Modeling and Simulation of a Carrier-based PWM Voltage Source Inverter for a Nine Phase Induction Machine Drive

International Journal of Power Electronics and Drive System (IJPEDS)
Vol. 5, No. 1, July 2014, pp. 1~14
ISSN: 2088-8694  1
Journal homepage: http://iaesjournal.com/online/index.php/IJPEDS
Modeling and Simulation of a Carrier-based PWM Voltage
Source Inverter for a Nine Phase Induction Machine Drive
Omonowo David Momoh
Department of Computer, Electrical and Information Technology, Indiana University-Purdue University (IPFW)
Fort Wayne, Indiana, United States
Article Info ABSTRACT
Article history:
Received Mar 29, 2014
Revised May 22, 2014
Accepted Jun 1, 2014
The analysis of a carrier-based PWM two level voltage source inverter for a
nine phase induction machine drive system is presented in this paper.
Methods for generating zero-sequence signals during balanced and
unbalanced condition are established. Simulation results for the analysis are
presented. Two fault conditions involving the voltage source inverter and the
nine-phase squirrel cage induction machine load are investigated. For the two
fault scenarios considered, the effects on the performance characteristics of
the induction machine load are highlighted. The simulation results obtained
show that the two imbalance conditions considered result in substantial
oscillations on the electromagnetic torque of the machine with attendant
reduction in the torque rating. There is also large slip in the rotor speed.
Keyword:
Existence function
Harmonic injection
Multiphase machines
Open-phase fault
Voltage-source inverter Copyright © 2014 Institute of Advanced Engineering and Science.
All rights reserved.
Corresponding Author:
Omonowo David Momoh
Department of Computer, Electrical and Information Technology
Indiana University-Purdue University (IPFW)
Fort Wayn, Indiana, United States
Email: momohd@ipfw.edu
1. INTRODUCTION
Multiphase machines are electrical generators or motors with the number of phases greater than
three (n > 3). When compared to three phase machines, multiphase machines have greater degrees of
freedom which has enabled some improvements in the system’s performance [1]-[5]. The advantages of
multiphase machine over their three phase counterparts are well documented in [6]-[12]. They include:
higher reliability and increased power density, enhanced fault tolerant capability, extended speed/torque
capability, reduced amplitude/increased frequency of pulsating torque, reduced rotor harmonic currents, and
reduced current per phase without increasing the voltage per phase. Also, in multiphase machine, extra-
torque can be produced from the interactions of current and spatial harmonics of the same order. For
instance, in nine phase machine, the third, fifth, and seventh harmonics can be harnessed to generate average
torque which adds up to the torque produced by the fundamental current component.
At the core of a multiphase machine drive is the power electronics technology. The advancement in
power electronics technology has made it possible to produce any number of phases using a DC/AC voltage
source inverter (VSI). Carrier-based sinusoidal pulse-width modulation (SPWM) is the most popular and
widely used PWM technique. This is because of the simple implementation in both analog and digital
realizations when compared to the space-vector PWM (SVPWM), which is found to be more intense from
computational and complexity viewpoints [13], [15]. Carrier-based SPWM also known as the comparison
pulse-width modulator compares a high-frequency triangular (double edge) or saw-tooth (single-edge) carrier
with reference signals (modulation signals) thereby creating gating pulses for the switches in the power
circuit [15], [16].
The neutral point of most ac motor drive and utility interface applications is isolated and

