EE 740 Professor Ali Keyhani Lecture

1
EE 740Professor Ali KeyhaniLecture 3

• Ideal Transformers

2
I1
I2
I2
IT
I1


V1
V2
-
-
V1
V2
N1
N2
I1
I2
Z2
V1
V2
N1
N2
I2
R1
jX1
R2
jX2
I1
I2/a
Ic
Im
Load
V1
V2
V1
Rc
jXm
N2
N1
3
I1
I2
I2
I1


V2
V1
V1
V2
-
-
N2
N1
IT
V1
N1
a

V2
N2
R1
jX1
I2/a
I1
I2
R2
jX2
Im
Ic
V1
Load
Rc
jXm
N1
N2
R2 a2R2
X2 a2X2
R1
jX1
R2
jX2
I2
I1
Ic
Im
Load
V1
Rc
jXm
N1
N2
4
I1
I2
IT
I1
I2


V1
V2
-
-
V1
V2
N1
N2
N1
V1
a

N2
V2
I2
R1
jX1
R2
jX2
I1
I2/a
Ic
Im
Load
V1
V2
V1
Rc
jXm
N2
N1
R2 X2 are referred to winding 1
R1
jX1
R2
jX2
I2
I1
Ic
Im
Load
V1
Rc
jXm
N1
N2
5
Req
jXeq
I2
V2
I1
V1
Load
N1
N2
Req R1 R2
Xeq X1 X2
Neglecting excitation current
V2
I2
jXeq
I1
V1
Load
N1
N2
6
Req
jXeq
Isc
Vsc
Vsc
Ideal Transformer
Real Transformer
jXeq
Req
Isc
Isc
Vsc
Vsc
7
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9
Rs
jXs
Rs
jXs
I1
I1
I2
V1(rated)
V2(rated)
V1(rated)
V2(rated)
N1
N2
N1
N2
LV
HV
S(rated)
N1
V1(rated)
S(rated)

a
N2
V2(rated)
10
Rs
jXs
V1(rated)
V2(rated)
N1
N2
Vb1
Vb2
Zpu
Vb1 V1(rated)
Sb S(rated 1 phase)
Vb2 V2(rated)
I1 pu
I2 pu
Zb1 (Vb1)2/Sb
Zb2 (Vb2)2/Sb
V1 pu
V2 pu
Zpu
Sb
Zpu
Vb1
Vb2
Vb1
Vb2
Zpu RsjXs/Zb1
11
Sb
Rs/a2 jXs/a2
Vb2
Vb1
Zpu
V1(rated)
V2(rated)
I1 pu
I2 pu
N1
N2
Sb
V1 pu
V2 pu
Vb1 V1(rated)
Sb S1(rated)
Vb2 V2(rated)
Zb1 (Vb1)2/Sb
Zb2 (Vb2)2/Sb
Zpu2 Rs/a2 jXs/a2 1/a2(RsjXs)(1/Zb2)
1/a2(RsjXs)(a2/Zb1) Zpu
Zb2 Zb1/a2
11
ZL