Expert Answer:Lab report (Three-Phase Transformers)

  

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Three-Phase Transformers
Abstract
In real life applications, power systems are three phase systems, and can be connected in
multiple ways, and one of the significant components of power systems, is a three-phase
transformer. Transformers can be described as isolators or components that isolate the system to
different blocks, and that is one of the most useful advantages of them. There are many types of
transformers such as a step up, a step down, and auto transformers. In this lab, a three-phase
transformer was used experimentally connected in multiple ways. A no-load test on a three-phase
transformer was first performed under six connections. Afterwards, a short circuit test on a threephase transformer was done under two connections. After that, a balanced three-phase load was
connected to the secondary side of the three-phase transformer, and measurements were obtained.
Additionally, the voltage regulation and efficiency of the transformer were calculated using the
measurements obtained for all cases required.
Introduction
This lab introduced the overall idea of the three-phase transformers, and provide all
needed concepts as well as methods of computing and preforming them in phasor and time domain.
The purpose of doing calculations, MATLAB programming, and implementing experiments in
this lab was to get acquainted with three phase transformers. In this lab, a real three-phase
transformer and measured phenomenon relating to real transformers was experimented. The
equivalent model for the transformer was also determined as well as performing harmonic analysis
to reconstruct the current and voltage waveforms of the transformer. This lab was started by doing
hand calculations, and confirming the results by writing MATLAB programs, then the experiment
Three-Phase Transformers
was implemented. All hand calculated results, MATLAB results, and experimental measurements
were compared in order to confirm the accuracy of the data obtained.
Procedure
As part of the pre-lab, various Matlab functions were written to calculate the properties of
an ideal transformer. Afterwards, short circuit measurements were also recorded for the Y-Y and
∆/YG connections. The 125/125 winding was used for each connection, and a 120v line voltage
was applied at 60 Hz.
No-Load measurements and analysis:
In this part of the lab, 120v line voltage at 60Hz was applied to the transformer connections.
There was no load connected to the secondary side of any transformer configurations. The current
and voltage waveforms were then captured and recorded for analysis. Also, for the ∆/Y connection
special care had to be taken to ensure that the primary side voltage was leading the secondary side
voltage by 30 degrees. This was achieved by connecting the delta or primary side in negative
sequence.
Performance of three phase transformer connections under balanced loads:
In the next part of the lab, the voltage regulation and efficiency of the transformer were
calculated at 100, 75, 50, and 25% of the transformers rated value using a purely balanced resistive
loads. The rated current for the windings of the transformer was 0.7 A. To achieve the rated load
percentages, the appropriate resistor values were calculated for the loads. Afterwards, the no-load
and full load voltages were measured along with the input and output power in order to calculate
Three-Phase Transformers
the voltage regulation as well as the efficiency of the transformer using Matlab. The voltage and
current waveform data was also collected for harmonic analysis purposes.
Performance of the open delta-V/V connection under balanced load:
For this part of the lab, the delta connections on both sides of the transformer. The line
voltage applied on the primary side was 120v at 60 Hz and the load connected to secondary was
in wye configuration. The loads on each phase were then adjusted to achieve 50% rated current.
Data was then collected to calculate the efficiency of the connection and compare it to closed delta
connection.
Tests for determining the equivalent model of the three phase transformer
bank:
In this part of the lab, we performed short and open circuit tests on the Y-Y and ∆-Y
connected transformers to determine the equivalent circuit model of the three phase transformer.
Using the data collected and the equivalent circuit modeled in Matlab, the efficiency and voltage
regulation of the transformer was calculated at 100, 75, 50, and 25% of rated current.
Three-Phase Transformers
Measurements and Experimental Results
This part of the report represents all the actual results of the experiments in organized
subsections that also contain all graphs and tables of this experiment. Most of the pre-lab
calculations were done using Matlab, and there were few parts that need some hand calculations.
The hand calculations and MATLAB results were fairly close to the experimental data obtained.
