The Practical Transformer
Ideal transformer:
 Lossless core
 Infinitely permeable core
∞
Practical transformer
Practical transformer is an ideal transformer with practical core:
Two circuit elements are introduced





Rm represents iron losses
Current in Rm is in phase with E1 (If)
Xm is measure of permeability of the core
Current in Xm lags E1 by 90o (Im)
Im is the magnetizing current needed to establish the flux φm
An imperfect core represented by a reactance Xm and a resistance Rm
Phasor diagram of a practical transformer at no-load
Io is the sum of If and Im and is called exciting current.
Primary and Secondary Leakage Reactance
Transformer with infinitely permeable core at no-load
Mutual fluxes and leakage fluxes produced by a transformer under load
The leakage fluxes are due to the imperfect coupling between the coils
Separating the various induced voltages due to the mutual flux and the leakage
fluxes
Voltages Ef1 and Ef2 induced by leakage fluxes φf1 and φf2
4.44
∅
4.44
∅
Voltages Ef1 and Ef2 are equivalent to voltage drop across leakage reactances:
Equivalent circuit of practical transformer:
Complete equivalent circuit of a practical transformer
Simplifying Equivalent Circuit
At no-load condition
Complete equivalent circuit of a transformer at no-load

=0 ⇒
0
 Only Io flows in

and
and
are small impedances ⇒ their voltage drop is negligible
Simplified circuit at no-load
At full-load condition:
is much larger than
⇒
can be neglected.
Simplified equivalent circuit of a transformer at full-load
If we shift all impedances to primary side:
Equivalent circuit with impedances shifted to the primary side
Voltage Regulation
With fixed primary voltage at rated value,
Voltage Regulation
100
Where
is secondary voltage at no-load
is secondary voltage at full-load
Measuring Transformer Impedances
Open Circuit Test
Rated voltage is applied to primary side.
Open-circuit test and determination of Rm, Xm, and turns ratio
Measured quantities:

 Active power
 Primary voltage
 Secondary voltage
Calculated quantities:
 Active power =
 Apparent power
= core losses
 Reactive power


 Turns ratio
Short Circuit Test
Small voltage,
(< 5% of rated voltage) is applied to primary.
Short-circuit test to determine leakage resistance and winding resistance
Measured quantities:
,
&
on primary side
Calculated quantities:
Transformer Phasor-diagram
Non-ideal transformer equivalent circuit:
With secondary impedances referred to the primary side:
Steps:
Draw
&
Add voltage components
Draw
in phase with
Draw
that lags
&
, where
by 90 , where
Ip X1
VP
If
aIs X2
Is /a
Im
Ip R1
E1
I0
aEs
aIs R2
Is
IP
Non-ideal transformer phasor diagram
Useful Definitions:
of a transformer:
% Impedance of a transformer:
%