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The Premier Electrical Maintenance and Safety Event
I Know How to Add the Numbers –
But What Is the Power Factor Telling
Me?
Keith Hill
Doble Engineering Company
1 - Hill
INTRODUCTION:
The purpose of this paper is to advance the technical ability of the tester to correctly
identify and interpret power factor test data. In the paper I Have a Lot of Numbers, What do they
Mean – Basic Interpretation of Two Winding Transformers, presented at PowerTest 2013, the
tester learned how to verify that the tests were performed correctly. In this paper, we will dig
deeper into the interpretation of irregular test data for the following types of transformers: twowindings, auto with tertiary and three winding. This data will include an excellent example of
what we mean by ‘average power factor”.
Several case studies for various types of transformers, along with various problems are
included in this paper. This data will point out problems that are often encountered in the field
and it is often times difficult for the tester to interpret the results. These case studies will detail
how to verify the test results and what to look for when analyzing the test data.
Some terminology listed in this paper may be new to you so an attempt is being made to
identify these components with a brief description. More detailed information can be located in
the operator’s manual provided by the manufacturer of your equipment. For this paper it will be
assumed that the tester knows how to operate the test set and how to verify that the tests were
performed properly. It is important that the tester fully understands the test forms or software
being used. It is imperative that the test data for the apparatus be analyzed in the field and not
back in the office after the apparatus has been returned to service. One of the most important
parts of analyzing test data is to make sure that the tests were performed correctly. Test data
will be invalid if the test procedures used were incorrect.
The following terminology will be used in this paper: CH, CL, CHL, CH’, CL’, and C1
CH is used to describe all of the high voltage components to ground. This will include the high
side insulation, high side bushings, structural insulating members, insulating fluid, and deenergized tap changed, if present.
CL is used to describe all of the low voltage components to ground. This will include the low
side insulation, low side bushings, structural insulating members, insulating fluid and load tap
changer, if present.
CT is used to describe all of the tertiary components to ground. This will include the low side
insulation, low side bushings, structural insulating members, and insulating fluid.
2 - Hill
CHL is used to describe the insulation between the windings, winding barriers, and the insulating
fluid.
CHL
HIGH
LOW
CH
CL
Tank & Core
Figure 1
Dielectric Circuit of a Two-Winding Transformer
The CH’ and CL’ may be new terminology to both inexperienced and experienced testers
who may normally use test equipment manufactured by various manufacturers.
CH’ is the CH insulation minus the sum of the C1 results for the primary bushings.
CL’ is the CL insulation minus the sum of the C1 results for the secondary bushings.
C1 is the test performed on the bushings (Figure 2), with a capacitance tap, by energizing the
main conductor and measuring to the tap in the Ungrounded Specimen Test (UST) mode.
3 - Hill
Figure 2
HANDY FORMULAS and THINGS TO KEEP IN MIND
Power Factor = watts x 10
mA
Capacitance = 265 x mA (60 Hz) (Rule of thumb is good up to about 15% power factor)
Capacitance = 318 x mA (50 Hz) (Rule of thumb is good up to about 15% power factor)
It must be remembered that a change in current or capacitance from prior tests is a
physical change, while a change in watts is usually from contamination or deterioration. From
the above power factor formula, one can see that if the capacitance and current are the same, as
in prior tests, that the change in power factor would have to be from a change in the watts.
One should remember that when we state “power factor” we should be stating “average power
factor” as good insulation and defective insulation are averaged together.
REVIEW OF TEST PROCEDURE VERIFICATION
By performing some simple math we can verify that the tests were performed correctly.
For the primary winding the summation of the currents and watts for Test 2 (CH) and Test 3
(CHL) add to be Test 1 (CH + CHL). Test 4 is the calculated CHL which is calculated by
subtracting the currents and watts of test 2 (CH) from test 1 (CH +CHL). As you can see the
CHs will cancel out leaving the CHL.
For the secondary winding the summation of the currents and watts for Test 6 (CL) and
4 - Hill
Test 7 (CHL) add to be Test 5 (CL + CHL). Test 8 is the calculated CHL which is calculated
by subtracting the currents and watts of test 6 (CL) from test 5 (CL +CHL). As you can see the
CLs will cancel out leaving the CHL.
For some test sets, all data is referenced to 10 kV. This means that the CHL insulation
tests 3, 4, 7, and 8 should be “equal” even when tested at different voltages. If a difference in the
data is noted there may be a voltage related test problem.