However, when doing the hand calculations and MATLAB, all system components were assumed
idea, while in real life applications they are not. This was one of the reasons behind the slight
differences between the experimental and calculated results using Matlab. The experimental
readings are included in the tables that are shown below instead of including the screenshots that
were taken to save the results. This helps in making the report more organized. It also helps when
comparing the theoretical and empirical results in the discussion part of this assignment.
1. GY/GY:
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
199
113.8
0.099
33.6
Secondary
215
123
0
0
Table1. No-load test collected data
The measurements obtained from the no-load test are shown in table 1.
Three-Phase Transformers
2. Y/Y :
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
193
112
0.0432
8.7
Secondary
211
121
0
0
Table2. No-load test collected data
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
15
8
0.713
18
Secondary
0
0
0.623
0
Table3. Short circuit test measurements
The measurements obtained from the no-load test and the short circuit test can be seen in
table 2 and 3.
• Balanced Load
Rated load
100 %
75%
50%
25%
Rdesired (Ω)
178.5
238
357
714
Ractual (Ω)
196
245
490
980
Table4. calculated load
Rated load
ᶇ(%)
100 %
91
75%
92.3
50%
88.7
25%
83.45
Voltage Regulation (%)
4.6
4.8
4.5
4.45
Table5. Efficiency and voltage regulation of different rated loads
Three-Phase Transformers
The calculated load at different percentages of current can be found in table 4, and table 5
shows the measurements obtained from the primary side and load side at different loads.
3. Y/GY:
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
193
112
0.0453
10
Secondary
216
121
0
0
Table6. No-load measurements
The measurements obtained from the no-load test can be seen in table 6 above.
4. ∆/GY :
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
112
68
0.05
8
Secondary
214
126
0
0
Table7. No-load measurements
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
13
5
0.734
24
Secondary
0
0
0.643
0
Table8. Short circuit test measurements
Three-Phase Transformers
Tables 7 and 8 contain the no-load and short ciriut tests meauserments.
• Balanced Load
Rated load
100 %
75%
50%
25%
Rdesired (Ω)
285
406
571
1127
Ractual (Ω)
196
(∆-connected)
Table9. calculated rated loads
326.6
490
Rated load
VL (V)
V1ϕ (V)
IL (A)
100%
120
67
1.5
Primary
75%
117
65
0.934
50%
117
64
0.79
side
25%
112
65
0.233
100%
206
123
0.323
75%
202
119
0.491
load
50%
209
125
0.378
25%
216
124
0.131
Table10. Balanced load of different rated loads
980
P3ϕ (w)
253
199
157
52
233
175
141
47
Rated load
100 %
75%
50%
25%
ᶇ(%)
93.25
91.33
92
86.19
Voltage Regulation (%)
2.5
2.7
2.3
1.976
Table11. Efficiency and voltage regulation of different rated loads
The determined loads as different percentages of the rated current are shown in table 9.
Also, the measurements obtained of the balanced load can be seen in table 10. Table 11 represents
the efficiency of each load at different percentages of the rated current.
Three-Phase Transformers
5. Y/∆:
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
193
115
0.08
7.9
Secondary
122
72
0
0
Table12. No-load measurements
The measurements obtained from the no-load test for the primary and secondary sides of the
transformer can be seen in table 12.
• Balanced Load
Rated load
100 %
75%
50%
25%
Rdesired (Ω)
174
233
348.31
485.72
Ractual (Ω)
196
245
326.6
490
Table13. calculated Rated loads
Rated load
Primary
side
load
VL (V)
V1ϕ (V)
IPH(A)
100%
211
123
0.691
75%
205
122
0.549
50%
202
119
0.432
25%
199
117
0.31
100%
129
72
0.633
75%
124
71
0.491
50%
123
72
0.371
25%
122
72
0.255
Table14. Balanced loads measurements
P3ϕ (w)
259
201
149
101
228
177
136
91.33
Three-Phase Transformers
Rated load
100 %
75%
50%
25%
ᶇ(%)
92.14
91.55
91.43
91.7
Voltage Regulation (%)
3.9
3.2
3.213
2.921
Table15. Efficiency and voltage regulation of different rated loads
The calculated loads for different percentages of the rated current and the measurements
obtained from the primary, and loads sides of the transformer can be seen in tables 13 and 14.
