electric power transformers
TRANSCRIPT
Electric Power Transformers
Some Images
Core-Type and Shell-Type• In practice, the primary
and secondary windings are wrapped one on top of the other.
• Transformer symbol (note the polarity markings)
Ideal Transformer
• No copper resistance• No core loss• No leakage flux• Infinite core permeability
(i.e., zero reluctance, and infinite inductance)
aNN
VV
s
p
s
p ==
aNN
II
p
s
s
p 1==
sp
windingssppsp
sp
sp
ZaZ
SIVIVSS
PP
2=
====
=
=
Practical Transformer• A practical transformer has
– Copper resistance– Leakage flux– Finite core permeability
(i.e., finite inductance)– Core loss
• Equivalent circuit model
Simplified Transformer Model
Model referred to primary side (r.t.p.)
Model referred to secondary side (r.t.s)
Approximate Transformer Model
Approximate model referred to primary side (r.t.p)
Approximate model referred to secondary side (r.t.s)
Simplest Transformer Model
Simplest model referred to primary side (r.t.p)
Simplest model referred to secondary side (r.t.s)
Determining the parameters of the transformer model
• Open circuit test (OCT): Apply rated voltage
PVR
QVXPSQVIS cm
2222 ==−==
Determining the parameters of the transformer model
• Short circuit test (SCT): Apply low voltage
2,2,22
IPR
IQXPSQVIS peqpeq ==−==
Per-Unit (pu) System
• Definition:• Common known bases: Vbase and Sbase
• Advantages of pu system:– Eliminates explicit voltage conversion at
every transformer,– pu impedance of a transformer r.t.p or
r.t.s is the same.– pu values fall within very narrow ranges
.,,,,,, ZIVSQPKKKK
base
actualpu ==
base
base
base
basebase
base
basebasebasebasebase S
VI
VZVSISQP
2,, =====⇒
Voltage Regulation
• Because of the transformer series impedance, the secondary voltage varies with the load (when the primary voltage is fixed).
• Phasor diagram:
%100*%100*,
,
,
,,
fls
flsp
fls
flsnls
V
VaV
VVV
VR−
=−
=
seqseqsp IjXIRVa
V++=
Transformer Efficiency
• Efficiency,
• Copper Loss,
• Core Loss,
%100*coscos%100*
)(%100*
ppp
sss
corecuout
out
in
out
IVIV
PPPP
PP
θθη =
++==
seqscu RIP ,2=
c
p
c
p
core RV
aRa
VP
2
2
2
/
)(==
Auto-Transformer• Used when changing the
voltage by small amounts.• No isolation between
primary and secondary sides.
cse
c
H
L
NNN
VV
+=
c
cse
H
L
NNN
II +
=
LLLHHHio IVSIVSS ====
seseccwinding IVIVS ==
se
cse
winding
io
NNN
SS +
=
3-Phase Transformers
• Three independent single-phase transformers
• Three-phase transformer wound on a single three-legged core.
• Possible connections:– Wye-Wye– Wye-Delta– Delta-Wye– Delta-Delta
Wye-Delta and Wye-Wye Connections
aVV
VV
S
P
LS
LP ==φ
φ
33
aVV
VV
S
P
LS
LP 33
==φ
φ
Per-Unit (pu) System in 3-Phase Circuits
• Definition:• Common known bases: VL,base and S3Ф,base
.,,,,,, ZIVSQPKKKK
base
actualpu ==
base
baseL
base
basebase
baseL
basebase
basebasebase
SV
IVZ
VSI
SQP
,3
2,,1
,
,3
,3,3,3
,3
,
φ
φ
φ
φφφ
==
=
==⇒
Transformer Ratings (V, f, S)• Voltage and frequency
ratings:– Prevents winding insulation
from breakdown,– Avoids operation in the deep
saturation region.– Reduction in supply
frequency also causes excessive magnetizing current.
• Apparent power rating sets the limits on the current flow (which controls transformer heating).
Homework
• Problems from Chapter 3: 5, 6, 7, 8, 12, 14, 18, 22.