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Open delta
A1
B1
C1 C2
B2
A2
Fed
from
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Open delta
A1
B1 B2
A2
b2
a1 a2
b1
c1 c2
Fed
from
Thr
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sou
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Open delta
A1
B1 B2
A2
b2
a1 a2
b1
c1 c2
b2
b1
a1
c1
c2
a2
Fed
from
Thr
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sou
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phas
e lo
ad
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Open delta
A1
B1 B2
A2
b2
a1 a2
b1
c1 c2
b2
b1
a1
c1
c2
a2
0∠=VVab
120−∠=VVbc
Fed
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Open delta
A1
B1 B2
A2
b2
a1 a2
b1
c1 c2
b2
b1
a1
c1
c2
a2
0∠=VVab
120−∠=VVbc
[ ]
120 )866.05.0(
866.05.0 1200
2222
∠=+=
++−=−∠−∠−=
+−=
VVj
VjVVVVVVV
:acb aVL in loopApplying K
bcabca
Fed
from
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Open delta
A1
B1 B2
A2
b2
a1 a2
b1
c1 c2
b2
b1
a1
c1
c2
a2
0∠=VVab
120−∠=VVbc
[ ]
120 )866.05.0(
866.05.0 1200
2222
∠=+=
++−=−∠−∠−=
+−=
VVj
VjVVVVVVV
:acb aVL in loopApplying K
bcabca
Fed
from
Thr
ee p
hase
sou
rce
Supp
lyin
g Th
ree
phas
e lo
ad
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022
∠=VV ba
120−∠=VVbc
120∠=VVca
b2
b1
a1
c1
c2
a2
022
∠= II ba
12022
−∠= II cb
12022
∠= II ac
Phase load currents and line currents in open delta:
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022
∠=VV ba
120−∠=VVbc
120∠=VVca
b2
b1
a1
c1
c2
a2
022
∠= II ba
12022
−∠= II cb
30120022222
−∠=∠−∠=−= IIIIII acbaa
12022
∠= II ac
Phase load currents and line currents in open delta:
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022
∠=VV ba
12022
−∠=VV cb
120∠=VVca
b2
b1
a1
c1
c2
a2
a2
b2 c2
022
∠= II ba
12022
−∠= II cb
30120022222
−∠=∠−∠=−= IIIIII acbaa
12022
∠= II ac
9012012022222
∠=−∠−∠=−= IIIIII cbacc
Phase load currents and line currents in open delta:
N.B.: Line currents have the same values and angles even if the load was star connected
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302
−∠= IIa
0:1
22∠=VV
rTransforme
ba
st
902
∠= IIc
120:2
−∠=VVrTransforme
bc
nd
902
−∠=− IIc
( )( )30
300
*1 222
∠=∠∠=
=
VIIV
IVS abaT
( )( )30
90120
)( *2 222
−∠=∠−∠=
−=
VIIV
IVS ccbT
LineLine I VSSS TTVV ×=+=→→→
321)(
21
21 LineLine IV QQTT
×=−=→→
VVS→
1TS→
2TS→
Active & reactive power of open delta:
2aI
2cI
°−30
2cI−
°+ 90 022
∠=VV ba
12022
−∠=VV cb
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De‐rating of open delta
A1
B1 B2
A2
PhaseLine II =
%7.573
1
3
)( 3
3
3
21
≈≈∴
×=
×=
×≈+=
×=
∆∆
→→→
SS
IV
IV
I VSSS
IVS
VV
PhaseLine
PhaseLine
LineLine
Phasephase∆∆
TTVV
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A1
B1 B2
A2
PhaseLine II =
%7.573
1
3
)( 3
3
3
21
≈≈∴
×=
×=
×=+=
×=
∆∆
→→→
SS
IV
IV
I VSSS
IVS
VV
PhaseLine
PhaseLine
LineLine
Phasephase∆∆
TTVV
De‐rating of open delta Fe
d fr
om T
hree
pha
se s
ourc
e
Supp
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phas
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A1
B1 B2
A2
%7.573
1
3
)( 3
3
3
21
≈≈∴
×=
×=
×=+=
×=
∆∆
→→→
SS
IV
IV
I VSSS
IVS
VV
PhaseLine
PhaseLine
LineLine
Phasephase∆∆
TTVV
PhaseLine II =
De‐rating of open delta Fe
d fr
om T
hree
pha
se s
ourc
e
Supp
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ree
phas
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ad
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Open delta
A1
B1 B2
A2
PhaseLine II =
Disadvantages: - De-rated operation, 57.7% of ∆∆ bank; × (3/2) = 86.6% of the capacity of the remaining two transformers -Average P.F. of V bank < Load P.F. (∼ 86.6% of balanced load P.F.); The two transformers operate at different power factors; for a balanced load P.F. of cosφ, one transformer has a P.F. of cos(30-φ) while the other has a P.F. of cos(30+φ), accordingly voltage regulation differs.
- Accordingly, increasing load (even if perfectly balanced), causes terminal secondary voltages to be unbalanced
IBC
IAB
IB
Fed
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Two single phase 150 kVA, 7200/600 V transformers are connected in open delta configuration. Find the maximum three phase load supplied.
Rated Secondary current of either transformer = 150 000 / 600 = 250 A This current should not be exceeded whatever was the type of connection, Accordingly:
( )
%./% DeratingkVArstransformetwoofratingAvailable
kVAVISLoad
6863002603001502
26025060033 maximum
===×=
=××==
One transformer is producing reactive power, while the other is consuming reactive power. This energy exchange between the two transformers is the reason for limited power output of 57.7% instead of an expected 66.7%
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Open Y – Open Delta
A1
B1 n
B2
A2
C1 C2 Fed
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Open Y –Open Delta
A1
B1 n
B2
A2 Disadvantages:
- Very large return current flow in neutral of primary
Fed
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