 Open Access
 Total Downloads : 1277
 Authors : R. Vijayakumar, C. Devilalitha, R. Mazhuventhi, Dr. Alamelu Natchiappan
 Paper ID : IJERTV4IS020583
 Volume & Issue : Volume 04, Issue 02 (February 2015)
 Published (First Online): 27022015
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Selective Harmonic Elimination PWM Method using Seven Level Inverters by Genetic Algorithm Optimization Technique
1R.Vijayakumar
Department of Electrical and Electronics Engineering Christ College of Engineering and Technology Puducherry, India
2Dr. Alamelu Natchiappan
Department of Electrical and Electronics Engineering Pondicherry Engineering College
Puducherry, India
3C. Devilalitha
Department of Electrical and Electronics Engineering Christ College of Engineering and Technology
Puducherry, India
4R. Mazhuventhi
Department of Electrical and Electronics Engineering Christ College of Engineering and Technology
Puducherry, India
AbstractThis paper proposes a method for optimization of the harmonic performance of inverters under selective harmonic elimination PWM modulation (SHEPWM) control. SHEPWM method is used to optimize harmonic stepped waveform for multilevel inverters using Genetic algorithm. It involves the solution of nonlinear transcendental equation sets representing the relation between the amplitude of the fundamental wave, harmonic components and the switching angles. The genetic algorithm obtains the being optimal solution set of switching angles for each obligatory harmonic profile. Optimized SHEPWM sequences obtained for various operating points under different sampling frequencies are exposed to result in significant reduction of major harmonics while upholding the waveform quality inside prescribed limits.
KeywordsSelective Harmonic Elimination PWM Method (SHEPWM), Genetic Algorithm (GA), Cascaded HBridge Multilevel Inverter, Optimization Technique.

INTRODUCTION
The two general group are mainly involved in all applications are electrical drives for all AC motors when dc supply is used and in systems including high voltage direct current transmission systems, customer power & flexible ac transmission systems(FACTS) devices and interconnection of distributed generation units to a grid. Modulation Strategy classified according to several switching algorithm such as Pulse width modulation (PWM), Sinusoidal Pulse Width Modulation (SPWM), Space Vector Modulation (SVM), Selective Harmonic Eliminated Pulse Width Modulation (SHEPWM) or Programmed Waveform Pulse Width Modulation (PWPWM) are applied widely to control and obtain switching angle to achieve the desired output voltage. In the recent era, a novel kind of inverter named multilevel inverter has been introduced. It can be used in high power and high voltage applications. Advantages of this multilevel approach include good power quality, good electromagnetic compatibility (EMC), low switching losses, and high voltage capability [1]. In order to extend the desired fundamental
component of voltage, all of several switching methods create harmonics and hence, it is of attention to select the finest method to succeed minimum harmonics and total harmonic distortion (THD) [2]. However, PWM techniques are not able to eliminate lower order harmonics totally [3]. Alternative approach is to select the switching angles consequently 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 practical literature [6]. A fundamental issue related with such method is to attain the arithmetic solution of nonlinear transcendental equations which include trigonometric terms and obviously existing several solutions [5]. This set of nonlinear equations can be solved by iterative techniques such as the NewtonRaphson method. SHEPWM provides highest power quality at fundamental switching frequency in comparison to other existing PWM methods like space vector modulation and carrier based PWM technique [7]. The applications of SHEPWM are power quality improvement, motor drives and high voltage DC transmission system & distributed system [8]. Genetic algorithm is used to solve the equation and determine the optimized switching angle [10]. It solves the problem with multiple solutions compared to Differential Evolution algorithm. It is method which is very easy to understand and practically does not demand the knowledge of mathematics [9].
In this paper, a harmony Genetic Algorithm (GA) approach will be presented. The problem can be solved with an easier formulation and with any number of levels without wide derivation of analytical expressions. It is also faster and more precise than other optimization techniques [11].

