Transformer Efficiency Analysis

This assignment presents an analysis of transformer efficiency under both resistive and inductive loads. It includes experimental data obtained through load testing, calculating the power factor, and analyzing the efficiency at various load levels. The discussion highlights the impact of load type on transformer performance and emphasizes that efficiency is influenced by factors beyond simply the full-load efficiency rating. Finally, the assignment concludes by discussing the practical implications of these findings for real-world transformer operation.

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TRANSFORMER EQUIVALENT CIRCUIT PARAMETER IDENTIFICATION AND
OPERATIONAL PERFORMANCE
Name of Student
Institution Affiliation

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Table of Contents
1.1 Introduction..........................................................................................................................2
1.2 Transformer Per-phase, Approximate Equivalent Circuit...................................................4
1.3 Discussion of Load Tests.....................................................................................................5
1.4 Results..................................................................................................................................8
1.5 Discussion of Results.........................................................................................................14
1.6 Conclusions........................................................................................................................15
1.7 References..........................................................................................................................16

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Power Transformer Characterisation and Load Prediction
1.1 Introduction.
The lab session was conducted in two phases. Laboratory 1 and laboratory 2.
In laboratory one an experiment was carried out to;
Determine the electrical equivalent circuit parameters for a single phase power.
By use of a purely resistive load to test the transformer from no-load to the full load.
After the lab session, the electrical equivalent circuit parameters which were determined
from the test model were used to determine and predict the performance of the transformer
from the open-circuit to the full-load (Engineers, 2012).
In laboratory 2; Single Phase Power Transformer Load Tests.
Experiments were carried out to;
Test the transformer from no-load to the full-load by use of a purely resistive load as it was in
the case of laboratory 1.
Use a resistive-inductive load to test the transformer from no-load to full-load.
Use a resistive-capacitive load to test the transformer from no-load to full-load.
The electrical equivalent circuit parameters which were determined ware used to calculate
and predict the performance of the transformer. From the open-circuit to the full load for all
the three scenarios.

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1.2 Transformer Per-phase, Approximate Equivalent Circuit.
Equivalent circuit of a 500VA transformer.
How to calculate the transformer performance.
Transformers are considered to be the backbone of power distribution system. The AV rating
refers to how much power a transformer can deliver the load in relationship to the power
supplied to it (Harlow, 2014).
To calculate the efficiency of a transformer one needs to know the amount of voltage and
current which is delivered to the load.
One needs to determine the primary and secondary voltages that can be achieved by referring
to the transformer specifications.
Once one knows the transformer specification, the efficiency of the transformer can be
determined by the formula. VA rating = (V secondary x I)/0.8," where V secondary is the
secondary voltage of the transformer and the 0.8 accounts for the power factor of the load
(Ghosh, 2012).

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1.3 Discussion of Load Tests.
Procedure;
The circuit was wired in such a way that the load impedance at the transformer output set of a
variable resistances.
The Variac voltage was set to zero.
The circuit was checked by the tutor (Harlow, 2014).
The circuit was connected to the mains supply.
The voltage of Variac output was increased until the input of the primary transformer was
200V.
The Load resistance which was connected to the secondary output was adjusted until the
primary transformer full load was 2.5A.
The required readings were recorded in the table below.
The load resistance was increased in such a way that the primary current reduced in 0.25A
steps until the current load was minimised. The readings were recorded at every step.
Primary Readings Secondary Readings
Power
(W)
Volts
(V)
Current
(A) Power Factor Power (W) Volts (V)
Current
(A)
Power
Factor
476 200 2.513 0.947 443.5 115.9 3.926 0.976
423.1 200 2.245 0.936 393.4 116 3.496 0.972
370.2 200 2 0.925 344.5 116.3 3.502 0.969
318 200 1.73 0.91 291.9 116.8 2.6 0.964
268 200 1.507 0.889 245 117.1 2.186 0.958
226.8 200 1.298 0.87 203 117.3 1.811 0.955

