Explaining Synthesis of Three-Phase Sinusoidal Voltages Using SV-PWM in the First Power Electronics Course

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1 Explining Synhi of hr-ph Sinuoil olg Uing S-PWM in h Fir Powr Elcronic Cour Moh, Philip Jo, Brkkn, Kruhn Mohpr Uniriy of Minno, Minnpoli, USA Wlmr Sulkowki, rik Uniriy, rik, orwy or Unl, U, ronhim, orwy Abrc-- In unrgru powr lcronic cour, un r ugh h inuoil pul-wih-moulion (Sin- PWM principl o ynhi hr-ph inuoil olg. I i wll known h h pc cor PWM pproch (S-PWM uili h ilbl c-bu olg of h inrr o i imum, ruling in impro olg cpbiliy of nrly 5% compr o Sin-PWM. Howr, S-PWM i no icu in h fir cour u o i prci complxiy in xplion implmnion. hi ppr crib how S- PWM c b icu in bic cour on powr lcronic. IRODUCIO hi ppr c b cgori in h pr. h fir pr riw nw pproch h u wiching powr-pol h builing block of wich-mo conrr []. I crib h choic of h crrir ignl for PWM h i br ui for hi builing-block pproch in ynhiing c c oupu. I lo how h limiion of Sin-PWM for hrph ynhi. h con pr crib h ron h pproch for uing pc cor PWM (S-PWM in ynhiing hr-ph oupu, how i uili h cbu olg of h inrr o i imum. h hir pr xplin how h crrir-b moulion, lik in Sin-PWM, c b u for implmning S-PWM. hi ig proi h frmwork furhr il woul b proi in h ppr. PWM OF SWICHIG POWER-POLE AS A BUILDIG BLOCK Fig. how wiching powr-pol which coni of bi-poiionl wich, conir o b il, wihin wo-por compri of olg-por currn-por. A crib in [], hi wiching powr-pol i h bic builing block which i rplic wic in conrr for c-moor ri -ph UPS, hric for hr-ph c ri UPS. crl, q ri crl, q ( up ˆri ri ( c ( Fig. Swiching powr-pol i wform. A crrir-b PWM wform i hown in Fig. b, whr conrol olg crl, i compr wih high-frquncy crrir ignl ri of rigulr wform h blih h wiching-frquncy f h wiching im-prio ( / f of h conrr. In conr o h riionl cripion, whr h crrir ignl i um o ry bwn ˆri ˆri [, ], i ri bwn ˆri o b br ui for hi builing-block pproch. I i imilr o h u of rmp ignl in c-c conrr, whr h ignl ri bwn ˆr. A hown by h ymmry in Fig. b, only on-hlf of h wiching im-prio n o b conir wihin which up / i h inrl uring which > h rul in h wiching-funcion q crl, ri

2 cu h wich o b in h up poiion; ohrwi q h wich i in h own poiion. h pol uy-rio ( / i h frcion of h im h h wich i in up h up poiion, which c b ri from h wform in Fig. b crl, ( ( < < ( ˆ ri whr h uy-rio ( in ( i h rg lu of h wiching-funcion q ( hown in Fig. b. h pol oupu olg ( qul q ( i rg lu pn on h uy-rio: ( ( < < ( whr h rg rfr o olg rg or on wiching im-prio i inic. From( (, hown in Fig. c by il-rformr rprnion crl, ( ( ( ˆ ( ri I i clr from Fig. h h oupu olg i rg r limi bwn. Howr, in pplicion uch moor ri, h oupu olg n o b boh poii ngi, which r rli by inroucing common-mo off in h oupu olg of ch pol. hi common-mo olg i nullifi in h iffrnil oupu crib in h following cion. hrfor, h oupu olg i ynhi o b cm (4 whr cm i h common-mo olg h llow h ir olg o bcom boh poii ngi roun hi common-mo olg. SYHESIS OF HREE-PHASE AC I DRIES AD UPS Conrr for hr-ph oupu coni of hr powrpol hown in Fig.. h pplicion i hown o b for moor ri bu h m ppli o ohr pplicion uch hr-ph UPS. In hi conrr, h rg oupu olg r ynhi ccoring o (4 cm b cm c cm cn b c 4 n Fig. hr-ph inrr. whr, cn r h ir blc hr ph lo olg, um o ro y im in. h oupu olg r hown in Fig. b. h common-mo olg, bing ro-qunc, o no ppr cro h lo only o h lo-nurl. (5,, cn ppr cro h lo wih rpc 4 SIE-PWM In Sin-PWM (imilr o conrr for c-moor ri -ph UPS h rg oupu of ch powr pol h common-mo c off olg qul o roun which,, cn c ry inuoilly hown in Fig. [- ]. h powr-pol oupu olg r hown in Fig. b. A h limi, c bcom imum of hnc ph ( ˆ. hrfor, h imum mpliu of h linlin olg in Sin-PWM, which occur in Fig., i limi o ( ˆ (6 LL

