Harmonic Orientation of Multi Carrier Modulation in Neutral Point Clamped Inverter

Transcription

1 SSN (Onlne) : SSN (Prnt) : nterntonl Journl of nnovtve Reserh n Sene, Engneerng nd Tehnology An SO 3297: 2007 Certfed Orgnzton, olume 3, Spel ssue 1, Jnury 2014 nterntonl Conferene on Engneerng Tehnology nd Sene-(CETS 14) On 10 th & 11 th Ferury Orgnzed y Deprtment of CL, CSE, ECE, EEE, MECHNCAL Engg. nd S&H of Muthymml College of Engneerng, Rspurm, Tmlndu, nd Hrmon Orentton of Mult Crrer Modulton n Neutrl Pont Clmped nverter Dhevn. R 1, Thmlrs. E 2 Assstnt Professor, Deprtment of EEE, veknnd nsttute of Engneerng nd Tehnology for women, Truhengode, Tml ndu, nd. 1 PG Sholr, Deprtment of EEE, veknnd nsttute of Engneerng nd Tehnology for women, Truhengode, Tml ndu, nd. 2 Astrt n ths pper, novel tehnque used to lnng the ptor voltge of neutrl pont lmped nverter wthout trnsformer nd lso redues the totl hrmon dstorton t the output y usng mult rrer pulse wdth modulton tehnque. Ths pper presents orentton of hgher order hrmons of ffteen level neutrl pont lmped nverter. The totl hrmon dstorton wll e rred out usng fst Fourer trnsformton. The effetveness of the proposed method s verfed y smultons. Keywords FACTS, GBT, multlevel, mult rrer PWM, NPC nverter, totl hrmon dstorton.. NTRODUCTON The neessty of nresng power qulty n the pst yers leds to the development of nverter due to ts effeny nd ontrol methods. An nverter s deve whh onverts the dret urrent (DC) nto n lterntng urrent (AC) wthout hngng the mgntude. The onverted urrent my ontn the requred voltge nd frequeny, swthng deves nd ontrol ruts. n order to mprove the qulty of n nverter y performs the power onverson of smll voltge steps resulted n lower hrmons. The output voltge of n AC sde ontns severl numers of dsrete levels of equl mgntude. The hrmon ontent of multlevel nverter s redued ompred to nverter voltge wveform. Ths method s known s multlevel nverter. Multlevel nverters re sgnfntly dfferent from the ordnry nverter where only two levels re generted. The semondutor deves re not onneted n seres for one sngle hgh-voltge swth. n whh eh group of deves ontrute to step n the output voltge wveform. The steps re nresed to otn n lmost snusodl wveform. The numer of swthes nvolved s nresed for every level nrement. Mult-level power nverters employ power semondutor swthes n the nverter to selet the DC voltge soure to produe strse voltge wveform t the output of nverter. The output of multlevel nverter s n the form of strse wveform, so tht the hrmons get redued therey the voltge gn get nresed nd the power qulty nreses. The generl purpose of the multlevel nverter s to synthesze nerly snusodl voltge from severl levels of d voltges, typlly otned from ptor voltge soures. As the numer of level nreses, the syntheszed output wveform hs more steps, whh produe strse wve tht pprohes desred wveform. Also s more steps dded to the wveform, the hrmon dstorton of the output wveform dereses, pprohng zero s the level nreses. As the numer of level nreses, the voltge tht n e summng multple voltge levels lso nreses. Severl multlevel nverter topologes re proposed over the pst few yers, the most populr multlevel nverters whh re mostly used re Dode-lmped, Flyng ptor nd the H-rdge multlevel nverter. Neutrl Pont Clmped nverter s