DQ Modeling and Dynamic Characteristics of a Three-Phase Induction Machine

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1 Aecan Jounal of Engneeng Reeach AJER 7 Aecan Jounal of Engneeng Reeach AJER e-issn: -847 p-issn : -96 olue-6, Iue-9, pp Reeach Pape Open Acce DQ oelng an Dynac Chaacec of a Thee-Phae Inucon achne Eanuel S. Oluwaogo *, Ignau K. Okakwu, Olanke O. Ae-Ikuean, Haee O. Sulean, Depaen of Eleccal & Copue Engneeng, Kwaa Sae Uney, Ngea. Depaen of Elec./Elec. Engneeng, Uney of Benn, Ngea. Depaen of Copue an Eleccal Engneeng, Ola Onaanjo Uney, Ago Iwoye,Ogun Sae. Depaen of Eleccal & Copue Engneeng, Kwaa Sae Uney, Ngea. Coeponng Auho: E. S. Oluwaogo Aac: AC oo a a e hae ecoe oe popula oe DC oo counepa Fo exaple Wa eona Sye n he aale pee e applcaon. The lae ue hee eleccal oang achne an ey coly o anan epe he low effcency offee y he. The foe offe upeo ynac pefoance. In h pape, he heoy of efeence fae ue o exane he ynac pefoance of he nucon achne. The efeence fae conee ynchonouly oang DQ-efeence fae. Th ecaue h efeence fae anfo he AC gnal o he eualen DC gnal. The ynac oel poe eale expeon fo he uy of anen an eay ae ehao of he achne. 4 h Oe Runge-Kua oe45 wa ue o ole he ffeenal euaon ung ATAB. Reul how ha ATAB a elale an ophcae ool o uy he anen an eay ae epone of he achne. Keywo: Refeence Fae, Inucon achne, Dynac Repone, ATAB, 4 h Oe Runge-Kua Dae of Suon: -9-7 Dae of accepance: I. INTRODUCTION Wh he huge ucce n he eco conol of AC oo, Inucon AC oo a e hae ecoe oe popula oe DC oo counepafo exaple Wa eona Sye n he aale pee e applcaon. The lae ue hee eleccal oang achne an ey coly epe he low effcency offee y he. Theefoe, eenal o analyze he ehao o pefoance of he nucon oo. Alhough, n he pa ecae lo of eeach ha een cae ou on he eay ae analy of he nucon oo whch wa poe o hae neglece he pefoance of he oo une peuaon a a eul of he loa change an flucuaon fo he upply. Theefoe, ecae al o uy he ynac epone of he nucon oo n oe o eene he anen ehao of h oo. To pec he ynac pefoance of he nucon oo [Khnan] conclue ha he ynac oel ee fo wo-phae fcou wnng n he ec an uaaue axe hough he efeence fae heoy u e ue. Wh h appoach, an n-phae achne can e euce o a e of wo phae wnng whch ae a an angle 9 o o each ohe. Hence, he eue aale olage, cuen an flux lnkage of he nucon oo anfoe o a efeence fae oang a an aay angula pee known a genealze efeence fae. I ey poan o enon hee ha hee ae hee coonly ue efeence fae ee fo he genealze aay efeence fae oel of nucon oo. They ae efly cue elow:. Saonay Sao Refeence Fae oel: The efeence fae pee zeo.e. I eualen o he ao aonay pee. Uually, aope y he ao cala conolle nucon oo e uch a: Inee-Paallel Thyoze conolle o Inee Fe nucon oo. w w w. a j e. o w w w. a j e. o g Page 7

