MV 1911
Single-phase transformer
Theory and Experiments
Contents
Introduction...............................................................................................................................1
Experiment 1 ............................................................................................................................3
1.1 Purpose ..........................................................................................................................3
1.2 Equipment.......................................................................................................................3
1.3 Theory.............................................................................................................................3
1.5 Load tests .......................................................................................................................6
1.6 Connection diagram........................................................................................................6
1.7 Procedure .......................................................................................................................7
1.8 Problems and tasks ........................................................................................................7
1.9 Measurement result table ...............................................................................................7
Experiment 2 ............................................................................................................................9
2.1 Purpose ..........................................................................................................................9
2.2 Theory.............................................................................................................................9
2.3 No-load test ..................................................................................................................11
2.3.1 Equipment ..............................................................................................................11
2.3.2 Procedure...............................................................................................................11
2.4 Measurement of winding resistances ...........................................................................12
2.4.1 Equipment ..............................................................................................................12
2.4.2 Procedure...............................................................................................................12
2.5 Short-circuit test............................................................................................................13
2.5.1 Equipment ..............................................................................................................13
2.5.2 Procedure...............................................................................................................13
2.6 Load test .......................................................................................................................14
2.6.1 Equipment ..............................................................................................................14
2.6.2 Procedure...............................................................................................................14
2.7 Measurement result table .............................................................................................15
2.7.3 No-load test............................................................................................................15
2.7.4 Measurement of winding resistances.....................................................................15
2.7.5 Short-circuit test .....................................................................................................15
2.7.6 Load test ................................................................................................................15
2.8 Problems and tasks ......................................................................................................16
Experiment 3 ..........................................................................................................................17
3.1 Purpose ........................................................................................................................17
3.2 Equipment.....................................................................................................................17
3.3 Theory...........................................................................................................................17
3.4 Procedure .....................................................................................................................19
3.5 Problems and tasks ......................................................................................................19
3.6 Measurement result tables ...........................................................................................20
Experiment 4 ..........................................................................................................................21
4.1 Purpose ........................................................................................................................21
4.2 Equipment.....................................................................................................................21
4.3 Theory...........................................................................................................................21
4.4 Procedure .....................................................................................................................23
4.5 Measurement result table .............................................................................................24
4.6 Problem ........................................................................................................................24
Introduction
Introduction
The single-phase transformer is used, above all, in mains power units for supplying different types of
electrical equipment. The transformer is then used to change the mains voltage to other voltages
that are required in the equipment.
The single-phase transformer consists of two windings on a common iron core. If one of the
windings is connected to an AC voltage V1, an alternating magnetic field will be set up in the iron
core. This field will then induce an AC voltage V2 in the other winding.
The ratio between these voltages is the same as the ratio between the number of tums on the two
windings:
V1 N 1
=
V2 N 2
The winding for the higher voltage is called the up winding and the other winding is called the down
winding.
If the transformer is connected in an electric circuit the input winding is called the primary winding.
The other winding, which gives out power, is called the secondary winding.
In reality the up and down windings of a transformer are wound on top of each other, and not side
by side as shown in the figure. This arrangement results in reduced leakage magnetic flux, and thus
a smaller voltage drop in the transformer on load. In transformer MV 1911, however, the windings
are laid side by side so that a larger, and hence easier to measure, voltage drop is obtained in the
transformer when carrying out the laboratory exercises.
1
Introduction
2
Experiment 1
Experiment 1
Performing a load test.
1.1 Purpose
To investigate how the secondary voltage of the transformer changes with different loads.
1.2 Equipment
Power pack MV 1300
T
= Transformer MV 1911
R
= Load resistor MV 1100
V1, V2
= Voltmeter 250 V, MV 1926
I1
= Ammeter 6 A, MV 1923
I2
= Ammeter 12 A, MV 1923
S
= Switch MV 1500
For later use:
Load reactor MV 1101
Load capacitor MV 1102
1.3 Theory
When a transformer is loaded, i.e. current flows through the secondary winding, the secondary
voltage will be reduced because of the voltage drop in the winding resistance and because of the
magnetic leakage flux.
In a model this leakage flux can be simulated by reactances and the following very familiar model for
a transformer is obtained, where the no-load current has not been taken into consideration.
3
Experiment 1
It can be shown that precisely the same effect can be simulated by replacing R2 on the right-hand
side of the model by a resistor on the left-hand side of the model, with a resistance value of:
 N1

 N2
2

 ⋅ R2

The same applies in the case of X2, which gives us a new model for the transformer:
If the two resistances are now combined to give one single value Rsc, and the two reactances to give
Xsc, the simple transformed model shown below is obtained.
