International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
Trapezoidal Inverted Sine PWM Techniques for
Fundamental Fortification in PV Fed Multilevel Inverters
S.Malathy1and Dr.R.Ramaprabha2
1
Assistant Professor, SSN College of Engineering, India.
Associate Professor, SSN College of Engineering, India.
2
1
malathys@ssn.edu.in
2
ramaprabhar@ssn.edu.in
To boost up the voltage and to adjust the load resistance,
a boost converter is placed between the PV panel and the
load. The duty cycle of the converter is adjusted so as to
equalise the load resistance with the internal resistance of
the PV panel. Perturb and Observe algorithm (P &O) is
used to track the maximum power point and duty cycle is
then adjusted accordingly. The developed PV model with
MPPT and boost converter is used to feed the cascaded five
level inverter circuit. The overall block diagram of the
system is given in the Fig 1.
Abstract— Renewable energy sources, especially solar
photovoltaic systems (PV) are gaining popularity as the
demand for electrical energy is increasing day by day. They
can act as a voltage source feeding the power circuit. This
work aims in utilising the PV system as a voltage source for a
cascaded five level inverter. Further the performance of the
PV panel fed cascaded multilevel inverter is analysed by
applying trapezoidal inverted sine PWM schemes. Many pulse
width modulation (PWM) techniques were proposed and
reported in literature with the aim of reducing the total
harmonic distortion and enhancing the fundamental output
voltage. Trapezoidal PWM scheme is one such scheme which
is found to enhance the fundamental output voltage than the
commonly used sine PWM scheme. This paper proposes a new
PWM technique where gating pulses are produced by
comparing a trapezoidal reference with multiple high
frequency inverted sine carriers. Perturb and Observe (P&O)
maximum power point tracking (MPPT) algorithm is used to
extract the maximum power form PV panel.
Keywords— PV, MPPT, P&O, PWM, TISC PWM, TTC
PWM, MLI,THD
I. INTRODUCTION
A single phase five level cascaded H bridge inverter
considered in this work requires two separate DC sources
and they are provided by two Photovoltaic (PV) panels.
Solar PV system is gaining popularity as the demand for
the power is on the rise. Moreover it is a clean source of
power and requires less maintenance. The power generated
by a single PV cell is small. Several cells are connected in
series and parallel, to attain the required current and the
voltage rating respectively. PV power generation is
dependent on the environmental factors like insolation and
temperature. The internal resistance of the PV panel is non
linear and it varies with the intensity of the Sun‘s radiation.
According to maximum power transfer theorem, maximum
power can be extracted from the panel if the load resistance
is made equal to the internal source resistance.
Fig.1. Block diagram of PV fed cascaded MLI
The harmonic content in the output of an inverter can be
reduced by increasing the number of levels and by applying
a suitable PWM technique. The concept of utilizing
multiple small voltages to generate a staircase like
waveform was introduced and this lead to a better and more
sinusoidal output waveform [1]-[2]. This approach not only
improved the spectral quality of the output voltage but also
reduced the voltage stress on each switch. With the aim of
fortifying the fundamental voltage and reducing the
harmonic distortion, many topologies and PWM techniques
were introduced [3]. The most commonly used PWM
technique is the sine PWM technique (SPWM).
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International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
In SPWM technique, a sine wave is compared with
multiple high frequency triangular waves to produce the
control signals which in turn control the operation of the
power circuit. Though the Total Harmonic Distortion
(THD) is less, this technique exhibits poor performance as
far as the fundamental output voltage is concerned. To
improve the harmonic performance and to enhance the
fundamental output voltage, third harmonic injected
reference with inverted sine carrier was proposed for three
phase inverters [4]. A new PWM technique with multiple
trapezoidal reference and single triangular carrier was
proposed by [5]. This method gave better fundamental
output voltage. A detailed comparative study of various
unipolar multi carrier PWM schemes was done by [6]-[7].
Various multi carrier (triangular) trapezoidal PWM
(MCTPWM) methods like Phase disposition (PD), phase
opposition disposition (POD), phase shift, carrier
overlapping PWM, variable frequency PWM were
discussed in detail [8]. Inverted sine carrier with sine
reference was proposed and it is found to enhance the
fundamental output voltage and spectral quality without
pulse dropping [9]. In general, trapezoidal PWM enhances
the fundamental voltage but increases the lower order
harmonics and the usage of inverted sine carriers enhances
spectral quality.
