Lab 3 Transformers short and open circuit test

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Lab 3 Transformers short and open circuit test
Transformers Short Circuit and Open Circuit Tests
Introduction
One of the universal electrical machines is the transformer, reciveing power at one voltage
and delivering it to another. Making use of the laws involving electromagnetism. Working
on the basis of Faradays law of induction stating that “ When the magnetic flux linking a
circuit changes, and electromotive force (EMF) is induced in the circuit proportional to the
rate of change of flux linkage”. This applies to the primary coils having current pushed
through it causing for a magnetic field to be produced, this in turn interacting with the
magnetic field of the secondary winding inducing an EMF and therefore a current.
Furthermore the the operation of these machines aids the effiecent long distance
transmission of electrical power from the generating stations. Since power lines incur
signinficant  2  losses, it is important to minimize these losses by the use if high voltages.
The same power can be delievered by high voltage circuits at a fraction of the current
required for low voltage circuits” reference hughes book
In this laboratory two transfomers were analysed during practical sessions where a number
of methods were undergone to enable for the extraction of values from the loaded
transformers. Results were recorded from both an open circuit test and a short circuit test
on each tranfomer ultimately allowing for calculations to be made in order to gain values for
the paramters of the equivalent circuit show in figure(). These results were then used to
calculate the effeincncy of each transformer.
 =     
 =     
 =      
 =       
The nominal values of the two transfomers parameters are shown in table ()
Transformer Design
frequency(Hz)
1
50Hz
2
50HZ
Nominal
VA
500
700
Nominal
Vin
240
240
Noimnal
Iin
2.083
2.917
Nominal
Vout
240
35
Nominal
Iout
2.083
20.0
Transformer 1 results
The first test was the open circuit (oc) the circuit of which can be seen in figure ()
The transformer was connected as seen above with the supply as the rated nominal voltage
and frequency as shown in table (). The ratio of the voltmeters V1/V2 gives the ratio of the
number of the turns. The ammeter labelled A provides the no-load current reading, allowing
for the values of the magnetic elements to be calculated. As the current across  and 
are negliable in comparison to the magnetic elements  and  the winding elements can
be disregarded. Therefore, the voltage and current values across and through the magnetic
elements are that of  and  . Thus finding values for  and  aids in the caluclations for
the values of the magnetic elements. The results obtained from the practical can be seen in
table ()
Transformer Frequency
1

1
50 Hz
240.5Vrms 26.2W
2
50.02 Hz
239.8Vrms 38.11W


67.61VA 0.387
109.2VA 0.349
1
0.281
0.456
20
248.7Vrms
35.92Vrms
The second test was the short circuit (sc) the circuit of which can be seen in figure()
The short circuit test works on the basis that the electrons will always flow in the shortest
route and therefore by shorting the circuit current will flow around the circuit not passing
through the magnetic elements of the transformer. Therefore across the two winding no
voltage is dropped; only the winding elemetns are effected. Thus finding  and  aids in
calculating the values of the winding elements  and  . Table () shows the results
obtained from this practical.
Transformer Frequency
1

1
49.3 Hz
8.43Vrms 18.1W
2
50.06 Hz
17.78Vrms 52.42W


18.45VA 0.982
53VA
0.989
1
2.209
2.970
2
2.127Vrms
19.55Vrms
Equations ()()() are used to calculate the power factor value in tables () and ().
 =  () ×   ()
  ()

The efficiency and voltage regulation can be calculated using the readings obtained from the
short and open circuit tests using equations ()()
  () =
Transformer 1 :
 =  + 
500 + (26.2 + 18.1) = 544.3
0
× 100 = 91.8%

assuming that the transformer is 100% efficient allows for the parameters to be calculated
as follows :
 () =
 =
 =
2 240.5 2
=
= 2207.64

26.2

240.5
=
= 108.94

2207.64
 = √0.2812 − 0.108942 = 259.02
 () =
 =
1
240.5
=
= 928.5

0.25902

928.5
=
= 2.96
2 2 × 50
These calculations show that the equivalent circuit during the open circuit test can can be
simplified down to the magnetic elements connected to the primary voltage. Below shows
the calculations required for the short circuit test to obtain the values of the winding
components connected to the supply voltage.
 () =

18.1
=
= 3.71
2

2.2092
 =  ×  = 2.209 × 3.71 = 8.2
 = √2 − 2 = √8.432 − 8.22 = 1.96
 =
 () =

2
=
1.96
2.209
= 0.89
0.89
= 2.84
2 ×  × 49.3
Now that the parameters of the circuit have been calculated the overall efficiency can be
computed this is done as follows:
500
 () =
= 2.083
240
240
 =
= 115.2
2.083
1 2
 = 115.2 × (
) = 107.75
1.034
2 =
2 =  //
2207.64 × 2 × 50 × 2.96
2207.64 + (2 × 50 × 2.96)
= 331.28 + 788.9
3 =  //2
3 =
107.75 × (331.28 + 788.91)
= 101.5 + 11.24
107.75 + (331.28 + 788.91)
Utlizing the voltage divider rule the calculations below could be made:
3
101.5 + 11.24
× =
240 = 231.41 − 1.025
1 + 3
101.5 + 11.24 + 3.713 + 0.87
Written is polar form as :
231.41∠ − 0.254°
1.034
 = (
) × 231.41 = 239.28
1
 2 231.412
 =
=
= 497.055

115.2
Thus to find the effeiceny the power loss in both the magnetic elements and the windings
must be calculated as follows:
 =
231.412
= 24.23
2207.64
240.5 − 231.41 = 8.59
 =
8.592
3.713
= 19.87
  = 24.23 + 19.87 = 44.01
497.055
% =
× 100 = 91.37%
500 + 44.01
Following the same method and procedure the parameters and efficiency of transformer 2
could be calculated, the results are shown below:
Efficiency from results obtained:
700 + (38.11 + 52.42) = 790.53
 () =
0
× 100 = 88.5%

Parameters:
 = 1388.087Ω
 = 0.173
 = 0.4219
 = 568.381Ω
 = 1.809
 = 3.71Ω
 = 8.2
 = 1.965
 = 0.89Ω
 = 2.84
 , 2 = 2.083
(VA and secondary voltage taken from table 4.6 and plugged into formula from the first part
of equation 4.15).
 = 77.886Ω
   = 0.1498
 = 107.962Ω
3 = 74.8891 + 9.6342
 = 221.93
 = 33.2432
 = 631.48
 = 54.16
 = 32.64
 = 87.92%
Discussion and evaluation
Calculating the parameters of each transformers required for the assumption that the
transformers were 100% efficient to be made or in other words the transformers were
ideal. In reality however transfomers are highly effieicent but not completely, these losses
that occur can be divided into two groups; the losses that occur in the primary and
secondary windings and the core losses due to hysteresis and eddy currents. The two
methods were used to calculate the effienecy of the transformers and it serves that the
second method (that using th parameters ) is the mores accurate of the two. None the less
the two methods and results mirror each other.
Conclusion
The oc and sc test permitted the characteristics of the transformers through influencing the
parameters in order to obtain the power losses within the winding and the core. This in turn
allowed for the efficiency of the transformers to be calculated. These values were then
double checked through mathematical calculations, these can be seen from equations ()
through to (). As the values calculated were similar to that from the practical work it helped
confirm and validate that the calculation was done correctly.
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