Download II. differntial evolution for shepwm

Selective Harmonic Elimination PWM Method in two
level inverter by Differential Evolution Optimization
Technique
Murali Murugan
PG scholar, Department of Electrical and Electronics,
Sri Manakula vinayagar engineering college
Pondicherry, India
[email protected]
Abstract—The Objective of the paper is to reduce the harmonic
order such as 5th, 7th, 11th, 13th, 17th, 19th and 23rd. The triplen
harmonic like 3rd, 9th, 15th, 21st are eliminated naturally by three
phase inverter. The proposed waveform is symmetric so that all
even order harmonics will be eliminated. In order to reduce
lower order harmonics, differential evolution optimization
technique is used to find the optimized firing angles. Using the
optimized firing angle, an inverter firing circuit is designed and
the FFT analysis is carried out. The analysis and simulation of
the three phase inverter is done in MATLAB, Using the
optimized firing angles obtained from the differential evolution.
Keywords—optimizationtechnique; differentialevolution;
selectiveharmonic elimination; pulse width modulaton.
I.
INTRODUCTION
In an industrialized nation today, an increasingly
significant portion of the generated electrical energy is
processed through power electronics for various applications
in industrial, commercial, residential, aerospace and military
environments .The technological advances made in the field
of power semiconductor devices over the last two decades,
have led to the development of power semiconductor devices
with high power ratings and very good switching
performances. Harmonics are undesirable currents or voltages.
They exist at some multiple or fraction of the fundamental
frequency. Harmonic pollution in static power converters is a
serious problem. For example in many residential, commercial
and office buildings the triplen harmonics create high neutral
currents to the extent that they may start fires, although the
fundamental neutral current is within allowable limits.
The possibility of applying GAs to obtain optimized SVM
sequences has been investigated .It has been defined with the
goal of minimizing the filtering requirement by lowering most
significant harmonics while conforming to the available
standards for voltage waveform quality [1]. The non-linear
load conditions are not considered. Build the dead-time effect
model in seven situations of inductor current and don’t need
Parthiban Balaraman
Assistant professor, Department of Electrical and
Electronics, Sri Manakula vinayagar engineering college,
Pondicherry, India
[email protected]
compensation in zero-crossing zone without ZCC. Present the
indirect inductor current by detecting784 load current instead
of inductor current. Confirm the effectiveness of the improved
inductor detection and the proposed dead-time compensation
method .It will also be extended for unipolar SPWM
controlled single-phase inverter and space-vector –
modulation (SVM)-controlled three-phase inverter with LC
filter.[2] The PSO-based algorithm is determined with a set of
solutions of switching angles with a relatively high speed
convergence. A nonlinear transcendental equations of the
selective harmonic elimination technique used in three-phase
PWM inverters feeding the induction motor by particle swarm
optimization (PSO). The fundamental component of the
output voltage has the desired magnitude, eliminating several
selected harmonics [3].
The objective function of the DE is designed to
minimize (to near zero) the selected harmonics and at the
same time allows for the fundamental component of the output
voltage to be controlled independently. It has been shown that
the method can accurately compute the HEPWM switching
angles without having to make correct guesses on the initial
values of the switching angles [4].The selective harmonic
elimination pulse width modulation (SHEPWM) switching
strategy has been applied to multilevel inverters to remove low
order harmonics. Eliminating harmonics is performed. Thus,
harmful harmonics such as the 5th harmonic still remains in
the output waveform. A reduction in the eliminated harmonics
results in an increase in the degrees of freedom. As a result,
the lower order harmonics are eliminated [5].
Harmonics must be reduced in order to reduce the
size of filters. In this paper a PWM applies a pulse train of
fixed amplitude and frequency, only the width of the pulse is
varied in proportion to the input, but with less wastage of
power at the output stage harmonics gets eliminated. This
paper eliminates 3rd, 5th, 7th and 9th harmonics [6].
Selective Harmonic Elimination Pulse-Width Modulation
(SHE-PWM) has been an inclusive research area in the field
of Power Converters. This paper involves the solution of non-
linear transcendental equation sets representing the relation
between the amplitude of the fundamental wave, harmonic
components and the switching angles through which several
harmonics are eliminated [7].
II.
B. Objective function for differential differential evolution
technique
By placing switching pattern in the output waveform
at proper locations, selected harmonics can be eliminated.
Fig 1. Generalized symmetric SHEPWM
The equation for eliminating the desired harmonic
which forms as the objective function for DE. By substituting
various values randomly by differential evolution technique, a
optimal firing angle is selected so that the selected harmonic
can be eliminated.
For 1st harmonic order equation is given by
4
1
1  2  1 cos  n1   M 