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Inductive Load Test
Procedure
The variable inductive load was connected to the transformer output.
The voltage of the Variac was set to zero.
The circuit was checked by the tutor.
The Variac voltage output was increased until the input voltage of the primary transformer
was 200V (Rebennack, 2013).
The variable inductive load which was connected to the primary transformer was adjusted
until the primary full load current was 2.5A
The required readings were taken and recorded in the table below.
The load resistance was increased in such a way that the primary current reduced in 0.25A
steps until the current load was minimised. The readings were recorded at every step.
The mains power was isolated by unplugging the Variac.
The variable resistance was disconnected.
Inductive Load (Measured
Value)
Primary Readings Secondary Readings
Power
(W)
Volts
(V)
Current
(A) Power Factor Power (W) Volts (V)
Current
(A)
Power
Factor
48.3 200 2.5 0.099 19.8 117 3.61 0.046
44.3 198 2.26 0.098 17 116.5 3.3 0.043
39.1 198 2.01 0.097 13.8 116.6 2.88 0.041
34.3 197 1.76 0.098 10.5 116.6 2.45 0.036
30.5 197 1.52 0.101 8 116.6 2.048 0.033
26.7 197 1.24 0.108 5.7 116.6 1.59 0.03

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Variable Capacitive Load Test
Procedure
The variable capacitance load was connected to the transformer output.
The Variac voltage was set to zero.
The circuit was checked by the tutor.
The circuit was connected to the mains supply.
The Variac output voltage was increased until the primary transformer input voltage 200V.
The variable capacitance load connected to the secondary transformer output was adjusted
until the primary transformer full load was 2.5 A
The required readings were recorded in the table below.
The load resistance was increased in such a way that the primary current reduced in 0.25A
steps until the current load was minimised. The readings were recorded at every step.
The mains power supply was isolated by unplugging the variable.
Primary
Readings
Secondary
Readings
Power
(W)
Volts
(V)
Current
(A) Power Factor Power (W) Volts (V)
Current
(A)
Power
Factor
36.9 200 2.5 0.074 3.3 119.3 4.6 0.005
33.8 119.6 2.45 0.076 3 118.8 4.25 0.005
31.5 119.4 2 0.078 2.6 119 3.86 0.004
29.4 200.7 1.75 0.083 2.2 119.4 3.44 0.005
27.3 200.5 1.5 0.089 1.7 119 3.01 0.004
25.3 200 1.25 0.117 1.5 118.8 2.59 0.004
All other pieces of equipment were disconnected.

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1.4 Results.
The data which was recorded and tabulated was further analysed, and the results were
presented in graphs and tables as shown below.
Resistive load test efficiency
Efficiency
Pout Pin %
443.5 476 0.931723
393.4 423.1 0.929804
344.5 370.2 0.930578
291.9 318 0.917925
245 268 0.914179
203 226.8 0.895062
Inductive Load efficiency
Efficiency
Pout Pin %
19.8 48.3 0.409938
17 44.3 0.383747
13.8 39.1 0.352941
10.5 34.3
0.3
06122
8 30.5 0.262295
5.7 26.7 0.213483

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Variable Capacitive Load efficiency
Efficiency
Pout Pin %
3.3 36.9 0.089431
3 33.8 0.088757
2.6 31.5 0.08254
2.2 29.4 0.07483
1.7 27.3 0.062271
1.5 25.3 0.059289
(i) Output power-factor (p.u.) (y-axis) versus real power (x-axis)
0 50 100 150 200 250 300 350 400 450 500
0
0.2
0.4
0.6
0.8
1
1.2
R Measured
RL Measured
RC Measured
R Calculated
RL Calculated
RC Calculated
Output power-factor (y-axis)
output real power (x-axis)

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(i) Secondary voltage (y-axis) versus secondary current (x-axis)
1 1.5 2 2.5 3 3.5 4 4.5 5 5.5
0
20
40
60
80
100
120
140
160
180
R calculated
RL calculated
RC calculated
R Measured
RL Measured
RC Measured
Secondary current (x-axis)
Secondary voltage (y-axis)
(ii) Output power-factor (p.u.) (y-axis) versus apparent power (x-axis)
150 200 250 300 350 400 450 500 550 600 650
0
0.2
0.4
0.6
0.8
1
1.2
R Measured
RL Measured
RC Measured
R Calculated
RL Calculated
RC Calculated
output apparent power (x-axis)
Output power-factor (y-axis)