more preferred thn other topology. n ths pper s onentrted for the mprovement of output voltge wveform, reduton of hrmons nd for retve power ompenston y usng mult rrer pulse wdth modulton (PWM) tehnque. t used to lne the d splt voltge nd mprove the effeny of the system nd redue the voltge flututon. To tke eneft of the dvntges of the multlevel nverter, Low Eletromgnet nterferene, Low Totl hrmon dstorton, redue onverson losses, t s used to oost the voltge sed on the requrement, Redue Swthng losses. n the proposed system Mult Crrer Pulse Wdth Modulton s used to ontrol the d splt ptor nd redue the hrmons. The smulton of the proposed ontrol method wll e rred out usng Mt l smulton tool wheren the detled nlyss nd desgn spets n e emphszed.. NEUTRAL PONT CLAMPED NERTER n response to the growng demnd for hgh power nverter unts, multlevel nverters hve een ttrtng Copyrght to JRSET 725

2 SSN (Onlne) : SSN (Prnt) : nterntonl Journl of nnovtve Reserh n Sene, Engneerng nd Tehnology An SO 3297: 2007 Certfed Orgnzton, olume 3, Spel ssue 1, Jnury 2014 nterntonl Conferene on Engneerng Tehnology nd Sene-(CETS 14) On 10 th & 11 th Ferury Orgnzed y Deprtment of CL, CSE, ECE, EEE, MECHNCAL Engg. nd S&H of Muthymml College of Engneerng, Rspurm, Tmlndu, nd growng ttenton from dem s well s ndustry n the reent dede. The multlevel nverter refers to usng onverter n the nvertng mode. Power n flow from DC sde to AC sde. Multlevel nverters re extensvely used n medum voltge levels wth hgh-power ppltons. The feld ppltons nlude use n lmntors, pumps, onveyors, ompressors, fns, lowers, nd mlls. Susequently, severl multlevel onverter topologes hve een developed. Multlevel nverter s power eletron deve ult to synthesze desred voltge from severl levels of d voltges. Suh nverters hve een reeved nresng ttenton n the pst few yers for hgh power pplton. A smll totl hrmon dstorton s the most mportnt feture of these nverters. n the djustle speed drve pplton, the multlevel nverters n e used for utlty omptle djustle speed drve (ASD) wth the nput from the utlty onstnt frequeny AC soure nd the output to the vrle frequeny AC lod. The mjor dfferenes when usng the sme struture for ASDs nd for k-to-k ntertes re the ontrol desgn nd the sze of the ptors. Beuse the ASD need to operte t dfferent frequenes, the DC lnk ptor needs to e lrge enough to vod lrge voltge swng under trnsent stte. Among the est known topologes re the H-rdge sde nverter, the ptor lmpng nverter (mrte ells), nd the neutrl pont lmped nverter. As reported n the lterture, the NPC nverter hs een used n severl prtl nstnes for rodstng mplfer, plsm, ndustrl drve s well s FACTS ppltons et. For FACTS pplton the power pulston t twe output frequeny ourrng wth the d lnk of eh H- rdge ell neessttes over-szng of the d lnk ptors. The ptor lmpng nverter, though the three-level sheme of whh ws pulshed n the erly 1980 s hd een rrely dsussed untl the ntroduton of the mrte ells. The ndvdul lmpng ptor needs only to smooth the swthng frequeny rpple voltge nd the requred pty for eh lmpng ptor s therefore smll. However, s the numer of level nreses, suh prolems s therml desgnng, lowndutne desgnng, s well s nsulton desgnng of the system wll eome rtl. Fg.1. A typl output wveform The neutrl pont lmped nverters provde hgh qulty output, low swthng frequeny