Space Vector Modulation of Dual Inverter Motor Drive
Compared with Single Inverter Drive
Melinda B. Fauziah, Yoshiaki Oto and Toshihiko Noguchi
Shizuoka University, JapanAbstract. This paper describes space vector modulation (SVM) techniques for different motor
drive systems. Two three-phase topologies are compared from the viewpoints of switchingsequences and the resultant voltage waveforms, i.e., an open-end winding motor fed by dual
inverters and a conventional star-connected three-winding motor fed by a single inverter. In thedual inverter system, both the inverters are supplied by batteries with a 1:1 DC-bus voltage
ratio, while in the single inverter system, the DC-DC converter is employed to supply theinverter. The simulation results compared with the single inverter system show that, with theidentical motor speed command value, the dual inverter motor drive system can generate 9level voltage waveforms which can suppress the total harmonic distortion (THD) of the voltage
down to 35.86% and THD of the current down to 6.39%.

1. Introduction
The increasing number of transportations on the road have led to the significant increase in the amountof carbon dioxide emissions. This is one of the considerations intensively focused on the whole world
as well as Japan. In particular, hybrid electric vehicles are being utilized and the manufactures have atask in developing technology in order to reduce the amount of the carbon dioxide emissions.
Nowadays, many of the hybrid electric vehicles employ three-phase permanent magnet (PM) motors
driven by a combination of a DC-DC converter and a three-phase two-level inverter. However, thissystem generates three-level voltage waveforms with a high dv/dt which cause increase of harmonics
in the output voltage waveforms [1] [2]. This condition can reduce the motor efficiency and can cause
electromagnetic interference (EMI) [3] [4]. To solve these problems, an open-end winding motor fed
by dual inverters has been examined in this research [5]-[10].
This paper presents both the single and the dual inverter motor drive systems which can beemployed in the hybrid electric vehicles. The computer simulations have been conducted to confirm
the performance of both systems, especially, regarding the reduction of the THD.
2. Principles of Single Inverter and Dual Inverter System
2.1. Circuit Configurations and SVM
The conventional system consisting of a three-phase PM motor driven by a combination of a DC stepup converter and a two-level inverter is depicted in Fig. 1. The voltage boosted by the DC-DC
converter is operated as the input of the inverter and the three windings of the motor are connected to aneutral point. On the other hand, in the open-end winding motor, the neutral point is opened, and two
inverters feed the windings from each end as shown in Fig. 2. In the dual inverter system, the inverteron the left side is called INV1 and the other is INV2. Each leg of INV1 and INV2 is operated
complementary.

Vdc
300 V
Three-Phasestar-connected motor

InverterStep-upconverter

Fig. 1. Conventional motor drive system.

Vdc 1300 V

Vdc 2300 V

Open-end
winding motor

INV1

INV2

Fig. 2. Open-end winding motor fed by dual inverter.
Fig. 3 shows the space voltage vectors which consist of the output voltage vectors in the cases ofthe single inverter and the dual inverter. As can be seen in Fig. 3 (a), the single inverter can generate 8voltage vectors, i.e., 6 non-zero vectors and 2 zero vectors. The output voltage vectors generated bythe dual inverter are the summing result of the basic voltage vectors of INV1 and INV2. Fig. 3 (b) isthe voltage vectors generated by the dual inverter with the battery-battery system in which both DCbuses are supplied by batteries with a 1:1 DC-bus voltage ratio.
INV1V120

INV2

V60

V90

V120

V180

V0V360Vz

V120in

V150

V60in

V300in
V330

V210

V240

(a) Single inverter.

V0V360Vz
V210in

V300

V30
V0in
V360inV180inV180V240

V60

V270

V300(b) 1:1 DC-bus voltage ratio in dual
inverter.

Fig. 3. Space voltage vectors.
Fig. 4 shows the expanded space voltage vectors of both the single inverter and the dual inverter
system in the electrical angle range of 0 to 60 deg. The binary numbers represent the ON-OFF statesof each inverter leg where the value 1 indicates that the upper transistor is turned on whereas the value
0 indicates that the lower transistor is turned on. For the single inverter, the corresponding

combinations of the switching states are shown in brackets as depicted in Fig. 4 (a). Since the dual
inverter is composed of the two voltage sources, the corresponding combinations of the switchingstates represented by ( ) and ( )’ indicate the voltage vectors of INV1 and INV2, respectively, as
shown in Fig. 4 (b). The voltage vectors can be obtained by multiple switching states having a specificmagnitude and a phase angle. This means that the dual inverter has switching state redundancy which
provides flexibility to generate multilevel voltage waveforms.
(110)(001)(000)(001)(010)(011)(100)(101)(110)(000)(110)(111)(111)(001)(011)(000)(000)(000)(111)(001)(001)(010)(010)(100)(100)(011)(011)(101)(101)(110)(110)(111)(000)(111)(111)

(001)

(000)
(111)

(100)(001)(110)(011)(a) Single inverter.