Table 15 shows the efficiency of each percentage of the rated load.
6. ∆/∆:
VL (V)
V1ϕ (V)
IL (A)
P3ϕ (w)
Primary
114
68
0.069
7.2
Secondary
122
69
0
0
Table16. No-load measurements
The no-load measurements obtained can be found in table 16.
• Balanced Load
Rated load
100 %
75%
50%
25%
Rdesired (Ω)
173.22
232.1
346.73
492.29
Ractual (Ω)
196
245
326.6
Table17. Calculated rated loads
Rated load
Primary
side
load
100%
75%
50%
25%
100%
75%
50%
490
VL (V)
IL(A)
IPH(A)
P3ϕ (w)
116
119
117
116
125
124
126
1.22
1.03
0.743
0.518
1.39
1.032
0.71
0.729
0.62
0.439
0.302
0.79
0.501
0.402
305
191
138
109
275.88
181
129
Three-Phase Transformers
25%
126
0.429
0.262
92
Table18. Balanced loads measurements
Rated load
100 %
75%
50%
25%
ᶇ(%)
86.1
87.9
89.7
87.8
Voltage Regulation (%)
2.0
2.1
1.8
1.7
Table19. Efficiency and voltage regulation of different rated loads
The loads calculated for different percentages of the rated current can be seen in table 17.
Table 18 shows the measurements taken for the balanced load for each percentage. The efficiency
of each perchance of the rated load can be found in table 19.
7. Open delta ( V/V ):
Side
VL (V)
IL(A)
IPH(A)
P3ϕ (w)
Primary
123
0.722
0.726
219
Load
118
0.8
0.370
127
Efficiency (%)
58.3
Table20. 50% rated balanced load measurements
Rated load
50%
Rdesired (Ω)
345.54
Ractual (Ω)
326.6
Table21. determined 50% rated load
The measurements recorded for the open-delta connection at 50% rated load can be found
in table 20. Also, table 21 represents the balanced load values used for 50% rated current.
Three-Phase Transformers
Equivalent circuit model of three phase transformer:
➢ Y/Y connection:


transformer ratings:
ZB = 156.25 Ω
Side
Referred to primary side
Referred to secondary side
Per unit system
300AV
216/ 216 V
Req
Xeq
Rc
13.67 Ω
4.01 Ω
4.278 K Ω
13.67 Ω
4.01 Ω
4.278 K Ω
0.0863 pu
0.243 pu
27.22 pu
Table22. Equivalent circuit model
Xm
3.509KΩ
3.509KΩ
22.54 pu
The parameters of the equivalent circuit of the three phase transformer referred on the
primary and secondary sides and in the per unit system as well are shown in table 22 above. It can
be seen that the values referred to both sides of the transformer are the same, and that was because
the ratio of the transformer was one.
➢ Delta / GY connection :


transformer ratings : 300AV 125/ 216 V
ZB1 = 52.08 Ω
, ZB2 = 156.25 Ω
Side
Referred to primary side
Referred to secondary
side
Per unit system
Req
13.66 Ω
Xeq
11.19 Ω
Rc
2.355 K Ω
Xm
1.321 KΩ
41.32 Ω
30.99Ω
7.12 KΩ
3.83 KΩ
0.267 pu
0.209 pu
40.23 pu
Table23. Equivalent circuit model
25.14 pu
The data shown in table 23 above are the parameters of the equivalent circuit of the three
phase transformer referred to the primary and secondary sides and in the per unit system as well.
As can be seen, the values referred to the secondary side are bigger which makes sense since the
secondary voltage is the high voltage.
Three-Phase Transformers
Analysis and Discussion
According to the measurements taken, all the experimental results were fairly close to the
expectations. Most of the small differences occurred were due to the fact that the equipments
used are not ideal, whereas when doing the calculations and to come up with expectations all the
circuits components were assumed ideal. The following paragraphs discuss every requirement
from 1 to 5 respectively based on the results obtained which can be found in the tables
represented in the previous section of this assignment.