nd hgh voltge plty. But these fetures re otned when the d splt voltge s lned. To lne the d splt voltge used pulse wdth modulton. n ths projet mult rrer pulse wdth modulton s used nd hysteress ontroller s used. Ths ontroller s used to vod unwnted rpd swthng. The hysteress ontroller s very populr euse of ts nexpensve, smple nd esy to use. And lso the totl hrmon dstorton s redued y usng of mult rrer pulse wdth modulton tehnque. PWM tehnques mnmze the mgntude of the hrmons ut not removed ompletely. The multlevel nverter s used to remove the prtulr hrmons ompletely. Fg 1 shows the mult level nverter wveform. n the mult level nverter the output level equl to the soure whh ppled to the nverter. n ths dgrm snusodl wveform nd multlevel pproxmton s ndted.. MULT CARRER PULSE WDTH MODULATON Mult Crrer pulse wdth modulton s the extenson of two level rrer sed modulton. The mult rrer pulse wdth modulton tehnque onssts of one referene sgnl nd severl trngulr rrer sgnls. The s prnple of mult rrer pulse wdth modulton (MC-PWM) s omprson referene wveform wth rrer wveform. To generte m level t requred m-1 rrer. Both rrer nd referene sgnls hve sme frequeny nd mpltude. A frequeny of sne referene wveform s f r nd pek to pek vlue of referene wveform s A r. Eh rrer s ompred wth Copyrght to JRSET 726

3 SSN (Onlne) : SSN (Prnt) : nterntonl Journl of nnovtve Reserh n Sene, Engneerng nd Tehnology An SO 3297: 2007 Certfed Orgnzton, olume 3, Spel ssue 1, Jnury 2014 nterntonl Conferene on Engneerng Tehnology nd Sene-(CETS 14) On 10 th & 11 th Ferury Orgnzed y Deprtment of CL, CSE, ECE, EEE, MECHNCAL Engg. nd S&H of Muthymml College of Engneerng, Rspurm, Tmlndu, nd modultng sgnl t every nstnt. f the trngulr rrer s greter thn referene sgnl the result s 1 otherwse 0. Sum of the dfferent omprson whh represents voltge level s output modultor. The sheme s hrterzed y mpltude modulton ndex m nd frequeny modulton ndex m f. For sne wveform (referene) ntered n the rrer nds, the durton of tme tht the wveform exsts. For n m-level nverter, m-1 rrers wth the sme frequeny f nd the sme mpltude A re dsposed suh tht the nds they oupy re ontguous. The referene wveform hs pek-to-pek mpltude A m, frequeny f m, nd ts zero entred n the dle of the rrer set. The referene s ontnuously ompred wth eh of the rrer sgnls. f the referene s greter thn rrer sgnl, then the tve deves orrespondng to tht rrer s swthed on; nd f the referene s less thn rrer sgnl, then the tve deves orrespondng to tht rrer s swthed off. n multlevel nverters, the mpltude modulton ndex, m, nd the frequeny rto, m f, re defned s Fg 2 shows tht the mult rrer pulse wdth modulton. Mult rrer pulse wdth modulton hs one referene wveform nd mult rrer wveforms. These rrer nd referene wveforms re produe pulses. These pulses re ppled to the onverter gte. The mult rrer Pulse Wdth Modulton produes hgh qulty output nd redues the hrmons. M = A m / (m-1). A M f =f /f m. Hvng more thn two levels to uld snusodl shpe t s nstntul tht t n redue the hrmons n lod. However, the mprovement of urrent s depends on the ontroller employed. The su hrmon pulse wdth modulton s more populr euse of ts smplty nd good result for ll the opertng ondton nludes over modulton. n the se of three phse nverter three legs re produed. Requrements of three phse system phse