This paper proposes trapezoidal inverted sine carrier
PWM technique (TISC) where the reference signal is
trapezoidal and carriers are inverted sine signals. The
cascaded five level inverter is powered by PV panels with
maximum power tracking and boost converter. The
harmonic content and Vrms of the output voltage for
different values of modulation index (ma) are computed.
The output current from PV panel is given as
I pv  I ph  I D  I sh
(1)
Photon generated current of the PV panel, Iph is given as

I ph  K i T  Tn   I pvn
GG
(2)
n
The current through the diode is calculated as



I D  I r exp ( Vpv  I pv R se ) Vta  1
(3)
and
Ir 
K i (T  Tn )  Iscn
expK v (T  Tn )  Vocn Vta   1
(4)
Where,
K
q
ID
Ish
a
Ir
Gn
Ipvn
Tn
Vocn
Iscn
Voc
Iph
Ipv
Vpv
Rse
Isc
Ki
Rsh
T
Vta
Vmp
Vdc
II. SOLAR PV PANEL MODELING
The standard one diode model is used to model solar PV
source (Fig.2.). The equations (1)-(4) are used for the
mathematical modeling [10].
-
Boltzmann‘s constant (=1.381x10-23 J/K)
Charge of electron (=1.602x10-19 C)
Current through the diode
Current through the shunt resistance
Diode Ideality factor (1< a< 2 for a single cell)
Diode reverse saturation current
Nominal Insolation level (1000 W/m2)
Nominal photocurrent of PV panel
Nominal Temperature (273K)
Nominal value of open circuit voltage
Nominal value of short circuit current
Open circuit voltage of PV panel
Photon generated current of the PV module
PV panel current
PV panel Voltage
Series Resistance
Short Circuit current of module
Short-circuit current temperature Coefficient
Shunt Resistance
Temperature
Thermal Voltage (=aKT/q)
Voltage at Maximum Power Point
DC voltage at the inverter input
The mathematical model of the PV panel is implemented
in Matlab/Simulink and the P-V and I-V characteristics for
different insolation levels are presented in Fig.3 and Fig.4
respectively.
Fig.2. Simple PV model
584
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
Fig.3. I-V Characteristics of PV panel at different insolation levels
Fig.5. Flowchart of P& O Algorithm
The voltage and current of the PV panel are measured
after one perturbation and the power is calculated. This is
then compared with the previous value of power and the
difference ∆P (∆P =P k –Pk-1) is calculated. If ∆P is
positive, perturbation is continued in the same direction.
For negative values of ∆P, the direction of perturbation is
reversed.
Fig.4. P-V Characteristics of PV panel at different insolation levels
III. MAXIMUM POWER POINT TRACKING ALGORITHM
The performance of the PV panel depends highly on the
environmental conditions which vary throughout the day. It
is observed from Fig.3 and Fig.4 that, as the insolation
decreases the I-V and P-V characteristic curves of the PV
panel shifts down and so does the maximum power point.
The efficiency of the PV panel is very less and hence it
becomes necessary to extract the maximum power from the
panel by shifting the operating point to the maximum
power point. The operating point of the PV panel is fixed
by the load resistance. Several MPPT algorithms are
proposed in the literature to track the maximum power
point. Perturb and observe (P&O) algorithm is adopted in
this work due to its simplicity[11]. In this algorithm, a
perturbation is made on the PV panel operating point to
force tracking in the direction towards maximum power
point [11]-[16]. The flowchart of the P& O algorithm and
the output of the Matlab /Simulink model developed are
shown in Fig.5.
Fig.6.Maximum power point for different insolation
The maximum power point for different insolation levels
is shown in the fig.6. Matlab/Simulink model is developed
for P&O algorithm and is tested under variable insolation
conditions. The insolation is varied in steps from 200 W/m2
to 1000 W/m2.The model tracked the maximum power
point and it is plotted on the PV characteristic curve.
585
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
As the insolation level changes, the maximum power
point also changes. The PV module voltage that
corresponds to the maximum power point under different
insolation levels is shown in Fig. 7.
Fig.9. PV model with MPPT and boost converter with R load
IV. MULTI LEVEL INVERTERS
Several multilevel inverter topologies are proposed in
literature. Cascaded multilevel inverter is the popular
topology as the structure is modular and it does not require
any clamping diodes or voltage balancing capacitors.