 ISSN: 2088-8694
IJPEDS Vol. 5, No. 1, July 2014 : 1 – 14
2
consequently, there is no neutral current path. The absence of the neutral current path in the load provides a
degree of freedom in determining the duty cycle of the inverter switches [17]. The difference in potential
between the load neutral point (‘n’) and the center point of the dc-link capacitor (‘o’) of the VSI is called the
zero-sequence voltage, nov . The zero-sequence voltage can take any value which can be subsequently
injected into the modulation signals to achieve any of the following desirable properties: reduced switching
losses, improved waveform quality, and increased linear modulation range [3]. If the injected zero-sequence
signal is continuous, it produces a continuous PWM (CPWM) scheme; however, when it is discontinuous
with the potential for the modulator to have phase segments clamped to the positive or negative dc rails, the
modulation scheme is called discontinuous PWM (DPWM). In DPWM, there is no switching (and
consequently no switching losses) in those intervals when there is discontinuous modulation. A carrier based
PWM method comprising of all DPWM schemes is called the generalized discontinuous PWM (GDPWM)
[13], [18].
Much ground has been covered on PWM schemes for a multiphase VSI using either carrier-based
PWM or SVPWM technique. The goal of this paper is to implement a thorough simulation and analysis of a
carrier-based SPWM voltage source inverter for a nine-phase induction machine drive. This is done through
modeling and simulation of the drive system. In so doing, the work proposed in [3] is extended to a nine-
phase system. Also, beyond the work done for five-phase VSI drive system in [3] and [15], plots showing the
performance characteristics of the nine-phase induction machine are presented in this paper. Figure 1 is a
simplified schematic diagram of a two-level converter (VSI) supplying a nine-phase squirrel cage induction
machine.
2
dcv
2
dcv
Figure 1. Two-level nine-phase VSI supplying a nine-phase squirrel cage induction machine
2. MODELING OF CONTINUOUS CARRIER-BASED PWM FOR NINE PHASE
The principles of carrier-based PWM for a three-phase VSI are also applicable to a multiphase VSI
[13]. Consequently, the load voltage equations for the nine-phase VSI supplying nine-phase squirrel cage
induction machine as depicted in Figure 1 are given as follows:
jsjsjsjsjn irpiLv  (1)
jnv are the phase to neutral output voltage from the VSI, jsi are the phase currents from the VSI to the load,
jsL are the induction machine stator inductances, jsr are the induction machine stator resistances, p is a
differential operator (d/dt), j = a, b, c, d, e, f, g, h, i.
The turn-on and turn-off of the switching devices for the nine-phase VSI shown in Figure 1 are
represented by an existence function. The existence function has a value of unity and zero when the
switching device is turned on and turned off respectively. In its simplest form, an existence function of a two-

IJPEDS ISSN: 2088-8694 
Modeling and Simulation of a Carrier-based PWM Voltage Source Inverter for… (Omonowo David Momoh)
3
level converter can be represented as ihgfedcbajS jk ,,,,,,,,,  and npk , . j depicts the load phase
to which the switching device is connected and k represents the top (p) and bottom (n) device of an inverter
leg. Consequently, from Figure 1, Sap and San take a value of zero or unity and the two constitute the
existence function of the top device and bottom device of the inverter leg connected to phase ‘a’ of the nine
phase induction machine load [3], [13].
There are 29
= 512 switching possibilities (arrangements) during the operation of a nine-phase VSI.
The operation of a carrier-based PWM can be divided into two modes-linear modulation mode and nonlinear
modulation mode. Under the linear modulation mode, the peak of a modulation signal is less than or equal to
the peak of the carrier signal and consequently the gain is approximately unity. However, when the peak of a
modulation signal is greater than the peak of the carrier signal, over-modulation occurs and the gain is
generally less than unity. For operation in the linear modulation region, modulation is defined as the ratio of
the fundamental component amplitude of the line-to-neutral (phase) inverter output voltage to one-half of the
DC bus voltage [3], [19]. This is given as:
dc
j
j
V
V
M
5.0
 (2)
Where Mj is the modulation index (magnitude of the modulation), Vj is the magnitude of the fundamental
inverter output voltage, and Vdc is the magnitude of the dc bus voltage.
The voltage between the jth
inverter phase and the center point of the dc-link capacitor (‘o’)
otherwise known as pole (switched) inverter phase voltage, jov , is related to the load phase voltage, jnv , as
follows:
nojnjo vvv  (3)
Where nov is the common-node zero-sequence voltage as defined in section I above. The constraint imposed
by Kirchhoff’s Voltage Law (KVL) on the two switches in an inverter leg is such that the existence functions
for the top and bottom devices must be complimentary of each other. This is expressed in (4).
1 jnjp SS (4)
Violating this constraint will cause the short circuiting of the dc bus voltage. However, for absolute control of
currents and output voltages, one device in each leg must be turned on at all operating tines. There is a
relationship between the switched voltage, the existence functions, and the dc bus voltage given as follows:
 jnjpdcjo SSvv 
2
1
(5)
From (4),
jpjn SS  1 (6)
The complimentary property of jpS and jnS can be further expressed as:
jpjn
jnjp
SS
SS


(7)
By substituting (6) into (5), we have:
 12
2
1
 jpdcjo Svv (8)

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4
The nine switched voltages expressed in (3) can be summed up as follows:
no
i
aj
i
aj
jnjo vvv 9  
(9)
A symmetrical induction machine in a normal operation condition represents a balanced star-connected load.
Consequently, the sum of the phase currents equal to zero. Thus:


i
aj
jsi 0 (10)
Substituting (10) into (1) implies that the sum of the inverter phase-to-neutral output voltage (load voltage)
equals to zero as shown in (11).