2 Aecan Jounal of Engneeng Reeach AJER 7. Roo Refeence Fae oel: Th noally ue y he nucon oo whoe pee conol one fo he oo e. The efeence fae pee of h oel eualen o ha of he oo..e. Whee he oo angula pee.. Synchonou Roang Refeence Fae oel: The efeence fae pee of h oel he ae a ha of he ao upply angula pee of he agnec flux e-up n he a gap y he ao upply cuen..e. f Whee f he upply feuency n Hz Fo he pupoe of h pape, he efeence fae conee ynchonou efeence fae. Th ecaue h efeence fae anfo he AC gnal o he eualen DC gnal nce he ffeence eween he efeence fae angula pee an upply angula pee zeo whch coepon o he DC angula pee o feuency. Th eakhough achee hough ynchonou efeence fae oel ha le o upeo pee conol eco Conol of nucon oo la o he epaaely exce c oo. In [], he ynac ehao of -φ nucon oo wee aee ae on a ualy aheacal oel an copue poga ulaon n a aonay efeence fae o ao he coplexy nole n he coue of olng e-ayng ffeenal euaon oane fo he ynac oel. Fouh Oe Runge- Kua wa aope o ge nuecal oluon of he ynac oel. Alo, Eneuoh e al oele nucon oo y anfong ac coonae o oang o coonae. The /f pee conol of he oo wa ulae n ATAB/SIUINK enonen ung Pule Wh oulaon PW echnue. They conclue ha wh he ue of efeence fae anfoaon ecoe pole o conol he pee of elecc oo a well a o conee he eleccal enegy Eneuoh e al,.. In he ae yea, Hay e al. peene a pape on analycal an expeenal pefoance an conol of a hee-phae nucon oo fe fo a ngle-phae upply a a ngle capaco. The anen an eay ae analy wee pece ung - oel epeenaon whoe fae wa choen aonay. The pee wa conolle ung a TRIAC couple n ee wh he upply. kewe, n a pape wok peene y Naeh e al, whee he hee-phae AC uane wee euce o wo DC uane y plfe calculaon hey cae ou. Theeafe, he nee anfoaon wa one o ecoe he acual hee-phae AC eul. Theefoe, neceay o oel he achne paaee n o efeence fae y anfong he alenang hee-phae paaee of nucon achne o wo- phae eualen an euce he ynac epone of he achne. II. SYSTE ODE The e of ffeenal euaon ecng he nucon oo hae een ae explcly n he leaue o e nonlnea whch ake pefoance analy ncae an he cala lnea conol aege aope n he pa unelale. Theefoe, neceay o anfo hee coplcae euaon no ple an cleae e of euaon fo whch he all-gnal euaon can e eelope an he conol echnue ecoe oe appaen. Cone he eualen ccu of he nucon oo n he o-efeence fae a hown n Fg. elow. The nucon oo aue o hae alance wnng, alance npu an he zeo euence ccu elnae fo he cuon. w w w. a j e. o w w w. a j e. o g Page 8

3 Aecan Jounal of Engneeng Reeach AJER 7 olage Euaon Takng he ao an he oo cloe loop of he eualen ccu of Fg. a, an applyng K an Faaay law aoun he loop, we hae: Sao oop: Whee... a IS... IS Apply K o oo loop of fgue a an fgue aoe, we hae; Whee I I Flux lnkage euaon Reong he ffeenal opeao IS IS I I... a.. fo euaon an... a Replacng λ y ψ an y fo euaon a o oan w w w. a j e. o w w w. a j e. o g Page 9

4 Aecan Jounal of Engneeng Reeach AJER 7 IS IS I Whee:. Fo euaon a le If f... c c enoe upply feuency ue n calculang nuce eacance uch ha: f o.. c Suue c no a an fo he ax Suue, an a no a an a epecely an le oo e locke.e. he oo e ho ccue.... an eual zeo nce he oo... 4 a... 4 a... 4 a... 4 a Repeenng he olage euaon n ax fo w w w. a j e. o w w w. a j e. o g Page

5 Aecan Jounal of Engneeng Reeach AJER a The oel fo - cuen of he hee phae nucon oo ae oane a follow: ulplyng euaon 4a y an 4a y an uacng he eul o oan 4.[ A ] ulplyng euaon 4a y an 4a y an uacng he eul o oan 4...[ B ] ulplyng euaon 4a y an 4a y an uacng he eul o oan 4...[ C ] ulplyng euaon 4a y an 4a y an uacng he eul o oan 4.[ D ] Toue Euaon An elecoagnec oue of powe eualence anfoaon eween he hee-phae an wo-phae oel expee a: e p...[e]] Whee P he nue of achne pole. e he eang oue pouce y he all eang e euaon ecoe: J e f Alo, Euaon [F] elow euce fo [E] an P J f f an he loa oue e. Theefoe, Newon F w w w. a j e. o w w w. a j e. o g Page

