International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
Wavelet Modulation for Neutral Point Clamped Multilevel
Inverters
Umabati Laishram1, A.M. Nagaraj2
1
M Tech Student, DSCE Bangalore, 2Associate Professor, DSCE Bangalore
Abstract— This paper implements a new type of
modulation known as Wavelet Modulation (WM) based on
non-uniform sampling and wavelet theory in a multilevel
neutral-point clamped inverter. The proposed scheme is
compared with other modulation techniques such as
Sinusoidal Pulse Width Modulation (SPWM) and Squarewave Pulse Width Modulation (SQPWM). Simulation results
show that the WM technique produces smoother current
output, better output voltage, and lesser Total Harmonic
Distortion (THD) as compared with the other modulation
techniques.
II. NEUTRAL-POINT CLAMPED MULTILEVEL INVERTER
The neutral-point clamped (NPC) multilevel inverter
was first introduced by [10] and generalization was done by
[11]. A 3-level neutral-point clamped multilevel inverter is
designed with 12 unidirectional active switches and 6
neutral point clamping diodes. Each switch blocks half of
the full dc voltage. In each phase leg, only 2 out of the 4
switches must be on at any particular instant. Two series
connected capacitors of the same rating splits the supply
voltage into 3-levels. The diodes are all similar so that the
same voltage level is clamped across the switch. A 3-level
neutral-point clamped multilevel inverter is shown in
figure I.
The structure of the NPC multilevel inverter provides
less voltage stress across the switch. The purpose of
producing different levels of voltage is to sequentially
activate only 2 switching elements in each leg. One of the
main advantages of neutral-point clamped multilevel
inverter is that they have twice the number of switching
elements as the six pulse 3- inverters, where each
switching element blocks only half the dc bus voltage.
Also, the increased number of switches guarantees reduced
switch utilization [7].
Keywords—modulation, neutral-point clamped multilevel
inverter, THD, wavelets, wavelet modulation.
I. INTRODUCTION
A wavelet is a waveform of limited duration that has an
average value of zero. Wavelets are mathematical functions
that group data into varied frequency components and
study each component with a resolution matched to its
scale. The fundamental idea behind wavelets is to analyze
according to scale [3].
S.A. Saleh, C.R. Moloney, and M.A. Rahman developed
a special wavelet-based non-dyadic MRA for implementing
wavelet modulation in single-phase voltage source Hbridge inverters [2]. The non-uniform recurrent sampling
model of single-phase inverters provided the framework for
3 inverters [1]. A non-uniform recurrent sampling model
for a 3 inverter is required for non-uniform recurrent
sampling and reconstruction of three CT signals with the
same frequency and shifted from each other by
radians from each other. WM technique for 3 inverter
requires establishing a unique non-dyadic MRA where each
subspace is time and frequency shifted to support the nonuniform recurrent sampling reconstruction of three CT
signals.
This paper presents using the backbone of WM
technique in 3 VS inverter [1] in implementing WM
technique in a neutral-point-clamped multilevel inverter.
Furthermore, this paper provides the effects of WM
technique on the output voltage, current and THD of the
neutral-point-clamped multilevel inverter. Furthermore, it
also provides comparisons in the basic output parameters of
WM technique with other PWM techniques such as SPWM
and SQPWM.
Figure I. Neutral-point clamped multilevel inverter.
61
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
III. SALEH AND RAHMAN’S WAVELET
The output of an inverter is usually composed of trains
of periodic rectangular pulses that have different durations
and the overall period is equal to the period of the
fundamental component of the inverter output. Such
rectangular pulses can be accorded as the successive stages
of interpolation to synthesize a CT signal from its samples.
This type of sampling is known as non-uniform recurrent
sampling. Single-phase inverters was modeled using nonuniform sampling where a sinusoidal CT signal is sampled
in a non-uniform recurrent manner so that groups
consisting of two samples each are created [2]. The
sampling model of single-phase inverters was extended to
the model of three-phase inverters [1], where three
sinusoidal CT signals are sampled in a non-uniform
recurrent manner. This sampling is to be applied to the
model of a 3-phase neutral-point coupling inverter. The
three sinusoidal signals have the same frequency with a
phase shift of
radians from each other.