Moreover it is easy to increase the number of levels by
stacking up the basic bridge circuit. The basic H bridge
circuit is modelled using MATLAB/SIMULINK (Fig.10).
This module produces three different voltage levels viz.
+Vdc, 0 and – Vdc. Two H bridge modules are connected in
series to generate output voltage with five different levels
viz. +2Vdc, +Vdc, 0,-2Vdc and - Vdc.
Fig.7.Maximum power point voltage as tracked by P&O algorithm
A. Boost converter
The boost converter has one controlled semiconductor
switch as shown in the Fig.8 and it is controlled by
applying appropriate gating pulses. The turn off resistance
of the switch is very much higher than the turn on
resistance. Thus by varying the duty cycle of the gating
pulse, the effective resistance offered by the circuit is
varied. The boost converter is placed right between the load
and the PV panel to ensure maximum power transfer
(Fig.9.). The resistance of the circuit as seen from the PV
panel must be equal to the internal resistance of the PV
module for maximum power transfer.
Fig.8.Boost converter
Fig 10. Matlab/Simulink model of H bridge module
The duty cycle of the boost converter is adjusted in such
a way that maximum power is transferred from the module
to the load.
In general 2N+1 levels are generated by ‗N‘ H bridge
modules and each module requires a separate DC voltage
source (Vdc).
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
The source can be a battery, fuel cell or a solar PV panel.
In this work PV panel with MPPT and Boost converter
provides the required voltage to the cascaded multilevel
inverter.
The overall all model developed for a PV panel fed
cascaded five level inverter is shown in Fig.13. Two H
bridge inverter circuits are connected in series to form a
five level inverter. Two PV panels with maximum power
point tracker and Boost converter feed the MLI circuit. The
gating pulses are generated by the PWM generator module.
Fig 11. Matlab/Simulink model of PV module with MPPT and Boost
converter
Cascaded five level inverter has two H Bridge modules
each with four controlled switches. It is required to
generate 8 gating pulses in the desired pattern so as to
obtain five different levels in the output voltage. In TISC
PWM technique the gating pulses are generated by
comparing two high frequency inverted sine carriers with a
unipolar trapezoidal reference wave. Fig.12 shows the
Matlab/Simulink model developed to generate gating
pulses. Trapezoidal triangular carrier PWM involves two
high frequency triangular carriers and a trapezoidal
reference.
Fig.13. MATLAB/SIMULINK model of 5 level cascaded inverter fed
by PV modules
V. TRAPEZOIDAL PULSE WIDTH MODULATION SCHEME
The scheme uses a single trapezoidal modulating signal
and the carrier can be triangular, saw tooth or inverted sine
signal. In Trapezoidal triangular carrier PWM (TTC PWM)
scheme, high frequency triangular carriers are compared
with trapezoidal reference. The intersection between the
trapezoidal signal and the carrier signals defines the
switching instant of the PWM pulse. The multiple carriers
used are positioned above zero level and the number of
carriers is dependent on the output voltage levels. For N
level inverter, (N-1)/2 carriers are used.
The amplitude of the reference wave is represented as
Am and the frequency as fm. Each of the carrier signals will
have amplitude of Ac and frequency fc. The modulation
index is calculated as ma=Am/2*Ac and the frequency ratio
is mf= fc/fm.
A. Trapezoidal Inverted sine PWM (TISC) scheme
In this proposed scheme, a unipolar trapezoidal signal
with an amplitude of Am and frequency fm is taken as
reference. Two high frequency inverted sine carriers with
frequency fc and amplitude Ac are compared with the
trapezoidal reference. Both the carriers are in phase with
each other. The frequency ratio is chosen to be 24 and the
modulation index is varied from 0.6 to 1 in steps of 1.
Fig.12.MATLAB/SIMULINK model of TISC PWM generator
587
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Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
The carrier arrangement along with the unipolar
trapezoidal reference is shown in Fig.14.
Fig.17. Output voltage by TTC PWM method
Fig.14. Arrangement of carrier and reference for TISC PWM scheme
VI.
SIMULATION RESULTS
The PV panel, Boost converter, P & O maximum power
point tracker and the cascaded five level inverter are
developed and integrated in Matlab /Simulink. The gate
signal generator is developed for the proposed trapezoidal
inverted sine PWM scheme and the trapezoidal triangular
carrier scheme using MATLAB and it is tested for various
modulation indices. The output waveform and the
harmonic profiles of the TISC and TTC PWM schemes are
presented in Fig.15 to Fig.18 for a modulation index of 0.8.