(100)(011)(000)(011)(100)(000)(100)(111)(101)(001)(110)(010)(111)(011)(b) Dual inverter.

Fig. 4. Switching states.
2.2. Sector Identification
The sector of the single inverter is identified, regarding the value of the phase angle in which eachsector has 60-deg difference. For instance, the sector from 0 to 60 deg is called sector 1, the next 60
deg is sector 2, and so on. In the case of the dual inverter system, the sector identification is proposedby using the space voltage vectors as shown in Fig. 5. The hexagon is divided into 6 regions with 60deg phase zone in which each region is also divided into 4 equilateral triangle sectors. The region from0 to 60 deg is called region 1 and the sectors located in region 1 are sector #11, #12, #13, and #14.
Boundary lines, which are a, b, c, d, e, and f limiting the sectors, are employed to identify the locationof the reference voltage vector.
VβV120eV90#23#31aV150

V60#22V60in#34#14V180in

V180

#42

V210

#64

#44

#41

#54

V240in#43cV300inbadV0in
V360inaV0VαV360#63

1 221 22b#13#11#12

#14ɵ

V330
#61

#53

V270

V240

V30

d : Vβ = 3 Vαa : Vβ = 1 24b : Vβ = 3 Vα 1 2 e : Vβ = 3 Vα2c : Vβ = 3 Vα 1 2 f :Vβ = 41 22Vref#11#62

#52
#51

#13
#12#24#33b#21V120in#32f

Overall boundary line equations :cdfVβdVβV3002 Vdc
32 2 Vdc
3e(a) Division of sector location.

Vβ1 243 Vα 1 223 Vα 1 22(b) Sector identification approach.

Fig. 5. Proposed sector identification in dual inverter system.

The equation of each boundary line can be calculated by considering the maximum voltage vector
amplitude and the reference voltage vector decomposed into αβ-axis. The maximum voltage vector
amplitude can be obtained as follows:

V0  V60  V120  V180  V240  V300  V360  22Vdc ,3(1)V30  V90  V150  V210  V270  V330  2Vdc , andV0in  V60in  V120in  V180in  V240in  V300in  V360in (2)2Vdc ,3(3)where Vdc is equal to Vdc1 = Vdc2, V0…V360 are large vectors, V30…V330 are medium vectors, andV0in…V360in are small vectors having a half magnitude of the large vector. Moreover, the voltage vector
can be calculated as follows:

Vref VV  ,cos  sin (4)where Vref is a reference voltage vector, Vα and Vβ are voltage vectors decomposed into αβ-axis, and θ
is a space vector angle. The overall line equations are presented in Fig. 5 (a). For instance, if thereference voltage vector is located in the sector #11, boundary line equations a, b, and d are required.
The sector can be selected using inequality equations of the boundary lines as shown in Fig. 5 (b).
If the position of the reference voltage vector has been determined, the three voltage vectors
surrounding the corresponding sector are employed to generate the reference voltage vector. For
instance, if sector #11 is detected, V0in, V0, and V30 are employed to generate the reference voltage
vector.
2.3. Switching State
The switching states in a SVM period should assure the symmetrical output voltage pulse sequence toimprove the THD and to reduce the switching losses. It is necessary to arrange the switching state
sequence in which during the transition of one switching state to the next one, only one leg is switchedover. Therefore, during 1 period, the appropriate switching states which are selected to achieve thesymmetrical voltage waveform both in the single and in the dual inverter system are depicted in Fig. 6.
In the case of the single inverter system, for instance, when the reference voltage vector is in sector #1,
the sequence of the switching states shown in Fig. 6 is selected. In the sector #11 of the dual inverter
system, since all are non-zero vectors, the sequence of switching states is determined by choosing theleast transition.
SVM 1 Period

Single inverter

Dual inverter

Vz

V0

V60

Vz

V60

V0

Vz

(000)

(100)

(110)

(111)

(110)

(100)

(000)

V0in

V30

V0V0in

V0

V30

V0in

(000)(011)(100)(000)(100)(111)(101)(001)(110)(010)(111)(011)(100)(001)(110)(011)(100)(011)(000)(011)(100)(000)(100)(111)(101)(001)(110)(010)(111)(011)(100)(011)(100)(001)(110)(011)(000)(011)(100)(000)(100)(111)(101)(001)(110)(010)(111)(011)

Fig. 6. Appropriate switching states selected to achieve symmetrical voltage patterns.

