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Lab 2
Power Transformers
Objectives
 To understand the voltage-current relationships of an ideal transformer.
 To understand how to refer impedances through an ideal transformer.
 To perform the open-circuit and short-circuit tests to obtain the physical model of the transformer.
Background Theory
Voltage and Current Relationships
An electrical transformer is constructed from copper windings around an iron core. Generally, there are two layers of
windings; one for the primary winding with N 1 turns of wire, and one for the secondary winding with N 2 turns. The
schematic symbol for the ideal transformer is show in Figure 2.1.
+
V1
I1
I2
N1
N2
-
+
V2
-
Figure 2.1 Ideal Transformer
For the ideal transformer, the primary and secondary voltages are related to the number of turns on the primary and
secondary windings:
V1
N
 1
V2 N 2
(2.1)
The primary and secondary currents have the inverse relationship:
I1 N 2

I2
N1
(2.2)
Impedance Referral
If an impedance Z2 is connected across the secondary winding of a transformer, it may be expressed as the ratio of
secondary voltage to secondary current:
Z2 
V2
I2
With Equations 2.1, 2.2, and 2.3, the ratio of primary voltage to primary current is written as
5.1
(2.3)
6
V1  N1

I1  N 2
2

 Z 2

(2.4)
Equation 2.4 reveals that the secondary impedance appears as a modified impedance on the primary side. Circuit
analysis is facilitated when the secondary impedance is referred to the primary side and the ideal transformer is
eliminated from the circuit. This procedure is illustrated in Figure 2.2.
a
a
2
Z' = (N1/N2) Z
Z
b
b
Figure 2.2 Secondary impedance referred to the primary.
Physical Transformers
The ideal transformer is lossless: all energy is transferred through the device. Physical transformers, however, have
internal inductances and resistances that result in power dissipation and lower secondary voltages. The physical
transformer model, shown in Figure 2.3, is approximated as an ideal transformer with series and parallel passive circuit
elements.
Figure 2.3 Physical Transformer Circuit
The magnetizing elements, Lm and Rm, are due to the current drawn by the transformer without a load connected to
the secondary. The magnetizing inductance draws the current that is necessary to sustain the magnetic field in the
core. The magnetizing resistance models the losses due to currents induced in the core. Since the magnetizing
elements cause losses in the iron core, they are often referred to as “iron losses”. The series element Rs, models the
copper losses, the resistive losses in the copper coils. The series element Ls, models the leakage inductance,
corresponding to the small fraction of the flux generated by the primary coil which is not coupled through the core to
the secondary windings (leakage flux). The values of these elements are determined by the open circuit and short
circuit tests of the physical transformer.
7
Short-circuit Test
In the short circuit test, the terminals of the secondary winding are shorted together. The secondary and primary
voltages in the ideal transformer of the model are therefore zero. Because of the short circuit, a very small source
voltage on the primary is sufficient to cause rated current to flow through the transformer windings.
Figure 2.4 Effect of secondary short circuit
Thus, the average power delivered by the source is contained in the series resistance
P  I s2 Rs
(2.5)
and reactive power is contained in the series reactance:
Q  I s2 X s
(2.6)
Open Circuit Test
In the open circuit test, the secondary winding is unconnected. Hence, the primary and secondary currents in the ideal
transformer of the model are zero. In order to compute the values of Xm and Rm, we must represent the parallel
elements as a series circuit . . .
Figure 2.5a Represent core effects as Series circuit
And sum impedances:
Figure 2.5b Combining Impedances
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We can now compute Xss and Rss as before:
P  I s2 Rss
(2.7)
Q  I s2 X ss
(2.8)
Using the values of Rs and Xs from the short circuit test, Rm and Xm may be computed.
Since Ls represents leakage flux, coupling coefficient k can be computed using
k
X m
X ss
(2.9)
Laboratory Procedure
Turns Ratio
Determine the nominal turns ratio of each primary winding (105, 115, 125 V) with each secondary winding (6, 12, 18,
24 V) on the Todd Systems transformer.
Connect the adjustable AC supply and the transformer as shown in Figure 2.6. Apply rated voltage (105 V) to the 105V
primary of the transformer and measure the RMS voltage at each secondary tap. Repeat the same procedure and
measurements with the 115V and 125 V primaries. Calculate all the available turns ratios with the measured primary
and secondary voltages.
Hampdon
Power Supply
0 - 135 VAC
105, 115, or 125
6, 12, 18, or 24
Todd Systems
Transformer
C
Figure 2.6 Circuit for Measuring Tap Voltages
Short-Circuit Test: Measurement of Winding Losses
With the AC power supply turned off, connect the 50 mV, 50 A shunt (0.001 ohm) across the 24 V secondary as shown
in Figure 2.7. Bring up the voltage slowly until 25 mVAC appears across the shunt as measured by the DMM,
corresponding to the rated transformer secondary current of 25 A. Measure the real and apparent powers again, along
with the source voltage. With these measurements, calculate the reactive power and the series resistance, the series
reactance, and the series inductance.
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Power Analyzer
A
BLK
YEL
Hampdon
Power Supply
0 - 135 VAC
125
Todd Systems
Transformer
24
Shunt
YEL
V
C
0
BLK
10 AWG wire
Figure 2.7 Short Circuit Test
Open Circuit Test: Measurement of Core Losses
Connect the variable AC supply and the power analyzer to the transformer as shown in Figure 2.8. Measure the real
and apparent powers with rated voltage applied. With these measurements, calculate the reactive power, the
magnetizing resistance, the magnetizing reactance, and the magnetizing inductance.
Power Analyzer
YEL
A
BLK
YEL
Hampdon
Power Supply
0 - 135 VAC
125
V
Todd Systems
Transformer
C
BLK
Figure 2.8 Open Circuit Test
THE LAB WRITE UP SHOULD CONFORM TO DEPARTMENTAL STANDARDS AS DESCRIBED IN THE
GUIDELINES FOR LABORATORY REPORTS. INCLUDE THE FOLLOWING :

Draw the equivalent circuit model of the 125/24 transformer with all resistances and inductances labeled
with their calculated values.

Diagrams

Measurements

Calculations