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- 1. Estimation of Optimized Power Quality In MicroController Based Cascaded Multilevel InverterP. Maruthu Pandi*, N.Devarajan†* Government College of Technology /Dept. of Electrical Engg, Coimbatore-641 013,Tamilnadu,India. maruthu74@yahoo.com.†Government College of Technology /Dept. of Electrical Engg, Coimbatore-641 013,Tamilnadu,India. profdevarajan@yahoo.com.Abstract- Nowadays high quality power is essential formedical, research and industrial applications to produce goodquality results and analysis. In this paper, an attempt hasbeen made to improve the quality of power. A single phaseseven level cascaded multi level inverter with identical dcsupply is designed to reduce the harmonic components of theoutput voltage. Genetic algorithm optimization technique isapplied to multilevel inverter to determine optimumswitching angles there by reducing some higher orderharmonics while maintaining the required fundamentalvoltage. This generalized technique can be extended to multilevel inverters with any number of levels. The switchingangles for each pulse are determined using Genetic Algorithmwhich is a evolutionary programming technique. Thesimulation is carried out in MATLAB/Simulink package andthe result is compared with the conventional methods likeNewton Raphson. The Total Harmonic Distortion ismeasured accordingly for different modulation indices. Aproto type model of microcontroller based seven levelinverter has been designed, fabricated and tested. The resultsare presented and analyzed and hence the hardware resultsare verified with the simulation results.Index terms- Multi level inverter, Selective HarmonicElimination, Genetic Algorithm, Total Harmonic Distortion.I. INTRODUCTIONMultilevel inverters have attracted a great deal ofattention in medium –voltage and high power applicationsdue to their lower switching losses , higher efficiency andmore electromagnetic compatibility than those ofconventional two-level inverters [1]-[4].The desiredoutput voltage of these converters is synthesized fromseveral levels of dc voltages. Among multi level inverterstructures the topologies based on series-connected H-bridge inverters are particularly attractive due to theirmodularity and simplicity of control [1],[2].The desired output of a multi level converter issynthesized with several methods including staircasemodulation, sinusoidal pulse width modulation (PWM)with multiple triangular carriers, and multilevel space-vector modulation. The elimination of specific low-orderharmonics from a given voltage /current waveformgenerated by a voltage/current source inverter using whatis widely known as optimal , “Programmed” or selectiveharmonic elimination PWM (SHE-PWM) techniques hasbeen deal with in numerous papers and for variousconverter topologies, systems, and applications [5]-[10].A fundamental issue associated with such method is toobtain the arithmetical solution of non lineartranscendental equation that contain trigonometric termsand naturally present multiple solutions. Numericaliterative techniques such as Newton-Raphson method areapplied to solve the SHE problems [2], [6], [7]; howeversuch techniques need a good initial guess that should bevery close to the exact solution. Although the Newton-Raphson method works properly if a good initial guess isavailable but providing a good guess is very difficult inmost cases. This is because the search space of the SHEproblem is unknown and one does not know whether asolution exists or not and if exists what is the good initialguess.The theory of resultants and its performance for amultilevel staircase waveform was reported in [8] in whichit is shown that the transcendental equations characterizingthe harmonic content can be converted to polynomial andthe latter can be solved to get the complete solution usingthe method of resultants from elimination theory[10].Theuse of symmetric polynomials combined with the resultanttheory for a multilevel converter to reduce the degree ofthe polynomial equations is reported in [9].The output waveforms of multilevel inverters are in astepped form resulting in reduced harmonics compared to asquare-wave inverter. To reduce the harmonics further,different multilevel sinusoidal PWM and space-vectorPWM schemes are suggested in the literature [11], [12];however, PWM techniques increase the control complexityand the switching frequency. Another approach to reducethe harmonics is to calculate the switching angles in orderto eliminate certain order harmonics. Chiasson et al. [13]derived analytical expressions using the mathematicaltheory of resultants to compute the optimum switchingangles. These expressions were polynomial of 22nddegree.In this paper, general genetic algorithm (GA) approachwill be presented. This solves the same problem with aIEEE Region 8 SIBIRCON-2010, Irkutsk Listvyanka, Russia, July 11 — 15, 2010 671978-1-4244-7626-8/10/$26.00 ©2010 IEEE