6 Aecan Jounal of Engneeng Reeach AJER 7 w w w. a j e. o w w w. a j e. o g Page The nananeou hee-phae oo aale ao an oo can e oane ung ynchonouly oang efeence fae a follow: e he alance hee-phae upply olage o he ao of he nucon oo e efne a: co co co c a Thee hee-phae e of olage anfoaon o - ynchonouly oang efeence fae one ung he wo followng euaon: 4... co n n co c c a kewe, he hee phae ao an oo cuen ae fnally e oane ung nee anfoaon a gen elow: 4... co n n co c 4... c c a Thee ge: 4 co n co n co n co n n co c c a In oe o oan he ynac chaacec of he nucon achne on -ax, euaon [A] o [F] ae ole ung 4 h Oe Runge Kua [Oluwaogo e. al.] III. COPUTER SIUATION AND RESUTS The opeang paaee of he hee-phae uel cage nucon oo ue fo h uy ae gen elow: = 79.6; R =.86Ω; =.46H; =.7H; P = 4; R =.45Ω; f = 5Hz =.7H; ω = 79.7p; ω = 76.99p; J =.89kg/ ; The ATAB -fle eelope o oan he pefoance chaacec of he hee-phae nucon oo wa achee ung he algoh ae n he flow-cha of fg. elow.

7 Aecan Jounal of Engneeng Reeach AJER 7 Fg. : Poga Flow Cha Fgue elow how he eul oane fo he ATAB -fle poga w w w. a j e. o w w w. a j e. o g Page

8 Aecan Jounal of Engneeng Reeach AJER 7 Fg. : Sulaon Reul. I. RESUT DISCUSSION The anfoaon of ac upply olage cone o wo-phae eualen ge an zeo olage epecely. The wo-phae eualen aale ao an oue an oue ocllae fo few econ afe whch eane ale. Wheea, he nee cuen of wo-phae achne -eualen nuoal ale.. CONCUSION Th pape ge a ep-y-ep aheacal oel of a hee-phae nucon achne n a ynchonouly oang efeence fae. The oel poe eale expeon fo he uy of anen an eay ae ehao of he achne. The epone oane fo he nuecal oluon o he oel ung 4 h Oe Runge-Kua execue y he ATAB -fle poga afacoy. Th conclue ha 4 h Oe Runge-Kua oe45 a elale an ophcae ool o ole ffeenal euaon. REFERENCES [] P. C. Kaue, O. Waynczuk, S. D. Suhoff Analy of Elecc achney an De Sye, IEEE Pe, A John Wley & Son, Inc. Pulcaon Secon Eon,. [] E.S. Oluwaogo, O.D. Oune, A.K. Baane, I.K. Okakwu, 5. The Dynac oellng an Eleccal Pofle of Thee Phae Inucon oo Ung ATAB Poga, Innoae Sye Degn an Engneeng. ol.6, No.. [] R. Khnan,. EECTRIC OTOR DRIES: oelng, Analy, an Conol. Pence Hall, Inc. New Jeey. w w w. a j e. o w w w. a j e. o g Page 4

9 Aecan Jounal of Engneeng Reeach AJER 7 [4] Eneuoh F. O., O. E.. oellng, Sulaon an Pefoance Analy of A aale Feuency De n Spee Conol Of Inucon oo. Inenaonal jounal of engneeng nenon, ol. an No.7. [5] K. Naeh,. R. 4. Sulaon fo Thee Phae o Two Phae Tanfoaon. nenaonaljounal of eegng enn Eleccal an Eleconc. ABOUT THE AUTHORS E.S. Oluwaogo gauae fo Uney of Ilon, Ngea, n 8. He ecee he.sc. egee fo he Uney of ago, Ngea, all n Eleccal Engneeng. He a lecue n he Depaen of Eleccal & Copue Engneeng a Kwaa Sae Uney, Ngea. He cuenly puung a PhD egee n Eleccal / Eleconc Engneeng, Uney of Benn, Ngea. H eeach nee nclue Powe Sye Saly an Conol, Conol of Eleccal achne, Opzaon an Rou Conol, Auoaon ec. He a ee of IEEE an a egee Engnee wh COREN. I.K. Okakwu gauae fo Aoe All Uney, Ekpoa Ngea n 8. He ecee.sc egee fo Uney of ago n all n Eleccal/Eleconc Engneeng. He cuenly puung a PhD egee n Eleccal/Eleconc Engneeng Uney of Benn, Ngea. H aea of nee nclue powe ye aly an conol, eleccal achne, powe ye elaly, econoc pach, FACTS an applcaon, Deegulaon E. S. Oluwaogo,.Sc. DQ oelng an Dynac Chaacec of a Thee-Phae Inucon achne. Aecan Jounal of Engneeng Reeach AJER, ol. 6, no. 9, 7, pp w w w. a j e. o w w w. a j e. o g Page 5