVM
and the capacitor voltage control can simultaneously be
carried out by selecting an appropriate switching state among
the redundant states. It should be noted that almost unity
power factor is assumed as an operating condition of the
motor in the example illustrated in Fig. 6.
B. Impact of Instantaneous Motor Power Factor
Fig. 7 shows a relationship between the motor line current
vector and the polarities of the motor line currents, where thepolarity signs indicate the current directions in the motor
windings, i.e., “+” means a direction from INV 1 to INV 2,
while “” does the opposite direction. The capacitor charging
mode or the discharging mode can be determined by thecurrent direction of the motor windings in every switchingstate.
It is, however, assumed that the PM motor is connected tothe dual inverter system as a load, which is inherently an
inductive load; thus, the motor line currents lag behind thevoltage vector generated by the SVM. Each line current

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
UV
W＋

Current
Polarity F
U＋
V
W＋

Fig. 7. Relationship between current vector and motor line currents.

The redundant switching states generating V30
Current Polarity（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. 8. Relationship between redundant switching states to output V30 andcapacitor voltage control modes.

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

i d*
*
m
＋
－

PI

T*

1/Ψ

i

* ＋
－
q

＋

PI

dq

*
q

v
PI

swu1

v*

vd*
αβ

－

swv1

*

v

sww1


i*
*
v

tan1
tan1

S
V
M

Vcap

m

iu
INV1

iv

iw

PM
Motor
swu2
swv2
INV2
sww2

1
s

id

αβ

i

uvw

iq

dq

i

αβ

Fig. 9. Control block diagram of dual inverter system for open-end winding PM motor drive.
TABLE I. COMPUTER SIMULATION CONDITIONS.
Switching frequency
10 kHzVoltage of battery (INV1)
300 V
Voltage of capacitor (INV2)
150±5 V
Capacitance of capacitor (INV2)
1320 F
Motor speed command value
10000 r/min
Dead time
0 s
Number of poles
2
Number of flux linkage
0.1 WbMoment of inertia
0.0001 kgm2
Motorparameters
Damping coefficient
0.002 N/rad/s
Phase resistance1Ω
Phase inductance
5 mH

direction changes according to the instantaneous motor power
factor, which may be affected by the motor operating
conditions and the motor parameters. This implies that the
instantaneous motor power factor must be taken into accountto control the capacitor voltage at a constant value.
Let’s assume the case where the commanded voltage vector
is in the hatched sector as illustrated in Fig. 7. The available
voltage vectors are V60, V60in, and V30 to synthesize thecommanded voltage vector in the case. The maximum
lagging phase angle between the voltage and the current
vectors is 90 deg., which means that the current direction is in
one of “B,” “A,” and “F.” Two of the redundant switchingstates to generate V30 voltage vector are shown in Fig. 8, forexample, where the relationship between the motor line
current direction and the capacitor charging or thedischarging mode. A switching state (110)(010)’ makes the
motor line current charge the capacitor in the case of thecurrent vector direction “B,” but the identical switching state
makes the capacitor discharging mode in the case of thecurrent vector direction “A” or “F.” In general, therelationship between the switching state and the capacitor
charging or discharging mode cannot uniquely be determined
if the motor line current vector phase angle changes due tothe instantaneous motor power factor. Therefore, it isindispensable for the SVM process to choose an appropriate
switching state among the redundant switching states that

Fig. 10. Simulation results.

Fig. 11. Expanded waveform of voltage across phase U winding terminals.

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Controller

INV1

INV2

Test Motor
Load Motor
Torque Pickup

Fig. 12. Experimental setup of dual inverter system.

Fig. 13. Experimental test result.

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)
1320 Fd-axis current command value
0A
q-axis current command value
1A
Motor speed
1100 r/min
Dead time
4 s
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

redundant switching states, as well as the feedback value ofthe capacitor voltage of INV 2.
TABLE I and Fig. 10 show the simulation conditions andthe operation waveforms obtained through the simulations,
respectively. The motor speed, the instantaneous motor
power factor, the capacitor voltage, and the voltage across thephase U winding terminals are shown from the top to thebottom of Fig. 10. 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 150±5 V.
Fig. 11 is an expanded waveform of the motor winding
voltage, where the 9-level voltage waveform is also properly
observed.

makes it possible to control the capacitor voltage at a constantvalue according to the instantaneous motor power factor.
V.

COMPUTER SIMULATION AND 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 capacitor
is installed across the DC bus of INV 2 and the proposed
control technique is introduced into the system. The control
block diagram is indicated in Fig. 9. The motor is controlledwith a field-oriented control (vector control) algorithm, so hasa speed control loop and a current control loops in thecontroller. The phase angle between the voltage vector andthe motor line current vector is calculated on thesynchronously rotating (d-q) reference frame, and is utilized
to select the most appropriate switching state among the

VI.

EXPERIMENTAL SETUP AND TEST RESULTS

Experimental tests have been conducted with anexperimental setup of the dual inverter system as shown in
Fig. 12. The open-end winding PM motor is controlled by afield-oriented control (vector control) algorithm, and its speed
is regulated at 1100 r/min by a load servo motor directly
connected to the test motor. The rated output power of thetest motor is 1 kW, and is fed by the two 5-kVA inverters inwhich one of the inverter has only the capacitor across theDC bus. Experimental test conditions are listed in TABLE II,
and the test result is shown in Fig. 13. As shown in the test
result, the multilevel voltage waveform is generated acrossthe open-end winding of the test motor, but contains a lot of
unexpected noise pulses in the waveform, which
detrimentally deteriorates the THD of the voltage waveform.
However, the three-phase line currents are balanced andinclude less harmonic components than the fundamental
components. In addition, the capacitance voltage is properly
controlled to be around 150 V within the specified hysteresis

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band. All in all, therefore, the proposed approach woks well,
but must be improved to compensate for the unexpectedvoltage pulses in the output multilevel voltage waveforms.