i
aj
jnv 0 (11)
By taking into consideration Equation (10) and (11), the common-node zero-sequence voltage can be
expressed in terms of the switched voltage as follows:


i
aj
jono vv
9
1 (12)
Also, by substituting (8) into (12), the zero-sequence voltage can be expressed in terms of the existence
function and the dc bus voltage as given in (13).






 
i
aj
jp
dc
no S
v
v
2
9
9
(13)
By substituting (13) and (8) into (3), the inverter phase-to-neutral voltage is expressed in terms of the
existence functions and dc bus voltage as follows:
ihgfedcbajq
SS
v
v
i
jq
aq
qpjp
dc
jn
,,,,,,,,,
,8
9











 


(14)
2.1. Nineth-Harmonic Injection
It has been proposed that the injection of the nth
-harmonic into the reference modulation signals of
an n-phase system effectively increases the linear modulation range without moving into over-modulation
region [20], [21]. This technique has led to higher output fundamental voltage than using simple sinusoidal
carrier based PWM [3], [15]. The optimal level of the nth
-harmonic component is found to be:
 
n
n
vv jn
2sin 
 (15)
Equation (15) takes a positive sign for n = 3, 7, 11, 15,…., and negative sign for n = 5, 9, 13, 17, ……. Thus,
for a nine-phase system, the injected nineth harmonic is negative and the resulting zero-sequence signal is
given as:
  )9sin(
9
18sin
)(9 tvtv jno 







 (16)

5
The maximum possible modulation index in the linear region in the case of the nth
harmonic injection has
been derived to be:
)2cos(
1
n
M

 (17)
It has been found that injecting the third harmonic leads to an increase of 15.47% in the fundamental output
voltage while there is an increase of 5.12% by injecting the fifth harmonic [15], [20]. Following the same
procedure, it can be derived that the injection of the nineth harmonic will lead to an increase of 1.54% in the
fundamental output voltage.
2.2. Determination of the Common-node Zero-sequence Voltage with Balanced Load
Existence functions are modulation pulses having values of zero or unity. The Fourier series
approximation of the existence functions are represented as follows [3], [13]:
 
 
 
 
 
 
 
 
 ipip
hphp
gpgp
fpfp
epep
dpdp
cpcp
bpbp
apap
MS
MS
MS
MS
MS
MS
MS
MS
MS









15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
15.0
(18)
Where Map, Mbp, Mcp, Mdp, Mep, Mfp, Mgp, Mhp, Mip are the carrier-based modulation signals. Their values
range between -1 and 1. For implementation, the existence functions are generated by comparing the high-
frequency carrier signal (triangle signal) having positive peak and negative peak values of 1 and -1
respectively. The frequency of the carrier signal adopted for this work is 10kHz. After some simplifications
that involve substituting (18) and (8) into (3), the modulation signals for the top nine switching devices can
be expressed as:
 
ihgfedcbaj
MM
v
v
v
v
v
vv
M ojp
dc
no
dc
jn
dc
nojn
jp
,,,,,,,,
222 **




(19)
Where
*
jpM are the reference modulation signals for the phases, jpM are the corresponding actual
modulation signals responsible for generating the switching functions,
*
oM is responsible for producing the
zero-sequence signal (common-node voltage) injection in the carrier-based PWM VSI. The modulations
signals synthesized in (19) are compared with the carrier signal such that the respective switch turns on when
the corresponding modulation signal is greater than the triangle carrier signal and vice versa. Furthermore, as
the device turns on, the complimentary switch on the particular leg turns off owing to the Kirchhoff’s
Voltage Law constraint imposed on the existence function as mentioned earlier.
A properly selected zero-sequence signal can extend the linearity region of the carrier-based PWM
VSI. From the earlier works on this subject [3], [13], the expression for generating the zero-sequence signal
(common-node voltage) is:
maxmin )1()21(5.0 vvvv dcno   (20)
Where vmin and vmax represent the instantaneous minimum and maximum magnitudes of the nine reference
modulating voltages as shown in (21).  can assume any value between zero and unity but 5.0 is
considered the best overall in every linear condition and it is the value chosen for this work. The value,

 ISSN: 2088-8694
6
5.0 , has also been found to give state vector PWM (SVPWM) scheme.
 