For other modulation indices, the results are presented in
Table I and Table II for TISC and TTC PWM schemes
respectively.
Fig.18. Harmonic profile by TTC PWM method
TABLE I
THD AND VRMS FOR THE PROPOSED TISC PWM SCHEMES
ma
0.6
TISC PWM Schemes
THD in % and Vrms in volts
THD
Vrms
16.51
47.81
0.7
12.0
51.3
0.8
0.9
13.21
14.08
53.22
55.44
1.0
14.74
56.76
TABLE II
THD AND VRMS FOR THE TTC PWM SCHEMES
Fig.15. Output voltage by TISC PWM method
ma
Fig.16. Harmonic profile by TISC PWM method
588
TTC PWM Schemes
THD in % and Vrms in volts
0.6
THD
16.41
Vrms
43.61
0.7
17.26
48.26
0.8
17.58
51.8
0.9
18.58
54.15
1.0
19.7
56.13
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 4, April 2012)
[6] B.Shanthi and S.P.Natarajan, ―Comparative study on various
The RMS value is found to increase with the increase in
the modulation index in steps of 0.1. The results of the TTC
PWM method, where triangular carriers are used are
presented in Table II. Though the variation in the Vrms
values between both the methods is small at higher
modulation indices, the harmonic distortion is considerably
reduced by employing the proposed TISC method.
unipolar
PWM strategies for single phase five level cascaded
inverter‖ ,International Journal of Power Electronics (IJPELEC),
Special issue
on: Power Converters: Modeling, Simulation,
Analysis, Topologies, Secondary issues and Applications,
InderScience publication,Switzerland, pp.36-50, 2009
[7] B.Shanthi and S.P.Natarajan, ―Carrier overlapping PWM methods
for single phase cascaded five level inverter‖, International Journal
of
Science and Techniques of Automatic control & computer
engineering
(IJ-STA, Tunisia), Special issue on Control of
Electrical Machines,
pp. 590-601, December 2008
VII. CONCLUSIONS
The simulation results of PV fed cascaded five level
inverter are presented. The trapezoidal ISC PWM
technique is proposed for the multilevel inverter and the
results are compared with that of the triangular carrier. It is
observed from the data presented that the TISC PWM
technique gives result with better spectral quality and
enhanced fundamental voltage. The insolation level is
assumed to be uniform and identical for both the PV
modules used. P & O MPPT algorithm is used to enhance
the performance. For higher voltage and current rating,
more PV panels are to be connected in series and parallel.
Since the performance of the PV module is dependent on
the environmental factors, effect of partial shading is to be
included in future study.
[8] R.Bensraj, S.P.Natarajan,‖Multicarrier Trapezoidal PWM Strategies
ACKNOWLEDGMENT
[12] Joe-Air Jiang, Tsong-Liang Huang, Ying-Tung Hsiao, Chia-Hong
The author wish to thank the management of SSN
College of Engineering, Chennai for providing all the
computational facilities to carry out this work
[13] K.H.Hussein, I. Muta, T. Hoshino and M. Osakada ―Maximum
Based on Control of Freedom Degree for MSMI‖, ARPN Journal of
Engineering and Applied Sciences , Vol. 5, No.5,May 2010, pp. 3241.
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reduction in power converters‖ proceedings of international
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feb,1995.vol.2 Pp560-564
[10] Marcelo Gradella Villalva, Jonas Rafael Gazoli, and Ernesto Ruppert
Filho, ―Comprehensive Approach to Modeling and Simulation of
Photovoltaic Arrays‖, IEEE Transactions on Power Electronics, vol.
24, no. 5, 2009, pp.1198-1208
[11] Vafaoui., B. Wu and R. Cheung ,‖ Implementation of maximum
power point tracking algorithm for residential photovoltaic systems ‖
2nd Canadian Solar Buildings Conference Calgary, June 10 – 14,
2007.
Chen, Maximum Power Tracking for Photovoltaic Power Systems,
Tamkang Journal of Science and Engineering, 2005, Vol. 8, No. 2,
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Photovoltaic Power Tracking: An Algorithm for Rapidly Changing
Atmospheric Conditions,‖ IEE Proceedings on Generation,
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