- 2. simpler formulation and with any number of levels withoutextensive derivation of analytical expressions. GA is asearch method to find the maximum of functions bymimicking the biological evolutionary processes. There arefew examples of GA applications for power electronics inthe literature [14]–[16].II. CASCADED H - BRIDGE MULTILEVELINVERTERAmong three types of topologies cascaded type multi-level inverter is considered for this work. In thisconfiguration, three single phase H-bridges are seriallyconnected for seven-level inverter. In general the numberof bridges required for an m level inverter is (m-1)/2. Allthe switches in the inverter are turned on only at thefundamental frequency and the voltage stress across theswitches is only the magnitude of DC source voltage. Inthe cascaded multilevel inverter all the voltage sourcesneed to be isolated from one another. Thus for seven-levelinverter three DC sources are needed. The switching stresscan be reduced because of its better switch utilization. Inthe proposed system, identical DC source voltages are usedfor the three H-bridges of the multi-level inverter.A. Structure of Single Phase Cascaded MultilevelInverterFigure .2.1 Block diagram for cascaded multilevel inverterThe block diagram of single phase cascaded the sevenlevel inverter is shown in the figure 2.1. Each bridgemodule comprises of four Metal Oxide Semi ConductorField Effect Transistors (MOSFET). Each bridge isenergized by separate sources. The cascaded multilevelinverter consists of a series of H-bridge (single phase, fullbridge) inverter units. As mentioned, the general functionof this multilevel inverter is to synthesize a desired voltagefrom several separate dc sources which may be obtainedfrom batteries, fuel cells, solar cells or ultra capacitors.Each separate dc sources is connected to a single-phasefull-bridge inverter. Each inverter level can generate threedifferent voltage outputs which are +Vdc, 0, - Vdc. The acoutput of each level’s full bridge inverter is connected inseries such that the synthesized voltage waveform is thesum of all of the individual inverter outputs. The numberof output phase voltage level in a cascaded multilevelinverter is then 2s+1, where s is the number of dc sources.With enough levels and appropriate switching algorithmthe multilevel results in an output voltage waveform whichis almost sinusoidal.B. Principle of Working of Seven Level InverterFigure.2.2. Output voltage of single phase cascaded seven-levelinverterThe output voltage of seven-level cascaded multilevelinverter is shown in the figure 2.2. The maximum outputphase voltage is given as V0=V1+V2+V3.The steps tosynthesize the seven-level voltage waveforms are asfollows.1. For an output voltage level V0=0, no switch in theH-Bridges are turned on.2. For an output voltage level V0=V1, turn on theswitches M11, M12, M22, M32.3. For an output voltage V0=V1+V2, turn on all theswitches as mentioned in step 2 and M21.4. For an output voltage level V0=V1+V2+V3, turnon all the switches in the step 3 and M31.where Mij is the switches in the individualbridge.i is the number of bridge and j switchnumber in the inverter.Table-2.1 shows the voltage levels and theircorresponding switch states in one quarter cycle of outputvoltage. State condition 1 means the switch is on and 0means the switch is off. Each switch is turned on only onceper cycle and therefore reduces switching losses.Table 2.1 Output voltage levels and their switching states for seven-level inverter.Switches Output voltage levelsV1 V1+V2 V1+V2+V3M11 1 1 1M12 1 1 1M13 0 0 0M14 0 0 0M21 0 1 1M22 1 1 1M23 0 0 0M24 0 0 0M31 0 0 1M32 1 1 1M33 0 0 0M34 0 0 0MicrocontrollerDCsupply(solarcells,fuelFilter1phase H-bridgeconverterACoutputDCsupply(solarcells,fuelFilter1phase H-bridgeconverterACoutput672 IEEE Region 8 SIBIRCON-2010, Irkutsk Listvyanka, Russia, July 11 — 15, 2010