 *********
max
*********
min
,,,,,,,,max
,,,,,,,,min
inhngnfnendncnbnan
inhngnfnendncnbnan
vvvvvvvvvv
vvvvvvvvvv


(21)
By dividing both sides of (20) by 0.5vdc, the expression for the average value of
*
oM is given as:
*
max
*
min
*
maxmin
)1()21(
5.0
)1(
5.0
)21(
5.0
MMM
v
v
v
v
v
v
o
dcdcdc
no




(22)
Where
*
minM and
*
maxM are the instantaneous minimum and maximum magnitudes of the reference
modulation signals for the nine phases.
Figure 2 is the schematic diagram representing the nine-phase carrier-based PWM voltage source
inverter incorporating both the ninth harmonic zero-sequence and the common-node zero-sequence injection
technique. A model corresponding to this schematic diagram was implemented using MATLAB/Simulink.
2.3. Determination of the Common-node Zero-sequence Voltage with Unbalanced Load
The common-node zero-sequence voltage signal for the nine-phase system will not be zero when the
load is unbalanced since there will be a resultant current jsi in (1) as a result of the imbalance. Consequently,
the procedure adopted to determine the common-node zero sequence signal will not be applicable here.
Following the procedure adopted for five-phase system in [3], the system voltage equation shown in (3) will
be re-arranged as follows:
**
nojnjo vvv  (23)
Figure 2. Nine-phase carrier-based PWM technique
In (23), the pole (switched) inverter voltage is expressed in terms of the reference inverter output voltage
*
jnv ,
and the average common-node neutral voltage
*
nov .
Equation (18) can be generically expressed as:

7
  ihgfedcbajMS jpjp ,,,,,,,,,15.0  (24)
Substituting (24) into (8) gives:
jpdcjo Mvv 5.0 (25)
Also, substituting (25) into (23) gives:
**
5.0 nojnjpdc vvMv  (26)
Equation (26) can be re-arranged to give:
**
**
5.05.0
ojpjp
dc
no
dc
jn
jp
MMM
v
v
v
v
M


(27)
Where,
dc
no
o
dc
jn
jp
v
v
M
v
v
M
5.0
5.0
*
*
*
*


(28)
From (27),
**
jpojp MMM  (29)
Equation (29) can be expressed in matrix form as follows:






























































































*
*
*
*
*
*
*
*
*
1100000000
1010000000
1001000000
1000100000
1000010000
1000001000
1000000100
1000000010
1000000001
ip
hp
gp
fp
ep
dp
cp
bp
ap
ip
hp
gp
fp
ep
dp
cp
bp
ap
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
M
(30)
Just like in [3], Equation (30) can be represented as follows:
yAx  (31)
Where,

 ISSN: 2088-8694
8






































1100000000
1010000000
1001000000
1000100000
1000010000
1000001000
1000000100
1000000010
1000000001
A (32)
On closer look at (32), there are ten columns and nine rows. This implies that there are nine
equations with ten unknown in (27). The solution to (31) is indeterminate and by invoking the Moore-
Penrose pseudo-inverse method. The solution is obtained as:
  yAAAx TT 1
 (33)
Consequently, the modulation signals are obtained as:










 


i
jk
ak
kpjpjp MMM **
9
10
1 (34)
By re-arranging (34), the common-node zero-sequence signal as a result of load imbalance is obtained as:


i
ak
kpo MM **
10
1 (35)
3. RESULTS AND ANALYSIS
The model of a carrier-based PWM two level voltage source inverter for 9-phase induction machine
drive was developed and simulated using MATLAB/Simulink. Detailed analysis encompassing the ninth
harmonic zero-sequence injection and common-node zero-sequence signal injection was implemented. The
analysis of the system under balanced and unbalanced load was also carried out. For this work, the frequency
of the carrier signal (Vtri) used is 10kHz and the value of the dc bus voltage (Vdc) utilized was 150 V. The
parameters for the nine-phase squirrel cage induction machine used as the system load are listed in Table 1.
The prototype machine used was a three-phase induction machine (with a rated peak voltage of 180
V) that was rewound to a nine phase machine. Consequently, the peak voltage for the nine phase machine is
60V.
Table 1. Parameters of the Nine-Phase Squirrel Cage Induction Machine
Parameter value
Rated Power 3 Horsepower (hp)
Stator Resistance (Rs) 0.99 Ω
Referred Rotor Resistance ( rR )
0.66 Ω
Magnetizing inductance (Lms) 0.0404 H
Stator Leakage Inductance ( lsL )
0.0034 H
Referred Rotor Leakage Inductance ( lrL )
0.0034 H
Number of Poles 4
Moment of Inertia (J) 0.089 kg.m2