3 ( ( ( cn b Fig. Sin-PWM. 5 SPACE ECOR PWM (S-PWM U of pc cor h bn rcnly inrouc in phyicl bi uch h i c b u in ching h fir cour ling wih -ph c mchin [4]. hi pproch h numrou bnfi. In h powr lcronic cour, lhough h ynhi of hr-ph c i gnrl, i i b o imgin h i i bing ynhi for hr-ph moor wih hr mgnic x pr in pc, hown in Fig.. In rm of h ir ph olg, h olg pc cor c b wrin by muliplying h ph olg by hir rpci x orinion in Fig. : / 4 / ( ( ( cn( (7 whr h pc cor ( i complx ribl xpr by rrow on op, i i h rg lu, u lik h ph olg. Eq. 7 how h h pc cor ( i compc noion uch h ingl ribl conin informion bou h olg of ll hr ph gin b c n c im. Gin (, y ph olg c b obin by h procion of ( on h xi muliplying i by fcor of /. If h hr-ph olg, ch of ph mpliu ˆph, ry inuoilly in im wih frquncy f ( ω /, hn h pc cor will h con mpliu ˆ ( ˆ will ro counrclockwi wih p of ω ( f r/. In Fig., in rm of h wiching powr-pol inou oupu olg wih rpc o h ngi c bu n; b n; cn c n (8 h bo quion will lo b li in rm of h rg quii: n; b n; cn c n (9 hrfor, ubiuing (9 ino (7 rcogniing h / 4 /, h rg olg pc cor c b wrin in rm of h rg oupu olg of h wiching powr-pol / 4 / ( ( b( c( ( A wich in wiching powr-pol of Fig. i ihr up or own, wih h inou oupu olg ihr or im. Wih hr pol, igh wich-u combinion r poibl. From (, h olg pc cor c inly um on of h ix iinc non-ro inou lu hown in Fig. 4, whr ph "" i rprn by h l ignific igi ph c by h mo ignific igi. h mpliu of ch of h ix cor qul. h ruling inou olg cor, which w will cll h bic cor, r hown in Fig. 4 forming ix cor. 7 r h ro cor bcu of hir ro lu. b xi ( 6 ( 7 ( III I ( II I ph ( I ( ( 4 5 ( c xi Fig. 4( Inou bic cor xi

4 4 y θ x ˆ, Fig. 4(b Synhi of (. h rg olg pc cor i ynhi by imwigh rging of h wo cn bic non-ro olg cor h form h cor in which h rg olg cor o b ynhi li, bu uing boh h ro olg cor of qul urion. In h following lyi, w will focu on ( hown in Fig. 4b, wih h im of gnrliing h icuion o ll cor. o ynhi ( in Fig. 4b, h cn bic cor r ppli for inrl x 7 r ppli for urion ch. By im-wigh rging ( [ x y ] x y ( y rpcily, h ro cor whr, x y. In (, xpring h bic cor in rm of hir mpliu ph gl rul in ˆ / ( θ ( x y ( ( From Fig. 4b (, i i clr h h rio y/ x ic h orinion θ of (, whr h mpliu ˆ i conroll by inroucing h wo ro. A h limi, whr hnc x y, h ip of h olg pc cor li on h righ lin conncing h wo non-ro bic cor, hown in Fig. 4b. Howr, normlly h hr olg o b ynhi ry inuoilly in im, mnion rlir, rul in roing olg cor of con mpliu, h h limi, hown by h h circl in Fig. 4b, h imum lu h gl of /6r: ( ˆ co( ( 6 h corrponing ph olg pk, im h pc cor pk, h h following imum from ( ( ˆ ph (4 hnc h imum lin-lin olg i ( ˆ LL (5 Comprion of (6 (5 how h S-PWM rul in highr limi on h ilbl oupu olg by fcor of, or by pproximly 5 prcn highr, compr o Sin- PWM. 6 CARRIER-BASED IMPLEMEAIO OF S-PWM h mor ifficuly in implmning S-PWM crib bo i h i rquir cor-b clculion. Howr, i c b xplin implmn uing crrir-b moulion imilr o Sin-PWM. o h in Fig. 4b in cor, wih h bic non-ro cor ( (, h ro-cor ( ( 7, h powr-pol c olg i lwy xcp for inrl corrponing o ( 7. hrfor, h rg lu of h powr-pol c oupu i c ( (6 Similrly, h wiching-pol olg i lwy xcp for inrl corrponing o (. hrfor, h rg lu of h wiching-pol oupu i ( (7 Equing h lu gin by (6 (7 o h wichingpol olg in Fig b, cn ( cm( (8 ( cm( (9 Soling (8 (9, ( cn( cm ( ( Eq. i li only for cor. o gnrli for ll cor, ( c b xpr

5 5 (,, cn min(,, cn cm ( ( k ( Eq. how h h common-mo olg in S-PWM coni of, in Sin-PWM, plu xr olg rm k (. A in Sin-PWM, i i poibl o chi S-PWM by uing high-frquncy rigulr-wform crrir h conrol olg (qul o if ˆ ri hown in Fig. 5, compr o h for Sin-PWM. crl, ˆ ri Sin-PWM S-PWM.5 crl, com, S PWM Fig. 5 Comprion of Sin-PWM S-PWM conrol olg in ph- for h m oupu. 7 COCLUSIOS hi ppr crib how S-PWM c b ugh in h fir cour in powr lcronic inc i h my g or Sin-PWM. h originl conribuion of hi ppr r follow: br crrir moulion in PWM, rionl for uing pc cor in h fir cour, clr xplion of crrir-b implmnion of S-PWM. REFERECES [] Moh,., Fir Cour on Powr Elcronic, MPERE,. [] Moh.., Unl.M., Robbin W.P., Powr Elcronic Conrr, Applicion Dign, /, John Wily & Son,. [] Holm, D.G., Lipo,.A, Pul Wih Moulion for Powr Conrr, IEEE Pr,. [4] Moh,., Elcric Dri: An Ingri Approch, MPERE,.