shfted modulton snusods re needed. Two possltes re renowned y use of rrer sgnl. The rrers hve the sme frequeny nd sme mpltude nd re dsposed so tht the nds re ontnuous. Ths method tkes the nstntneous verge of the mxmum nd mnmum of the voltges (v,v ) nd sutrts ths vlue from eh of the ndvdul referene voltges.e v v v where, v v v mx( v ) mn( v 2 ) Fg:2.Multlevel Crrer Bsed PWM Showng Crrer Bnds. HYSTERESS CONTROLLER The urrent ontrol plys n mportnt role n power eletrons ruts. The mn role of the ontrol systems n urrent regulted nverters s to fore the urrent n the three phse lod. Among the severl PWM tehnques, the hysteress urrent ontrol s used very often euse of ts smplty mplementton. Also gve fst response urrent ontrol loop nd t does not need ny knowledge of lod prmeters. But t hs the dsdvntge when the urrent ontrol wth fxed hysteress nd tht the frequeny vres wthn nd. t ontrols the swthes of the voltge soure nverter nd to rmp the urrent, so tht t follows the referene urrent. f the vlue for the mnmum nd mxmum error should e the sme, the hysteress ndwdth s equl to two tmes of error. When the error rehes n upper lmt, the trnsstors re swthed to fore the urrent down Copyrght to JRSET 727

4 SSN (Onlne) : SSN (Prnt) : nterntonl Journl of nnovtve Reserh n Sene, Engneerng nd Tehnology An SO 3297: 2007 Certfed Orgnzton, olume 3, Spel ssue 1, Jnury 2014 nterntonl Conferene on Engneerng Tehnology nd Sene-(CETS 14) On 10 th & 11 th Ferury Orgnzed y Deprtment of CL, CSE, ECE, EEE, MECHNCAL Engg. nd S&H of Muthymml College of Engneerng, Rspurm, Tmlndu, nd Fg.3. Hysteress Controller Eletr dsplement feld D of ferroeletr mterl s the eletr feld E s frst deresed, then nresed. The urves form hysteress loop. The rmpng of the urrent etween the two lmts where the upper hysteress lmt s the sum of the referene urrent nd the mxmum error or sutrton of the referene urrent nd mxmum error s shows n the fgure 4. re the dodes D 1 nd D 2. These two deves lmp the swth voltge to hlf the level of the d-us voltge. n generl the voltge ross eh ptor for n N level dode lmped nverter t stedy stte s 1/ n d. Although eh tve swthng deve s only requred to lok, the lmpng deves hve dfferent rtngs. The neutrl pont lmped nverter provdes multple voltge levels through onneton of the phses to seres of ptors. Aordng to the orgnl nventon, the onept n e extended to ny numer of levels y nresng the numer of ptors. Erly desrptons of ths topology were lmted to three-levels where two ptors re onneted ross the d us resultng n one ddtonl level. The ddtonl level ws the neutrl pont of the d us, so the termnology neutrl pont lmped (NPC) nverter ws ntrodued. Due to ptor voltge lnng ssues, the neutrl pont lmped nverter mplementton hs een lmted to the three levels. Beuse of ndustrl developments over the pst severl yers, neutrl pont lmped nverter s now used extensvely n ndustry ppltons. n generl for n N level dode lmped nverter, for eh leg 2 (N-1) swthng deves, (N-1) (N-2) lmpng dodes nd (N-1) d lnk ptors re requred. When N s suffently hgh, the numer of dodes nd the numer of swthng deves nrese nd mke the system mprtle to mplement. f the nverter runs under pulse wdth modulton (PWM), the dode reverse reovery of these lmpng dodes eomes the mjor desgn hllenge. Fg.4. Hysteress Bnd. ANALYSS OF FFTEEN LEEL NEUTRAL