It is of course also possible to construct another model with Rsc and Xsc drawn on the right-hand side
of the model, but they will then have different numerical values.Suitable designations are included in
the model in order to study the voltage drop in the transformer. V2 stands for the voltage on
transformer side 2 transferred over to side 1.
V2' = V2 ⋅
N1
N2
4
Experiment 1
The voltages are calculated, in complex form, in accordance with the following expressions:
V2' = V1 − Rsc ⋅ I 1 − jX sc ⋅ I 1
For practical transformer use the approximate formula:
V2' = V1 − Rsc ⋅ I 1 ⋅ cos ϕ 2 − X sc ⋅ I 1 ⋅ sin ϕ 2
Where φ2 is the phase angle between V2 and I2.
From this formula it can be seen that if the feeding voltage V1 is constant, the secondary voltage V2
will decrease when the load , that is to say I1, increases. However, one exception to this is a
capacitive load, when I2 is negative. Sinφ2 is then also negative, and hence the last term in the
expression for the secondary voltage is positive. Thus if the load is sufficiently capacitive there will
be a negative voltage drop.
The transformer characteristic is shown below:
5
Experiment 1
1.5 Load tests
The transformer has four windings on the down side, each of which give 55 V. These windings are
connected in series and parallel so that the voltage on the down side is 110 V. See the connection
diagram below.
The rated power of the transformer is 1 kVA. Calculate the rated current on the down side:
I 2n =
S n 1000
=
= _____ A
110
Vn
This current must not be exceeded during the experiment .
1.6 Connection diagram
6
Experiment 1
1.7 Procedure
1. Connect three phases in parallel across the load resistor. Switch on the variable AC voltage
and adjust the voltage to 220 V. This must be maintained constant during all the
measurements.
2. Load the transformer in steps of 1 A up to the rated current by adjusting the load resistor.
Make a note of I1, V2 and I2 for each step.
3. Switch off the AC voltage and replace the load resistance by one phase on the load reactor
and repeat the same measurements (it is sufficient to go up to about 7 A).
4. Replace the load reactor by the load capacitor and repeat the same measurements up to
about 3 A.
1.8 Problems and tasks
1. Draw the graphs of measurements on V2 = f(l2) for the three sets of measurements in the
same diagram.
2. Calculate a suitable value of resistance Rsc in a model for this transformer. Take the
numerical values from the values measured with resistive load and rated current, and
substitute these figures in the formula for the voltage drop.
3. Calculate a suitable value for the reactance xsc in a corresponding way, using the figures
from the measurement with inductive load.
1.9 Measurement result table
I2n = _____A
Max 5A I1
Parallellkopplade resistorer
I1 (A)
R
I2 (A)
V2 (v)
Alla lägen
En spole
I1 (A)
L
I2 (A)
V2 (v)
Alla lägen
Parallellkopplade kond.
I1 (A)
C
I2 (A)
V2 (v)
Xk=_____Ω
7
Experiment 1
8
Experiment 2
Experiment 2
Measurement of efficiency and shortcircuit impedance.
2.1 Purpose
To measure efficiency and short circuit impedance, from no load test, winding resistance,
short circuit test and load test.
2.2 Theory
The efficiency can be determined by measuring the input power P1 and the output power P2.
The efficiency is then given by
η=
P2
P1
In practice it is often difficult to obtain access to the large powers involved in the case of full
load for a large power transformer.
Consequently, only the losses in the transformer are measured and the efficiency calculated
using the following expression:
η=
P1 − Pf
P1
= 1−
Pf
P1
= 1−
Pf
P2 + Pf
The losses Pf consists of the no-load losses plus the load losses.
The no-load losses constitue the power the transformer consumes when it is not loaded.
The load losses constitute the power which is consumed when the rated current flows in one
winding and the other winding is short-circuited.
When measuring the load losses the short-circuit impedance of the transformer can also be
determined. The model is then as in the diagram:
In order to carry out this short-circuit test, the feeding voltage Vsc is of course reduced to a
few per cent of the rated voltage.
The short-circuit impedance Zsc is given by
Z sc =
Vsc
I 1n
9
Experiment 2
The short-circuit resistance Rsc is determined with the aid of the power Psc which is measured
when carrying out the short-circuit test:
Psc = Rsc ⋅ I 1n2
The short-circuit impedance and resistance are often given as percentages. It can be shown
that they can be calculated from the following formulas :
vz =
v sc
vn
vr =
Psc
Sn
v x = v z2 − v r2
where Sn is the rated power of the transformer
10
Experiment 2
2.3 No-load test
2.3.1 Equipment
Power pack MV 1300
T
= Transformer MV 1911
I
= Ammeter 1A, MV 1922
V
= Voltmeter 250 V, MV 1926
P
= Wattmeter 5 A, 250 V, MV 1928
2.3.2 Procedure
1. Connect the circuit as shown in the diagram.
2. Do not change to a smaller measuring range on the wattmeter despite the fact that
only a small reading is obtained when carrying out this measurement. As the voltage
is 230 V it is not possible to connect in a measuring range that is less than 230 V, and
as the current is about 0.3 A it is not possible to connect in a measuring range that is
less than 0.3 A. The small reading of the wattmeter is due to the fact that the phase
shift in a transformer on no load is very big ( P = V ⋅ I ⋅ cos ϕ ).