CASCADED MULTILEVEL INVERTERS
A novel scheme for an mlevel (m 3) cascaded multilevel hybrid inverter is proposed. In the proposed method, a simple algorithm of founding switching sequence is applied that leads
to lowest change in voltage. An actual hybrid multilevel inverter must safeguard that the total harmonic distortion (THD) in the voltage output waveform is small sufficient [13]. This paper proposes a new algorithm for the hybrid multilevel inverter with uneven or varying voltage steps under the selective harmonic elimination PWM modulation. The algorithm results in the minimum THD of output voltage of the cascaded multilevel inverter with unequal voltage steps. A new expression of THD is existing to shorten the derivation [12].
Fig. 1. Mlevel Cascaded HBridge Multilevel Invereter
A single Hbridge is a threelevel converter. The four switches S1, S2, S3 and S4 are controlled to generate three
i = the switching angle
h = harmonic order

CONVENTIONAL METHOD
In conventional method, additional number of switches used to attain the switching angle and used to rises the output voltage level. For seven level inverters, fifth and seventh harmonics are lessening by using switching angle. In this method, low harmonics are allowable; an extensive solution space is available [14].
discrete outputs Vout with levelsVdc , 0 and Vdc . When S1
and S4 are on, the output isVdc ; when S2 and S3 are on, the output is Vdc ; when either pair S1 and S2 or S3 and S4 are on, the output is 0.
In this paper, seven level cascaded HBridge multilevel inverter used. Its obtaining the higher voltage level and increases the voltage level of the inverter using reduced number of switches. Easy to reduces total harmonic distortion [15].
The Fourier series of a 7 level unit dc source is shown in figure,
Fig. 2. Seven Level HBridge Multilevel Inverter
f t
f1 t
f 2 t
f 3 t
(1)
cos(p ) cos(p ) cos(p )
p
(2)
4Vdc
3
cos(h )sin(ht)
(3)
Where
i
h
p i1
Vdc = Voltage source for each cell that is unity
Fig. 3. Seven Level Output Voltage Waveform
produce a quarterwave symmetric stepped voltage waveform synthesized by several DC voltages [16].
By applying Fourier series analysis, the output voltage can be expressed as
n
V (t) 4 (V cos(n ) V cos(n ) … V cos(n )) sin(nt)
1
1 2 2 s s
n1,3,5…
Fig. 4. Total Harmonic Distortion For Conventional Method
(4)
Where s is the number of DC sources, and V1 , V2 Vs is the level of DC voltages. The switching angles must satisfy the
Numerous set of solution are available by definite modulation indices. Possible to evaluation THDs for each solution set
condition
0 1
2
s
2 . However, if the
and its gives the lower THD. Figure shos seven level voltages waveform for modulation index [17].

CONTROL AND MODULATION TECHNIQUES OF MULTILEVEL CONVERTERS

Multilevel SPWM
Multilevel SPWM usually needs multiple carriers. Each DC source needs its own carrier. Several multicarrier techniques have been developed to reduce the distortion in multilevel converters, based on the classical SPWM with
switching angles do not satisfy the condition, this method no
longer exists. IfV1 V2 … Vs , this is called equal DC voltages case. To minimize harmonic distortion and to achieve adjustable amplitude of the fundamental component, up to s1 harmonic contents can be removed from the voltage waveform. In general, the most significant lowfrequency harmonics are chosen for elimination by properly selecting angles among different level converters, and highfrequency harmonic components can be readily removed by using additional filter circuits [18]. To keep the number of eliminated harmonics at a constant level, all switching angles
triangular carriers. Some methods use carrier disposition and
others use phase shifting of multiple carrier signals. This
must satisfy the condition
0 1
2
s
2 , or
common SPWM method is the extension of bilevel SPWM. One reference signal is used to compare to the carriers.
The advantage of the method is it is very simple. But it has two disadvantages. The first is the method cannot completely eliminate the low order harmonics. Therefore the low order harmonics cause loss and high filter requirements. The second is the high switching frequency causes high switching loss and low efficiency.