( )
(
( )
(
⁄ )
( )
( )
(
⁄ )
( )
)
( )
(
(
( )
(
(
( )
(
)
)(
( )
)
)(
( )
)
)(
( )
∏(
)
( )
( )
∏(
)
( )
(
( ))
∑∑
(
)
(
)
(
( ))
∑∑
(
)
(
)
(
( ))
∑∑
(
)
(
)
( )
(
)
(
(
)
(
)
(
(
)
)(
( )
)
)(
( )
)
)(
( )) , (
( )) and (
( )) are the
Where (
reconstructed versions of the three sinusoidal CT signals.
Equations (10)-(12) relates the ac output voltage to its dc
input voltage VDC through stages of periodic and timelocalized interpolating functions. The time-localization
property of the interpolating function implies that each
interpolating function is defined for one group of nonuniform recurrent samples.
IV. IMPLEMENTING THE WAVELET MODULATION
TECHNIQUE FOR A NPC MULTILEVEL INVERTER
( )
)
The WM technique developed for 3 VS inverter can be
implemented in a similar fashion to a 3 NPC multilevel
inverter. According to [1], the technique is divided into two
parts:
( ),
( ) and
( ) in a nonPart 1) Sampling
uniform recurrent manner by using a set of basis functions.
The created samples in sample groups da, db, and dc are
located at the boundaries of the intervals [
],
[
] and [
]. These time locations are
determined as follows:
( )
)
( )
(
)
( ),
( ) and
( ) are the Lagrange
Where
interpolating function over the sample groups da, db and dc
given by
( )
∏(
The intervals [
], [
] and [
]
are the time intervals for the three interpolating functions
( ),
( ) and
( ) respectively. The periodicity of
the sample groups and the time localized feature of the
interpolating functions ensure their periodicity with a
period of Tm.
The reconstructed version of the three sinusoidal CT
signals are given as follows:
Where
and
is the frequency of each
sinusoidal signal.
In general, the reconstruction of a CT signal from its
non-uniform samples can be achieved using Lagrange’s
Interpolating functions. In order to reconstruct three
sinusoidal CT signals from groups of non-uniform
recurrent samples, stages of periodic interpolating functions
are employed. Each stage of these interpolating functions is
defined for one sample group of each sampled sinusoidal
signal. The interpolating functions for sample groups da of
( ), db of
( ) and dc of
( ) is as follows:
(
( )
)
( )
62
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
For SMa(t),
VI. PERFORMANCE RESULTS
Simulation is done using the following parameters:
Output frequency, f =50 Hz.
Switching frequency, Fs =250 Hz.
For SMb(t),
Pulse frequency, fp = 1080 Hz.
No. of pulses, p = 10.
For performance comparison purposes, the same inverter
is activated using Sinusoidal Pulse Width Modulation
(SPWM) and Square Pulse Width Modulation (SQPWM)
techniques.
For SMc(t),
Where d=0,1,2……D-1 and D is the number of sample
groups created over Tm; j=0,1,2…….
Part 2) Generating switching pulses created as a dilated
(by scale j) and translated (by shift value k) version of the
synthesis scaling functions. Each of these generated
switching pulses will have its duration determined in
Part 1.
Changes in the scale j and the translation k leads to a
change in the time interval and location of each sample
group of each CT reference modulating signal.
V. SIMULATION USING MATLAB
The step-by-step-procedure for implementing the WM
technique in NPC multilevel inverter is realized using a
MATLAB code that generates switching pulses to activate
a SIMULINK model of a NPC multilevel inverter. The
simulation model is as shown below:
Figure III. Output waveform for SPWM NPC multilevel inverter.
Figure IV. Output waveform for SQPWM NPC multilevel inverter.
Figure II. Simulink model of NPC multilevel inverter.
63
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
Table I summarizes the performance simulation results
for all the three modulation techniques tested. The
comparative performance results in Table I clearly
demonstrates that significant improvements in the outputs
of a NPC multilevel inverter can be achieved using WM
technique.