9
3.1. PWM Algorithm for Balanced Modulation Signals and Balanced Load
Simulation results for the carrier-based PWM voltage source inverter in which the modulation
signals for all the nine phases are balanced and the load is also balanced are presented here. The value,
5.0 , was chosen for the common-node zero-sequence voltage injection. The effect of this value of 
on the modulation signal can be seen in Figure 3 part (b). Figure 4 part (a) shows the inverter output phase ‘a’
voltage while part (b) shows the load current when a load torque of 9 Nm was applied to the induction motor.
Figure 5 shows the inverter output line-to-line voltage for adjacent phases (phase ‘a’ and phase ‘b’), and
nonadjacent phases (phase ‘a’ and phase ‘c’).
Figure 3. Phase ‘a’ modulation signal (a) Given reference modulation signal (b) actual modulation signal
with 5.0
In Figure 6, the electromagnetic torque and rotor speed characteristics of the induction machine are
presented. It can be seen from the figures that the rated electromagnetic torque of the nine-phase squirrel cage
induction machine is about 12Nm. Parts (a) and (b) respectively show the electromagnetic torque and rotor
speed of the machine during free acceleration period while parts (c) and (d) show same after a 9Nm load
torque is applied to the machine at 3 seconds. The nine-phase stator currents of the squirrel cage induction
machine are shown in the plot of Figure 7.
Figure 4. (a) Phase ‘a’ load voltage (b) phase ‘a’ stator current
5.97 5.975 5.98 5.985 5.99 5.995 6
-1
-0.5
0
0.5
1
Time[s]
maref
5.97 5.975 5.98 5.985 5.99 5.995 6
-1
-0.5
0
0.5
1
Time[s]
ma
(a)
(b)
5.94 5.95 5.96 5.97 5.98 5.99 6
-200
-100
0
100
200
Time[s]
van
[V]
5.94 5.95 5.96 5.97 5.98 5.99 6
-10
-5
0
5
10
Time[s]
ias
[A]
(a)
(b)

 ISSN: 2088-8694
10
Figure 5. (a) Line-to-line voltage for phase ‘a’ and phase ‘b’ (b) line-to-line voltage for phase ‘a’ and phase
‘c’
3.2. PWM Algorithm for Unbalanced Modulation Signals and Balanced Load
In this segment of simulation results analysis, the carrier-based PWM voltage source inverter has
unbalanced modulation signals. However, it is made to supply a balanced load (symmetrical nine-phase
induction machine). The imbalance was occasioned by interchanging the phase angles of the modulation
signals (reference voltages) for phase ‘a’ and phase ‘b’; also, the magnitude for phase‘d’ modulation signal
was changed from 0.8 to 0.78. This translated to the peak value of phase‘d’ reference voltage changing from
60 V to 47 V. The common-node neutral voltage is generated through the procedure laid down in section 2
subsection 2.3 above.
Figure 6. Plots of electromagnetic torque and rotor speed
5.97 5.975 5.98 5.985 5.99 5.995 6
-200
-100
0
100
200
Time[s]
vab
[V]
5.97 5.975 5.98 5.985 5.99 5.995 6
-200
-100
0
100
200
Time[s]
vac
[V] (a)
(b)
0 1 2 3
-10
0
10
20
Time[s]
T
e
[Nm]
3 4 5 6
-5
0
5
10
Time[s]
T
e
[Nm]
0 1 2 3
-200
0
200
400
Time[s]
w
r
[rad/s]
3 4 5 6
320
340
360
380
Time[s]
w
r
[rad/s]
(a) (c)
(d)(b)

