§ 12-2 Three-phase Y-Y connection
Three-phase sources have three
terminals called the line terminals(a,b,c).
Neutral connection--n
Balanced three-phase sources may
be defined as having
0????? ??? cnbnancnbnan VVVa n dVVV
These three voltages,each existing between one line and the
neutral,are called phase voltages ( ),cnbnan VVV ???,,
?
?
?
a b
c
n
? bnV?
?
? ?
?
? ?
anV
?
cnV
?
Let
?0??? pan VV
?120???? pbn VV
?120???? pcn VV
Vp--rms magnitude of any of the phase voltages.
?????? ?????? 2 4 01 2 00 pcnpbnpan VV,VV,VVor
?
?
?
a b
c
n
? bnV?
?
? ?
?
? ?
anV
?
cnV
?
Phase sequence(相序 )
(-) phase sequence(+) phase sequence
0??? ??? cnbnan VVV
bnV
?
cnV
?
anV
?
bnan VV
?? ?
anV?
bnV
?
cnV
?
bnan VV
?? ?
-- positive phase sequencecba ??
-- negative phase sequenceabc ??
0??? ??? cnbnan VVV
The line voltage--the line to line voltage.
bcV
?
caV
?
abV
?
bnV
?
cnV
?
anV
?
?? 303303 ?????? ???? panbnanab VVVVV
?? 903303 ??????? ???? pbncnbnbc VVVVV
?? 2 1 03303 ??????? ???? pcnancnca VVVVV
?
?
?
1 2 0
1 2 0
1 2 03
byVl e a d sV
byVl e a d sV
byVl e a d sVa n dVV
abca
cabc
bcabpL
??
??
??
??
)s ou r c eba l an c e d(VVV cabcab 0??? ???
?30
Y-Y connected
p
an
aA Z
VI ?? ? ?? 120120 ??????? ?
??
?
aA
p
an
p
bn
bB IZ
V
Z
VI
?
?
120120 ??????? ?
??
?
aA
p
an
p
cn
cC IZ
V
Z
VI
0???? ???? cCbBaANn IIII
aAI?
bBI?
cCI?
anV?
bnV?
cnV?
?
?
?a b
c
n
? bnV
?
?
? ?
?
? ?
?
?
?A B
C
?
pZ
pZ
pZ
N
cnV?
anV?
If an impedance ZL is inserted in series with each of
the three lines and ZN is inserted in the neutral.
0??
?
?
?
?
?
?
?
?
???
????
N
Nn
pL
cnNn
pL
bnNn
pL
anNn
Z
V
ZZ
VV
ZZ
VV
ZZ
VV
0)13( ?? ?????
???
?
pL
cnbnan
NpL
Nn ZZ
VVV
ZZZV 0??
?
NnV
?
?
?a b
c
n
?anV
?
?
? ?
?
? ?
?
?
?A B
C
?
pZ
pZ
pZ
N
bnV?
cnV?
LZ
LZ
NZ
LZ
pL
na
aA ZZ
VI
??
?
?
?120???
??
?
?
?
Aa
pL
nb
bB IZZ
VI
?120???
??
?
?
?
Aa
pL
nc
cC IZZ
VI
0???? ???? cCbBaANn IIII
0??
?
?
N
Nn
Nn Z
VIor
If we have balanced sources,balanced loads,and balanced
line impedance,a neutral wire of any impedance may be
replaced by other impedance,including a short circuit and an
open circuit.
?
?
?a b
c
n
?anV
?
?
? ?
?
? ?
?
?
?A B
C
?
pZ
pZ
pZ
N
bnV?
cnV?
LZ
LZ
NZ
LZ
0?? ? NnV
Example,Find,Ia n dZ A?
2 Solution:
VVL et an ?03300 ???
A./I A ?01 5 5133 0 02 0 01 ???? 8.033 0 04 0 0 2 ?? I
AIII AAA ?6.2687.321 ???? ???
AZ ?? 9.36609.3689.2 3/3 0 02 ??????
1AI?
2AI?a
??
AI?
P Fl ea d in g.
W
80
400V/ ?03300 ?
W200
n
2Za
??
AI?
??
??
b
c
W200
P Fl ea d in g.
W
80
400
V/ 3300
2Z
AI A ?9.3689.22 ??? ?