Transformer 1 Test Data
Two Winding
Test
#
1
2
3
4
5
6
7
8
9
10
ENG
H
H
H
1-2
L
L
L
5-6
67 kV/12.47 kV
Test
kV
10
10
10
10
10
210
mA
Watts
31.889
10.287
21.605
21.602
66.615
45.013
21.613
21.602
6.550
35.312
1.063
0.408
0.655
0.655
2.557
1.930
0.622
0.627
0.243
1.534
15 MVA
% PF
Meas
----0.40
0.30
0.30
----0.43
0.29
0.29
0.37
0.43
% PF
Corr
0.39
0.29
0.29
----0.42
0.28
0.28
0.36
0.42
Corr
Factor
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
0.98
Cap
Meas.
8458.8
2728.7
5730.9
5730.1
17669.8
11939.8
5732.9
5730
1737.47
9366.64
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
CH’
CL’
Figure 3
After doing the “math” for Transformer 1, the tester should feel comfortable that the tests
performed on the primary were performed correctly since tests 2 and 3 add to be test 1 and that
tests 3 and 4 are “equal”.
The secondary tests were also performed correctly since tests 6 and 7 add to be test 5 and
that tests 7 and 8 are “equal”. To verify the results, tests 3, 4, 7, and 8 should be “equal”. (These
four tests should be “equal” even when the windings are tested at different voltages).
The data for the CH’ and CL’ are the CH and CL without the bushings If taps are not
present or the C1 tests were not performed CH’ and CL’ cannot be calculated.
Now since the tests were performed correctly the tester should analyze the corrected
5 - Hill
power factor results. The measured power factor results have not been compensated for the oil
temperature. The apparatus or top oil temperature can often time greatly affect watts which will
affect the corrected power factor results. All oil filled equipment should be corrected to 20
degree C (68 degree F). This temperature correction factor compensates for the different
temperatures that may occur for different test periods (hot vs. cold) or loading factors which can
often times affect the temperature of the insulating fluid. From the data above you can see that
the oil temperature resulted in a correction factor of .98. The measured power factors are
multiplied by the correction factor .98 to determine the corrected power factors. The data for
Transformer 1 is acceptable as the “numbers” add up correctly and the corrected power factor is
below the expected limit of 0.5% for this type of transformer.
Transformer 2 Test Data
Two Winding
Test
#
1
2
3
4
5
6
7
8
9
10
ENG
H
H
H
1-2
L
L
L
5-6
2400/480 volt
Test
kV
2.5
2.5
2.5
----1.0
1.0
1.0
-----
mA
Watts
12.920
4.911
8.018
8.018
18.710
10.700
8.018
8.010
3.605
1.268
2.338
2.337
5.620
3.282
2.336
2.338
D-Y
% PF
Meas
----2.58
2.92
2.92
----3.07
2.91
2.92
% PF
Corr
----2.06
2.34
2.34
----2.46
2.33
2.34
750 kVA
Corr
Factor
.80
.80
.80
.80
.80
.80
.80
.80
Cap
Meas.
3426
1302
2125
2124
4963
2838
2125
2125
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
CH’
CL’
Figure 4
As Found Test Results
After doing the “math” for Transformer 2, the tester should feel comfortable that the
tests performed on the primary were performed correctly since tests 2 and 3 add to be test 1 and
that tests 3 and 4 are “equal”.
The secondary tests were also performed correctly since tests 6 and 7 add to be test 5
and that tests 7 and 8 are “equal”. To verify the results, tests 3, 4, 7, and 8 are “equal” even
when the windings were tested at different voltages.
There will be no data for the CH’ and CL’ since the bushings did not have taps. If taps
6 - Hill
are not present or the C1 tests were not performed CH’ and CL’ cannot be calculated.
From the data above you can see that the oil temperature resulted in a correction factor
of .80. The measured power factors are multiplied by the correction factor .80 to determine the
corrected power factors.
Noting that all of the power factor results exceed the recommended limits (1.0%) the
tester must determine some of the possible causes for the abnormal test results. Using the
information provided that described CH, CL, and CHL the tester can narrow the possible
problems.
Since CH, CL, and CHL are all higher than the recommended limits, the only thing
common to all three insulation systems is the insulating fluid, so if we have contaminated fluid,
we have contaminated windings.