3. Switch on the variable AC voltage and adjust the voltage to 220.0 V.
4. Read off and make a note of the current I0 and the power P0.
5. Switch off the AC voltage.
11
Experiment 2
2.4 Measurement of winding resistances
2.4.1 Equipment
T
R
= Transformer MV 1911
= Ohmmeter with high accuracy in the range 1-10 ohms .
2.4.2 Procedure
1. Connect up the circuit as shown in the diagram
2. When carrying out the measurement of resistance of the down winding, the winding
must be connected in the same way as it is for the remainder of the laboratory
exercises. The resistance is then measured between the terminals to the winding as
shown on the diagram.
3. Read off and make a note of the resistances of the up and down windings of the
transformer.
12
Experiment 2
2.5 Short-circuit test
2.5.1 Equipment
Power pack MV 1300
T
= Transformer MV 1911
V
= Voltmeter 50 V, MV 1926
I
= Ammeter 6 A, MV 1923
P
= Wattmeter 50 V, 5 A, MV 1928
2.5.2 Procedure
1. Connect the circuit as shown in the diagram.
2. Calculate the rated current of the transformer. Since the transformer is short-circuited,
the current will be large even with quite a small voltage. Switch on the variable
AC voltage and increase the voltage very slowly until the current is equal to the rated
current.
3. Make a note of the voltage Vsc, the current Isc and the power Psc.
13
Experiment 2
2.6 Load test
For comparison purposes the efficiency will be measured directly.
2.6.1 Equipment
Power pack MV 1300
T
= Transformer MV 1911
V1 , V2
= Voltmeter 250 V, MV 1926
I1
= Ammeter 6 A, MV 1923
I2
= Ammeter 12 A, MV 1923
P
= Wattmeter 250 V, 5 A, MV 1928
R
= Load resistor MV 1100
2.6.2 Procedure
1. Connect the circuit as shown in the diagram.
2. Note that the wattmeter must again have the measuring range 240 V.
3. Calculate the rated current of the transformer on the down side.
4. Set the load resistor to the position giving the smallest current, and then switch on the
variable AC voltage. Adjust the voltage to 220.0 V.
5. Adjust the load resistor so that the current on the transformer down side is equal to
the rated current of the transformer.
6. Make a note of I1, P1, V2 and I2.
7. Vary the current on the down side of the transformer in steps of 2.0 A down to zero.
8. Make a note of I1, P1, V2 and I2 for each step.
9. Switch off the AC voltage.
14
Experiment 2
2.7 Measurement result table
2.7.3 No-load test
V (V)
I0 (A)
P0 (w)
220.0
2.7.4 Measurement of winding resistances
Up winding R1 (Ω)
Down winding R2 (Ω)
2.7.5 Short-circuit test
Vsc (V)
Isc (A)
Psc (W)
2.7.6 Load test
Measured values
V1 (V)
I1 (A)
P1 (W)
Calculated values
V2 (V)
220.0
15
I2 (A)
P2 (W)
η (%)
Experiment 2
2.8 Problems and tasks
1. Calculate the efficiency of the transformer at the given full rated power and with a
power factor of 1.0, using the loss summation method.
η = 1−
Pf
=1P0 + Psc
=
P2 + Pf 100 ⋅ 1.0 + P0 ⋅ Psc
2. Calculte the given power P2 = V2 ⋅ I 2 ⋅ 1.0 for measurement 2.6. The power factor is
1.0 because the load consisted of a pure resistance.
Then calculate the efficiency η =
P2
P1
3. Why does the efficiency measured using the loss summation method differ from the
efficiency measured by the direct method?
4. What are the advantages and disadvantages of measuring the efficiency direct?
5. Calculate the copper losses
PCu = R1 ⋅ I 12 + R2 ⋅ I 22
with the resistances from measurement 2.4 and with the rated current of the
transformer on the up and down sides respectively.
6. Why do the calculated losses in the windings PCu differ from the measured Psc?
16
Experiment 3
Experiment 3
Waveform of the no-load current
3.1 Purpose
To examine and measure the no load current.
