SEI 9 5 h Inrnionl Confrn: Ss of Elroni, hnologis of Inforion nd louniions Mrh -6, 9 UNISIA Quliy Ipron of Unlnd hr-phs ols Rifiion Fi Zhr AMAOUL *, Musph.RAOUFI * nd Mouly hr LAMCHICH * * Dprn of physis, Fuly of Ss Slli Unirsiy Cdi Ayyd P.O. BOX 9, Mrrksh, Moroo fz.oul@u.. roufi@u.. lhih@u.. Asr: In his ppr w r h s whr unln is on h ll of h powr supply, nd prsn hod o opns his unln of h nwork. his hod is sd on onsidrg gnrl hr phs ols of unqul pliud nd rirry phs. his ol sys is hn oposd wo squns: posii nd ngi squn. h zro squn is ssurd o zro. For h squn, odulion swihg funion is drd. h ol h d sid is hn xprssd s funion of wo squns ol, nd h rld swihg. In h o DC ol xprssion, hr r rs h gnr hronis, w k hoi h h su of hroni rs quls zro. A glol swihg funion is hn drd. Ky words: PMW rifir, unln ol, uni powr for (UPF). INRODUCION h lril nwork sud o n nironn so i sr, is h s of idns whih us disurns of h powr supply du gnrl o syris of dns of h ls of h nwork, wih h rious ffs of shor-irui of origs ffg h nwork, wih h unln of h sour, h srong sgl-phs lods or d disriuion of h lods on h lril nwork. Whn suh df ours, hr is irh of non syry of orn ol whih n ndngr h sfy of h popl nd drior h xisg sllions h lril nwork, if i is no quikly lid [CHE 6]. his ppr proposs nw onrol sh for h /d hr-ll PWM rifir undr gnrlizd unlnd oprg ondiions. h qunifiion of his unln is sd on h ols doposiion ordg o h syril oponn of Forsu [GRA ]. his hod pris o spr h hrphs unlnd ols on hr lnd dpndn syss known s dir (posii squn), opposi (ngi squn) nd hoopolr. Siulion ws ondud undr wo diffrn ss of unlnd oprg ondiions. h firs s is 9% unln on phs pu ol. h sond unln s is doul susoidl pu. his sond unln s is on xpl of h xr unlnd oprg ondiions. his priulr oprg ondiion is lso oonly found rsidnil rs whr oh nd pu ols r ill [SUH ]. A dild siulion progr is prprd y usg Ml/Siulk. Siulion nd xprl rsuls onfir h proposd onrol hod. Figur. PWM /d onrr undr gnrlisd unlnd oprg ondiions. - -
SEI9 - -. Rifir wih ouion ford wih sour of unln ol: opnsion of unln Considrg hr-phs pu ols (unqul pliuds nd rirry phss) wihou zro squn s h orhogonl su of posii nd ngi squn, hrfor h pu n wri h nry lik or of hr lns: i () Aordg o h quion of Eulr, h ol of phs n rprsnd y h su of wo oplx sizs, for xpl, for phs : () () (5) nd r rspily h phsor of pliud nd his od oplx. (6) (7) h s forlis is pplid o ohr phss. h sp phsor of h hr-phs sys n xprssd s: i (8) i (9) W noi h h nsion i is oposd of posii squn nd ngi squn of ol. h posii squn is dfd s: p R () p R () hrfor, h hr ols of h posii squn r wr: p p p Wih h s nnr, h ngi squn is: n R Fro whr h hr ols of h ngi squn r wr: n n n And h oupu ol onuous sid n dsrid wih h followg quion: d (5) Whr, r h swihg funions rli o h hr rs of h PWM rifir, whih n k h lu () or (-), quion (6) n wr oril for: d (6) h firs wo rs produ h onsn ol d, whil h wo ohr rs produ hroni h frquny of h l. [GRA ] If h nsions of h posii squn r wr: p p p p p p p p p (7) h orrspondg swihg funions r hn () () () ()
