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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 n1 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. REFERENCES [1] Ali Mehrizi-Sani, Student Member, IEEE, and Shaahin Filizadeh, Member, IEEE. “ An Optimized Space Vector Modulation Sequence for Improved Harmonic Performance”IEEE Transction on industrial electronics, vol 56, no. 8 , august 2009 [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] 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 DOI: 10.5370/JEET.2011.6.3.334., N. Bahari, Z. Salam, Taufi “Application of Differential Evolution to Determine the HEPWM Angles of a Three Phase Voltage Source Inverter” Reza Salehi, Naeem Farokhnia, Mehrdad Abedi, and Seyed Hamid Fathi “ Elimination of Low Order Harmonics in Multilevel Inverters Using Genetic Algorithm” Journal of Power Electronics, Vol. 11, No. 2, March 2011. Selective Harmonic Elimination by Programmable Pulse Width Modulation in Inverters., International Journal of Engineering Trends and Technology (IJETT) - Volume4Issue4- April 2013., M. Kiran kumar, A. Madhu Sainath, V. Pavan Kumar. J.Baskaran, S.Thamizharasan, R.Rajtilak “GA Based Optimization and Critical Evaluation SHE Methods for Three-level Inverte”. International [4] [5] [6] [7]