Copia de transformador.pptaaaaaaaaaaaaaaaa

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1. Transformer
Professor Mohamed A. El-Sharkawi

2. 2
Why do we need transformers?
•Increase voltage of generator output
–Transmit power and low current
–Reduce cost of transmission system
•Adjust voltage to a usable level
•Create electrical isolation
•Match load impedance
•Filters

3. 3
Basic Components
Iron Core
Insulated Copper Wire

4. 4

5. 5

6. 6
i
1 i
2
N
1
e
1
+
_
N
2
e
2
+
_



dte
N
1
dt
d
Ne
1
1
11


dt
d
Ne

22
Primary
Secondary

7. 7


2
1
2
1
2
1
N
N
dt
d
N
dt
d
N
te
te



2
1
2
1
N
N
E
E


2
2
1
1
N
E
N
E


Basic Analysis:Voltage
i
1
i
2
N
1e
1
+
_
N
2 e
2
+
_
•Volts/turn is constant
•Voltages are in phase (no phase shift)
•Magnitudes vary with turns ratio.

8. 8
Basic Analysis: Power and
current
21
SS
*
22
*
11
IEIE
1
2
1
2
*
2
*
1
N
N
E
E
I
I

1
2
2
1
N
N
I
I

2211 ININ
i
1
i
2
N
1e
1
+
_
N
2 e
2
+
_
•Currents are in phase.
•Current ratio is opposite to the voltage ratio

9. 9
Basic Analysis: Reflected impedance
I
1
I
2
E
1
E
2
+
-
+
-
Z
2
N
1
N
2
I
1
E
1
+
-
Z
1
111
222
EIZ
EIZ


2
1
2
1
2
1
2
2
1
1
2
1
2









N
N
N
N
N
N
I
I
E
E
Z
Z
2
1
2
1
2









N
N
Z
Z

10. 10
Ideal Transformer: Ratings
100 MVA, 13.8/138 KV
Apparent Power
Primary VoltageSecondary Voltage
N
2
N
1
+
-
V
1
I
1 I
2
+
-
V
2

11. 11
Ideal Transformer: Ratings
100 MVA, 138/13.8 KV
MVAIVIVS 100
2211

A 725
kV 138
MVA 100
1
1

V
S
I
A 7250
kV 13.8
MVA 100
2
2 
V
S
I
10
kV 13.8
kV 381
2
1
2
1

N
N
V
V
N
2
N
1
+
-
V
1
I
1 I
2
+
-
V
2

12. 12
Actual Transformer
•Windings:
–Resistance
–Inductance
•Core:
–Eddy Current
–Hysteresis
i
1
i
2
N
1e
1
+
_
N
2 e
2
+
_

13. 13
R
1
X
1
N
1 N
2
R
2 X
2
Ideal Transformer
Windings Impedance

14. 14
Core Hysteresis
B
H
i
N
e
+
_
dtefB

ifH

15. 15
i

e

16. 16
Core Model
e
i
R
Let
tEe sin
max

t
E
dte 

cos
max

t
R
E
R
e
i sin
max

i

e

17. 17
Core Model
Let
tEe sin
max

t
E
dte 

cos
max

t
L
E
dte
L
i
dt
di
Le


cos
1
max



i

e
i
e X
l

18. 18
e
i
R X
l
i

e
i

e

19. 19
R
o
X
o
R
1
X
1 R
2
X
2
V
1
I
1
I
o
'
2I
I
2
V
2
E
1 E
2
N
1N
2
Equivalent Circuit
2
1
2
1
2
1
V
V
N
N
E
E

2
1
1
2
2
'
2
I
I
N
N
I
I
