Triangular Multicarrier SPWM Technique for Nine Level Cascaded Inverter

Abstract

In this paper, novel pulse width modulation technique which uses triangular carrier waveform is proposed for nine-level cascaded inverter. In triangular carrier waveform, different techniques such as phase disposition (PD), inverted phase disposition (IPD), phase opposition disposition (POD) and alternative phase opposition disposition (APOD) are implemented. The fundamental output voltage and harmonics obtained in each method are compared with each other. The proposed switching technique enhances the fundamental component of the output voltage and improves total harmonic distortion. The different PWM methodologies adopting the constant switching φrequency multicarrier are simulated φor a 1KW, 3φ inverter using MATLAB/SIMULINK. The eφφect oφ switching frequency on the fundamental output voltage and harmonics are also analyzed.

Full text

International Journal of Scientific & Engineering Research, Volume 4, Issue 5, May 2013
ISSN 2229-5518
IJSER © 2013
http://www.ijser.org
Triangular Multicarrier SPWM Technique for Nine
Level Cascaded Inverter
A.Mahendran, K.Muthulakshmi, R.Nagarajan
Abstract-In this paper, novel pulse width modulation technique which uses triangular carrier waveform is proposed for nine-level
cascaded inverter. In triangular carrier waveform, different techniques such as phase disposition (PD), inverted phase disposition (IPD),
phase opposition disposition (POD) and alternative phase opposition disposition (APOD) are implemented. The fundamental output
voltage and harmonics obtained in each method are compared with each other. The proposed switching technique enhances the
fundamental component of the output voltage and improves total harmonic distortion. The different PWM methodologies adopting the
constant switching φrequency multicarrier are simulated φor a 1KW, 3φ inverter using MATLAB/SIMULINK. The eφφect oφ switching
frequency on the fundamental output voltage and harmonics are also analyzed.
Index Terms-Sinusoidal Pulse Width Modulation (SPWM), Triangular Multicarrier SPWM (TMC SPWM), Total Harmonic Distortion (THD).
—————————— ——————————
1 INTRODUCTION
ultilevel inverter is an effective solution for increasing pow-
er and reducing harmonics of ac waveform [1]. Multilevel
inverters are suitable for high voltage and high power ap-
plications due to their ability to synthesize waveforms with better
harmonics and important for power electronics applications such
as flexible ac transmission systems, renewable energy sources,
uninterruptible power supplies, and electrical drives and active
power filters. In this paper, constant switching frequency multi-
carrier [2], [3], pulse width modulation method is used for the
multi level inverter. The control objective is to compare the refer-
ence sine wave with multicarrier waves for three phase nine level
cascaded inverter.
Multilevel voltage source inverter (MVSI) structure is very
popular especially in high power DC to AC power conversion
applications. It offers several advantages that make it
preferable over the conventional voltage source inverter (VSI).
These include the capability to handle higher DC link voltage,
improved harmonics performance, reduced power device stress [4].
There is a problem in controlling a VSI with variable amplitude
and frequency to obtain an output voltage waveform with
sinusoidal shape by using simple control techniques and it can be
overcome by MVSI.
The general structure of the MVSI is to synthesize a staircase
or multilevel output sinusoidal voltage out of several levels of dc
voltages and it can therefore be described as a voltage synthe-
sizer. In conventional VSI, the maximum output voltage is deter-
mined by the blocking capability of each device. By using a mul-
tilevel structure, the stress on each switching device can be
reduced in proportional to the higher voltages. Consequently, in
some applications, it is possible to avoid expensive and bulky
step-up transformer. Another significant advantage of a multilevel
output is better and more sinusoidal voltage waveform. As a re-
sult, a lower total harmonic distortion (THD) is obtained.
In motor applications, high dv/dt in power supply generates high
stress on motor windings and requires additional motor insu-
lation
Fig.1. One leg or single phase of the power circuit of a three phase
CCMLI
Further, high dv/dt of semiconductor devices increases the
electromagnetic interference (EMI), common-mode voltage and
possibilities of failure on motor. By increasing the number of levels
in the output waveform, the switching dv/dt stress is reduced in the
multi level inverter [5], [6].
It is reported that the development of multilevel voltage
source inverter topology has began in early 1980’s when
Nabae at el proposed a three-level neutral point clamped (NPC)
Inverter [7]. Later, several multilevel topologies have evolved,
such as the Diode Clamped Multilevel Inverter (DCMLI) also
known as Neutral Point Clamped (NPC) Inverter, Flying
Capacitor Multilevel Inverter (FCMLI) and Cascaded Multilevel
Inverter (CCMLI) [8]-[11].
Among them, CCMLI topology is the most attractive, since
it requires the least number of components and increases the
number of levels in the inverter without requiring high ratings
on individual devices and the power rating of the CCMLI is also
increased [12]. It also results in simple circuit layout and is modu-
lar in structure. Furthermore, CCMLI type of topology is free of
M
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DC voltage balancing problem, which is a common issue facing in
the DCMLI and FCMLI topologies. The nine level single phases
Cascaded Inverter topology is shown in Fig.1.
2 CASCADED MULTILEVEL INVERTER
The CCMLI consists of a series connection of separate single (full-
bridge) or three-phase inverter modules on the ac output termi-
nals [13], [14]. Each dc to ac module requires an isolated dc input.
The nine-level CCMLI is having four input DC sources as shown
in fig 1. The value of each source is Vdc.
Each inverter module can generate three different output
voltage levels +Vdc, 0 and –Vdc, by connecting the dc source to
the output terminals utilizing different switching
combinations of the four semiconductor switches in each inverter.
The CCMLI is producing nine level output, they are 4Vdc, 3V
dc
, 2V
dc ,Vdc , 0 , -Vdc , -2Vdc , -3Vdc and -4Vdc . This topology is suita-
ble for applications where separate dc voltage sources are availa-
ble, such as photovoltaic (PV) generators, fuel cells and batteries.
The phase output voltage is generated by the sum of four output
voltage of the full bridge inverter modules. Fig.1 shows the pow-
er circuit of one leg of a three phase CCMLI.
The multilevel inverter of Fig.1 utilizes four independent dc
sources and consequently will create an output phase voltage
with nine levels. In general, if NSis the number of
independent dc sources per phase, then the following relations
apply [13]:
1N2m S (1)


