IEEE International Conference on Recent Advances and Innovations in Engineering (JCRAIE-2014),May 09-11, 2014, Jaipur, India

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

muralimouragane@gmail.com

Abstract-The Objective of the paper is to reduce the harmonic

order such as 5th, 7th, 11th, 13th, 17th, 19th and 23' .... The triplen harmonic like 3n., 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 optim ized 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-optimization technique; differential evolution; selective harmonic 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. Harmonics exist natural1y in inverters. Harmonic pol1ution 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 the allowable limits.

The possibility of applying GAs to obtain optimized SYM 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. But the dead-time effect model in several situations of inductor current and don't need

[978-1-4799-4040-0/14/$31.00 ©2014 IEEE]

Parthiban Balaraman Assistant professor, Department of Electrical and

Electronics, Sri Manakula vinayagar engineering college, Pondicherry, India

parthipondicherry@gmail.com

compensation in zero-crossing zone without ZCC. Present the indirect inductor current by detecting the 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 control1ed single-phase inverter and space-vector modulation (SYM)-control1ed 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 al10ws 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 switching technique has been applied in inverters to remove low order harmonics.The unwanted harmful1 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 can be reduced by reducing the size of filters. In this reference 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 reference 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 reference paper involves the solution of non-linear equations which represents the relation

between the amplitude of the fundamental wave, harmonic components and the switching angles through which several harmonics are eliminated [7].

II. DlFFERNTIAL 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 competitive form of evolutionary computing more than a decade ago. It is capable of handling non-differentiable, nonlinear, and multi modal 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.

B. Objective functionfor differential differential evolution technique

By placing switching pattern in the output waveform at proper locations, selected harmonics can be eliminated.

I I I

I 11

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 15t harmonic order equation is given by

(1)

Where M is the modulation index

To eliminate the nth harmonic order

To eliminate the harmonic order

4 [ 8 . ] E23 -;- 1 + 2 f; (-1)' cos(na,)

C. Optimization technique differential evolution

(2)

(3)

(4)

(5)

(6)

The general structure of a DE program for SHEPWM is shown in Fig.2. The algorithm starts by initializing the desired population of switching angles as an objective function. The DE parameters are considered as follows, The population size ie., NP = 80, mutation factor (also known as the scale factor) F = 0.6, crossover probability CR = 0.9, values to reach VTR = 0.0000001 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 Xv min. It has been found that the choice of the boundary has little effect on the performance of the algorithm, the wideness of the bounds requires more iteration; however the projection remain the same, so long as the conditions are satisfied. The above values can be varied according to the design path.

For the next steps, the fitness value of each switching angles of the population is analyzed. If the fitness satisfies the predefined criteria, the final value is considered as the best value and the iteration is stopped. Otherwise, it will proceed to the mutation process. The mutation operation generates a mutant vector based on the initial target population. The derived mutant vector is considered as the second target population. Then the crossover operator is applied to the initial target and secondary target according to probabilistic scheme. 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.

INITIALIZE THE

PARAMETERS

EVALUATE THE FIRST BEST

VECTOR

MUTUATION

PROCESS

RECOMBINA TION

PROCESS

SELECTION PROCESS

Fig 2. Flowchart for SHEPWM

� 1(1-J. COO'JP.J1J::OI1C:p. c.ha,ac£. .. tic_" drr J.5,---�----�----�---

2.lJ

0.5 \ u ���,�--�--��� o 5 � 1 00 50 200 250 300

Fig 3. Convergence characteristics of DE

A.

After obtaining the switching pattern from the optimization technique, a three phase voltage source inverter is designed and the required pulse is given using an embedded MATLAB program and the profile of harmonic analysis is performed. The specifications of the VSI are as follows: VDC=300Vdc, fundamental frequency=50Hz, Rl=R2=R3=lO

� + R

Y 300 V B

�

Fig 4. Three phase voltage source inverter

III SIMULATION RESULTS AND DISCUSSION

A. 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 151 and 2nd time run

Run al a2 a3 a4 as a6 a7 a8 time

\0 0 0\ "'1' If) ...... \0 t-o ...... 0\ N 0 0\ t- 0\ t- o "'1' If) 0 \0 \0 M

1 "'1' \0 N 00 0\ 0\ N M ...... t- "'1' 00 t- \0 0\ "'1' "'1' t- C; � M t- "'1' t- oO If) M N N ..t ..t N N M t- t- oo 00

M If) 0 ...... "'1' 0 N N 0\ ...... If) M \0 t- 0\ \0 0 0\ N 0 00 M 0\ t- M t- N 0\

2 0 "'1' M 0\ M 00 t- t-0\ 0\ If) C; "'1' ...... oc: \0 � oc: "'1' t-N M loCi ...... � � M ..t ...... N N 00 00

The table 1 illustrates two different run time for the unoptimized firing angles.

I·················

......... .. L ...

... • ..........

..........

• .......... ...

Fig 5. Pulse pattern for inverter obtained from unoptimized DE

Fig 6. Output voltage waveform for the unoptimized value of the inverter

:0-

m-

iO-

iO-

:0-�

0)-

:0-

;0-

10- I I • I I . I 1\ ill 2) JU J:

Hrm :ri: :r:cr

Fig 7. FFT analysis for the unoptimized switching values

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 lO shows the output voltage waveform, THD and harmonic distortion values.

Table 2: comparison table for lSI and 2nd time run.