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(iii) Efficiency (%) (y-axis) versus real power (x-axis)
0 50 100 150 200 250 300 350 400 450 500
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
R Measured
RL Measured
RC Measured
R Calculated
RL Calculated
RC Calculated
Output real power (x-axis)
Efficiency (%) (y-axis)
(iv) Efficiency (%) (y-axis) versus real apparent power (x-axis)
150 200 250 300 350 400 450 500 550 600 650
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
R Measured
RL Measured
RC Measured
R Calculated
RL Calculated
RC Calculated
output apparent power (x-axis)
Efficiency (%) (y-axis)

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Resistive load test
Power Factor
Apparent
Power
Real
Power N
Voltage
secondary Current secondary
0.974675149 455.0234 443.5
1.72562
6 115.9 3.926
0.970074173 405.536 393.4
1.72413
8 116 3.496
0.845850031 407.2826 344.5 1.71969 116.3 3.502
0.961209168 303.68 291.9
1.71232
9 116.8 2.6
0.957103781 255.9806 245
1.70794
2 117.1 2.186
0.955607557 212.4303 203 1.70503 117.3 1.811
Inductive Load
Power Factor
Apparent
Power
Real
Power N
Voltage
secondary Current secondary
0.046878329 422.37 19.8 1.70940 117 3.61

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2
0.044219014 384.45 17
1.69957
1 116.5 3.3
0.041094911 335.808 13.8
1.69811
3 116.6 2.88
0.036755697 285.67 10.5
1.68953
7 116.6 2.45
0.033501286 238.7968 8
1.68953
7 116.6 2.048
0.030745332 185.394 5.7
1.68953
7 116.6 1.59
Variable Capacitive Load
Power Factor
Apparent
Power
Real
Power N
Voltage
secondary Current secondary
0.006013339 548.78 3.3
1.67644
6 119.3 4.6
0.005941771 504.9 3
1.00673
4 118.8 4.25
0.005660295 459.34 2.6
1.00336
1 119 3.86
0.005356239 410.736 2.2
1.68090
5 119.4 3.44
0.004746084 358.19 1.7 1.68487 119 3.01

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4
0.004875005 307.692 1.5
1.68350
2 118.8 2.59
1.5 Discussion of Results.
Resistive load test was measured after the power had not passed through the transformer for a
long time. From the results of resistance load test whereby the voltage and the current were
measured at the same time, it was very clear that the current was very close to the current
which is rated on the transformer ratings (Horton, 2011).
From the result, the power factor of the transformer was used to detect the dryness of the
insulation of the transformer. It was calculated by dividing the input volt-ampere and then
multiplied by 100 (Losi, 2014).
The results of purely resistive load shows that the transformer's efficiency was very high in
both the full load and to no-load scenarios.
From the result when the input and the output were high the Inductive Load efficiency
percentage was also high.
1.6 Conclusions.
In conclusion, like any other electric types of equipment, the efficiency of the transformer is a
function of the power output and the power input. In most cases, the transformers are
considered as one of the most efficient electrical devices. From the study carried out most of
the transformers have a full load efficiency which ranges between 95% and 98.5 % (Proulx,
2016).
From the test carried out, it is very clear that the efficiency of the transformers cannot be
judged by this efficiency, but different transformers have different ways in which they are

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energised. For the case of distribution transformers, they have their primaries more energised
all the time, but in most cases, they have their secondary supply having a little load or no-
load during most of the time (Rebennack, 2013).
1.7 References
Engineers, I. o. (2012). CIRED: 16th International Conference & Exhibition on Electricity
Distribution, Volume 5. London: Institution of Electrical Engineers.
Ghosh, A. (2012). Power Quality Enhancement Using Custom Power Devices. London:
Springer Science & Business Media.
Harlow, J. H. (2014). Electric Power Transformer Engineering. London: CRC Press.
Horton, W. F. (2011). Power Frequency Magnetic Fields and Public Health. Paris: CRC
Press.
Losi, A. (2014). Integration of Demand Response Into the Electricity Chain: Challenges,
Opportunities, and Smart Grid Solutions. Chicago: John Wiley & Sons.

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Proulx, T. (2016). MEMS and Nanotechnology, Volume 4: Proceedings of the 2011 Annual
Conference on Experimental and Applied Mechanics. Chicago: Springer Science & Business
Media.
Rebennack, S. (2013). Handbook of Power Systems II. London: Springer Science & Business
Media.
Vendelin, G. D. (2012). Microwave Circuit Design Using Linear and Nonlinear Techniques.
Texas: John Wiley & Sons.
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