1/16/2013. Overview. 05-Three Phase Analysis Text: Three Phase. Three-Phase Voltages. Benefits of Three-Phase Systems.

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1 oltge () 1/16/21 Overview 5Three Phse Alysis Text: ECEGR 451 Power Systems ThreePhse Soures Delt d Y Coetios ThreePhse Lods ThreePhse Power ThreePhse Alysis PerPhse Alysis Dr. Louie 2 ThreePhse oltges Three Phse deg time (s) Note: istteous vlues sum to vetor digrm Power systems use phse We re oered with led phse Bled iruit oditios: impedes re equl for eh phse voltge soure phsors hve equl mgitude d hve 12 deg. phse shift,, phse rottio Dr. Louie Dr. Louie 4 Beefits of ThreePhse Systems Effiiet use of odutors over three, sigle phses Rottig field is eeded for some lods (eg three phse motors) Effetive for power trsfer Perphse lysis e used i my ses Costt power delivery to three phse lods Three Phse Three phse geertors oeted s Y or Y (Wye) Delt Dr. Louie 5 Dr. Louie 6 1

2 1/16/21 Three Phse oltge Three Phse oltge Phse voltge: the voltge ross eh soure (, d ) Lie voltge: the voltge ross the lies of the soures (lso lled LietoLie oltge ) For Yoeted soures: Phse oltges y KL Lie oltges ( ) ( ) ( ) Y Delt Dr. Louie 7 Dr. Louie 8 Three Phse oltge Three Phse oltge For Deltoeted soures: Phse oltges Do ot ofuse phse voltge with perphse voltge s disussed lter Lie oltges oltges (lie or phse) sum to zero ddig vetors results i Deltoetios: phse voltges = lie voltges Dr. Louie 9 Dr. Louie 1 Three Phse Curret Phse urret: urret flowig through the voltge soures i threephse iruit Lie urret: urret flowig from threephse soure to lod Eh set of phse urrets d sets of lie urrets re led: Sum to zero Equl i mgitude Displed y 12 degrees Three Phse Curret Phse urrets i Yoeted soures: etor Digrm I I 12 o I Lod I I I is used s referee Dr. Louie 11 Dr. Louie 12 2

3 1/16/21 Three Phse Curret Phse urrets i Yoeted soures: lie urret Three Phse Curret Phse urrets i Deltoeted soures: etor Digrm I I I Lod Yoetios: phse urret = lie urret I I I Lod I 12 o I I is used s referee Dr. Louie 1 Dr. Louie 14 Three Phse Curret Summry Lie urrets i Deltoeted soures: I I I I ( ) 12 I I I I ( ) 56 I4 I I I( ) KCL t odes,, lie urret Lie Curret = Phse Curret Lie oltge = Phse oltge x o Lie Curret = Phse Curret x o Lie oltge = Phse oltge I 12 I I I I 4 I 56 Lod Y (Wye) Delt Dr. Louie 15 Dr. Louie 16 Y Soure Coversio Y Soure Coversio Eh ofigurtio hs idetil lielie voltges, lie urret, d omplex power delivered to the lod Eh ofigurtio hs idetil lielie voltges, lie urret, d omplex power delivered to the lod perphse voltge of delt is the lielie voltge divided y sqrt() Dr. Louie 17 Dr. Louie 18

4 1/16/21 Exmple Covert the show threephse soure to its Y equivlet give: 48 Exmple Covert the show threephse soure to its Y equivlet give: Note: usully we redefie the referee oltge to e so tht 277 Dr. Louie 19 Dr. Louie 2 Three Phse Lods Three phse soures re oeted to three phse lods i two ommo ofigurtios Y (wye) Delt Y soures e oeted to delt d/or Y lods Delt soures e oeted to delt d/or Y lods Three Phse Lods Ciruit lysis is esier if lods re oeted s Y We trsform led Delt oeted lods ito led Y oeted lods mthemtilly y Y Y : omplex impede of Yoeted lod (Ohms) : omplex impede of Deltoeted lod (Ohms) Results oly pply to termil oditios Y Delt Dr. Louie 21 Dr. Louie 22 Covetios & Assumptios oltge: lietolie i rms Curret: lie i rms Curret diretio: soure to lod Bled three phse Three Phse Power Totl power delivered is the sum of power delivered y eh phse S = I * I * I * = I * (due to symmetry) = S where S : totl three phse omplex power (A) S: sigle phse omplex power (A) Dr. Louie 2 Dr. Louie 24 4

5 1/16/21 Three Phse Power ThreePhse Alysis Similrly P = Re{ I * } Re{ I * } Re{ I * } = Re{ I * } = P d Q = Im { I * } Im { I * } Im { I * } = Im{ I * } = Q Rell tht we mke hypothetil oetio etwee eutrls without ffetig the iruit Neutrl Codutor For led soures d lods, o urret flows o the eutrl odutor I = Dr. Louie 25 Dr. Louie 26 ThreePhse Alysis Phses e oeptully deoupled No eed to solve ll three phses Solve for phse (urret or voltge) Shift 12 o for phse, d 12 o for phse We therefore do perphse lysis ThreePhse Alysis Bled ThreePhse Theorem Assume: led threephse system ll lods d soures re Yoeted (or overt them to Yequivlet y dividig delt lods y usig perphse voltge of delt soures ) o mutul idutes etwee phses the ll eutrls hve the sme voltge the phses re ompletely deoupled ll orrespodig etwork vriles our i led sets of the sme sequee s the soures Dr. Louie 27 Dr. Louie 28 Exmple Cosider the followig iruit where the lielie voltge is 12.47k, d the lod impede is 12 j. Determie the totl omplex power osumed y the lod. Exmple 1. erify tht the iruit is led Dr. Louie 29 Dr. Louie 5

6 1/16/21 Exmple 2. Covert soures d lods to Yoetios Exmple 2. Covert soures d lods to Yoetios 12.47k 12.47k 12.47k shift y degrees for oveiee Lod is lredy Yoeted Dr. Louie 1 Dr. Louie 2 Exmple. Drw perphse equivlet iruit Exmple irtul oetio etwee d j Dr. Louie Dr. Louie 4 Exmple 4. Solve resultig iruit for sigle phse omplex power d totl omplex power Exmple 4. Solve resultig iruit for sigle phse omplex power d totl omplex power I S I 4,654 j1,16 A S ltertively S j 4,654 j1,16 A S S 121,96 j,49 A S 121,96 j,49 A j Dr. Louie 5 Dr. Louie 6 6

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