Chapter 5
Transformer
Part 2
Prepared by Dr. Mohd Azrik Bin Roslan
What you should know at the end of
this chapter
What is transformer
Mutual inductance
Ideal transformer
Non-ideal transformer
Open circuit test
Short circuit test
Per unit system
Autotransformer
3-phase transformer
Application of transformer
Transformer model parameters
It is possible to experimentally determine the
values of the inductances and resistances in
the transformer model
An adequate approximation of these values
can be obtained with only two tests
 the open-circuit test
 the short-circuit test
Open circuit test
 Conducted to determine Rc and XM
 Obtained components are connected in parallel
 One transformer winding is open-circuited, and the other
winding is connected to full rated line voltage
 The input voltage, input current, and input power to the
transformer are measured. (This measurement is normally
done on the low~voltage side of the transformer, since
lower voltages are easier to work with.)
Open circuit test
 All the input current must be flowing through the excitation
branch of the transformer.
 The series elements , Rp and Xp are too small in comparison
to Rc and XM to cause a significant voltage drop, so
essentially all the input voltage is dropped across the
excitation branch.
 From this information, it is possible to determine the power
factor of the input current and therefore both the magnitude
and the angle of the excitation impedance.
Open circuit test
Admittance
Yo c
I oc

Vo c
Open circuit Power Factor
Poc
PF  cos  
Voc I oc
R  Resistance
X  Reactance
Z  Impedance
1
Y 
 G  jB  Admittance
Z
G  Conductance
B  Susceptance
Open circuit Power Factor Angle
  cos
1
Poc
Voc I oc
I oc
1
1
Yoc      GC  jBM   j
Voc
RC
XM
Short circuit test
 Conducted to determine combined leakage reactance and
winding resistance
 Obtained components are connected in series
 Low-voltage terminals of the transformer are short-circuited,
and the high-voltage terminals are connected to a variable
voltage source (This measurement is normally done on the
high-voltage side of the transformer, since currents will be
lower on that side, and lower currents are easier to work
with.)
Short circuit test
 The input voltage is adjusted until the current in the short
circuited windings is equal to its rated value
 The input voltage, current, and power are measured.
 Since the input voltage is so low during the short-circuit test,
negligible current flows through the excitation branch
 If the excitation current is ignored, then all the voltage drop
in the transformer can be attributed to the series elements
in the circuit.
Short circuit test
Impedances referred to the primary side
Psc
PF  cos  
Vsc I sc
Power Factor of the current
Angle Power Factor
Therefore
Z sc
Vsc

I sc
Psc
  cos
Vsc I sc
1
Vsc 00
Vsc
0
Z sc 


0
I sc   
I sc

 
Z sc  Req  jX eq  R p  a 2 Rs  j X p  a 2 X s

Voltage regulation (VR)
 Because a real transformer has series impedances within it,
the output voltage of a transformer varies with the load
even if the input voltage remains constant.
 The voltage regulation of a transformer is defined as the
change in the magnitude of the secondary voltage as the
current changes from full load to no load with the primary
held fixed.
VR 
Vs ,nl  Vs , fl
Vs , fl
Vs 
At no load,
Vp
VR  a
X 100%
Req s
jX eq s
Is
Vp
a
Vp
 Vs , fl
Vs , fl
aI p
a
X 100%
Vs
Voltage regulation (VR)
Lagging PF
Vp
 Vs
a
so VR  0
Unity PF
Vp
 Vs
a
so VR  0
Leading PF
Vp
 Vs
a
so VR  0
Transformer Efficiency
Transformers are also compared and judged
on their efficiencies.
The efficiency of a device is defined by the
equation
Pout

100%
Pin

Pout
Pout   P losses
X 100%
Transformer Efficiency
There are three types of losses present in
transformers
 Copper (I2R) losses. These losses are accounted
for by the series resistance (Rp and Rs) in the
equivalent circuit.
 Hysteresis losses. These losses are included in
resistor Rc.
 Eddy current losses. These losses are also
included in resistor Rc.
Output power is given by Pout  Vs I s cos 
so
Vs I s cos 