SEI9 p p p p p p p p p Wh produs: p p Afr lulion, w fd: ( ) (8) (9) () p p h s nnr for h ngi squn, if w k s xpl: n n n n n n n ( ) n n n n n And ( ) n n p n n n W fd: ( ) () () () n p n () n p If hs quniis r srd o forul (9), h ls wo rs i yilds: ( ) p p If w hoos: p n (5) (6) p n hus h wo undsirl rs r nlld wn h. And h forul (9) os: (8) d n d p p p (9) hrfor, h funion of odulion whih pris o produ onuous nd onsn ol for ny ondiion usg n unln is: () i p i ( ) p W no h only h pliud of h posii squn pprs h xprssion (), whih p n surd y filrg. h xprssion () is usd o dlop h dir of h l lok of h Fig.. Non-syry ol is hrrizd y is dgr whih is dfd y usg h hod of h oponns of Forsu y h opposi h rio of h pliuds of h rs nd dir ol [CHE 6], hrfor h for of non-syry or unln is dfd y h followg rlionsh: U n () p hn quion () os: ( U ) ( ) () d p p hrfor, h xprssion of h xiu lu of h ol is: d ( ) () U () d p Equion () shows h rlionsh wn h onuous ol nd h for of unln, s long s his ls rss, whih dus rduion on h ll of d ol nd rrolly. h Fig. shows h oluion of h xiu lu of h ol d ordg o h for of unln. hn (7) - -
SEI9 L,, L L R, R, R Dphsg of 9 * s ο s( ) ο s( ) l..prrs usd siulion for s Dphsg of 9 * Fig. illusrs h hr phs ols, whr h ol hs n unln of 9% h pliud, Fig. shows h phs () pu urrn, nd h phs () pu ol, flly, Fig. illusrs h onrr oupu d ol. Dphsg of 9 p Figur. Modulion wih orrion of unln. d p * 5 6 hr Ls phs rois nsion ols du résu (), (), (), () () - - - -.8....6.8.. ps(s) i (s) () Figur. ol unl. U (%) d ordg o h for of. Siulion Rsuls nd disussions o pro h fsiiliy nd h prforn of h proposd onrol sh undr rious gnrlizd unln oprg ondiions, siulion ws d for wo diffrn unlnd oprg ondiions. Cs I: 9% of unln on phs pu ol his kd of unlnd pu ondiion is qui oon wk sys [SUH ]. h prrs of our sys for his ondiion r surizd l. ol nsion nd ourn urrn d of phs () (), I (A) I () ol DC() nsion d() - - - - 8 7 6 5 I.5.56.58.6.6.6.66.68 ps(s) i (s) () -.....5.6.7.8.9 ps(s) i (s) () - -
SEI9 8 ol nsion DC() d() 7 6 5 -.5.5.55.6.65.7.75.8 ps(s) i (s) (d) Ls rois nsions du résu (), (), () hr hr phs phs ols ols (), (), (), (), () () - - - -.5..5.5 ps(s) i (s) () Figur. Rsuls of siulion h s of 9% of unln on h ll of h pliud : () hr phs ols; () ol of h phs (); () urrn of h phs (); (d) DC ol. Aordg o Fig., w s h h urrn is prilly susoidl nd phs wih h ol of h phs (). Fig. shows h h d ol follows is rfrn. Cs II: A doul susoidl pu Alhough his yp of unlnd oprg ondiion is no s oon s h of s, doul susoidl pu is onsidrd o on of h os xr unlnd oprg ondiions. Consqunly, i is suil xpl o x h prforn piliy of proposd hod. h sys prrs of his ondiion r rpiuld l. nsion ourn d () I(A) ol nd urrn of phs (), I () ol nsion d() DC() - - - I -.5.5.55.6 ps(s) 8 7 6 5 i (s) () s ο s( ) l. Prrs usd siulion for s Fig. prsns h hr ols, Fig. illusrs h ol nd h urrn of h phs (), w s h h urrn is prilly susoidl nd phs wih h ol, flly h Fig. shows h h ol follows is rfrn u wih h prsn of h rpl. ol nsion DC() d().....5.6.7.8.9 ps(s) 8 7 6 5 i (s) ().55.6.65.7.75.8.85.9 ps(s) i (s) (d) Figur 5. Rsuls of siulion h s of u on h ll of h hird phs: () hr phs ols; () ol of h phs (); () urrn of h phs (); (d) DC ol. - 5 -
SEI9 Figur 6. Siulk odl usd for h opnsion of unln. Figur 7. Blok of opnsion of unlund pu ols.. Conlusion his ppr proposs nw hod for hr-ll PWM rifir oprg undr gnrlizd unlnd oprg ondiions. An xr unlnd oprg ondiion of pu ol s on of wo xpl ondiions for h siulion his ppr. h d oupu nd nrly uniy powr for sid of h rifir show h ffss of h hod. REFERENCES [FE 6] CHERIF FEHA, "nlys éliorion d l di d l non-syéri d nsion dns l qulié d l énrgi élriqu", hès d Door d E, Unirsié d Bn, Fulé ds Ss d l géniur, pp., pp., Mi 6. [GRA ] D.Grh Hols, hos A.Lo, "Puls Wih Modulion for Powr Conrrs : Prls nd Pri", pp.-5, -, 59-597, IEEE Copur Soiy Prss, Oor. [SUH ] Y.Suh,. irs,. A. Lo, "A Nonlr Conrol of h Insnnous Powr dq Synhronous Fr for PWM AC/DC Conrr undr Gnrlizd unlnd Oprg Condiions", Unirsiy of Wisons- Mdison ol, oor. - 6 -