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Transformer Voltage Regulation
Fact: As the load current is increased, the voltage (usually) drops.
Transformer voltage regulation is defined as:
VR 
Vs ,nl  Vs , fl
Vs , fl
Other useful formulas
VR 
VP / a  Vs , fl
Vs , fl
VR 
Vs ,nl  Vs , fl
VR 
Vs , fl
VP  Vs , fl
Vs , fl
Prefer small VR
For an ideal transformer : VR=0
Note: If there were only resistive loads, the VR would
not be much large in real transformers, but because loads
normally have different power factors, VR may be
considerably large in real transformers.
VR in real transformers
VR 
VP / a  Vs , fl
Vs , fl
V P / a  V s  Req . I s  jX eq . I s
V P / a  V s  Req . I s  jX eq . I s
At unity power factor
Resistive load
At lagging power factor
Inductive load
At leading power factor
Capacitive load
Transformer Taps
The voltage in a distribution line is not constant.
It may be 1.05 p.u. at generator terminal and 0.95 at the
load side.
Depending on the place the transformer is used, we may
need to adjust the transformer ratio to get similar load
voltage. That’s why we need Tap
In Tap Changing
Under Load (TCUL)
transformer, the tap
changes automatically
to keep the output
voltage constant
Current Inrush
If a transformer is switched to a system, there may be
some current with large magnitude (Current Inrush), in the
first few milliseconds after the switch is closed.
The reason behind the current inrush is transient
Transients
Transient in electrical systems
is the severe changes in
current and voltage after a
switch is closed or opened
Vm
e  Vm . cos t   
. sin t
N .
Special Transformers
-Instrument Transformers
-Autotransformers
Instrument Transformers
Power Transformers (PT)
Current Transformers (CT)
We need voltage and current samples for:
-measurement (voltmeters, ammeters, wattmeters, scopes)
-Protection
-Control
In instrument transformers, accuracy is very important.
In their design they do their best to make it as close as
possible to ideal transformers.
Accuracy is important in magnitude and phase.
They make it shell type to reduce the flux leakage
Power Transformers (PT)
Specially wound transformer with a high-voltage
primary and low-voltage secondary (0-120 V), very
low power rating, almost no load.
Insulation on high voltage is very important.
Thousands of turns of very thin conductors.
Current Transformers (CT)
Reduces the line current to a safe (measurable) level (0-5 A)
The secondary should be connected to an instrument or short-circuited
Autotransformers
This form of transformers are more economical if
the voltage level of the primary and the secondary
is almost the same. For example if we want to
change the voltage from 110 to 120 or 13.2 kV to
13.8 kV.
Conventional Transformer
Step-up autotransformer
Step-down autotransformer
New terminology in autotransformers:
Common coil : The coil common in the primary and secondary
Series coil : The coil in series with the common coil
We write the equation based on the voltages and current
in the common coil and series coil. These relations can
be used for both cases (step-up and step-down)
It is easy to prove (assuming ideal transformer)
VL
NC

,
VH N C  N SE
I L N C  N SE

IH
NC
An autotransformer to get a adjustable magnitude
sinusoid voltage from zero to nominal value
(the one in the lab)
Apparent Power Advantage of Autotransformers
Remember, we emphasized that a transformer designed
for a particular voltage and apparent rating can not be
easily used for other ratings
Now we show that if a transformer designed to work
for a particular ratings, is reconnected to work as an
autotransformer, it can handle much more apparent
power
Let’s define
Winding apparent power
Input-output apparent power
In conventional transformers
SW  IW .VW
S IO  VP . I P  Vs . I s
S IO  SW
But in autotransformers:
SW  I C .VC  I SE .VSE
S IO  VL . I L  VH . I H
SW  I C .VC  VL .( I L  I H )  VL . I L  VL I H
NC
N SE
 VL . I L  VL I L .
 VL I L .
N SE  N C
N SE  N C
N SE
S IO N SE  N C
 S IO .


N SE  N C
SW
N SE
The autotransformer can handle more apparent power specially
when the series windings is small. The closer the two voltages
are the greater the autotransformer power advantage
The disadvantage of increased apparent power is that the
parameters of transformer is decreased in p.u. values. This
will cause higher currents during faults in power systems
Example: