International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 2, February 2013)
A Review on Mitigation of Harmonics in Cascaded H-Bridge
Multilevel Inverter using optimization Techniques
Amrita Tuteja 1, Dr. Amita Mahor2, Aarti Sirsat3
1
P.G. Scholar, NIIST, Bhopal (M.P.), India
2
H.O.D. Electrical & Electronics Department, NIIST, Bhopal (M.P.)
3
P.G.Scholar, SOI DAVV Indore (M.P.),
The key issue in designing an effective multilevel
inverter is to ensure that the total harmonic distortion
(THD) of the output voltage waveform is within acceptable
limits. To control the output voltage and to eliminate the
undesired harmonics in multilevel converters various
modulation methods such as sinusoidal pulse width
modulation (PWM) and space-vector PWM techniques are
suggested[6],[7]. However, PWM techniques are not able
to eliminate lower order harmonics completely. Another
approach is to choose the switching angles so that specific
higher order harmonics such as the 5th, 7th, 11th, and 13th
are suppressed in the output voltage of the inverter. This
method is known as selective harmonic elimination (SHE)
or programmed PWM techniques in technical literature
[8]–[10]. A fundamental problem with such method is to
obtain the arithmetic solution of nonlinear transcendental
equations which contain trigonometric terms and naturally
present multiple solutions.
This set of nonlinear equations can be solved by iterative
techniques such as the Newton–Raphson method [8]–
[11].However, such techniques need a good initial guess
which should be very close to the exact solution patterns.
Therefore, the Newton–Raphson method is not feasible to
solve the SHE problem for a large number of switching
angles if good initial guesses are not available. To solve the
SHE problem another approach based on mathematical
theory of resultant is proposed[12],where the SHE problem
are converted into an equivalent set of polynomial
equations and then the mathematical theory of resultant is
utilized to find all possible sets of solution. This approach,
however, appears to be unattractive because as the number
of inverter level increases, so does the degree of the
polynomials of the mathematical model. This is likely to
lead to numerical difficulty and substantial computational
burden as well. The Particle Swarm Optimization (PSO)
approach is developed to deal with the SHE problem with
unequal Dc sources. Particle Swarm Optimization (PSO) is
a relatively recent heuristic search method whose
mechanics are inspired by the swarming or collaborative
behavior of biological populations.
Abstract - Multilevel inverters have been drawing growing
attention in the recent years especially in the distributed
energy resources area due to the fact that several batteries,
fuel cells, solar cell, wind and micro turbines can be connected
through multilevel inverter to feed a load or the ac grid.
Multilevel inverter becomes an alternative in the area of highpower medium-voltage energy control. Therefore, Harmonic
Reduction in multi level inverters are considered very
important task.
For eliminating the harmonics lot of
researchers have suggested modifications in the circuit
topology and optimal selection of firing angle using
conventional and nonconventional optimization algorithms.
This paper presents a review application by different
optimization techniques for harmonic reduction in multilevel
inverters.
Keywords- Cascaded Multilevel Inverter, Genetic
Algorithm (GA), H-bridge, Multilevel Inverter, Particle
Swarm optimization (PSO), Total Harmonic Distortion
(THD).
I.
INTRODUCTION
A multilevel converter is a power electronic system that
synthesizes a desired output voltage from several levels of
dc voltages as inputs. With an increasing number of dc
voltage sources, the converter output voltage waveform
approaches a nearly sinusoidal waveform while using a
fundamental frequency-switching scheme. The primary
advantage of multi level inverter is their small output
voltage, results in higher output quality, lower harmonic
component, better electromagnetic computability, and
lower switching losses. [1][2]
Multilevel inverters also have interest in the field of
high-voltage high-power applications such as laminators,
mills, conveyors, compressors, UPS systems. Some of the
fundamental multilevel topologies include the diodeclamped [3], flying capacitor [4], and cascaded H-bridge
structures [5]. The most familiar power circuit topology for
multilevel converters is based on the cascade connection of
an s number of single-phase full-bridge inverters to
generate a (2s + 1) number of levels.
30
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 2, February 2013)
As an optimization technique, PSO is much less
dependent on the start values of the variables in the
optimization problem when compared with the widely used
Newton-Raphson
Another approach i.e. The Genetic Algorithm (GA) is
stochastic optimization techniques. Genetic Algorithm is
applied to compute the switching angles in a cascaded
multilevel inverter to produce the required fundamental
voltage. The problem of harmonic elimination is converted
into an optimization task using binary coded task. It deals
with all the problems that usually considered very hard
such as integer variables, non-convex functions, no
differentiable functions, domains not connected, badly
behaved functions, multiple local optima, and multiple
objectives. For these reasons, GA has been adopted in this
study.
II.
C ASCADED H-B RIDGE MULTILEVEL INVERTER
The cascaded multilevel inverter consists of a series of H
bridge (single-phase full-bridge) inverter units. Each fullbridge can generate three different voltage outputs: +Vdc,
0, and −Vdc. However, all three multilevel inverters can
produce staircase waveform as shown in Fig. 2. The
number of output phase voltage levels in a cascaded
multilevel inverter is 2S + 1, where S is the number of dc
sources. For example, phase voltage waveform for a 7-level
cascaded multilevel inverter with three isolated dc sources
(S = 3) is shown in Fig. 2. Each H-bridge unit generates a
quasi-square waveform by phase-shifting the switching
timings of its positive and negative phase legs.
III.
Fig. 1. Cascaded multilevel inverter with separate dc sources.
SELECTIVE H ARMONIC E LIMINATION
A 7-level inverter waveform shown in fig.2 has three
variables θ1, θ2, and θ3, where Vdc1, Vdc2, and Vdc3 are
assumed to be equal. Considering equal amplitude of all dc
sources, the Fourier series expansion of the output voltage
waveform, shown in Fig.2, will be written:
Fig. 2. The output voltage waveform of a 7-level inverter.
31
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 2, February 2013)
∞
V ( t) = ∑ Vn sin (n t)
n=1
M. Sabahi et al. – This paper developed an optimal
solution to the harmonic reduction problem in a cascade
multilevel inverter with non equal DC sources using
genetic algorithm. In this paper switching angles are
generated for different values of Modulation index,
considering minimum voltage total harmonic distortion
(THD), where as selected harmonics are controlled within
the allowable limits at all desired modulation indices. The
computed angles are used in simulated circuit in
MATLAB/Simulink to validate the results.
N. Yousefpoor et al. proposed the optimal minimization
of total harmonic distortion (OMTHD) technique, which is
an efficient method for determining the switching angels to
minimize the total harmonic distortion (THD). This paper
compares OMTHD technique in cascaded multilevel
inverter with constant DC sources & adjustable DC sources
which can be controlled. Comparison results show that
employing adjustable DC sources which can be controlled
results in substantial improvement in the harmonic
minimization.
Burak Ozpineci & Leon M-Tolbert et al. developed p a
genetic algorithm (GA) optimization technique which is
applied to multilevel inverts for eliminating some higher
order harmonics while maintaining the required
fundamental voltage. This technique can be applied to
multilevel inverters & the optimum switching angels are
calculated to eliminate the harmonics. Then these angles
are used in an experimental setup to validate the results.
K. Haghdar et al.focuses an elimination of harmonics in
a H- bridge multi level voltage source inverter. The basic
concept is to eliminate specific harmonics by the proper
selection of switching angle. In this paper generalized
pattern search (GPS), Simulated Annealing (SA) & genetic
algorithm (GA)are used to determine proper switching
angles to eliminate harmonics in 13 level inverter. The
proposed methods can be applied to all of the multilevel
inverter. The simulation results showed that GPS & SA
methods are more efficient than GA.
S.H.Fathi & N.Yousefpoor et al. proposed an optimized
harmonic stepped waveform technique (OHSW) for
reducing harmonics in multilevel inverter. This technique
is very efficient for improving the quality of multilevel
inverter output voltage. In this paper three phase & single
phase OHSW techniques are applied to the cascaded
multilevel inverter with adjustable DC sources and constant
DC sources .Comparison show that employing adjustable
DC sources which can be controlled results in substantial
improvement in the total harmonic distortion.
John N. Ehissan et al.describes a method to compute the
switching angles in a multilevel converter to produce the
required fundamental voltage.
(1)
Where, Vn is the amplitude of nth harmonic. Switching
angles are limited between zeros and
(0
Because of odd quarter- wave Symmetric characteristics,
harmonics with even order become zero. Consequently, Vn
becomes:
{
∑
(
}
For odd ns
0
for even ns
(2)
The Fourier expansion for generated voltage waveform
using the SHE-PWM method is given be
V(
∑
(cos(n ) + cos(n )
+ cos (n )+….cos(n
(
The switching angles
condition:
-
0
(3)
must satisfy the following
(4)
The number of harmonics which can be eliminated from
the output voltage of the inverter is (s-1). For example, to
eliminate the fifth –order harmonics for a five level
inverter, equation set (5) must be satisfied. Note that the
elimination of triple harmonics for the three –phase power
system applications is not necessary, because these
harmonics are automatically eliminated from the linevoltage
cos + cos = (
cos(
+ cos(
=0
(5)
In (5), modulation index M is defined as
M=
and
is the fundamental of the required voltage.