- 3. III. HARMONIC MINIMIZATION PROBLEM IN MULTILEVEL INVERTERThe output voltage waveform of cascaded multi levelinverter has m levels. The problem under consideration isto find appropriate switching angles namely θ1, θ2,θ3……… θn so that the n-1 nontriplen odd harmonics can beeliminated and control of the fundamental is also achieved.The Fourier series expansion of the SHE-PWM waveformis given by equation 1 assuming all the dc sources areequal value.v(wt)=(1)Each H-bridge inverter unit has a conduction anglewhich is calculated to minimize the harmonic components.The conduction angles are the factors determining theamplitude of the harmonic components. This paper dealswith a three H-bridge cascaded inverter because its 7- leveloutput voltage can be almost sinusoidal. In that case theconventional method can eliminate the 5thand7thharmonics except for the fundamental wave. In seven levelinverter three dc sources are needed so that the dc voltagelevels are chosen so as not to generate the fifth and seventhorder harmonics while achieving the desired fundamentalvoltage. The mathematical statements of these conditionsare obtained by modulation index defined as andis magnitude of fundamental frequency of given voltage.(2)(3)(4)This is a system of three simultaneous equations withthree unknowns θ1, θ2 and θ3. These values are found bysolving the simultaneous equations (2)-(4).IV. CONVENTIONAL METHOD FOR HARMONIC REDUCTIONA. Newton Raphson MethodThe conventional method has the merit of eliminatingthe required harmonic component but it has someproblems. First it is difficult to solve simultaneousequations which are a set of nonlinear transcendentalequations. These equations can be solved by an iterativemethod such as Newton–Raphson. If the number ofsimultaneous equations increases so does the time and theamount of calculations to obtain the conduction angles.Moreover the method is an approximate one depending onthe iteration which leads to the inclusion of some errors.Secondly conducting angles are calculated through anoffline operation. Therefore they have to be arranged in thelook-up table. It needs much data in order to implementswitching angles with an accurate resolution. If the scale ofthe modulation index is divided in detail, the data of theconducting angles increases. In other words, the data of theconducting angles depends on the resolution of themodulation index. Therefore the conventional method hasa limitation in its application to an adjustable motor drive.The conventional method does not solve the set of nonlinear transcendental equations but calculates severaltrigonometric functions.The objective is to choose the levels of the DC voltagesso as to get the required fundamental voltages Vf andspecific higher order harmonics of v(ωt) equals to zero.The circuit shown in figure 5.2 is simulated and theresults are presented in figure 5.3 and figure 5.4.B. Limitations of Conventional Method• The solution obtained depends on the initial guessand no guarantee to be optimum.• It has computational burden and is timeconsuming.• More than one solution is possible with differentmodulation indices.• To obtain convergence with the numericaltechnique, the starting values must be selectedconsiderably close to exact solution.• It is difficult to presume the starting values.Divergence problem may occur.V. PROPOSED TECHNIQUE FOR SWITCHING ANGLEGENERATIONThe limitations of the Newton Raphson method iseliminated by using Genetic algorithm based optimizationtechnique. The switching angles are determined using GA.The steps for formulating a problem and applying a GA areas follows.1. Select binary or floating point strings.2. Find the number of variables specific to theproblem; this number will be the number of genesin a chromosome. In this application the numberof variables is the number of controllableswitching angles which is the number of H-bridges in a cascaded multilevel inverter. Aseven-level inverter requires three H-bridges;thus, each chromosome for this application willhave three switching angles, i.e., { }.3. Set a population size and initialize the population.Higher population might increase the rate ofconvergence but it also increases the executiontime. The selection of an optimum-sizedpopulation requires some experience in GA.The population in this paper has 20chromosomes, each containing three switchingIEEE Region 8 SIBIRCON-2010, Irkutsk Listvyanka, Russia, July 11 — 15, 2010 673
- 4. angles. The population is initialized with randomangles between 0 degree and 90 degree takinginto consideration the quarter-wave symmetry ofthe output voltage waveform.4. The most important item for the GA to evaluatethe fitness of each chromosome is the costfunction. The objective of this study is tominimize specified harmonics; therefore the costfunction has to be related to these harmonics. Inthis work the fifth and seventh harmonics at theoutput of a seven-level inverter are to beminimized. Then the cost function (f) can beselected as the sum of these two harmonicsnormalized to the fundamental,(5)where are the switching angles and are theorder voltage harmonics.For each chromosome a multilevel output voltagewaveform