X 100%
Vs I s cos   Pcu  Pcore
Pcu  Pcopper losses
Pcore  Peddy current  Physterisis
Example 5
The equivalent circuit impedances of a 20-kVA, 8000/240 V, 60Hz transformer are to be determined. The open-circuit test was
performed on the secondary side of the transformer (to reduce
the maximum voltage to be measured) and the short circuit test
were performed on the primary side of the transformer (to reduce
the maximum (current to be measured). The following data were
taken:
POC
Find the impedances of the approximate equivalent circuit
referred to the primary side, and sketch that circuit.
Example 5
Example 5
Example 5
Example 6
Example 6
S
S
Example 6
Example 6
Example 6
Per unit system
The per unit value of any quantity is defined as
Actual Quantity
Per Unit, pu 
Base value of quantity
Quantity – may be power, voltage, current or
impedance
Per unit system
In normal practice Sbase and Vbase are defined
Then the other base value can be determined
Sbase
I base 
Vbase
Pbase ,Qbase , Sbase  VbaseI base
Zbase
Vbase Vbase 2


I base Sbase
Ybase
I base

Vbase
Example 7 : Per Unit System
Example 7 : Per Unit System
Example 7 : Per Unit System
Example 7 : Per Unit System
Example 7 : Per Unit System
Example 7 : Per Unit System
Autotransformer
On some occasions it is desirable to change voltage
levels by only a small amount.
 110 V  120 V
 13.2 kV  13.8 kV
These small rises may be made necessary by voltage
drops that occur in power systems a long way from the
generators.
In such case, it is wasteful and excessively expensive
to wind a transformer with two full windings, each
rated at about the same voltage.
A special-purpose transformer, called an
autotransformer is used instead. Both the primary and
the secondary are in a single winding.
Autotransformer
Conventional transformer
Autotransformer
Autotransformer
Step-up autotransformer
 the first winding is shown connected in an additive manner
to the second winding.
 the voltage at the output of the whole
transformer is the sum of the voltage on
the first winding and the voltage on
the second winding.
 The first winding here is called
the common winding.
 The smaller winding is called
the series winding
Autotransformer
Step-down autotransformer
 the voltage at the input is the sum of the voltages on the
series winding and the common winding.
 the voltage at the output is just the voltage on the
common winding.
Autotransformer
Because the transformer coils are physically
connected, a different terminology is used for
the autotransformer than for other types of
transformers.
 The voltage on the common coil is called the
common voltage Vc and the current in that coil is
called the common current Ic.
 The voltage on the series coil is called the series
voltage VSE and the current in that coil is called the
series current ISE.
 Voltage and current on the low-voltage side of the
transformer are called VL and IL respectively
 Voltage and current on the high-voltage side of the
transformer are called VH and IH respectively
Autotransformer
Voltage and current relationship
VC
NC

VSE N SE
VL  VC
I L  IC  I SE
I SE NC

I C N SE
VH  VC  VSE
I H  I SE
NC
VL I H


VH I L NC  N SE
Autotransformer
Input apparent power is equal to output apparent power for an
ideal autotransformer:
Sin  VL I L
Sout  VH I H
Sin  Sout  SIO
The apparent power in transformer winding:
Sw  VC IC  VSE I SE
The ratio of apparent power in the
primary and secondary of the
autotransformer to the apparent
power actually travelling through
Its winding is
S IO NC  N SE

SW
N SE
Apparent power rating advantage of an autotransformer over a
conventional transformer. The apparent power that actually travelling
through the transformer’s winding is less than the apparent power
entering the primary and leaving the secondary of the transformer.
Three phase transformer
3-phase transformer connections
 Wye-wye (Y-Y)
 Wye-delta (Y-∆)
 Delta-wye (∆-Y)
 Delta-delta (∆ -∆)
N p1
Vp1
I s1


a
N s1 Vs1 I p1
N p2
Ns2
N p3
Vp 2
Is2


a
Vs 2 I p 2
Vp 3
I s3


a
N s 3 Vs 3 I p 3
Phase
1
2
3
Primary phase
voltage
Vp1
Vp2 Vp3
Secondary
phase voltage
Vs1
Vs2
Vs3
Primary phase
current
Ip1
Ip2
Ip3
Secondary
phase current
Is1
Is2
Is3
Primary turns
Np1
Ns1
Np2 Np3
Ns2 Ns3
Secondary
turns
Three phase transformer
Wye-wye
(Y-Y)
Three phase transformer
Wye-delta
(Y-∆)
Three phase transformer
Delta-wye
(∆-Y)
Three phase transformer
Delta-delta
(∆ -∆)