3. Simulation and Result
The computer simulations have been conducted to observe the operation waveforms of the space
vector modulation in single inverter and the dual inverter system. The overall block diagrams of thesingle inverter and the dual inverter systems are shown in Fig. 10 and 11, respectively. A vector
control algorithm is utilized to control the motor in which closed-loop current controllers and a speed
controller are used to improve the performance.
The simulation is examined based on the condition and the motor parameters as shown in Table 1.
The simulation results are motor rotation speed, U-phase voltage and three-phase currents for both thesingle inverter and the dual inverter depicted in Fig. 9 (a) and (b), respectively. THD of the voltage
and the current has also been measured in each system. From both simulation results, the performanceof the motor rotation speed can reach the command value at 5000 r/min. By examining the U-phasevoltage of the motor windings, the 5-level voltage waveform can be achieved in the single inverter
system and the 9-level voltage waveform can be achieved in the dual inverter system. Three phasecurrents of the single and the dual inverter system show sinusoidal waveforms. Compared Fig. 9 (a)with (b), it can be found that the THDs of the voltage and the current are significantly reduced. The
dual inverter system can generate more voltage levels and can create smoother waveforms than thoseof the single inverter system. Moreover, phase current waveforms of the single inverter have many
harmonics, compared with the dual inverter system.
Table 1. Simulation conditions and parameters.
Inductor
Capacitor
Duty Cycle
Switching frequency of Converter
Input Voltage of Converter
Switching frequency of Inverter
Voltage of battery (INV1 and INV2)
Dead time
Motor speed command value
Number of poles
Number of flux linkage
Moment of inertia
Damping coefficient
Phase resistancePhase inductance

DC-DCconverterparameters
Inverterparameters

Motorparametersid*
ω*mPIT*PIi*
q1/ΨPIvd*dqvq*αβωm75 H
67 F
0.525 kHz
300 V
10 kHz300 V0 s
5000 r/min
40.1 Wb
0.0001 kgm20.002 N/rad/s
1Ω
5 mHvα*vβ*

tan-1 ᶿSW u1
SW v1

SVM SWw1*v

PMMotor1
sidiqαβdqiu
iv
iw

INViαiβuvw
αβFig. 7. Block diagram of PM motor drive fed by single inverter system.

id*
ω*mPITPIi*q*1/ΨPIvd*

vα*dqv*qSW u1
SW v1vβ*αβiuiviwINV1

SWw1ωmᶿ

-1tan

*vPM
MotorSVM
SW u1
SW v1

INV2

SWw1
1sidiqαβdqiαiβuvw
αβ

THD = 68.06%

40200-20-400.00

THD = 12.64%

0.02

0.04

0.06

0.08

0.10

Motor Rotation
Speed (r/min)
U-PhaseVoltage (V)rpm
rpm_ref

5000
4000
3000
2000
10000rpm
rpm_ref

400
2000-200-400

Three Phase
Current (A)Motor Rotation
Speed (r/min)

600
400
2000-200-400-600

Three Phase
Current (A)

5000
4000
3000
2000
1000
0U-Phase
Voltage (V)Fig. 8. Block diagram of open-end winding PM motor drive fed by dual inverter
system.

6040200-20-40-600.00

Time (s)THD = 35.86%

THD = 6.39%

0.02

0.04

0.06

0.08

Time (s)(a) Single inverter.

(b) Dual inverter.
Fig. 9. Simulation results.

4. Conclusion
The simulations of the single and the dual inverter motor drive systems have been presented. In thedual inverter system, the sector identification is determined by using the approach of the boundary line
equations. The selection of the appropriate switching states in the dual inverter among the redundancy
must be considered regarding the switching losses. The simulation results show that, with the identical
motor speed command value, the dual inverter motor drive system can generate 9-level voltage
waveforms which can suppress the THD of voltage down to 35.86% and the THD of the current down
to 6.39%. Therefore, it can be concluded that it is beneficial to use the open-end winding motor fed by
the dual inverter employed in the hybrid electric vehicles.
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