3.2 Equipment
Power pack MV 1300
T
= Transformer MV 1911
R
= Resistor 1.0 ohm, 100 W
OSC
= Oscilloscope, double beam, VC 6015
I1
= Ammeter 1 A, moving coil, for example universal instrument 3010
I2
= Ammeter 1 A, moving iron, MV 1922
V
= Voltmeter 250 V, MV 1926
3.3 Theory
The no-load current in a transformer is usually so small that the voltage drop in the winding
resistance on no load can be ignored. An impressed voltage is then assumed to be opposed
only by the induced e.m.f. Take the normal case, when the voltage is sinusoidal, the induced
e.m.f. will then also be sinusoidal. This means that the magnetic flux in the iron core of the
transformer will be sinusoidal
(e =
dφ
)
dt
Since the magnetization curve of the iron is bent (hysteresis curve), a sinusoidal flux will give
rise to a non-sinusoidal current. The figure below shows a part of the waveform of the current
derived from a sinusoidal flux via a hysteresis curve.
17
Experiment 3
Complete the derivation of the current waveform in the figure.
18
Experiment 3
3.4 Procedure
1. Connect the circuit as shown in the circuit diagram.
2. The oscilloscope is connected so that beam A shows the mains voltage and beam B
the voltage drop in R, which is proportional to the no-load current.
3. Switch on the variable three-phase voltage and adjust it to 220.0 V.
4. Make a note of I1 and I2.
5. Draw the oscilloscope picture of the current.
6. Read off on the oscilloscope the phase difference between the voltage and current.
7. Increase the voltage to 240.0 V.
8. Make a note of I1 and I2.
9. Draw the oscilloscope picture of the current.
10. Reduce the voltage to 200.0 V.
11. Make a note of I1 and I2.
12. Draw the oscilloscope picture of the current.
3.5 Problems and tasks
1. I1 and I2 are different despite the fact that they are the same current. Why?
2. Explain why the waveform of the current changes when the voltage is increased or
decreased.
19
Experiment 3
3.6 Measurement result tables
V (V)
200.0 V
220.0 V
240.0 V
I1 (A)
I2 (A)
V = 200.0V
Scale:
Y: 1cm =
X: 1cm =
V = 220.0V
Scale:
Y: 1cm =
X: 1cm =
V = 240.0V
Scale:
Y: 1cm =
X: 1cm =
20
Experiment 4
Experiment 4
Inrush current
4.1 Purpose
To study and measure the inrush current.
4.2 Equipment
Power pack MV 1300
T
= Transformer MV 1911
R
= Resistor 1 ohm, MV 1953
OSC
= Memory oscilloscope, double beam VC 6015
4.3 Theory
When a transformer is connected to the mains voltage, very large currents may be obtained
during the first few cycles of the AC voltage. The amplitude of this inrush current depends on
the phase of the AC voltage at the instant that it is connected to the transformer, and in the
worst case it can amount to 10-100 times the rated current.
This inrush current depends on the magnetization curve of the iron core, in precisely the
same way as the no-load current waveform. In Experiment 3, Theory, it was shown that the
magnetic flux in a transformer varies sinusoidally. We assume that before switching on there
is a certain residual magnetic field Φr in the iron core, what is known as remanence. We can
then derive the inrush current in the following way. The derivation is an exact analogy of that
in Experiment 3, Theory, and it is assumed that switching on takes place at an instant when
the magnetic field passes through zero.
21
Experiment 4
1. What is the value of AC voltage at the switching-on instant in the above figure?
(The answer should be max., zero or min.)
2. At what value of switch-on voltage do we obtain the highest inrush current?
(The answer should be max., zero or min.)
In practise this inrush current can cause problems as blown fuses and tripping of transformer
protections.
22
Experiment 4
4.4 Procedure
Measurement of inrush current
1. Connect the circuit as shown in the circuit diagram.
2. Set up the memory oscilloscope as follows: YA axis 100 V/cm (it is necessary to use a
high voltage probe), YB axis 10 V/cm, X axis 10 ms/cm, trigger on YA single sweep
and memory function.
3. Switch on the fixed three-phase voltage on MV 1300. Read off on the oscilloscope
the amplitude of the maximum half cycle of the current, which is of course the first half
cycle. Read off also the phase angle of the voltage at which connection takes place.
4. Make a note of the values in the measurement result table.
5. When using the switch on the power pack it is difficult to determine the phase angle
of the voltage at which connection occurs, and hence it is necessary to repeat the
connection process a number of times until it can be assumed that in all probability
the worst possible case has been included.
6. Switch off the AC voltage. Reset the oscilloscope so that the oscilloscope picture is
erased. Carry out a new measurement by again switching on the three-phase
voltage. Repeat the measurement ten times.
23
Experiment 4
4.5 Measurement result table
Ipeak (A)
Phase
angle (°)
4.6 Problem
At what phase angle is the maximum inrush current measured?
24