Transcript transformer 1

POWER CIRCUIT &
ELECTROMAGNETICS
EET 221
Transformer
Introduction
A transformer is a device that changes ac electric energy at one voltage
level to ac electric energy at another voltage level through the action of
a magnetic field.
The most important tasks performed by transformers are:
•
•
•
changing voltage and current levels in electric power systems.
matching source and load impedances for maximum power transfer
in electronic and control circuitry.
electrical isolation (isolating one circuit from another or isolating dc
while maintaining ac continuity between two circuits).
It consists of two or more coils of wire wrapped around a common
ferromagnetic core. One of the transformer windings is connected to a
source of ac electric power – is called primary winding and the second
transformer winding supplies electric power to loads – is called secondary
winding.
Ideal Transformer
An ideal transformer is a lossless device with an input winding and
output winding.
v p (t )
v s (t )

i p (t )
Np
Ns
1

i s (t ) a
Sp
SS
1
lossless
a
N p i p ( t )  N s is ( t )
a = turns ratio of
the transformer
Power in ideal transformer
Pout  Pin  V p I p cos
Qout  Qin  V p I p sin 
S out  S in  V p I p sin 
Where  is the angle between voltage and current
Impedance transformation through the
transformer
The impedance of a device – the ratio of the phasor voltage across it in
the phasor current flowing through it:
ZL
VL

IL
Z L'  a2Z L
The equivalent circuit of a transformer
The major items to be considered in the construction of such a model are:
•
Copper (I2R) losses: Copper losses are the resistive heating in the primary
and secondary windings of the transformer. They are proportional to the
square of the current in the windings.
•
Eddy current losses: Eddy current losses are resistive heating losses in the
core of the transformer. They are proportional to the square of the voltage
applied to the transformer.
•
Hysteresis losses: Hysteresis losses are associated with the arrangement
of the magnetic domain in the core during each half cycle. They are
complex, nonlinear function of the voltage applied to the transformer.
•
Leakage flux: The fluxes ΦLP and ΦLS which escape the core and pass
through only one of the transformer windings are leakage fluxes. These
escaped fluxes produce a self inductance in the primary and secondary
coils, and the effects of this inductance must be accounted for.
Nonideal or actual transformer
Mutual flux
Nonideal or actual transformer
Nonideal or actual transformer
Transformer equivalent circuit, with secondary impedances referred to the
primary side
Ep = primary induced voltage
Vp = primary terminal voltage
Ip = primary current
Ie = excitation current
XM = magnetizing reactance
RC = core resistance
Rs = resistance of the secondary winding
Xs = secondary leakage reactance
Es = secondary induced voltage
Vs = secondary terminal voltage
Is = secondary current
IM = magnetizing current
IC = core current
Rp = resistance of primary winding
Xp = primary leakage reactance
Nonideal or actual transformer
Transformer equivalent circuit
Dot convention
1. If the primary voltage is positive at the dotted end of the winding with
respect to the undotted end, then the secondary voltage will be
positive at the dotted end also. Voltage polarities are the same with
respect to the dots on each side of the core.
2. If the primary current of the transformer flows into the dotted end of
the primary winding, the secondary current will flow out of the dotted
end of the secondary winding.
Exact equivalent circuit the actual transformer
a) The transformer model referred to primary side
b) The transformer model referred to secondary side
Approximate equivalent circuit the actual
transformer
a) The transformer model referred to primary side
b) The transformer model referred to secondary side
Exact equivalent circuit of a transformer
Ep = primary induced voltage
Vp = primary terminal voltage
Ip = primary current
Ie = excitation current
XM = magnetizing reactance
RC = core resistance
Rs = resistance of the secondary winding
Xs = secondary leakage reactance
Es = secondary induced voltage
Vs = secondary terminal voltage
Is = secondary current
IM = magnetizing current
IC = core current
Rp = resistance of primary winding
Xp = primary leakage reactance
Primary side
Secondary side
I p  Ie  Is / a
ES  I s ( Rs  jX s )  Vs
Ie  IC  I M
Vs  I s Z L
V p  I p ( R p  jX p )  E p
E p  I C RC
E p  I M ( jX M )
E p  I e ( RC // jX M )
Vp
Ep
Is N p
a



Vs Es I p N s
Exact equivalent circuit of a transformer referred to
primary side
Rp
Ip
a2Xs
Xp
Is/a
a2Rs
Ie
Vp
Ep
aVs
Exact equivalent circuit of a transformer referred to
secondary side
Rp/a2
aIp
Xp/a2
Rs
Is
Xs
aIe
Vp/a
aIc
Rc/a2
aIm
Ep/a = Es
XM/a2
Vs
Example
A single phase power system consists of a 480V 60Hz
generator supplying a load Zload=4+j3W through a
transmission line ZLine=0.18+j0.24W. Answer the following
question about the system.
a) If the power system is exactly as described above ,
what will be the voltage at the load be? What will the
transmission line losses be?
b) Suppose a 1:10 step-up transformer is placed at the
generator end of the transmission line and a 10:1 step
down transformer is placed at the load end of the line.
What will the load voltage be now? What will the
transmission line losses be now?
Example
ILine
ZLoad=0.18+j0.24W
IG
ILoad
+
VLoad
V=48000V
ZLoad=4+j3W
(a)
T1 ILine
IG
1:10
T2
ILoad
ZLine=0.18+j0.24W
+
10:1
V=48000V
VLoad
(b)
-