Transformer 2 Test Data – after repairs
Test
#
1
2
3
4
5
6
7
8
9
10
ENG
H
H
H
1-2
L
L
L
5-6
Test
kV
2.5
2.5
2.5
----1.0
1.0
1.0
-----
mA
Watts
11.810
4.552
7.271
7.258
17.040
9.777
7.271
7.263
0.327
0.143
0.182
0.184
0.541
0.356
0.179
0.185
% PF
Meas
----0.31
0.25
0.23
----0.36
0.25
0.25
% PF
Corr
----0.28
0.23
0.23
----0.32
0.23
0.23
Corr
Factor
.90
.90
.90
.90
.90
.90
.90
.90
.90
.90
Cap
Meas.
3134
1207
1928
1927
4521
2593
1928
1928
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
CH’
CL’
Figure 5
As Left Test
After baking the windings and replacing the insulating fluid the transformer now has
power factors that are normally expected on a new transformer. A new power transformer (over
500 kVA) would normally be specified to have a power factor less than 0.5%, but in reality one
would normally expect to see a power factor that is in the 0.25% to 0.30% range. This 25 year
old transformer now has power factor results expected on a new transformer.
7 - Hill
Transformer 3 Test Data
Two Winding
230 kV/25 kV
Y-D
Test
#
ENG
Test
kV
mA
Watts
% PF
Meas
1
2
3
4
5
6
7
8
9
10
H
H
H
1-2
L
L
L
5-6
10
10
10
262.11
258.45
3.633
3.660
677.76
674.08
3.639
3.680
251.373
640.064
10.905
10.918
0.0210
-0.013
27.797
27.728
0.0180
0.069
10.732
26.768
----0.42
0.06
-0.04
----0.41
0.05
0.19
0.43
0.42
3.
3
2.
%
PF
Corr
----0.42
0.06
-.04
----0.41
0.05
0.19
0.43
0.42
900 MVA
Corr
Factor
Cap
Meas.
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
69525.8
68555.6
963.55
970.200
179779.7
178803.1
965.27
976.600
66678.49
169780.4
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
CH’
CL’
Figure 6
Please note the data for Figure 6 as the primary currents and watts for tests 1 and 2 are
basically the same while the currents and watts for tests 3 and 4 are basically zero. The same is
true for the secondary as tests 5 and 6 are basically the same while tests 7 and 8 are zero. This
two winding transformer was used in an application from a very high voltage (230 kV) to a
much lower voltage (25 kV). Electrostatically shield transformers are used to protect sensitive
electrical equipment from undesirable high frequency signals commonly generated by lighting,
switching surges, motors, and SCR feeds.
Electrostatic Shield
Figure 7
Shielded Transformer
8 - Hill
This shield (Figure 7) is not always represented on a transformer nameplate and this can
be very troublesome to a tester since the power factor test results for a shielded transformer will
be very different compared to the expected non-shielded results.
Since the currents and watts for tests 3, 4, 7, and 8 are often “0” we do not pay a lot of
attention to the measured or corrected power factors. A very small current can often result in a
very high power factor which in this case is not accurate for the condition of the windings.
Transformer 4 Test Data
Three Winding
Test
#
1
2
3
4
5
6
7
8
9
10
11
12
13
ENG
H
H
H
1-2
L
L
L
5-6
T
T
T
9-10
All
Test
kV
10
10
10
4
4
4
1
1
1
mA
Watts
61.430
18.110
43.300
43.300
23.260
6.411
16.840
16.849
52.890
52.690
0.179
.200
2.044
0.502
1.553
1.542
1.020
.425
0.612
0.595
2.688
2.676
0.006
0.102
% PF
Meas
----0.28
0.36
0.36
----0.66
0.36
0.35
----0.52
0.34
0.60
% PF
Corr
----0.27
0.35
0.35
----0.64
0.35
0.34
----0.49
0.33
0.58
Electrostatic
Shield
Corr
Cap
Factor
0.97
19556
0.97
5765
0.97
13785
0.97
13791
0.97
7405
0.97
2040
0.97
5362
0.97
5365
0.97
16837
0.97
16774
0.97
57.040
0.97
63
Meas.