IV.
REVIEW ON THE APPLICATION OF D IFFERENT
T ECHNIQUES IN MULTILEVEL INVERTER
Said Barkati et al. – This paper presents two
evolutionary algorithms for the optimized harmonic
stepped waveform. Genetic Algorithm & Particle Swarm
Optimization are applied to compute the switching angels
in a three phase seven level inverter to produce the required
fundamental voltage. In addition to this, these algorithms
are also used to solve the starting point problem of the
Newton Raphson Method.
32
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 2, February 2013)
In these a complete analysis is done for a seven level
converter, Where for a change of modulation index M1,the
switching angles can be chosen to produce the desired
fundamental voltage V1=M1(4sVdc/ while making the
fifth & seventh harmonics identical zero.
Ayoub Kavousi et al. present the Bee optimization
method for harmonic elimination in a cascaded multilevel
inverter. The main objective in selective harmonic
elimination pulse width modulation is eliminating low
order harmonics by solving non linear equations. In this
paper, the Bee Algorithm (BA) is applied to a seven level
inverter for solving the equations. The algorithm is based
on food foraging behavior of a swarm of a honeybees. This
method has higher precision & probability of convergence
than genetic algorithm (GA). MATLAB Software is used
for optimization comparisons of GA & BA.
H. Taghizadeh and M. Tarafdar Hagh present the novel
particle swarm optimization technique to determine the
optimum switching angles of multilevel converters to
produce the required fundamental voltage while at the same
time not generate lower order harmonics. This optimization
method is applied to transcendental equations
characterizing the harmonic content to minimize low order
harmonics. Comparing the results of PSO with
mathematical. Methods for seven and eleven level inverter.
It finds that PSO can simply find the optimum switching
angles and also with comparing with Genetic Algorithm
and it is clear that PSO has faster convergence with better
quality solutions than GA approach to solve this problem.
Mehrdad Tarafdar Hagh et al. developed an algorithm
based on species-based PSO (SPSO) to deal with the
problem where the number of switching angles is increased
and their determination using conventional iterative
methods in addition to GA and simple PSO techniques is
not possible. So an MSPSO algorithm with adaptive
adjustment of niche radius has been proposed to determine
the optimum switching angles of multilevel inverters.
Simulation and experimental results are provided for an 11level cascaded H-bridge inverter to validate the accuracy of
computational results. Results show that all undesired
harmonics up to 50th order have been effectively
minimized at the output voltage waveform of inverter.
Comparison of results with active harmonic elimination
technique shows that the THD and the switching frequency
of output voltage decreased dramatically.
M. Sarvi M. R. Salimian used two algorithms: 1-genetic
algorithm and 2- PSO is used to optimize THD in
Multilevel inverters. Theoretical and simulated results are
used to compare these techniques.
Also in this paper proposes a method for optimization of
specific harmonics and improving the characteristics of
switching in multilevel inverters. In this method, the
switching angle of each levels and the output voltage of
them is determined and is used for optimization. Then the
effect of changing in the output voltage of each inverter on
reduction of one or more specific harmonic is analyzed. In
this paper result of GA and PSO is compared and shows
that GA is better for optimizing THD in multilevel
converters. The amplitude of specific harmonics can be
decreased better by changing the amplitude of each level in
comparison of assuming constant amplitude.
F.J.T Filho & T.H.A. Mateus et al. presents a new
approach for real time computation of switching angles
using artificial neural networks. The solutions were found
off line using Genetic Algorithm (GA) to obtain the data
set for use during the training process of the neural network
& to explore the advantage of approximate solutions
obtained by the GA. The trained neural network is used
then for on-line real time determination of the angles. The
paper gives details on the approach used together with the
simulation & experimental results.
S. Sangeetha & S. Jeevananthan proposed a
programming tool to calculate the switching angles for
eliminating the selected harmonics in a multilevel inverter
(MLI).This paper presents the systematic analysis &
algorithm based off-line precalculation of switching angle
for a range of modulation index using resultant theory. In
this the problem of selective harmonic elimination together
with the voltage control is formulated as Fourier analysis
,simplified using resultant theory, reduced using
Mathematica 6 and then solved by visual C++ programme
by calulation of all possible triplent roots .