Where M is the modulation index
En 
8
4 

i
1

2
 1 cos  n i  


 
i 1

(2)
To eliminate the harmonic order
DIFFERNTIAL EVOLUTION FOR SHEPWM
A. General
Differential evolution (DE) is arguably one of the
most powerful stochastic real-parameter Optimization
algorithms in current use. The DE algorithm emerged as a
very competitive form of evolutionary computing more than a
decade ago. It is capable of handling non-differentiable,
nonlinear, and multimodal objective functions. Its simplicity
and straight forwardness in implementation, excellent
performance, fewer parameters involved, and low space
complexity, has made DE one of the most popular and
powerful tool in the field of optimization. It works through a
simple cycle of stages.
E1 
To eliminate the nth harmonic order
(1)
8
4

i
1

2
 1 cos  n i  


 
i 1

8
4

i
E7 
1  2  1 cos  n i  

 
i 1

E5 
(3)
(4)
...
.
E23 
8
4

i
1

2
 1 cos  n i 


 
i 1

E total =E1 +E5 +E 7 +E11 +E13 +E17 +E19 +E 23
(5)
(6)
C. Optimization technique differential evolution
The general structure of a DE program for SHEPWM
is shown in Fig.2. The algorithm starts by initializing the
target population of switching angles as an objective function.
The DE parameters are set as follows: the population size, NP
= 80, mutation factor (also known as the scale factor) F = 0.6,
crossover probability CR = 0.9, values to reach VTR =
0.000000001 and the stopping criterion of the maximum
number or generations is 300. In the initialization operation,
the target population (SHEWM angles) is randomly chosen
within defined bounds, as Xv max and Xvmin. It was found
that the choice of the boundary has little effect on the
performance of the algorithm, the wideness of the bounds
required more iteration, however the projection remand the
same, so long as the conditions are satisfied.
For the next steps, the fitness value of each switching
angles of the population is evaluated. If the fitness satisfies the
predefined criteria, the final value is saved and the process is
stopped. Otherwise, it will proceed to mutation operation. The
mutation operation generates a mutant vector based on the
initial target population. The derived mutant vector is
considered as the secondary target population. Then the
crossover operator is applied to the initial target and
secondary target according to probabilistic scheme which is
binomial and exponential crossover scheme to generate the
trial vector within the crossover probability setting. Finally,
the trial vector of competes with its initial target population of
switching angles for a position in the next generation. The
aforementioned steps of the DE are repeated iteratively until
the objective function of an individual vector is lower than
predefined threshold or until a predefined total number of
generations have been generated.
After obtaining the switching pattern from the
optimization technique, a three phase voltage source inverter
is designed and the required pulse is given using the
embedded MATLAB program and the harmonic analysis is
performed. The specifications of the VSI are as follows:
VDC=300Vdc,
fundamental
frequency=50Hz,
R1=R2=R3=1Ω
START
INITIALIZE
THE
PARAMETERS
EVALUATE THE
FIRST BEST
VECTOR
MUTUATION
PROCESS
RECOMBINATION
PROCESS
Fig 4. Three phase voltage source inverter
SELECTION
PROCESS
III
A.
NO
VTR CHECK OR
MAX
GENERATION
YES
STOP
A.
SIMULATION RESULTS AND DISCUSSION
UNOPTIMIZED SIMULATION RESULTS
The DE algorithm for solving the SHEPWM angles
are programmed in MATLAB using Embedded matlab
function. Pulse pattern which is obtained from the
unoptimized DE result is shown in figure 5. Fig 6 and 7 shows
the output voltage waveform, THD and harmonic distortion
values.
Table 1: comparison table for 1st and 2nd time run
Fig 2. Flowchart for SHEPWM
Fig 3. Convergence characteristics of DE
1
72.79005
72.369691
84.792676
84.443397
2
27.433014
27.187950
83.872232
84.767902
α8
33.288524
α7
11.097691
α6
25.042499
α5
6.453990
α4