INV1
1

INV2
i

1

Switching State A

VII.

0

DISCUSSION ON IMPACT OF DEAD TIME

0

Particular switching sequences are included on the dual
inverter system with the 2:1 DC-bus voltage ratio described
INV1
INV2
so far, which synchronously turns on or turns off the
10i
switching devices in the same phase of the both inverters. As
Dead-Timeshown in Fig. 14, for example, let’s assume the transition
0
1
from a switching state “A” to “B”, where the upper arms of
the both inverter are turned on in “A,” while the both lower
arms are on in “B.” Since the switching state during the dead
INV1
INV2
time is determined by the line current direction, the error
voltage vector is generated because the switching state during00i
the dead time is “0” and “1.” In other words, it is difficult to
Switching State B
avoid such an unexpected switching state during the dead1
1time because the switching state “A” cannot directly be
Fig. 14. Impact of dead time in simultaneous switching.
changed to “B” due to the dead time. Fig. 15 shows anexample of the unexpected error voltage generated during the
V60
dead time. If the commended voltage vector is located in the
Current Direction B
Discharging Mode
specific hatched sector, the three- voltage vectors V60, V60in,
V60in
V30
and V30 are used for the SVM. Although the proper
V(V120in)switching sequence is V60in → V30 → V60 → V60 in → ∙∙∙,
(V0)
the unexpected irregular voltage vectors such as V120in, V0,(Vz)
and Vz are inserted in every transition of the switching states.
V60in
V30
V60
V60in
However, the conventional single inverter and the dual
・・・(000)(001)(100)(101)(110)(111)(111)(001)inverter system with the 1:1 DC-bus voltage ratio do not have
The irregular voltage vector
V120inV0
Vz
this problem because there are not transitions that require
generated in dead-time(000)(101)(100)(111)(111)(111)synchronous turning on or turning off of the same phaseFig. 15. Unexpected error voltages during dead time.
switching devices in the both inverters.
The dead time is indispensable to prevent the DC bus of theinverters from the short circuit. Therefore, elimination of the
REFERENCES
unexpected error voltage during the dead time is important [1] Y. Kawabata, M. Nasu, T. Nomoto, Emenike C. Ejiogu, and T.
point in the dual inverter system that has the capacitors
Kawabata, “High-Efficiency and Low Acoustic Noise Drive System
Using Open-Winding AC Motor and Two Space-Vector-Modulated
instead of the DC power source and that has the DC-bus
Inverters,” IEEJ Transactions on Industrial Electronics, vol. 49, no. 4,
voltage ratio of 2:1. The investigation on the technical2002, pp. 783-789.
problem is one of the future works of the authors’.
[2] J. Kim, J. Jung, and K. Nam, “Dual-Inverter Control Strategy for HighVIII.

CONCLUSION

This paper has described an SVM technique of the dual
inverter system feeding an open-end winding PM motor,
where one of the DC busses in the system is replaced withcapacitors. The SVM is achieved by selecting an optimal
switching state among the redundant states that can generate
multilevel voltage waveforms across the open-end windings
and can simultaneously control the capacitor voltage at a
fixed value. The paper has pointed out that the instantaneous
motor power factor is important to take into account as wellas the switching states of the dual inverter system.
It has also been suggested in the paper that the dead timecauses unexpected error voltage pulses in the multilevel
voltage waveforms, which will be investigated in detail in the
future study.

[3]

[4]

[5]

[6]

[7]

Speed Operation of EV Induction Motors,” IEEJ Transactions on
Industrial Electronics, vol. 51, no. 2, 2004, pp. 312-320.
K. A. Corzine, M. W. Wielevski, F. Z. Peng, and J. Wang, “Control of
Cascaded Multi-Level Inverters,” IEEE Transactions on PowerElectronics, vol. 19, no. 3, 2004, pp. 732-738.
K. Mitsudome, H. Haga, and S. Kondo, “Improvement of Output
Voltage Waveform in Dual Inverter Having a Different DC Power
Supply,” IEEJ Technical Meeting on Rotating Machinery,
Semiconductor Power Converter and Motor Drive, 2015, pp. 77-82.
H. Machiya, H. Haga, and S. Kondo, “High Efficiency Drive Method of
an Open-Winding Induction Machine Driven by Dual Inverter using
Capacitor Across DC Bus,” IEEJ Transactions on Industry
Applications, vol. 135, no. 1, 2015, pp. 10-18.
J. Ewanchuk, J. Salmon, and C. Chapelsky, “A Method for Supply
Voltage Boosting in an Open-Ended Induction Machine Using a Dual
Inverter System With a Floating Capacitor Bridge,” IEEJ Transactions
on Power Electronics, vol. 28, no. 3, 2013, pp. 1348-1357.
Y. Ohto, T. Noguchi, and T. Sasaya, “Space Vector Modulation of Dual
Inverter Taking Power Factor of Open-End Winding Motor,” IEEJ
Annual National Conference, 2016, pp. 71-72.

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