VII. CONCLUSION
In this paper, WM technique developed for
VS
inverters is implemented in NPC multilevel inverter using a
simple switching pulse generation code. This pulse
generation code is applied to a SIMULINK model of a 3level NPC multilevel inverter developed using MATLAB.
Simulation results of the NPC multilevel inverter shows
that outputs have high fundamental component magnitude
and low harmonic components. Furthermore, a
performance comparison between the WM technique and
other PWM techniques such as SPWM and SQPWM shows
that WM inverters produce outputs with lower harmonic
content or improved THD than the other traditional inverter
modulation techniques.
The advantages of WM inverters can be listed as
follows:
 The inverter function with non-uniform recurrent
sampling reconstruction of reference modulating
signal means that the output pulses have a quarter
cycle symmetry.
 It is able to produce output voltages and currents
with higher magnitudes of the fundamental
component and lower harmonic contents better
than the other types of modulation techniques.
 The effect of harmonics on the source is low and
switching losses are low.
 Controllability is easy and implantation is simple.
Figure V. Output waveform for WM NPC multilevel inverters.
Figures III, IV and V demonstrate the output voltage
waveforms of the NPC multilevel inverter on the
implementation of SPWM, SQPWM and WM respectively.
The quality of inverter output voltage and load current is
usually expressed in terms of the THD factor defined as
Where
is the rms value of the fundamental
component of the inverter output voltage or load current.
is the summation of the rms values of all the other
harmonic components, which is given by
√
Where h=2,3,…..,n indexes of the harmonic component.
THD factors can be evaluated using in-built MATLAB
tools.
REFERENCES
TABLE I
[1]
SPW
M
SQP
WM
WM
THDV
13.72
3.58
1.90
[2]
THDI
7.54
13.42
1.94
[3]
[4]
64
S. A. Saleh, C. R. Moloney, and M. A. Rahman, ―Analysis and
development of wavelet modulation for three-phase voltage-source
inverters,‖ IEEE Trans. Ind. Electron., vol. 58, no. 8, pp. 3330–3348,
Jul. 2009.
S. A. Saleh, C. R. Moloney, and M. A. Rahman, ―Development and
testing of wavelet modulation for single-phase inverters,‖ IEEE
Trans. Ind. Electron., vol. 56, no. 7, pp. 2588–2599, Jul. 2009.
Amara Graps, ―An introduction to wavelets,‖ IEEE Computational
Science and Engineering, vol. 2, num. 2 ,Summer 1995.
A. Aktaibi, M. A. Rahman, A. Razali, ―A critical review of
modulation techniques,‖ Proc. IEEE 12th DSP Conf., Jackson Lake
Lodge, WY, pp. 544–549, Sep. 2006.
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 3, March 2014)
[5]
[6]
[7]
Jan IWASZKIEWICZ, Jacek PERZ, ―Fourier series and wavelet
transform applied to stepped waveform synthesis in multilevel
convertors,‖ Proceedings of Electrotechnical Institute, Narwicka 1,
80-557 Gdansk, Issue 229, 2006.
Panagiotis Panagis, Fotis Stergiopoulos, Pantelis Marabeas, Stefanos
Manias, ―Comparison of State of the Art Multilevel Inverters,‖
Power Electronics Specialists Conference, IEEE 2008.
S.A. Saleh, M. Azizur Rahman, ―An introduction to wavelet
modulated inverters,‖ IEEE Press Series on Power Engineering.
[8]
[9]
www.ConceptualWavelets.com
John Owens, ―Introduction to wavelets,‖ CS448: Topics in
Computer Graphics, Stanford University.
[10] A. Nabae, I. Takahashi, H. Akagi, ―A new neutral-point clamped
PWM inverter,‖ IEEE Transactions on Industry Applications, IA-17,
No. 5, pp. 518-523, September/October 1981.
[11] P.M. Bhagwatt , V.R. Stefanovic, ―Generalized structure of a
multilevel PWM inverter‖, IEEE Transactions on Industry
Applications, IA-19, No.5, pp 1057-1069, November/December,
1983.
65