11
Figure 7. Nine-phase induction machine stator currents
Figure 8 part (a) shows the inverter output phase ‘a’ voltage while part (b) shows the load current
when a load torque of 9 Nm was applied to the induction motor.
Figure 8. (a) Phase ‘a’ load voltage (b) phase ‘a’ stator current
In Figure 9, the electromagnetic torque and rotor speed characteristics of the induction machine are
presented. Parts (a) and (b) respectively show the electromagnetic torque and rotor speed of the machine
during free acceleration period while parts (c) and (d) show the same after a 9Nm load torque is applied to
the machine at 3 seconds. Due to the imbalance in the modulation signals, the electromagnetic torque exhibits
some oscillations and the rated value has decreased to about 10Nm. There is a larger slip in rotor speed on
application of load torque as compared to the first (section 3.1) scenario
The complete nine-phase stator currents of the squirrel cage induction machine during this faulty
inverter operating condition are shown in the plot of Figure 10. The magnitudes of the load currents flowing
in the two phases (phase ‘a’ and phase ‘b’) with the wrong modulation signal phase angles can be seen to be
larger than the rest.
3.3. PWM Algorithm for Balanced Modulation Signals and Unbalanced Load
In this final part of the analysis, the carrier-based PWM voltage source inverter has unbalanced
modulation signals just like in section 3, subsection 3.2 above. However, unlike section 3.2, it is made to
supply an unbalanced load (asymmetrical nine-phase induction machine). The imbalance in the load is
caused by the loss of one phase in the stator winding (open-stator fault) of the machine. In this particular
5.97 5.975 5.98 5.985 5.99 5.995 6
-10
-8
-6
-4
-2
0
2
4
6
8
10
Time[s]
iabcdefghis
[A]
ias
ibs
ics
ids
ies
ifs
igs
ihs
iis
6.94 6.95 6.96 6.97 6.98 6.99 7
-200
-100
0
100
200
Time[s]
van
[V]
6.94 6.95 6.96 6.97 6.98 6.99 7
-40
-20
0
20
40
Time[s]
i
as
[A]
(a)
(b)

 ISSN: 2088-8694
12
case, phase ‘a’ of the stator windings was opened. The common-node neutral voltage is generated through the
procedure laid down in section 2 subsection 2.3.
In Figure 11, the electromagnetic torque and rotor speed characteristics of the induction machine
under this asymmetrical operation are presented. Parts (a) and (b) respectively show the electromagnetic
torque and rotor speed of the machine during free acceleration period while parts (c) and (d) show same after
a 9Nm load torque is applied to the machine at 3 seconds. It can be see that the electromagnetic torque
exhibits more oscillations as compared to those in Figure 9. The machine rated electromagnetic torque has
further decreased to about 9 Nm. There is also a large slip in rotor slip experienced on application of load
torque under this faulty condition. Slip is the difference between the synchronous speed and the rotor speed.
The effects of the imbalance in the inverter and the load can be seen on the complete nine-phase
stator currents of the squirrel cage induction machine as shown in the plot of Figure 12. The magnitude of
phase ‘a’ current is zero while the magnitude of phase ‘b’ current can be seen to be considerably higher than
the rest.
0 1 2 3
-5
0
5
10
15
20
Time[s]
Te
[Nm]
4 5 6 7
-5
0
5
10
15
Time[s]
Te
[Nm]0 1 2 3
-100
0
100
200
300
400
Time[s]
wr
[rad/s]
4 5 6 7
320
340
360
380
Time[s]
wr
[rad/s]
(a)
(b)
(a) (c)
(b) (d)
6.97 6.975 6.98 6.985 6.99 6.995 7
-30
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-10
0
10
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30
Time[s]
iabcdefghis
[A]
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13
4. CONCLUSION
In this paper, a carrier-based PWM two level voltage source inverter for nine phase induction
machine drive was developed. Detailed equations for modeling the nine-phase VSI were clearly laid out and
simulation results are presented. The effects of imbalance in the modulation signals of the carrier based VSI
and imbalance on the induction machine load were investigated. The imbalance in the modulation signals of
the VSI resulted in some oscillation of the electromagnetic torque of the machine with a relative drop in the
torque rating. For the imbalance involving the modulation signals and the load, the oscillation of the
electromagnetic torque were quite severe. Also, compared to the normal inverter and induction machine
operation, there are substantial drops in rotor speed (slip) on application of load torque in the two imbalance
scenarios considered.
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0 1 2 3
-5
0
5
10
15
Time[s]
Te
[Nm]
4 5 6 7
-5
0
5
10
15
Time[s]
Te
[Nm]
0 1 2 3
-200
0
200
400
Time[s]
wr
[rad/s]
4 5 6 7
320
340
360
380
Time[s]
wr
[rad/s]
(a) (c)
(d)(b)
6.97 6.975 6.98 6.985 6.99 6.995 7
-30
-20
-10
0
10
20
30
Time[s]
iabcdefghis
[A]
ias
ibs
ics
ids
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ifs
igs
ihs
iis

 ISSN: 2088-8694
14
[5] H Tao, et al. Magnetostructural coupling field analysis on the end winding of a multiphase induction machine.
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Modeling and Simulation of a Carrier-based PWM Voltage Source Inverter for a Nine Phase Induction Machine Drive

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