Run a1 a2 a3 a4 a5 a6 a7 a8 time

00 .",. M M V) ,...., .",. \0 0\ 00 M 0\ M ,...., N N ,...., M t- M t- V) ,...., 00 \0 0\ 00 0\ \0 ,...., 1 .",. V) V) t- .",. 00 N V)

\0 � .",. � M 'c: 0\ ,...., t- o ..,f 0 M '" ,...., M V) ,...., ,...., N N M M t- t-

o N N M 0\ \0 ,...., \0 00 .",. 0 ,...., .",. 0 M V) ,...., 00 0 .",. N t- M 0

2 .",. 00 M 0\ 0\ 0\ M M 00 M 0\ 0 0\ M 00 00 .",. oc: \0 '! V) 00 00 \0 r--: ,...., 0 M ..,f vi 0\ 0\ ,...., N N M M \0 \0

The table 2 illustrates two different run time for the optimized firing angles.

• .... 1

, I

, i .

Fig 8. Pulse pattern for inverter obtained from optimized J?E

Fig 9. Output voltage waveform for the inverter

D

6)

6)

3J

. )

F .II:j;ln :lljll5:-.:I- 2�:"'L . liO- : �.L�

I

) 1 ___ 1 ____ 1 ____ 1 _________ ___ 1 o 5 '0 '5 iO is J:

H:lIU.rII,::lLl!'

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 23'd and the triplen harmonics.

IV RESULTS COMPARISON

The table 2 illustrates the comparison of the 15t and the 3001h iteration. The FFT analysis of figure 10 shows the presence of harmonic order such as 51\ 7'\ and lith whereas in the fig 9 it clearly states, the absence of the harmonics which is the best optimized switching pattern.

Table 3: comparison table for 151 and 300lh iteration for the optimized values

Least al a2 a3 a4 as a6 a7 a8 error

t- "'I' ;:!: '" � 0\ 0\ '" 0\ 0\ 0\ '" t- "'I' 0\ '" � 0 V"l <'"l t- 0\ 0 0\ V"l '" '" '-0 '-0 00 V"l '-0 t- <'"l � '" '" 00 ...... 0 t- '-0 t-o t- o 0; M .,r "'I' 0; 0 0 � ...... ...... '" <') <'"l '-0 t-

t- "'I' <'"l <'"l V"l ...... '" 00 0\ 00 <'"l 0\ <'"l 0\ � '" '" ...... <'"l t- <'"l � '-0 ...... '-0 ...... V"l "'I' 00 '-0 0\ 00 0\ '" V"l 0 '-0 V"l V"l t- "'I' 00 0\ ...... 0 t- C; "'I' "! <'"l '.c: 0 "': V"l � ...... 0 <'"l .,r V"l N ...... '" '" <') <'"l t- ......

t-

The table 3 shows the optimized firing angle values and the unoptimized firing angle values for two different iterations namely 151 and 300lh iteration. Very least error provides the optimized value and the fft analysis is shown in fig. 10

F.n1iIllI�lIa :'i:-",) ?J}.nm !((.:.'V. , ,

" --_ . _ 1 _-_ 1_ 1 ___ 1 _ . , _ _ 1 _ 1 __ - _ _ _ _ 1_ 1 __ " �o lilm:rito'd�'

·t:

Fig 11. FFT analysis for the unoptimized switching values

Table4: Comparison table for the optimized and unoptimized values

Harmonic order unoptimized optimized

I 231.98 234.38

5 2.36 0.01

7 6.65 0.01

II 7.4 0.04

13 15.49 0.05

17 9.84 0

19 2.68 0.01

23 7.5 0

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

250

200

150 • unoptimized

100 .optimized

50

0 - - • - -

1 5 7 11 13 17 19 23

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. The results are seen clearly that the major harmonics such as as 5t\ 7th, 11th, 13th, 17th, 19th and 23rd are eliminated. Other harmonics such as 25t\ 29th, and 31st can be easily eliminated by using the external filter circuit.

REFERENCES

[I] Ali Mehrizi-Sani and Shaahin Filizadeh " An Optimized Space Vector Modulation Sequence for Improved Harmonic Perfonnance"IEEE Transction on industrial electronics, vol 56, no. 8 , august 2009

[2] Hongliang Wang,Xuejun Pei,Yu Chen,Yong Kang. "An Adaptive Dead­time Compensation Method for Sinusoidal PWM-controlled Voltage Source Inverter with Output LC Filter" IEEE, 20 II

[3] Mohamed Azab "Harmonic Elimination in Three-Phase Voltage Source Inverters by Particle Swarm Optimization" Journal of Electrical Engineering & Technology Vol. 6, No. 3, pp. 334-341,2011 001:

[4]

[5]

[6]

I 0.5370/JEET.201 1.6.3.334.,

N. Bahari, Z. Salam, Taufi "Application of Differential Evolution to Determine the HEPWM Angles of a Three Phase Voltage Source Inverter"IEEE procedings 20 10.

Reza Salehi, Naeem Farokhnia, Mehrdad Abedi, and Seyed Hamid Fathi " Elimination of Lower Order Harmonics in Multilevel Inverters Using Genetic Algorithm" Journal of Power Electronics, Vol. II, No. 2, March 2011 .

Selective Harmonic Elimination by Programmable Pulse Width Modulation in Inverters., International Journal of Engineering Trends and Technology (UETT) - Volume4lssue4- April 2013., M. Kiran kumar, A. Madhu Sainath, V. Pavan Kumar.

[7] lBaskaran, S.Thamizharasan, R.Rajtilak "GA Based Optimization and Critical Evaluation Selective harmonic elimination Methods for Three­level Inverter". International Journal of Soft Computing and Engineering (USCE)., ISSN: 2231-2307, Volume-2, Issue-3, July 2012.,