1m2p  (2)
Where m is the number of levels and p is the number of switch-
ing devices in each phase.
Fig 2: Simulation model of a three phase nine level CCMLI
The most well known SPWM which can be applied to a
CCMLI is the Phase-Shifted SPWM. This modulation tech-
nique is the same as that of the conventional SPWM technique
which is applied to a conventional single-phase full-bridge invert-
er, the only difference being that it utilizes more than one carri-
er. The number of carriers to be used per phase is equal to twice
the number of dc voltage sources per phase (2Ns) [13].
Fig.2 presents the simulation model of a three-phase nine-level
CCMLI and is developed using MATLAB/SIMULINK. The simula-
tion results are obtained for the output phase voltage and
line voltage of the three-phase nine-level CCMLI with 1KW, 3f
resistive loads for various PWM techniques.
3 MODULATION TECHNIQUES
Pulse Width Modulation (PWM) control strategies
development tries to reduce the total harmonic distortion
(THD) of the output voltage. Increasing the switching
frequency of the PWM pattern reduces the lower frequency
harmonics by moving the switching frequency carrier
harmonic and associated sideband harmonics away from the
fundamental frequency component [15]. This increased
switching frequency reduces harmonics, which results in a
lower THD with high quality output voltage waveforms of
desired fundamental RMS value and frequency which are as
close as possible to sinusoidal wave shape.
Any deviation in the sinusoidal wave shape will result in
harmonic currents in the load and this harmonic current
produces the electromagnetic interference (EMI), harmonic
losses and torque pulsation in the case of motor drives. Higher
switching frequency can be employed for low and medium
power inverters, whereas, for high power and medium
voltage applications the switching frequency should be low.
Harmonic reduction can then be strictly related to the perfor-
mance of an inverter with any switching strategy. The three
phase multi level inverter requires three modulating signals or
reference signals which are three sine-waves with 120 degree
phase shift.
In this paper, triangular multicarrier sinusoidal PWM (TMC
SPWM) technique is developed. Each carrier is to be compared
with the corresponding modulating sine wave. The reference
or modulation waveform has peak-to-peak amplitude Amand
frequency fmand it is centered in the middle of the carrier set.
The general principle of a carrier based PWM technique is
the comparison of a sinusoidal waveform with a carrier
waveform, this typically being a triangular carrier waveform.
The reference is continuously compared with the carrier
signal. If the reference is greater than the carrier signal, then
the active device corresponding to that carrier is switched on,
and if the reference is less than the carrier signal, then the
active device corresponding to that carrier is switched off [16].
The carrier frequency defines the switching frequency of
the converter and the high order harmonic components of the
output voltage spectrum and the sidebands occur around the
carrier frequency and its multiples. In multilevel inverters, the
amplitude modulation index, Maand the frequency ratio, Mf
are defined as [17],
c/ma A)1m(AM 
(3)
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fmcf /fM (4)
Where Amand Acare amplitude of modulating and carrier
signal respectively. fmand fcare frequency of modulating and
carrier signal respectively. In this paper, modulation index
used is unity. For multilevel applications, carrier based PWM
techniques with multiple carriers are used. The Multicarrier
Modulation (MCM) techniques, can be divided in to the fol-
lowing categories [18] such as,
Phase disposition (PD) where all the carriers are in
phase.
Inverted phase disposition (IPD) where all the carriers
are in phase and is inverted.
Phase opposition disposition (POD) where the carriers
above the zero reference are in phase but shifted by
180 degrees from those carriers below the zero
reference.
Alternative phase opposition disposition (APOD)
where each carrier band is shifted by 180 degrees from
the adjacent carrier bands [19].
The above modulation strategies are implemented in
triangular multi carrier waveform. The line voltage waveform
and harmonic spectrum of the line voltage are shown for
different modulation techniques by doing simulation using
MATLAB/SIMULINK for a nine level CCMLI. The results
obtained are compared.
3.1 Triangular Multicarrier Sinusoidal PWM
(TMC SPWM)
The performance of the multilevel inverter is based on the
multi-carrier modulation technique used. Two-level to
multilevel inverters are made using several triangular carrier
signals and one reference signal per phase. Carrara [3]
developed multilevel sub harmonic PWM (SH-PWM) is as
follows,
For m-level inverter, m-1 carriers [15] with the same
frequency fcand same peak to peak amplitude Acare disposed
such that the bands they occupy are contiguous. They are
defined as
 