Space Vector PWM Modulation
The space vector PWM modulation technique is popular for bilevel PWM converter control. It can be extended to multilevel converters. Space vectors for the traditional three, five, and sevenlevel converters. These vector diagrams are universal regardless of the topology of multilevel converter. Therefore it can be used for diodeclamped, capacitor clamped, or cascaded converters.
These advantages make it popular for converter control. But one disadvantage is as the number of levels increases,
the total harmonic distortion (THD) increases dramatically.
Fig. 5. Output Waveform of Virtual Stage PWM Method
By applying Fourier series analysis, the output voltage can be expressed as
V (t) 4 (V cos(n ) V cos(n ) V cos(n ) … V cos(n ))sin(nt)
1
1 2
redundant switching states and the complexity of selecting switching states increase dramatically. Another disadvantage is it cannot completely eliminate the low order harmonics.
n1,3,5… n
2 3 3
s s
(5)

Selective Harmonic Elimination
The popular selective harmonic elimination method is also
Based on the harmonic elimination theory, if one wants to
eliminate the n th harmonic, then
called fundamental switching frequency method which is based on the harmonic elimination theory developed by Patel et al. As shown in Figure. , a multilevel converter can
cos(n1 ) cos(n2 ) cos(n3 ) … cos(ns ) 0
(6)
V1 cos(1 ) V2 cos(2 ) V3 cos(3 ) … Vs cos(s ) m
V cos(5 ) V cos(5 ) V cos(5 ) … V cos(5 ) 0
The above equations are nonlinear transcendental equation in nature, known as SHEPWM equation. Consequently,
1 1 2
V cos(n ) V
2 3 3 s s
cos(n ) V cos(n ) … V cos(n ) 0
multiple solutions are possible. This solution of these equations is achieved by means of evolutionary process method (Genetic algorithm) and to obtain switching angles to
1 1
cos
2
1
2 3
cos2
3
cos3
s
V1
4Vdc
(8)
s
(7)
overcome the problems.


GENETIC ALGORITHM

Introduction
cos51
cos52
cos53
0
(9)
Genetic Algorithm is direct, parallel, stochastic method for global search and optimization. It is the part of group of
cos71 cos72 cos73 0 (10) To simplify the expression, (3.4) can be written as cos1 cos2 cos3 m (11)
Where
m V1
4Vdc
(12)
evaluatory algorithm. It is a search technique used in computing to find true or approximate solution to optimization and search problem. The selection principle is applied by using criteria, giving an evaluation for the individual with respect to the desired solution. Algorithm is started with set of solution called generation. Solution of one generation is used to form a new population. This is motivated by a hope, that the new generation will be better than the old one. Solutions which are selected according to their fitness are more suitable and there are the more chances
Is defined here as the modulation index. So
4
they have to reproduce.

Flow chart
1
V
max
sVdc
(13)
The genetic Algorithm is classified into three types of operation. There are encoding, cross over, selection and
Where s is the number of DC sources.
7
5
By applying the resultant method, the solution of fundamental frequency switching angles for 5, 7, 11 and 13level can be obtained. In this thesis, the THD is computed throughout the nth as
mutation. The evaluation usually starts from a population of randomly generated individuals and happen in generation. In each generation, the fitness of every individuals in the generation is evaluated, multiple individuals are selected from the current generation based on their fitness value, and modified (recombined and possibly mutated) to form a new
THD
V 2 V
2 V 2
n
V
2
1
(14)
generation. The new generation is then used in the next iteration of the algorithm. Commonly, the algorithm terminates when either a maximum number of generations has been produced or a satisfactory fitness level has been
For all the cases except indicated. The even and triple
harmonics are not computed in THD because they do not appear in the lineline voltages.
For the 7level multilevel converters, the harmonic equations are:
cos1 cos2 cos3 m
reached for the generation. If the algorithm has terminated due to a maximum number of generations, a satisfactory solution may or may not have been reached.
cos51 cos52 cos53 0 cos71 cos72 cos73 0
(15)
Population Index
Generation Index
Randomize angle 1 through n
corresponding to number of population
No
Repeat Next
Start
Repeat Next Generation
and set size of the population. The rate of convergence is rises by using higher population and also increases the execution time. Each population contains some switching angles. The population is initialized with randomly preferred angle between 0 to 90 degree and its considering the quarter wave symmetry of output voltage. The genetic algorithm is to evaluate the fitness value of each individual. The objective of the function is to minimize specified harmonics. The most important thing for GA to evaluate the fitness values of individual in each population. The switching angle expression can be formulated as
Generation
Is
f 1 , 2
,3
100 V5

