Transcript Lecture Notes EEE 360 - Warsaw University of Technology

EEE 360
Energy Conversion and
Transport
George G. Karady & Keith Holbert
Chapter 5
Transformers
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Lecture 10
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Transformers
A) Core type
B) Shell type
Figure 5.22 Single phase transformer construction
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5.3.1 Ideal Transformer
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Transformers
5.3.1 Ideal transformer
•
•
Winding resistances are zero, no leakage inductance and iron loss
Magnetization current generates a flux that induces voltage in both
windings
N p m 
Ep 
Es 
Im
m
2
Ns m 
Ep
Vp
E s = Vs
2
Fig 5.23 Current, voltages and flux
in an unloaded ideal transformer
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Transformers
5.3.1 Ideal transformer
•
Loaded transformer
Im + Ip
Vp
Ep
Is
m
p
s
Es
Vs
Load
Figure 5.24 Currents and fluxes in a loaded ideal transformer
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Transformers
5.3.1 Ideal transformer
•
Turn ratio is:
T
•
Np
Ns

Ep
Es
The input and output complex powers are equal
E p I  S p  S s  Es I
*
p
T
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Ep
Es
*
s
Is

Ip
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Transformers
5.3.1 Ideal transformer
Ip = Is /T
T
Vp
Ep
Is
Es = Vs
Vp = Ep = T Es
Figure 5.25 Equivalent circuit of an ideal transformer
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Transformers
5.3.1 Ideal transformer
•
Transferring impedances through a transformer
VP T VS
2 VS
ZP 

T
IP  IS 
IS
 
T 
IP
Vac
T
VP
Z P  T 2 Z load
IS
VS
Zload
Figure 5.26 Thévenin
equivalents of transformer
circuit
a) Original circuit with ideal
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Transformers
5.3.1.1 Transferring impedances through a
transformer
Figure 5.26 Thévenin equivalents of
transformer circuit
IP
Vac
T2Zload
VP
b) Equivalent circuit when secondary
impedance is transferred to primary side
and ideal transformer eliminated
IS
Vac/T
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VS
Zload
(c) Equivalent circuit when primary source is
transferred to secondary side and ideal
transformer eliminated
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5.3.2 Real transformer
Transformer
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Transformers
5.3.1 Real transformer
m
s_leakage
p_leakage
Figure 5.30 Leakage flux in the real transformer
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Transformers
Xp
Rs
T
Im
Ip
Vp
Ist
Rp
Xm
Rc
Xs
Is
Ep
Es
Vs
Figure 5.31 Equivalent circuit of a real
transformer
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Transformers
Xp
Rp
Im
Ip
Vp
Rst
Xm
Xst
T
Is
Ist
Rc
Ep
Es
Vs
Figure 5.32 Modified equivalent circuit of
a real transformer
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5.3.4 Determination of
transformer parameter by
measurement
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Transformers
5.3.4 Determination of transformer parameter
by measurement
• Open circuit test
– Provides magnetizing reactance and core loss resistance
– Obtain components are connected in parallel
• Short circuit test
– Provides combined leakage reactance and winding
resistance
– Obtain components are connected in series
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Transformers
Short Circuit Test
Figure 5.35
Xp
Rp
Xs
W
Equivalent circuit for
short circuit test,
measurement at the
secondary side
Ish_s
equivalent circuit for
short circuit test
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I
V
Vsh_s
Xp / T2
Figure 5.36 Simplified
Psh_s
Rs
Rp / T2
Xs
Psh_s
Rs
W
Ish_s
I
V
Vsh_s
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Transformers
5.3.1 Short Circuit Test
Xe_s
Primary and
secondary
impedances
are combined
Psh_s
Re_s
W
Ish_s
I
V
Vsh_s
Figure 5.37 Simplified circuit for
calculation of series impedance
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Re _ s 
Xe_s 
Rp
2
 Rs
2
 Xs
T
Xp
T
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Transformers
Short circuit test evaluation
Re_s  
Psh_s
Ish_s
Zsh_s  
2
Vsh_s
Ish_s
2
2
Xe_s  Zsh_s  Re_s
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Transformers
Open circuit test
Po_p
I
Xp
Rp
Xs
Rs
W
Io_p
V
Xm_p
Rc_p
Vo_p
Figure 5.38 Equivalent circuit for open circuit test, measurement at the
primary side.
Po_p
I
Figure 5.39 Simplified
equivalent circuit
W
V
Io_p
Xm_p
Rc_p
Vo_p
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Transformers
Open circuit test evaluation
Rc_p 
Y
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Vo_p 
2
Yo_p  
Po_p
1
1
 2
2
R
X
Io_p
Vo_p
1
Xm _p  
2
Yo_p 
360 Chapter 5 Transformers
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2
Rc_p
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Transformers
Equivalent circuit obtained by measurement
Xe_s
Xm_p
Re_s
Rc_p
Figure 5.40 Equivalent circuit for a real transformer resulting
from the open and short circuit tests.
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Exercises using MAT CAD
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