 
 
 
1m,........1i
,)2/m(t,
cc
y
if
1
c
A
i
C






 (5)
Where ycis a normalized symmetrical triangular carrier
defined as,
   
 
  
2/112mod1,
cc
y

 (6)
cc f2/)t(  (7)
φ represents the phase angle of yc. ycis a periodic function
with the period cc /2T  . It is shown that using
symmetrical triangular carrier generates less harmonic distor-
tion at the inverters output [20], [21] and is shown in Fig.3.
Fig 3: Triangular carrier waveform
The multicarrier modulation techniques (PD, IPD, POD, and
APOD) are implemented using triangular multicarrier signals
and are shown in Fig. 4(a), 4(b), 4(c) and 4(d) respectively.
Fig 4(a): PD TMC SPWM
Fig 4(b): IPD TMC SPWM.
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Fig 4(c): POD TMC SPWM
Fig 4(d): APOD TMC SPWM
In TMC SPWM, so far only the PD, POD and APOD
techniques are discussed earlier in the literature. In this paper,
IPD scheme is also applied to TMC SPWM and it is found that
this scheme gives the lowest THD among all other PWM
schemes.
4. SIMULATION RESULTS
A nine level cascaded multilevel inverter model was
implemented in MATLAB/SIMULINK software to
demonstrate the feasibility of PWM techniques. Phase
disposition, inverted phase disposition, phase opposition
disposition and alternative phase opposition disposition
techniques are used for the Triangular multicarrier Sinusoidal
PWM techniques.
The line voltage waveform with its harmonic spectrum at
fundamental frequency of 50Hz and switching frequency of 2
KHz and 10 KHz is obtained for the proposed CCMLI. For
comparison, the total harmonic distortion (THD) was chosen
to be evaluated for all the modulation techniques. In order to
get THD level of the waveform, a Fast Fourier Transform (FFT)
is applied to obtain the spectrum of the output voltage.
Here the %THD is calculated up to a harmonic order which is
twice the switching frequency. For 2 KHz switching frequency
up to 80th order harmonics is taken in to account for calculat-
ing THD and for 10 KHz switching frequency up to 400th order
harmonics is taken in to account for calculating THD.
4.1 Triangular Multi Carrier Modulation
Techniques (TMC SPWM)
Fig 5(a): Line Voltage forTriangular Multi Carrier Phase Disposition SPWM
Fig 5(b): Percentage Line Voltage THD forTriangular Multi Carrier Phase
Disposition SPWM
Fig 5(a) and 5(b) show the line voltage and the percentage
THD of the line voltage for the triangular multi carrier
sinusoidal PWM using phase disposition technique.
Fig 6(a): Line Voltage forTriangular Multi Carrier Inverted Phase
Disposition SPWM
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Fig 6(b): Percentage Line Voltage THD for forTriangular Multi Carrier
Inverted Phase Disposition SPWM
Fig 6(a) and 6(b) show the line voltage and the percentage
THD of the line voltage for the triangular multi carrier
sinusoidal PWM using inverted phase disposition technique.
Fig 7(a): Line Voltage forTriangular Multi Carrier Phase Opposition
Disposition SPWM
.
Fig 7(b): Percentage Line Voltage THD for Triangular Multi Carrier
Phase Opposition Disposition SPWM
Fig 7(a) and 7(b) show the line voltage and the percentage
THD of the line voltage for the triangular multi carrier sinus-
oidal PWM using phase opposition disposition technique.
Fig 8(a): Line Voltage forTriangular Multi Carrier Alternative Phase
Opposition Disposition SPWM
Fig 8(b): Percentage Line Voltage THD forTriangular Multi Carrier
Alternative Phase Opposition Disposition SPWM
Fig 8(a) and 8(b) show the line voltage and the percentage
THD of the line voltage for the triangular multi carrier
sinusoidal PWM using alternative phase opposition
disposition technique.
Table.1 show the percentage line voltage THD, fundamental
phase and line voltage, and dominant harmonic factor are
obtained for the different multicarrier PWM techniques with a
switching frequency of 2 KHz and 10 KHz respectively.
From the simulation result in the triangular multi carrier