V7
V1
(16)
0< 1 < 2 <.
< m <
2
Yes
For each generation, the output voltage waveform in multilevel inverter which is produced using switching angle in the population and the required harmonic magnitude is attaining using FFT techniques. Fitness value is calculated for each individuals using
Minimize Fitness F (Z) subject to 1 =M and
FitnesVal 1 ,2
,3
100 V5

V7 V1
(17)
V5 1 ,V7 7 …..Vn n
Pick the best individual
Create new offspring using crossover and mutation operation
No
Solution converged?
Yes
Output 0< 1 < 2 <. < m
Stop
Fig. 6. Genetic Algorithm Flow Chart


FORMULATING THE PROBLEM
The genetic algorithm approach is similar way for any application. Genetic algorithm works to be set only a few parameters. The formulating a problem and GA are applied. Binary and floating point sequence will select and attain the number of switching angle in an individual. The number of variable are considered as the number of switching angle in individual. The switching angle and its given to the Hbridge cascaded multilevel inverter a seven level inverter requires five hbridge inverter and each population will have three switching angle. First initialize the population of the interface
Genetic algorithm is set to run a definite number of generations to estimate the solution. Subsequently first generation, fitness values are used to attain the novel generation. Then it goes through the crossover and mutation process which creates new generation the similar cycle starting from fitness value estimation. By using MATLAB source code, it can find the optimal switching angles solution for a cascaded multilevel inverter with any number of output voltage levels and for the elimination of desired any number of harmonics.

SIMULATION RESULTS
The SHEPWM technique strategy of single phase cascaded seven level inverter using genetic algorithm and switching angle variation technique are simulated with the use of MATLAB R2012a. For seven level inverters, reduced number of switches using Hbridges is needed for simulation. MOSFET switches are used as power switches. Figure 5 shows the simulation circuit for seven level inverter using PWM technique.
In order to validate the computational results as well as the simulations results are presented for a single phase 7 level cascaded Hbridge inverter. The circuit configuration is shown in the Fig. 6 the inverter uses MOSFETs as the switching devices, and the nominal dclink voltage for each Hbridge is considered to be 138V. The gate control signals are generated by a dedicated unit is provided to the each H bridge.
Fig. 7. Simulation Diagram of the Single Phase Cascaded HBridge Multilevel Inverter using Genetic Algorithm
Fig. 8. Output Voltage Waveform of Proposed System (Seven Level)
Fig. 9. Fitness Value and Generation Stopping Criteria Of Genetic
Algorithm
Fig. 10. Voltage Total Harmonic Distortion Plot For Proposed Method
Fig. 11. Current Total Harmonic Distortion Plot For Proposed Method

CONCLUSION
The selective harmonic elimination PWM method at fundamental frequency switching arrangement has been simulated using the Genetic Algorithm that creates all possible solution sets when they exist. In comparison with other suggested methods, the proposed technique has several advantages such as: it can produce all probable solution sets for any numbers of multilevel inverter without considerable calculation burden; speed of convergence is fast etc. The proposed technique was successfully simulated for attaining the optimum switching angles for 7level Cascaded HBridge Multilevel Inverter. An extensive analysis for 7 level inverter has been presented and it is shown that a significant amount of THD reduction can be achieved if all possible solution sets are computed.
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