is created using the switching angles in thechromosome and the required harmonic magnitudes arecalculated using FFT techniques.The fitness value (FV) is calculated for eachchromosome inserting. In this case,(6)The switching angle set producing the maximum FV isthe best solution of the first iteration.5. The GA is usually set to run for a certain numberof iterations (100 in this case) to find an answer.After the first iteration, FV’s are used todetermine new offspring. These go throughcrossover and mutation operations and a newpopulation is created which goes through thesame cycle starting from FV evaluation.Sometimes, the GA can converge to a solution wellbefore 100 iterations are completed. To save time, in thispaper, the iterations have been stopped when the absolutevalue of the cost function goes below 1, in which case thesum of the fifth and the seventh harmonics is negligiblecompared to the fundamental.Note that after these iterations, the GA finds onesolution; therefore, it has to be run as many times as thenumber of solutions required to cover the wholemodulation index range.For the seven level inverter, switching angles whichminimize the fifth and seventh order harmonics are shownin the table 5.1 for various ranges of modulation indicesusing GA. Figure 5.1 shows the fitness values for variousgenerations.Table 5.1 Calculated switching angles for various modulation indexModulationIndex LevelModulationIndex1.05 12.57 23.81 54.331.0 11.83 30.58 59.18High0.90 23.17 49.37 64.540.7 38.5 59 82.880.6 39.5 58.6 83.10Middle0.5 18.9 66.01 80.180.4 44.17 74.38 87.400.3 29.24 39.25 53.010.2 50.92 63.36 73.19Low0.1 55.85 63.43 83.02Figure.5.1 GA result for fitness vs generationsA. Simulation Circuit for Seven Level InverterThe single phase cascaded seven level inverter usingPWM technique and switching angle variation techniqueare simulated with the use of MATLAB R2007b.For sevenlevel inverter three H-bridges are needed for simulation.MOSFET switches are used as power switches. Figure.5.2. shows the simulation circuit for seven level inverterusing PWM technique.Figure. 5.2. Simulation circuit for seven level inverter using PWMtechnique.674 IEEE Region 8 SIBIRCON-2010, Irkutsk Listvyanka, Russia, July 11 — 15, 2010
- 5. Figure 5.3.Output using switching angle variationB. Simulation ResultsFigure. 5.2 shows the circuit which is simulated inMatlab simulink package. The supply voltage in each H-bridge is 40V and MOSFET is used as power switch. Theload is considered as pure resistance 50Ω.The switchingangles are obtained using GA approach in the off line.The figure 5.3 shows output voltage waveform of theseven level inverter .The Figure 5.4 shows the harmonicprofile of the output voltage when the power circuit issimulated with switching angles calculated by Newton-Raphson method and Figure 5.5 is for the switching anglesestimated from genetic algorithm. From the spectrumanalysis it is inferred that the THD in GA based is 24.52%and that for Newton-Raphson is 53.08%.Figure.5.4. FFT analysis for seven level inverter using newton raphsonmethodFigure.5.5. FFT analysis for seven level inverter using GABy comparing the two Figures 5.4 and 5.5 it is clearlyidentified that the harmonics are reduced effectively bycomputing the switching angles by GA compared toNewton Raphson method.C. Hardware ResultsA proto type model of seven level cascaded multilevelinverter has been fabricated and tested. The switchingsignals for the model are generated from8051microcontroller.The driver circuits are also used togive pulse for switches in the power circuit.The pulses for the H-bridge inverters are shown inFigures 5.6, 5.7, and 5.8 respectively. The inverter outputvoltage waveform is also shown in Figure 5.9 and thecorresponding frequency spectrum is shown in Figure5.10.Figure 5.6. Pulses for switches M11, M12, M13, M14Figure 5.7. Pulses for switches M21, M22, M23, M24Figure 5.8. Pulses for switches M31,M32,M33,M34Figure 5.9. Output voltage wave form for seven level inverterIEEE Region 8 SIBIRCON-2010, Irkutsk Listvyanka, Russia, July 11 — 15, 2010 675