SPWM technique PD and IPD PWM schemes, from 3rd order
harmonics to 17th order harmonics and higher odd order
harmonics (above 17th harmonics) are less than 1%. Few of the
even order harmonics from 18th harmonics to 54th harmonics
for the above mentioned scheme are less than 2%. The
dominant 57th harmonic factor is about 2% for the PD and IPD
schemes.
In the POD scheme, from 3rd order harmonics to 19th order
harmonics and higher even order harmonics (above 20th har-
monics) are less than 1%. Few of the odd order harmonics
from 21st harmonics to 69th harmonics are 1% to 2%. The
dominant 39th and 41st harmonic factor are 5.37% and 5.59%
respectively for the POD scheme.
In the APOD scheme, from 3rd order harmonics to 25th order
harmonics and higher even order harmonics (above 26th
harmonics) are less than 1%. Few of the higher odd order
harmonics above 27th order are present. The dominant 29th and
51st harmonic factor are 4.70% and 4.59% respectively for the
APOD scheme.
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It is observed that, when the switching frequency of the
CCMLI is increased, the percentage line voltage THD, the
fundamental phase and line voltage are decreased very slight-
ly for the PD and IPD schemes. In the POD and APOD
schemes, if the switching frequency is increased, the
percentage line voltage THD is increased very slightly and the
fundamental phase and line voltage are decreased very slight-
ly. Also the fundamental line voltage is maximum for POD
scheme and is minimum for PD and IPD schemes.
TABLE.I
Line voltage %THD, Fundamental voltage per phase,
Fundamental line voltage and dominant harmonic factor for
triangular multicarrier SPWM
Modulation
Technique
Line
voltage
%
THD
Voltage
per phase
(volts)
Line
voltage
(volts)
Dominant
harmonic
factor (%)
FS
(2KHz)
PD
8.21
227
391.2
H
57
=1.83
IPD
8.19
227
391.2
H
57
=1.84
POD 11.45 227.1 392.8
H
39
=5.37
H
41
=5.59
APOD 12.22 227 392.7
H
29
=4.70
H
51
=4.59
FS
(10KHz)
PD
8.18
226.4
389.9
H
377
=1.65
IPD
8.17
226.4
389.9
H
377
=1.66
POD 12.49 226.7 392.
H
199
=6.01
H
201
=5.99
APOD 12.71 226.9 392.1
H
189
=4.85
H
211
=4.85
5 CONCLUSION
The simulation results for a three phase cascaded nine-level
inverter which use triangular carrier wave as novel
multicarrier Modulation technique is obtained through
MATLAB/SIMULINK. In triangular carrier waveform,
different techniques such as phase disposition (PD), inverted
phase disposition (IPD), phase opposition disposition (POD)
and alternative phase opposition disposition (APOD) are
implemented. The output quantities like fundamental phase
and line voltage, percentage THD of the line voltage and
percentage dominant harmonic factor are being found. When
the switching frequency is 2 KHz, phase opposition
disposition (POD) scheme gives maximum line voltage and
triangular (IPD) scheme gives minimum % THD for line
voltage. If the switching frequency is 10 KHz, alternative
phase opposition disposition (APOD) scheme gives maximum
line voltage and triangular (IPD) scheme gives minimum
% THD for line voltage. The proposed methods offer better
harmonic performance and selection of proper switching
frequency in the pulse width modulation strategies enhances
the fundamental output voltage.
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————————————————
A.Mahendran is currently pursuing master’s degree program
in Applied Electronics, Kamaraj College of Engineering and Technology in Anna
University, Viruthunagari, Tamilnadu, India. E-
mail: maha17am@gmail.com
K.Muthulakshmi is currently working as Associate Professor in Electrical and Elec-
tronics Engineering Department, Kamaraj College of Engineering and Technology
,Viruthunagar,Tamilnadu, India
R.Nagarajan is currently working as Associate Professor in Electrical and Electronic
Engineering Department, Raja College of Engineering and Technology in An-
na University, Madurai, India. E-mail: knaga71@yahoo.com
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