PONT CLAMPED NERTER The most ommonly used multlevel topology s the neutrl pont lmped nverter, n whh the dode s used s the lmpng deve to lmp the d us voltge so s to heve steps n the output voltge. The key dfferene etween the two-level nverter nd the three-level nverter Fg.5. A typl Multlevel nverter. The struture s more omplted thn two level nverter; the operton s strghtforwrd nd well known. n summry, eh phse node (,, or ) n e onneted to ny node n the ptor nk ( 3, 2, 1 ). Conneton of the -phse to postve node, 3 our Copyrght to JRSET 728

5 SSN (Onlne) : SSN (Prnt) : nterntonl Journl of nnovtve Reserh n Sene, Engneerng nd Tehnology An SO 3297: 2007 Certfed Orgnzton, olume 3, Spel ssue 1, Jnury 2014 nterntonl Conferene on Engneerng Tehnology nd Sene-(CETS 14) On 10 th & 11 th Ferury Orgnzed y Deprtment of CL, CSE, ECE, EEE, MECHNCAL Engg. nd S&H of Muthymml College of Engneerng, Rspurm, Tmlndu, nd when S 1p nd S 2p re turned on nd to the neutrl pont voltge, when S 2p nd S 1n re turned on nd the negtve node 1 s onneted when S 1n nd S 2n re turned on. There re some omplementry swthes nd n prtl mplementton, some ded tme s nserted etween the gtng sgnls nd ther omplements menng tht oth swthes n omplementry pr my e swthed off for smll mount of tme durng trnston. However, for the dsusson heren, the ded tme wll e gnored. Swthng stte, the -phse urrent wll flow nto the junton through dode D 1 f the urrent s negtve or out of the junton through dode D 2 f the urrent s postve. The d urrents 3, 2, nd 1 re the node urrents of the nverter. A pr of dodes s dded n eh phse for eh of the two juntons. The operton s smlr to the threelevel. For prtl mplementton, the swthng stte needs to e onverted nto trnsstor sgnls. One the trnsstor sgnls re estlshed, generl expressons for the phse lne-to-ground voltge nd the -phse omponent of the d urrents n e wrtten s H H.... H o o o H H N No N No N No H H N1 N1 N1 N1o N1o N1o 1 1o.... H 1 1o.... H 1 1o The node urrents for the N level nverter re gven y H H H N N N H H N 1 1 N H H 1 N 1 N H 1 H N 1 vlue of the duty yle. ts shows n the followng expresson: d ' v v 1 2v n p off By ddng n to the modulton sgnls, the duty yle d s hnged. The NP urrent n e lulted s follows. ' d ( k 1) d' ( k 1) d' ( k o ( k 1) ( k 1) Fg 6 shows tht the urrent n the ptors. The ove expressons re used to found the ptor urrent. The mthemtl proess for the other phses s the sme s the phse. The equtons defne the optml vlue they nlude the relevnt vrles nd the system dynms, the modulton ndex, the rrer frequeny, the d splt ptor vlues nd the orrespondng ptor voltges. 1) f the vlue s low, slow voltge-lnng dynm on the d-splt ptors s produed. f the vlue of the s hgh the system dynm s slow. The voltge lnng ontrol vrle s the neutrl pont urrent o. n the stedy stte ondton the verge vlue of ths vrle s zero. The urrent njeted nto the neutrl pont nverter whh the output phses re onneted to tht pont nd the output urrents re {,, }.y the followng expresson re desred the urrents 1 nd 2: 1 2 m m o 2 o 2 The reltonshp etween the modulton sgnls nd the ompenston s determned y tkng nto ount the Fg.6. Current n the Cptors.. SMULATON RESULT n ths symmetr multlevel nverter 28swthes s used. n ths the dode lmped nverter. Bslly the nverter operton s to onvert the vrle DC nto n AC. The nput d soure s gven y usng tteres. Here hysteress ontroller s used to ontrol the output voltge of the nverter. The output voltge hs some hrmon. Ths hrmons re redued y the usng of flter. Fourteen soures re used these re ptor soures. Eh soure hs 100. Ths d splt ptor s lned y usng the Mult Crrer Pulse Wdth Modulton. And lso ths Pulse Wdth Modulton Strtegy redue the hrmons. The Copyrght to JRSET 729

