IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 13, No. 3; June 2006
477
The Impulse Design of Transformer Oil-Cellulose Structures
J.K. Nelson and C. Shaw
Rensselaer Polytechnic Institute.
Dept. of Electrical, Computer and Systems Engineering
Troy, NY 12180-3590, USA
ABSTRACT
Transformer oil/cellulose structures are often designed based on a cumulative stress
criterion derived from experimental tests at power frequency. However, such
structures must also meet stringent impulse requirements defined by a Basic Insulation
Level (BIL). The industry has tried to establish an equivalence factor to permit power
frequency cumulative stress methods to be used to estimate impulse withstand strength.
Since the mechanisms of failure differ substantially under surge conditions, there
would seem no good reason to suppose that a universal equivalence factor is
appropriate. Tests are reported using a 2.3 MV generator to document impulse failure
of a number of bulk, creep and hybrid structures to establish the nature of this
relationship through statistical comparisons with the established 50/60 Hz methods.
Factors varied from 1.94 to 3.34, depending on the configuration. The methodology is
described and the results discussed in the context of the design of oil-cellulose
structures, having regard to complicating factors such as waveshape and electrode
covering. The study permits some speculation about impulse design under hybrid
situations (i.e. failure paths involving both creep and bulk liquid).
Index Terms — Insulation design, oil/cellulose structures, cumulative stress, impulse
withstand.
1 BACKGROUND
THE “cumulative stress” method is in industrial use for the
design of composite (oil-paper) structures, particularly for
large transformers. It has evolved to provide a design tool for
use under alternating voltage conditions and is based on
numerous experimental test results. The economic design of
complex liquid-solid dielectric structures in divergent electric
fields is problematic since the electric stresses involved are
usually substantially non-uniform, may not change
monotonically, and a plurality of materials and geometries are
prevalent. Furthermore, the problem is further complicated by
the combined nature of many of the critical paths (i.e. part
creep, part bulk). Despite the semi-empirical nature of the
method, there is a theoretical basis for the technique [1] based
on known physics when applied for 50/60 Hz stresses. The
method has served the transformer industry well, and avoids
establishing a withstand voltage simply on the basis of the
maximum prevailing electric field which is clearly an
ineffective and uneconomic criterion.
1.1 THE CUMULATIVE STRESS CRITERION
In applying the cumulative stress technique, the structure is
examined and paths thought to be critical are identified. Such
Manuscript received on 14 September 2005, in final form 14 November 2005
paths may be categorized as either “bulk” through oil
volumes, “creep” along cellulose surfaces (paper or
pressboard) or some combination of the two. The
prevailing electric field is computed along each chosen
path, usually by the application of finite element flux
plotting software. Starting at the point of highest stress
(which is usually at one end of the path, but not always
so), the stress is calculated over a fixed increment in the
direction which maximizes the stress. In a stepwise
manner, the track is extended along the path by
considering each successive increment and computing the
largest cumulative stress i.e. the total voltage divided by
the corresponding portion of the path. The resulting
profile (cumulative stress as a function of position on the
path) is then compared with design curves used by
individual industrial designers. An example taken from
Moser [2] is depicted in Figure 1 for bulk oil and creep
paths under 50/60 Hz ac stresses. A detailed example of
the method may be studied in [3] which describes the
development of a computer-based algorithm to automate
the process
A profile which is totally under the respective design
curve is deemed to be a satisfactory design, and,
conversely, if any part of the profile lies above the curve,
the design (for that path) is considered unsafe. The
margin of safety can be assessed from the relative
positions of the curves. It is important to recognize that
1070-9878/06/$20.00 © 2006 IEEE
J.K. Nelson and C. Shaw: The Impulse Design of Transformer Oil-Cellulose Structures
100
1000
breakdown under sustained voltages and underlie the
design curves in Figure 1 will no longer be relevant.
There are no curves that are equivalent to Figure 1 which
pertain to impulse failure, and, indeed if the physical
basis for the form of Figure 1 is taken into account, there
are good reasons for surmising that the cumulative stress
method would not be likely to provide a valid basis for
impulse design.
10
(a)
(b)
1
Electric Field (kV/cm)
478
0.10
1.00
10.00
100.00
Path Length (cm)
3
Figure 1. Power Frequency acrms design curves for (a) bulk
oil, (b) creep.
this is a design criterion and not a breakdown estimate.
Statistical margin is already built into the design curves which
represent approximately a 1% failure probability. Figure 1
represents the two basic criteria for bulk and creep cases.
However, in practice, additional curves are sometimes used to
allow for gas content, electrode covering, non-continuous
operation, etc. An interesting feature of the bulk cumulative
stress curve is that its power law relationship may be
expressed as:
E = 75 d –0.38
(1)
Where d is the oil path length. It may also be shown that the
volume effect [1,4] associated with oil breakdown may also be
defined empirically as E ∝ v –0.137, where v is the volume
within a 90% equigradient contour. This would imply that, for
example, a plane parallel gap would exhibit an area which
increased approximately as the square of the gap spacing. This
is clearly erroneous unless the volume involved is not that
between the electrodes, but rather a hemispherical volume
surrounding each initiating event at the electrode. In these
circumstances the two representations are entirely compatible.