- 6. Figure 5.10. FFT analysis for the seven level inverter.VI. CONCLUSIONIn this work Genetic algorithm optimization technique isapplied to find the switching angles of the cascadedinverter for the reduction of harmonics. The resultsobtained show that fifth and seventh order harmonics arereduced effectively. As in this approach, GA can beapplied to any type of optimization problems.GA reducesthe harmonic content more predominantly than any otherconventional technique such as Newton Raphson. Thiswork can be extended by applying GA to reduce theharmonics in inverters with any number of levels.REFERENCES[1] J. S. Lai and F. Z. Peng, “Multilevel converters—A new breed ofpower converters,” IEEE Trans. Ind. Appl., vol. 32, no. 3, pp. 509–517, May/Jun.1996.[2] J. Rodriguez, J. Lai, and F. Z. Peng, “Multilevel inverters: A surveyof topologies, controls and applications,” IEEE Trans. Ind.Electron., vol. 49, no. 4, pp. 724–738, Aug. 2002.[3] L. M. Tolbert, F. Z. Peng, and T. G. Habetler, “Multilevel converterfor large electric drives,” IEEE Trans. Ind. Appl., vol. 35, no. 1, pp.36–44,Jan./Feb. 1999.[4] J. Wang and F. Z. Peng, “Unified power flow controller using thecascade multilevel inverter,” IEEE Trans.Power Electron., vol. 19,no. 4, pp. 1077–1084, Jul. 2004.[5] P.N.Enjeti and J.F.Lindsay, “Solving nonlinear equation ofharmonic elimination PWM in power control”,“Electron.Lett.vol.23, no.12, pp.656-657, Jun.1987.[6] H. S. Patel and R. G. Hoft, “Generalized harmonic elimination andvoltage control in thyristor inverters: Part I—Harmonicelimination,” IEEE Trans. Ind. Appl., vol. IA-9, no. 3, pp. 310–317,May/Jun. 1973.[7] H. S. Patel and R. G. Hoft, “Generalized harmonic elimination andvoltage control in thyristor inverters: Part II—Voltage controltechnique,” IEEE Trans. Ind. Appl., vol. IA-10, no. 5, pp. 666–673,Sep./Oct. 1974.[8] J.N.Chiasson,L.M.Tolbert,K.J.McKenzie,and Z.Du, “Control of aMultilevel converter using resultant theory,”IEEETrans.Contr.syst.Technol,vol.11,no.3,pp.345-354,May-2003[9] J.N.Chiasson, L.M.Tolbert ,K.J.McKenzie, and D.Zhong,“Elimination of harmonics in a multilevel converter using the theoryof symmetric polynomials and resultants,”IEEETrans.Contr.Syst.Technol,vol.13,no.2,pp.216-223,Mar.2005[10] J.N.Chiasson,L.M.Tolbert,K.J.McKenzie,and Z.Du, “ A completesolution to the harmonic elimination problems,” IEEE Trans.PowerElectron,vol.19,n0.2,pp.491-499,Mar.2004[11] L.M.Tolbert, F.Z.Peng, T.G.Habetler, “Multilevel PWM methods atlow modulation indices,” IEEE Transactions on Power Electronics,15(4), July 2000, pp.719-725.[12] L.M Tolbert, T.G.Habetler, “Novel multilevel inverter carrier-basedPWM method,”IEEE Transactions on Industry Applications, 35(5),Sept-Oct.1999, pp.1098-1107.[13] J. Chiasson, L. M. Tolbert, K. McKenzie, and Z. Du, “Eliminatingharmonics in a multilevel converter using resultant theory,” in Proc.IEEE Power Electronics Specialists Conf., 2002, pp. 503–508.[14] B. Ozpineci, J. O. P. Pinto, and L. M. Tolbert, “Pulse-widthoptimization in a pulse density modulated high frequency AC-ACconverter using genetic algorithms,” in Proc. IEEE Int. Conf.Systems, Man, and Cybernetics,2001, pp. 1924–1929.[15] I. Maswood, S.Wei, and M. A. Rahman, “A flexible way togenerate PWM-SHE switching patterns using genetic algorithms,”in Proc. IEEE Applied Power Electronics Conf. Expo., 2001, pp.1130–1134.[16] Houck, J. Joines, and M. Kay. The Genetic AlgorithmOptimization Toolbox (GAOT) for MATLAB 5. [Online].Available:http://www.ie.ncsu.edu/mirage/GAToolBox/gaotP. MaruthuPandi received BE degree inElectrical and Electronics Engineering fromGovernment College of Engineering,Tirunelveli, India, in 1995 and ME degree inpower electronics and drives from College ofEngineering,Guindy Chennai, India in 2002and is currently pursuing Ph.D. degree inelectrical engineering from Anna University,Coimbatore. He has 13 years of experience inteaching. He is currently working as a lecturerin the department of electrical engineering ofGovernment College of Technology, Coimbatore, India. His field ofinterests includes power quality, power electronics and electrical drives,simulation of power electronic converters and Virtual Instrumentation.N. Devarajan received B.E. degreein Electrical and Electronics Engineering andM.E. degree in Power System Engineeringfrom Government College of Technology,Coimbatore, India in the year 1982, 1989respectively. He received Ph.D. degree inControl System Engineering from PSGCollege of Technology, Coimbatore, India.He has more than two decades of teachingand research experience. He joined inGovernment College of Technology in theyear 1984 and he is currently the Assistant Professor of ElectricalEngineering department. He has produced six Ph.D scholars so far andguiding more than ten scholars. He has published more than forty papersin national and international reputed journals. He has attended more thanhundred national and international conferences. He is a reviewer of manyInternational journals. His fields of interests include control systems,Design of electrical machines, Optimization techniques and softcomputing techniques.676 IEEE Region 8 SIBIRCON-2010, Irkutsk Listvyanka, Russia, July 11 — 15, 2010

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