6 SSN (Onlne) : SSN (Prnt) : nterntonl Journl of nnovtve Reserh n Sene, Engneerng nd Tehnology An SO 3297: 2007 Certfed Orgnzton, olume 3, Spel ssue 1, Jnury 2014 nterntonl Conferene on Engneerng Tehnology nd Sene-(CETS 14) On 10 th & 11 th Ferury Orgnzed y Deprtment of CL, CSE, ECE, EEE, MECHNCAL Engg. nd S&H of Muthymml College of Engneerng, Rspurm, Tmlndu, nd hrmons pushes y PWM nto hgh frequeny rnge round the swthng frequeny. The frequenes t whh the voltge hrmons our n e desred. By usng mult rrer PWM the totl hrmon dstorton s redued. ts shows n the smulton result. And lso ompenste the retve power. The effeny s hgh. By usng grphl user nterfe the totl hrmon dstortons re otned. The totl hrmon dstorton s lulted y the fst foureby usng mult rrer pulse wdth modulton tehnque the trggerng pulse gven to the swthes re ontrolled. The nput voltge to the d soure s 100.The level retor prt produes n output voltge whh s lwys postve nd the rdge prt s to hnge the polrty of the output. The THD get redued to 4.28%. ts shows n fg.7. v o l t g e ( ) hrmon dstorton, for 150HZ t gves the 1.82% totl hrmon dstorton. Ths multlevel nverter ontns fourteen swthes. Eh d soures hs 100 t produes 1000 output voltge. Ths output voltge ontns fewer mounts of hrmons. The output voltge of neutrl pont lmped nverter s shows n the fg.9. Ths output voltge of neutrl pont lmped nverter ontns some hrmons. By usng low pss flter ths hrmons re redued. The fltered output voltge of neutrl pont lmped nverter s shows n fg.10. Then ths fltered output voltge s seprted y usng of soltor nd ths output voltge wthout ertn order hrmons s ppled to hgh power ppltons, FACTS ppltons nd renewle energy nterfe phse output voltge Fg.7.FFT Anlyss tme(s) Fg.9. Smulton Result For 3 Phse Output oltge phse fltered output voltge 500 v o l t g e ( ) Fg.8. FFT Anlyss 2 Fg 8. shows tht totl hrmon dstorton of 100HZ nd 150HZ. For 100HZ t provdes the 3.27% totl tme(s) x 10 4 Fg.10. Three Phse Fltered Output oltge. Copyrght to JRSET 730

7 SSN (Onlne) : SSN (Prnt) : nterntonl Journl of nnovtve Reserh n Sene, Engneerng nd Tehnology An SO 3297: 2007 Certfed Orgnzton, olume 3, Spel ssue 1, Jnury 2014 nterntonl Conferene on Engneerng Tehnology nd Sene-(CETS 14) On 10 th & 11 th Ferury Orgnzed y Deprtment of CL, CSE, ECE, EEE, MECHNCAL Engg. nd S&H of Muthymml College of Engneerng, Rspurm, Tmlndu, nd. CONCLUSON The dsturnes n power eletrons equpment re often perod nd rh n hgher hrmons. They hve een frequenes nd re often ove the ndwdth of regultors used to ontrol fundmentl omponents. Therefore the regulr ontrol n only prtlly redue ther effets on the dstorton of ontrol vrles. Ths hysteress ontrol tehnque enles us to otn etter seletve hrmon reduton n the output AC voltge. Fnlly, we otned the output AC voltge wveform. Besdes tht, t relzed etter multlevel output nd heved desred results. Blne the voltge of the d splt ptors of 15-L