SLOVAK UNIVERSITY OF TECHNOLOGY
Faculty of Material Science and Technology in Trnava
ELECTRICAL ENGINEERING AND
ELECTRONICS
Laboratory exercises
Róbert Riedlmajer
TRNAVA 2007
ELECTRICAL ENGINEERING AND ELECTRONICS
Laboratory exercise 10 - Transformer measurements.
Introduction
Figure 1 shows the transformer schematic symbol and
the corresponding commonly used Steinmetz model is
shown in Figure 2. Therein, the model voltage and
current phasors are defined as:
Vˆ1
Iˆ
1
I2
N1 N2
+
+
Primary side voltage (V)
V1
V2
Primary side current (A)
-
-
Vˆ2'
Iˆ '
Referred secondary side current (A)
Iˆφ
Magnetizing current (A)
2
I1
Referred secondary side voltage (V)
Figure 1. Transformer symbol.
The model parameters are:
R1
Xl1
Rc
Xm
R2'
Xl2'
N1/N2
Primary coil resistance (Ω)
Primary coil leakage reactance (H)
Core loss resistance (Ω)
Core magnetizing reactance (Ω)
Referred secondary coil resistance (Ω)
Referred secondary coil leakage reactance (H)
Transformer turns ratio
I1
+
V1
R1
Xl1
X'l2
R'2
I'2
+
Iφ
Xm
V2
-
-
Figure 2. Steinmetz model of a transformer.
Note that this Steinmetz model utilizes the referred secondary quantities related to the
physical quantities by
N 
Vˆ2' =  1 Vˆ2
 N2 
(1)
N 
Iˆ2' =  2  Iˆ2
 N1 
(2)
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ELECTRICAL ENGINEERING AND ELECTRONICS
2
N 
R2' =  1  R2
 N2 
(3)
2
N 
X l 2' =  1  X l 2
 N2 
(4)
Furthermore, this Steinmetz model can be augmented with a core loss term Rc in parallel
with Xm that approximately accounts for the hysteresis and eddy current losses.
Determining resistance
The resistance parameters R1 and R2 can be found by applying DC voltage to the
respective windings. For example, if a DC voltage is applied to the primary winding, the
Steinmetz model predicts the equivalent circuit shown in Figure 3. The primary
resistance can then be determined by
R1 =
VDC
I DC
(5)
The same procedure can be used to find the secondary resistance R2. Note that the turns
ratio is needed to refer this resistance to the primary. This is usually given by the
transformer manufacturer.
R1
Idc
+
Vdc
Figure 3. Steinmetz model DC test.
Reactances
If the secondary of the transformer is short-circuited, the equivalent circuit can be
approximated as shown in Figure 4. In this case, the magnetizing impedance is
assumed to be much larger than the secondary resistance and leakage impedance. This
is typically a good assumption for practical transformer designs. From the voltage,
current, and power measurements, the magnitude and angle of the short-circuit
impedance can be determined as
VAsc = Vˆsc Iˆsc
(6)
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ELECTRICAL ENGINEERING AND ELECTRONICS
Z sc =
Vˆsc
(7)
Iˆsc
 P 
∠Z sc = cos −1  sc 
 VAsc 
R1
Isc
Xl1
X'l2
(8)
R'2
+
Vsc
Zsc
Figure 4. Approximated Steinmetz model for short-circuti test.
From the imaginary part of this impedance, the sum of the primary and secondary
leakage reactances can be found. In particular,
X l1 + X l 2' = Im{Z sc }
(9)
The individual leakage reactances can be determined if it is assumed that
X l1 = X l 2'
(10)
Although it is possible to perform other tests on the transformer to determine a more
exact relationship between Xl1 and Xl2', (10) is a good approximation. An alternate
method of determining the leakage reactances is to set (7) equal to the short-circuit
impedance magnitude which can be written as
Z sc =
(Rl1 + Rl 2' ) 2 + ( X l1 + X l 2' ) 2
(11)
Using (11) along with the resistances, the sum of Xl1 and Xl2' can be determined. This
method is convenient when watt-meters are not accessible.
The next test involves open-circuiting the secondary winding and applying rated voltage
to the primary winding. Under this condition, the Steinmetz equivalent circuit,
including the core loss term, reduces to that shown in Figure 5. As can be seen, the
open-circuit impedance is
VAoc = Vˆoc Iˆoc
(12)
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ELECTRICAL ENGINEERING AND ELECTRONICS
Z oc =
Vˆoc
(13)
Iˆoc
P 
∠Z oc = cos −1  oc 
 S oc 
Ioc
R1
(14)
Xl1
+
Voc
Rc
Xm
Figure 5. Steinmetz model for open-circuit test.