CH+CHL
CH
CHL(UST)
CHL
CL+CLT
CL
CLT(UST)
CLT
CT+CHT
CT
CHT(UST)
CHT
CH,CL,CT
Figure 8
After performing the math for the primary and secondary windings, for the three
winding transformer (Figure 8), it appears the tests were performed correctly. The test results
for the tertiary may be questionable as the test results for the tertiary winding are similar to the
results for the shielded transformer (Transformer 3).
Transformer 4 is not a shielded transformer, however the low voltage winding for this
transformer is acting as a “shield” since the low voltage is “guarded” or taken out of the test
when performing the tests on the tertiary winding. For test 9 the winding is guarded, test 10 the
9 - Hill
winding is guarded, and for the UST test the winding is grounded in which case ground current
is not measured. Please note Figure 9 for the winding layout.
CHL
Figure 9
Three Winding Transformer
10 - Hill
Transformer 5 Test Data
Two Winding Transformer
Test
#
1
2
3
4
5
6
7
8
9
10
ENG
H
H
H
1-2
L
L
L
5-6
Test
kV
10
10
10
2
2
2
mA
Watts
32.380
9.969
22.390
22.411
40.720
18.320
22.400
22.400
7.753
2.558
1.855
0.694
0.703
1.484
0.737
0.734
0.747
-0.15
% PF
Meas
----1.86
0.31
0.31
----0.40
0.33
0.33
-0.19
% PF
Corr
----1.86
0.31
0.31
----0.40
0.33
0.33
-0.19
Corr
Factor
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
Cap
Meas.
8591
2644
5941
5947
10803
4860
5942
5943
2058.8
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
CH’
CL’
Figure 9
Analysis of the data in Figure 9 reveals a very high power factor for test 2 which is the
CH. Since CH is the only insulation system that has a very high power factor we do not suspect
the oil or any items that part of the secondary winding. From the data on line 9 we determine
that C1 tests have been performed on the primary bushings and the CH, without the bushings,
now has negative watts.
The C1 test data for the primary bushings were:
H1
H2
H3
mA
Watts
0.761
0.736
0.719
0.798
0.653
0.555
% Power Factor
10.5
8.87
7.72
Figure 10
We can see from the above data (Figure 10) that the summation of the watts (0.798 +
0.653 + 0.555 = 2.006 watts) for the C1 test exceeds the watts for the CH (1.855 watts) which
makes the watts for test 9 negative ( 1.855 – 2.006 = -0.19).
11 - Hill
Transformer 6 Test Data
2 Winding Transformer
Test
#
1
2
3
4
5
6
7
8
9
10
ENG
H
H
H
1-2
L
L
L
5-6
Test
kV
10
10
10
10
10
10
mA
Watts
33.080
12.860
20.210
20.220
59.360
39.140
20.210
20.220
8.133
35.668
16.220
3.612
12.610
12.608
23.630
11.040
12.610
12.590
3.495
10.813
% PF
Meas
----2.81
6.24
6.24
----2.82
6.24
6.23
4.30
3.03
% PF
Corr
----2.84
6.30
6.30
----2.85
6.30
6.29
4.34
3.06
Corr
Factor
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
1.01
Cap
Meas.
8765
3411
5352
5354
15734
10380
5353
5354
2157
9459
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
CH’
CL’
Figure 11
The data in Figure 11 indicates that the power factor without the bushings (Line 9) is
greater than the power factor with the bushings (Line 2). Review of the data indicates that all of
the overall power factors are above the acceptable limits for this transformer. Since all of the
power factors are elevated one would first suspect that the insulating fluid and windings are
contaminated. As stated earlier we are reviewing the average power factors of the insulations.
The good bushings made the contaminated winding look “better”.
12 - Hill
Transformer 7 Test Data
Auto Transformer with a Tertiary
Test
#
1
2
3
4
5
6
7
8
ENG
HL
HL
HL
1-2
T
T
T
5-6
Test
kV
10
10
10
10
10
10
mA
Watts
50.720
22.200
28.490
28.520
95.080
66.550
28.490
28.530
1.039
0.528
0.518
0.511
1.752
1.228
0.520
0.524
% PF
Meas
----0.24
0.18
0.18
----0.18
0.18
0.18
% PF
Corr
----0.24
0.18
0.18
----0.18
0.18
0.18
Corr
Factor
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
Cap
Meas.