neutrl pont lmped nverter, nd redue the hrmons when mult rrer PWM modulton s employed. The totl hrmon dstorton s redued to 4.58%.The numer of level s nrese n the Neutrl pont lmped multlevel nverter n order to redue the seletve hrmons elmnton nd to nrese the voltge gn nd power qulty. REFERENCES [1]. Dongsheng Zhou, Senor Memer, EEE (2002) A Self- Blnng Spe etor Swthng Modultor for Three- Level Motor Drves EEE trnstons on power eletrons, vol.17, no.6. [2]. E.Smth, S.P. Ntrjn, C.R.Blmurugn, (2012) Performne Evluton of Mult Crrer Bsed PWM Tehnques for Sngle Phse 5L H-Brdge Type FCML, OSR journl of engneerng (OSRJEN) ssn: vol.2, no.7. [3]. H Klpesh, Bhlod, nd Prmod Agrwl, (2010) Spe etor Modulton wth DC-Lnk oltge Blnng Control for Three-Level nverters, ACEEE nterntonl on ommuntonol.1, no.1. [4]. Jord Zrgoz, Josep Pou, nd Montse Corln, (2011) oltge-blne Compenstor for Crrer-Bsed Modulton n the Neutrl-Pont-Clmped Converter, EEE, trnstons on poweer delveryol.26, no.1. [5]. Ku Wng, Zedong Zheng, Le Xu, nd Yongdong L, (2013) A Four-level Hyrd-Clmped Converter wth Nturl Cptor oltge Blnng Alty EEE trnstons on power eletronsol.56, no.2. [6]. M. Leon, Tolert, Fng Zheng Peng, nd G Thoms. Hetler, (2000) Multlevel PWM Methods t Low Modulton ndes EEE trnstons on power eletrons, vol. 15, no. 4. [7]. M. Nsr, G. B. Ghrehpetn nd J. Mlmonfred, (2012) Comprson of Multrrer PWM Strteges for Fve-level Z-Soure Dode-Clmped nverter for On-Grd Renewle Energes Appltons nterntonl onferene on renewle energes nd power qulty vol.6, no.8. [8]. Ms.T.Prth. Ph.D, Dr.P.Renug, (2010) Mult Crrer PWM sed Mult Level nverter for Hgh Power Applton, nterntonl journl of omputer ppltons ( )ol.1, no.9. [9]. Sergo Busquets-Monge, Jose Dnel Orteg, Josep BordonuJose, Antono Berstn, (2008) Closed-Loop Control of 3Phse NPC nverter Usng n Optmzed 2 PWM, EEE, trnstons on ndustrl eletronsol.55, no.5. [10]. Srnvs Dsm, B..Snkerrm, (2013) oltge Blnng Control Strtegy n Converter System for Three-Level nverters, nterntonl journl of eletrl nd omputer engneerng (JECE) pp. 7~14 SSN: ol.3, no.1. [11]. St. Lous, Mssour, (1998) Novel Multlevel nverter Crrer-Bsed PWM Methods, EEE, journl of nformton engneerng nd ppltons, pp ol.8, no.5. [12]. T.Prth, P.Renug, (2011) Hrmon orentton of pulse wdth modulton tehnque n multlevel nverters, EEE, power engneerng nd eletrl engneerngol.9, no.1. [13]. U-Mn Cho nd Kyo-Beum Lee, (2013) Neutrl-Pont oltge Blnng Method for Three-Level nverter Systems wth Tme-Offset Estmton Sheme, EEE, journl of power eletronsol.13, no.2. [14]. We-dong Jng, Sho-wu Du, Lu-hen Chng, Y Zhng, nd Qn Zho, (2010) Hyrd PWM Strtegy of SPWM nd SPWM for NPC 3L S, EEE trnstons on power eletronsol.25, no.10. [15]. Wensheng Song, Xoyun Feng, nd Keyue M Smedley,(2003) A Crrer-Bsed PWM Strtegy wth the Offset oltge njeton for Sngle-Phse Three-Level Neutrl-Pont-Clmped Converters, EEE trnstons on power eletronsol.43, no.6. [16]. Xomng Yun, Memer EEE, nd vo Br, Senor Memer, EEE, (2000) Fundmentls of New Dode Clmpng Multlevel nverter, EEE trnstons on power eletronsol.15, no.4. [17]. Zhe Zhng, Ole C. Thomsen, nd Mhel A. E. Andersen, (2013) Dsontnuous PWM Modulton Strtegy Wth Crut-Level Deouplng Conept of Three-Level Neutrl- Pont-Clmped (NPC) nverter, EEE, journl of power eletronsol.13, no.2. Copyrght to JRSET 731