LECTURES 4 AND 5 THREE-PHASE CONNECTIONS (1)
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1 ECE 330 POWER CIRCUITS AND ELECTROMECHANICS LECTURES 4 AND 5 THREEPHASE CONNECTIONS (1) AcknwledgmentThese handuts and lecture ntes given in class are based n material frm Prf. Peter Sauer s ECE 330 lecture ntes. Sme slides are taken frm Ali Bazi s presentatins Disclaimer These handuts nly prvide highlights and shuld nt be used t replace the curse textbk. 9/4/2017 Cpyright 2017 Hassan Swidan
2 WHY THREEPHASE? Mst effective in terms f equipment and wires. Prduces smth rtating magnetic field. Cnstant instantaneus pwer. 9/4/ Cpyright 2017 Hassan Swidan
3 THREEPHASE OLTAGES The three phases are usually referred t as abc. Anther standard ntatin is RYB (RedYellwBlue). ltages: Same magnitude. Same frequency. Out f phase by 120. a a' b b' c c' 9/4/ Cpyright 2017 Hassan Swidan
4 THREEPHASE OLTAGES Psitivesequence vltages are mst cmmn (abc). v ( t ) cs( t ) aa ' v ( t ) cs( t 120 ) bb ' v ( t ) cs( t 120 ) cc ' m m m Negativesequence vltages, flip b and c (acb). v ( t ) cs( t ) aa ' v ( t ) cs( t 120 ) bb ' v ( t ) cs( t 120 ) cc ' m m m 9/4/ aa' bb' cc' aa' bb' cc' Cpyright 2017 Hassan Swidan m 2 m 2 m m 0 2 m m 120 2
5 THREEPHASE OLTAGES If phase a has angle θ v, the psitive sequence is (yu practice the negative sequence): v ( t) cs( t ) aa' m v v ( t) cs( t 120 ) bb' m v v ( t) cs( t 120 ) cc' m v Phasr representatin: aa' bb' cc' m v 2 m v m v cc 120 θ v aa bb 120 θ v aa bb 120 Psitive Sequence cc 120 Negative Sequence 9/4/ Cpyright 2017 Hassan Swidan
6 THREEPHASE CONNECTIONS In general, psitive sequence is used unless therwise specified. Tw main cnnectins: Wye (Y) Delta (Δ) a Y n Cnnectin c c a a b b c b Delta Cnnectin 9/4/ Cpyright 2017 Hassan Swidan
7 PHASE AND LINE Phase vltage ( ø ) and phase current (I ø ) are defined acrss an element: Surce Linetline (r line) vltage ( ll ) and line current (I ) l are defined n the line: a 9/4/ φ ll Cpyright 2017 Hassan Swidan I φ ll b ll c φ Lad I φ I l I l I l
8 THREEPHASE CONNECTION WYE CONNECTION: The three windings are represented by cils. In the wye cnnectin, terminals a, b, and c are jined and labeled as terminal n, als called the neutral terminal 9/4/ Cpyright 2017 Hassan Swidan
9 DELTA CONNECTION: THREEPHASE CONNECTION In the delta cnnectin, terminal a is cnnected t b, and t c Finally, c can be cnnected t terminal a. The vltage acrss identically equal t zer v = v ( t) v ( t) v ( t) ac aa bb cc and is b 9/4/ Cpyright 2017 Hassan Swidan
10 YCONNECTION ltages can be linetline ( ll ) r linetneutral ( ln ). Currents can be line (I ) l r phase (I ø ). Linetline vltages can be referred t as line vltages ( ). l Linetneutral vltages can be referred t as phase vltages ( ø ). 9/4/ Cpyright 2017 Hassan Swidan
11 YCONNECTION Linetline vltages are v ab, v bc, and v ca. Linetneutral vltages are v an, v bn, and v cn which are als 0, 120, 120. an bn cn Example: ab an bn bc bn cn c a cn a n and s n. c v cn v an i c a n i a v bn b i n i b 9/4/ Cpyright 2017 Hassan Swidan
12 YCONNECTION Thus: ab bc ca ab 3 30 bc 3 90 ca ca bn ab cn 30 ll 3 an Il I bc 9/4/ Cpyright 2017 Hassan Swidan
13 Y OR CONNECTION? 9/4/ Cpyright 2017 Hassan Swidan
14 Y OR CONNECTION? In distributin, the secndary winding is ften in wye, as it prvides a neutral fr single r three phase lads. The primary is ften in delta, as it allws 3rd harmnics t flw within the transfrmer and prevent it flwing int the supply. 9/4/ Cpyright 2017 Hassan Swidan
15 Y OR CONNECTION? In Y cnnectin, vltage acrss each cil is smaller than the line vltage, s it is preferable where high line vltage are used as in high vltage pwer systems, t prtect cils frm high vltage. In delta cnnectin current passing thrugh cils are smaller than line currents, therefre cils can be rated fr smaller current. 9/4/ Cpyright 2017 Hassan Swidan
16 YSOURCE, YLOAD bn Ic n an cn I a I n Z n I b Z n L Z Z I Z I Z an a n n I Z I Z bn b n n I Z I Z cn c n n add : 0 I I I Z 3I Z a b c n n 9/4/ Cpyright 2017 Hassan Swidan but by KCL, I I I I I Z 3Z 0 I n n 0 n a b c n Ia, Ib, Ic Z Z Z an bn cn
17 YSOURCE, YLOAD Fr a lad impedance Z Z, 0 an I a I I l Z Z 120 bn I b I Z Z I 120 cn I c I Z Z I l l 9/4/ Cpyright 2017 Hassan Swidan
18 YSOURCE, YLOAD S 3 S a S b S c S n, if S n 0 i. e. balanced lad I I I * * * an a bn b cn c I I ( I I ) * * * * an a bn b cn a b I I * * an cn a bn cn b I I * * bc b ca a 9/4/ Cpyright 2017 Hassan Swidan
19 YSOURCE, YLOAD S 3 90 I I I I 3 cs j 3 sin S 3 I S 3 I ll l 9/4/ Cpyright 2017 Hassan Swidan
20 YSOURCE, YLOAD Therefre, S 3 P Q I ll l 3 I cs( ) ll l 3 I sin( ) ll l Nte that ( ll ) can als be written as ( l ). 9/4/ Cpyright 2017 Hassan Swidan
21 READING MATERIAL Reading material: Sectins and Recmmended reading fr next time: Cntinue sectin and sectin /4/ Cpyright 2017 Hassan Swidan
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