8.776010
α3
3.894375
α2
2.7414706
α1
2.690863
Run
time
The table 1 illustrates two different run time for the
unoptimized firing angles.
B.
OPTIMIZED SIMULATION RESULTS
The DE algorithm for solving the SHEPWM angles
are programmed in MATLAB using Embedded matlab
function. Pulse pattern which is obtained from the optimized
DE result is shown in figure 8. Fig 9 and 10 shows the output
voltage waveform, THD and harmonic distortion values.
Table 2: comparison table for 1st and 2nd time run.
71.315156
α8
69.683056
70.926714
α7
69.883331
35.689331
α6
35.839706
34.348795
α5
34.599249
23.279333
α4
23.309413
20.456183
11.058294
α3
20.693002
2
α2
11.838842
1
6.764128
Fig 5. Pulse pattern for inverter obtained from unoptimized
DE
α1
7.484180
Run
time
The table 2 illustrates two different run time for the optimized
firing angles.
Fig 6. Output voltage waveform for the unoptimized value of
the inverter
Fig 8. Pulse pattern for inverter obtained from optimized DE
Fig 7. FFT analysis for the unoptimized switching values
Fig 9. Output voltage waveform for the inverter
The table 3 shows the optimized firing angle values
and the unoptimized firing angle values for two different
iterations namely 1st and 300th iteration. Very least error
provides the optimized value and the fft analysis is shown in
fig. 10
Fig 10. FFT analysis of voltage waveform for the
optimized angles of the inverter
The above is the THD and the harmonic distortion
values of the optimized technique (Differential Evolution)
which clearly shows the absence of the harmonic order such
as 5th, 7th, 11th, 13th, 17th, 19th and 23rd and the triplen harmonics.
IV RESULTS COMPARISON
Table4: Comparison table for the optimized and unoptimized
values
The table 2 illustrates the comparison of the 1st and
the 300 iteration. The FFT analysis of figure 10 shows the
presence of harmonic order such as 5th, 7th, and 11th whereas
in the fig 9 it clearly states, the absence of the harmonics
which is the best optimized switching pattern.
th
st
th
Table 3: comparison table for 1 and 300 iteration for the
optimized values
34.05979
34.76049
69.67992
34.348795
35.689331
70.92619
70.73529
23.18721
23.279333
α8
71.31516
19.8632
α7
20.456183
α6
10.26514
α5
11.058294
α4
6.722094
α3
6.764128
α2
0.012197
α1
2.5005E-27
Least
error
Fig 11. FFT analysis for the unoptimized switching
values
Harmonic
order
unoptimized
1
231.98
5
2.36
0.01
7
6.65
0.01
11
7.4
0.04
13
15.49
0.05
17
9.84
0
19
2.68
0.01
23
7.5
0
optimized
234.38
The table 4 provides the switching angles between
the optimized and the unoptimized technique. In optimized
technique the values are found to be nearer to zero whereas in
the case of unoptimized technique values are not zero
Journal of Soft Computing and Engineering (IJSCE)., ISSN: 22312307, Volume-2, Issue-3, July 2012.,
Fig 12 bar chart for two different iterations
The above chart shows the comparison of the two
different iterations and the in case of the optimized value the
harmonic order is completely eliminated as said from the
objective function.
CONCLUSION
This paper investigates and successfully implements
optimal switching strategies for harmonic elimination in three
phase voltage-source inverters. Optimal switching patterns for
the voltage-source inverter configurations were generated
through optimized technique (differential evolution). Thus an
inverter is designed to implement the switching strategies and
the harmonic profile is analyzed. Other harmonics such as
25th, 29th, and 31st can be easily eliminated by using the
external filter circuit.
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[1]
Ali Mehrizi-Sani, Student Member, IEEE, and Shaahin Filizadeh,
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[2]
Hongliang Wang,Xuejun Pei,Yu Chen,Yong Kang.
“An Adaptive Dead-time Compensation Method for Sinusoidal
PWM-controlled Voltage Source Inverter with Output LC
Filter” IEEE, 2011
[3]
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