ELP 101
Lab 7
Steady state performance of a
single-phase transformer
Sneha Bhargava
2022TT12152
Group 33
1
Aim:
To deduce the model and nd the parameters of
a single-phase transformer.
Apparatus:
1.
2.
3.
4.
5.
Single phase transformer
Single phase auto transformer
Low power-factor wattmeter
AC ammeter
AC voltmeter
Theory:
A current I1 induces a ux Φ in a loop of wire. The voltage across this
loop of wire, V1, is dΦ/dt. When there are N1 turns of the wire, the
voltage across the loop of wire is N1dΦ/dt. Flux can be linked with
the help of an iron/magnetic core. When the same core is shared by
another loop of wire, the same ux,Φ is induced through the loop. If
there are N2 turns of this secondary wire, the voltage induced
across the secondary, V2, is N2dΦ/dt.
As long as I1 is changing with time, V1/V2=N1/N2.
The concept of a transformer is generalized in a mutual inductance.
The popular symbol for a mutual inductance is shown below.
fi
fl
fl
2
In the above, the mutual inductance is characterized by the following
equation-set:
v1(t)=L1(di1(t)/dt)+M(di2(t)/dt)
v2(t)=M(di1(t)/dt+L1(di2(t)/dt)
When the currents and voltages are sinusoids in steady state, the
above pair of equations can be reduced appropriately and expressed
as phasors:
V1=jωL1I1+jωMI2
V2=jωMI1+jωL2I2
The value of M is related to L1 and L2 as:
M=k√L1L2 where k is de ned as the coupling coe cient.
A transformer is an example of a mutual inductance and follows the
above general relationships. The coupling coe cient in an ideal
transformer is 1.
As you observe in the above pair of equations, the mutual inductance
can be conveniently represented as a two-port network with the
help of an impedance matrix (Z parameters). In such a case,
Z11=jωL1, Z12=Z21=jωM, and Z22=jωL2. Further, a convenient
representation of a Z-parameter set is a T-network. This allows us to
model the transformer as a two-port network of the form shown
below:
ffi
ffi
fi
3
Unfortunately, it is not possible to measure the Z-parameters of the
transformer using the standard two-port network measurement
experiments. We will be estimating the two-port parameters of the
network using open-circuit and short-circuit tests.
Two approximations are typically used for characterization of the
transformer.
1. The impedance R0 ∥ jX0 is much much larger than R1+jX1and
R2+jX2. Conversely, R1+jX1 and R2+jX2 are much much
smaller than R0
∥ jX0.
2. The impedances R1+jX1 and R2+jX2 are related as a ratio
N1^2/N2^2. As such if we know one of the two, the other can
be estimated.
Setup:
A) Open-circuit test
The open-circuit test is performed on the low-voltage side, keeping
the high-voltage side open.
Set up the circuit as shown below.
Apply rated voltage (V0), and note the corresponding power (W0) at
4
Complete setup:
Wattmeter
the input and the current drawn (I0). Use a low power factor
wattmeter for the experiment.
B) Short circuit test
5
The short circuit test is performed with the input on the high voltage
side and the short circuit on the low voltage side. Make connections
as shown in the circuit diagram below.
Apply the required voltage (Vsc) so that the current drawn (Isc) is
equal to the rated current. Since the transformer is shorted, a voltage
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of only 5-10% of the rated voltage in the HV side will be needed.
Note the corresponding power input (Wsc). Repeat the above for
di erent values of short circuit currents and tabulate the readings.
Observations:
A) Open-circuit test
Wattmeter at 300V, Multiplying Factor = 2
S.No.
Voltage applied Current Drawn
Voc(V)
Ioc(A)
Power Input(W)
Core Loss
1
117.8
0.48 17.4x2=34.8
2
100.7
0.36 13.3x2=26.6
3
80.0
0.28 9.2x2=18.4
4
60.1
0.23 6x2=12
Readings:
1. Voc
Ioc
Power input
ff
7
2. Voc
3. Voc
4. Voc
Ioc
Ioc
Ioc
Power
Power Input
Power Input
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Calculations:
No load PF(cosΦ)=W/VI
Iw=I0 cosΦ
Iμ=I0 sinΦ
R0=V0/Iw
X0=V0/Iμ
S.No.
Voc(V)
Ioc(A)
Power
cosΦ
sinΦ
Iw(A)
Iμ(A)
R0(Ω)
X0(Ω)
(W)
1
117.8
0.48
34.8
0.62
0.78
0.30
0.37
392.67
453.08
2
100.7
0.36
26.6
0.73
0.68
0.26
0.24
387.31
419.58
3
80.0
0.28
18.4
0.82
0.57
0.23
0.16
347.83
500
4
60.1
0.23
12
0.87
0.49
0.20
0.11
300.5
546.36
0.76
0.63
0.25
0.22
357.08
479.76
Avg
cosΦ=0.76
sinΦ=0.63
R0=357.08 Ω
X0=479.76 Ω
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B) Short-circuit test
Wattmeter at 150V, Multiplying Factor = 2
S.No.
Voltage applied Current Drawn
Vsc(V)
Isc(A)
Power Input(W)
Couple Loss
1
11.36
8.2 30x2=60
2
8.95
6.3 20x2=40
3
6.8
4.3 10x2=20
Readings:
1. Vsc
Isc
Power Input
2. Vsc
Isc
Power Input
10
3. Vsc
Isc
Power Input
Calculations:
Total impedance referred to secondary side Z2=Vsc/Isc
R2=Wsc/Isc^2
X2^2=Z2^2-R2^2
S.No.
Vsc(V)
Isc(A)
Power
Z2(Ω)
input(Wsc)
R2(Ω)
X2(Ω)
1
11.36
8.2
60
1.38
0.89
1.05
2
8.95
6.3
40
1.42
1.01
0.99
3
6.8
4.3
20
1.58
1.08
1.15
1.46
0.99
1.06
Avg
R1=R2(n1/n2)^2=0.99Ω (since n1=n2, we have n1/n2=1)
X1=X2(n1/n2)^2=1.06Ω (since n1=n2, we have n1/n2=1)
The coupling coe cient k = M/√(L1L2) = X0/√(X1+X0)(X2+X0).
Hence, k=0.998
ffi
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Conclusion:
From the above experiment, we have been able to
calculate the various circuit parameters of a real
transformer using the open circuit and the short
circuit tests.
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Sources of Error:
1. Scale of multimeter/DSO not appropriate for
measurements
2. Loose Connections
3. Resistance of wires not considered and giving rise
to inconsistency
due to increase in resistance due to heating.
4. Change in the connections while circuit is closed.
Precautions:
1. Make the connections neat and tight
2. Dont leave the switch on for long continuous
periods of time
3. Wear proper shoes and use insulated tools.
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