This phase shift was by design as per the lab requirements. For the rest of the connections,
the primary and secondary voltages were in phase as expected. The magnitudes of the line voltages
in the ∆-YG and Y-∆ connections were a factor of √3 off. This was due to the fact that the line
voltage could not exceed 120v and therefore for these two connections approximately 69v had to
be applied to each phase of the delta connection. The magnitudes of the line and phase voltages
for the rest of the connections were nearly the same or as expected; there were differences caused
by the unideal characteristics within the equipment itself.
Third harmonic content was found to be present in each phase of each connection.
However, in the delta connected circuits, either primary, secondary, or ∆-∆, it was found that the
harmonic content was isolated from the rest of the system in that it was forced to circulate within
the ∆ connection itself. In the YG connection, the third harmonic was also isolated in that it was
shunted to ground. However, in the case where there was an ungrounded Y connection, the third
harmonic was not isolated from the system and therefore would be transferred to the load.
In terms of power delivery, it was found that the ∆-YG connection delivered the most
Three-Phase Transformers
power. The Y-Y and ∆-∆ connections delivered nearly the same amount of power, however, it was
also found that the power delivered by the ∆-YG connection was significantly greater. This result
was unexpected since the line voltage on the secondary side of the ∆-YG connection should have
been higher and thus less current should been provided to each phase of the Y connected load.
This unexpected result might be due to using the software to take wrong measurements.
The ∆-Y connection delivered the most power and thus had the greatest efficiency. For the
voltage regulation, however, the advantage was found with the Y-Y configuration. This
observation can be confirmed by looking at the tables of voltage regulation and efficiency that
represented in the results section of this report.
There are advantages and disadvantages to disconnecting a Y-Y connection and replacing
it with a ∆-∆ connection. One advantage is that if the Y-Y connection was not grounded on both
sides, the ∆-∆ connection will get rid of any problems that existed due to the third harmonics of
current. A disadvantage to replacing the Y-Y connection would be cost of replacement. Other than
that, there is no real reason to have a Y-Y connection as even the book says there are very few
real-world applications of Y-Y connected transformers.
The main harmonic content present in our testing was the tripling harmonic content or
mainly the third harmonic. Three of the four transformer connections encountered in this lab can
be used to isolate third harmonic components of the current from the power system. The YG-∆
and ∆-YG connections isolate the third harmonic components on the delta side because the current
is able to circulate on the delta side. This acts as a drain of sorts because in a Y-Y connection that
is not grounded, excess current is not able to disperse so it builds up and creates a problem. This
is because the third harmonic of each phase is in phase with the other third harmonics. This causes
Three-Phase Transformers
voltages to become non-sinusoidal if the load is not balanced. The ∆-∆ connection also isolates the
third harmonic components of the current from the power system because the current can flow on
both sides of the transformer bank.The efficiency of three phase transformers is very close to what
was experimentally determined in a single phase transformer. However, it is better to use three
phase transformers when having 3 loads because it is more economical even though a single phase
transformer would give better results. The open delta connection was found to have the lowest
efficiency and it does not provide any advantage to mitigate the effects of the third harmonic from
reaching the load. Furthermore, if one of the 2 phases of the open delta connection was to
disconnect, the system would experience greater instability. Also, the Y-Y connection has little
advantage when it comes to mitigating the effects of the third harmonics on the load thus it is
another connection to possibly avoid.
Conclusion
In this lab, the three-phase transformer analysis and implementation were learned. Also,
one of the important concepts and methods that was learned in this lab was how to come up with
an equivalent module for the three-phase transformer as an efficient way to analyze it under
multiple different conditions. Overall, the meter readings were relatively close to the hand and
Matlab calculations. The voltage regulation and efficiency of the transformers were calculated
multiple times under different connections of the two sides of the transformer. In addition, one of
the procedure parts was to observe the behavior of the three-phase transformer under balance
loaded conditions, and that part was done successfully shown in the results section of this
assignment. The only errors that occurred were due to the fact that transformers are non-ideal
components in reality. All objectives of this lab were successfully met.

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