Using the measured open-circuit impedance as well as R1 and Xl1, the core admittance
can be determined by
Yc =
1
Z oc − (R1 + jX l1 )
(15)
Using this admittance, the magnetizing reactance and core loss resistance can be found
from
Xm =
−1
Im{Yc }
(16)
Rc =
1
Re{Yc }
(17)
An alternate method for determining Xm is to set the magnitude of the measured opencircuit impedance equal to
Z oc = R12 + ( X l1 + X m )
2
(18)
This method does not require measurement of power. However, there is not enough
information to calculate the core loss resistance.
Activity:
Experimental determination of all elements in the transformer equivalent circuit
involves three tests:
• measurement of the primary resistance
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ELECTRICAL ENGINEERING AND ELECTRONICS
• open-circuit test
• short circuit test
The laboratory transformer has the ratings listed in Table I. From the voltage ratings, it
can be seen that the turns ratio is N1/N2 = 2.
Table I. Transformer parameters: S=1kVA
Vˆ1 = 240 V
Vˆ2 = 120 V
Iˆ1 = 4.54 A
Iˆ2 = 9.08 A
DC Resistance Test
Connect the transformer as shown in Figure 6. In this case, a DC power supply with a
current limit is used to supply the primary winding. Increase the DC voltage until the
primary current is equal to the rated RMS current (2A). Record values of VDC and IDC
for calculation of R1. Perform the same DC test on the secondary coil to find R2.
H1
DC Supply
Power Supply
(Set to 2A)
X1
+
Vdc V
-
Single Phase
Transformer
H4
X2
Figure 6. Laboratory setup for transformer DC test.
Short-Circuit Test
The short-circuit test is used to determine the total winding resistance and leakage
inductance losses in the windings at full-load current. In this test, one pair of terminals
is short-circuited while the voltage of the other winding is raised until full load current
flows in the short-circuited, and the voltage, current, and power input are recorded. The
voltage that is required for the full-load current in the short-circuit test is determined by
the low impedance of the windings and should be equal to 5% of the rated voltage of the
winding.
Using two phases of the AC source panel and a resistance from the load panel, connect
the transformer as shown in Figure 7. Increase the voltage applied to the primary until
the primary current reaches its rated value. Record the primary voltage and current. In
this case, the power is too low to be measured by the laboratory watt-meters so (7) and
(10-11) can be used to calculate Xl1 and Xl2'.
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ELECTRICAL ENGINEERING AND ELECTRONICS
50 Ω
(from load panel) Isc = 2A
H1
X1
+
AC/DC
Source Panel
Vsc V
-
Single Phase
Transformer
H4
Short
circuit
wire
X2
Figure 7. Transformer short circuit test.
Open-Circuit Test
The open-circuit test gives information regarding the losses in the core, the parameters
Rm, Xm, and the turns ratio. Rated voltage is applied at the terminals of one winding
while the other winding terminals are open-circuited. Voltage, current and power is
measured. The current that flows in the primary winding during this test is called the
excitation current. The excitation current component of the primary current is needed to
produce the resultant mutual flux. This current has two components: the magnetizing
current and the core loss current.
Remove the resistor and short-circuit wire from the transformer so that the setup is that
shown in Figure 8. Apply rated voltage to the transformer and determine the magnitude
of the open-circuit impedance. Since the power is not measurable, use the impedance
magnitude and (18) for determining Xm.
Ioc = 2A
H1
X1
+
AC/DC
Source Panel
Voc V
-
Single Phase
Transformer
H4
X2
Figure 8. Transformer open circuit test.
Transformer Load Test
Connect the transformer to the three-phase source and load as shown in Figure 9.
Apply rated voltage to the primary winding and record the primary and secondary
voltages and currents. Perform this test for all combinations as shown in Table II.
Lower the voltage to zero before switching from one load configuration to another.
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ELECTRICAL ENGINEERING AND ELECTRONICS
I2
I1
H1
+
AC/DC
V
V
Source
1
Panel
-
Three-Phase Load Penal
X1
+
Single Phase V
Transformer 2 V
-
H4
X2
Figure 9. Transformer load test.
L
C
R
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
Table II. Load test measurements.
Vˆ
Iˆ
Vˆ
1
1
2
Iˆ2
Calculations
1. Using the above measurements, calculate the parameters of the Steinmetz model for
the laboratory transformer.
2. Using the Steinmetz model, calculate the transformer primary current, secondary
voltage, and secondary current for all configurations of the transformer load tests.
Estimate the load parameters from the data of Experiment 1. Compare these
calculations to the measurements of the load test.
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