Chuang Liu et al. presents a Stochastic Newton method
to compute the switching angle in multilevel converters so
as to produce the required fundamental voltage while at the
same time not generate higher order harmonics. In this
paper stochastic techniques are used to find the possible
initial values, such as beginning process of Particle Swarm
Optimization (PSO).This synthetic method is called
Stochastic Newton Method (SNM), which is applied to
solve the selective harmonic elimination problem for
multilevel inverters.All sets of solutions are found for
found for elevan & nineteen levels converters to show the
simplicity,effictiveness & easy implementation of SNM.
Zhi Zeying Liu Hui et al. presents the curve fitting
techniques (CFT) & MATLAB programmes to determine
the values of switching angles. All the initial switching
angles are obtained by using MATLAB’S fsolves.
33
International Journal of Emerging Technology and Advanced Engineering
Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 3, Issue 2, February 2013)
[4 ] T.A. Meynard and H. Foch, "Multi-level choppers for high voltage
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[8 ] H. S. Patel and R. G. Hoft, ―Generalized harmonic elimination and
voltage control in thyristor inverters: Part I—Harmonic elimination,‖
IEEE Trans. Ind. Appl., vol. IA-9, no. 3, pp. 310–317, May/Jun.
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[10 ] W. Fei, X. Du, and B. Wu, ―A generalized half-wave symmetry
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[11 ] P. N. Enjeti, P. D. Ziogas, and J. F. Lindsay, ―Programmed PWM
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[12 ] J. N. Chiasson, L. M. Tolbert, K. J. McKenzie, and Z. Du, ―Realtime computer control of a multilevel converter using the
mathematical theory of resultant,‖ Math. Comput. Simul, vol. 63, no.
3–5, pp. 197–208, 2003.
[13 ] Barkati S, Baghli L, Berkouk E.M, Boucherit M.S. "Harmonic
elimination in diode-clamped multilevel inverter using evolutionary
algorithms". Electric Power Systems Research 78 (2008) 1736–
1746.
[14 ] Chuang Liu; Jianze Wang; Dan Luo; Fei Sha; , "Elimination of
Harmonics in Multilevel Converters Using Stochastic Newton
Method," Power and Energy Engineering Conference (APPEEC),
2010 Asia-Pacific , vol., no., pp.1-4, 28-31 March 2010
[15 ] Taghizadeh, H.; Hagh, M.T.; , "Harmonic Elimination of Cascade
Multilevel Inverters with Nonequal DC Sources Using Particle
Swarm Optimization," Industrial Electronics, IEEE Transactions on ,
vol.57, no.11, pp.3678-3684,Nov.2010
[16 ] Hagh, M.T.; Taghizadeh, H.; Razi, K.; , "Harmonic Minimization in
Multilevel Inverters Using Modified Species- Based Particle Swarm
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[17 ] Sarvi, M.; Salimian, M.R.; , "Optimization of specific harmonics in
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pp.1-4, Aug. 31 2010- Sept. 3 2010
In this paper a method to selected harmonic elimination
(SHE) choosing initial values was presented in a singlephase full bridge voltage source inverter.The on-line real
time control of SHE was realized. The simulation & the
experimental results were separately done by MATLAB.
Akira Nabae et al. proposed a new neutral point clamped
pulse width modulation inverter composed of main
switching devices to clamp the output. In these paper two
inveter are compared .The neutral point clamped pulse
width modulation (NPC PWM) inverter shows improved
result and is appropiate for a wide range variable speed
drive.Two inverter are compared analytically &
experimentally .The neutral point clamped pulse width
modulation inveter adopting new PWM techniques was
used to eliminate higher order harmonics .
Jagdish Kumar et al. implement the selective harmonic
elimination method at fundamental switching frequency
using Newton Raphson method that produces all possible
solution sets. The proposed technique has many advantages
such as it can produce all possible solution sets for any
numbers of multilevel inverter without much computational
burden, speed of convergence is fast. The proposed
technique was successfully implemented for computing the
switching angles for a seven level & eleven level cascade
multilevel inverter.
V.
CONCLUSIONS
The different techniques that is GA,PSO OSHW etc has
been proposed to solve SHE problem with equal and non
equal dc source in H-bridge cascaded multilevel
inveter.The proposed methods is able to find the optimum
switching angles in a simple manner. They also reduce the
computational burden and running time and ensure the
accuracy and quality of the calculated angles.
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34