13456
5890
7557
7566
25220
17655
7557
7565
CH+CHT
CH
CHT(UST)
CHT
CT+CHT
CT
CHT(UST)
CHT
Figure 12
An auto transformer with a tertiary is actually a two winding transformer. Interpretation
of an auto with tertiary is the same as for the two winding. The currents and watts add up
correctly so are comfortable that the tests were performed correctly. All of the power factors
are below the acceptable limits so this transformer is acceptable.
Transformer 8
Two Winding Transformer – Acceptance Tests
The following transformer data can be devastating for a testing company as it may cost
you an excellent customer. The owner of the transformer questioned if you can have “negative”
results. He was informed that it was possible but that it was very abnormal and usually was the
result of a test procedure error.
The first dataset was the results attained by testing company number #1 while the second
dataset was provided by testing company #2.
13 - Hill
Data provided by Testing Company #1
Test
#
1
2
3
4
5
6
7
8
ENG
H
H
H
1-2
L
L
L
5-6
Test
kV
2
2
2
1
1
1
mA
Watts
11.76
3.040
8.729
8.720
15.23
6.514
8.729
8.716
0.600
0.955
-0.350
-0.355
1.634
1.952
-0.330
-0.318
ACCEPTANCE TEST
% PF
Meas
----3.14
-0.40
-0.41
----3.00
-0.38
-0.36
% PF
Corr
----2.23
-0.3
-0.3
----2.13
-0.3
-0.3
Corr
Factor
0.71
0.71
0.71
0.71
0.71
0.71
0.71
0.71
Cap
Meas.
3121
805.9
2315
2315
4041
1727
2315
2314
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
Figure 13
The numbers add up (Figure 13) to indicate that the test were performed correctly but
the power factors for tests 2 and 6 are well above the recommended limits for a new power
transformer. Tests 3, 4, 7, and 8 have negative power factors since the watts for test 2 were
greater than the watts for test 1. The watts were also great for test 6 than test 5. The troubling
thing about these results is that the tester was asked if the transformer was grounded for the
tests and he stated that it was grounded for all of the tests. This “tester” (really a button pusher)
had no concern for the high power factors, the negative results for watts and power factors, and
the inaccurate report that was provide to his customer.
Data provided by Testing Company #2
RETEST
Test
#
1
2
3
4
5
6
7
8
% PF
Meas
----0.35
0.24
0.24
----0.18
0.22
0.25
ENG
H
H
H
1-2
L
L
L
5-6
Test
kV
10
10
10
1
1
1
mA
Watts
11.82
3.206
8.616
8.614
15.49
6.874
8.616
8.616
0.314
0.111
0.205
0.203
0.335
0.123
0.191
0.212
Figure 14
14 - Hill
% PF
Corr
----0.28
0.19
0.19
----0.14
0.18
0.20
Corr
Factor
0.80
0.80
0.80
0.80
0.80
0.80
0.80
0.80
Cap
Meas.
3135
850.4
2285
2284
4109
1823
2285
2286
CH+CHL
CH
CHL(UST)
CHL
CL+CHL
CL
CHL(UST)
CHL
The math for the retest adds up (Figure 14) and the power factors are well below the
acceptable limits for a new power transformer. When questioned about these results and what
he identified when he arrived on site the 2nd tester stated that the transformer was not grounded.
The tester for the second testing company connected the substation ground to the transformer as
it was sitting on the concrete pad ungrounded. Who would you call in the future?
Conclusion:
As one can see, interpretation of power factor test data can be involved and very often
time consuming. As mentioned earlier in the paper, it is imperative that the data is analyzed in
the field in case other diagnostics tests need to be performed. Do not wait until you get back into
the office to perform the math and to analyze the power factors. Do not be a “button pusher”!
Biography
Keith Hill has been employed at Doble Engineering since 2001, and currently works as a
Principal Engineer in the Client Service Department. Keith has over 38 years of experience in
substation maintenance, electrical testing, and project management. Mr. Hill is a member of
IEEE, a former NETA certified technician, and is a level I and II certified thermographer. Prior
to Doble, Mr. Hill was the Electrical Supervisor of Engineering Services for a major refinery.
Mr. Hill has published several papers relating to equipment testing and maintenance for various
conferences and publications. At the present time, Keith serves as the secretary of the Doble
Arresters, Capacitors, Cables, and Accessories committee. Keith received his BS from the
University of Houston with a major in Electric Power.
15 - Hill