Such a description is also thus consistent with a weak link
theory of breakdown which can be represented by one of the
asymptotic distributions of extreme values [5] as given in
Section 2.3. The nature of Figure 1 explains why liquids are
particularly weak when path lengths are long, and why
barriers are effective in improving dielectric integrity.
1.2 IMPULSE FAILURE
Under impulse conditions, it is clear that some of the
mechanisms known to influence power frequency breakdown
are inoperative. Clearly, those agencies which require a
considerable period of time to operate such as
electrohydrodynamic motion producing flow-induced
cavitation, dielectrophoretic particle migration, large bubble
formation etc. will effectively be frozen out leaving fast
processes like streamer propagation as likely mechanisms. Asa
result, many of the mechanisms which are known to trigger
DIL Factor
2.5
2.5 - Full Wave
Impulse
1.7- Switching
Impulse
2
1.5
1 - Applied
1
0.8 - Induced
0.5
0
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
Time (s)
Figure 2. Design Insulation Levels (factors) for typical
ANSI dielectric tests.
Notwithstanding that, the transformer industry needs to
be able to account for impulse breakdown in the design in
order to insure that the structures meet the Basic
Insulation Level (BIL). One common method of design
assessment is to use the power frequency criteria with a
factor to account for the surge conditions. The factor is
varied according to the duration of the impulse applied.
This factor is known as the “Design Insulation Level”
(DIL). A plot of the DIL versus the time duration of the
applied voltage is given in Figure 2. However, the
obvious differences in breakdown mechanism calls into
question the use of a constant conversion factor for any
insulation system. Clearly, a comprehensive empirical
study to document this relationship would be a formidable
undertaking. The results reported here provide a modest
start in the process of providing a better basis for the
impulse design of composite structures.
2 EXPERIMENTAL ARRANGEMENTS
2.1 TEST STRUCRURES
In order to represent a number of different breakdown
path configurations, eight different test structures
(designated A – H) were developed and are described in
Table 1. These provide for breakdown paths which are
predominantly through bulk oil, along creep surfaces or
mixed configuration situations (i.e. failure paths where
IEEE Transactions on Dielectrics and Electrical Insulation
Figure 3. Three of the 8 oil-cellulose structures.
Table 1. Descriptions of the structures.
Creep
A
B
C
D
Bulk Oil
E
F
Combination
G
H
479
Vol. 13, No. 3; June 2006
4 cm x 10 cm cylinder with 2 cm
standoffs holding the rings
2 cm cylinder cut to 5 cm in length
between disc electrodes
2 cm cylinder cut to 8 cm between
disc electrodes
2-2x2.7 cm cylinders separated by
6 mm x 3 cm pressboard disc between
disc electrodes
for that [2] when applying the design criteria as discussed
in Section 4.
2.2 PULSE SOURCE
The structures were accommodated in a sealed oilfilled cell, with optical windows, which in turn was
mounted on the oil-filled high-voltage termination of a
2.3 MV Febetron™ providing a steep-fronted impulse
(0.024/3.2 µs waveshape). The test enclosure is depicted
in Figure 4. This generator was a 160-stage Marx circuit
(modified to operate at only half its voltage capacity) in a
grounded enclosure insulated with Freon™-12 gas. The
rig was controlled with a trigatron on the first stage
together with voltage control through N2 stack pressure
adjustment. The negative-going applied voltage and
waveform were determined by a 500 MHz digitizing
oscilloscope coupled through a matched 32,000:1 built-in
divider. Where the impulse failure occurred on the
1.59 cm oil gap between disc
electrodes
2.86 cm oil gap between disc
electrodes
2 cm x 10 cm cylinder with 1 cm
standoffs holding the rings
2 cm x 10 cm cylinder with 2 cm
standoffs holding the rings.
part is creep and part is through bulk liquid). Three typical
examples are depicted in Figure 3. The samples were
primarily based on pressboard cylinders placed between
contoured electrodes and vacuum oil impregnated to usual
industrial standards. By using two different diameters of
pressboard tube (4 cm and 2 cm), it was possible to provide a
pure creep surface or a combination of bulk oil and surface
creep (for the 2 cm cylinder where the pressboard was not in
intimate contact with the doughnut-shaped metallic ring – see
Figure 3 right-hand image.). The structures were immersed in
a standard transformer oil (Shell Diala B) with a moisture
content of 7 ppm determined by a Karl Fischer electrometric
titration. The oil was filtered through a 1 µm edge filter and
degassed to 1.3 Pa (10-2 Torr) in a degassing chamber in
which the oil made multiple passes down plates in the vacuum
enclosure at 70°C. The known difficulties [6] of lapped paper
insulation on the electrodes prompted the use of bare
electrodes in this study. However, proper allowance was made
Figure 4. Test enclosure mounted on the terminal of the 2.3 MV
Febetron™.
outside of the structure, a camera system (not shown in
Figure 4) was able to document the breakdown path
through the windows provided. It is recognized that the
impulse tests were not undertaken with a standard 1/50 µs
wave which would have been desirable. However the
unique multi-MV impulse generator available was not
capable of front and tail time extended to the standard
waveshape. The implications of the non-standard wave
are further discussed in Section 4.
2.3 PROCEDURES
To determine the impulse characteristics, samples were
tested according to the step up method [7], where the
actual breakdown voltage value was recorded. The
parameter estimates, were obtained from a Weibull
J.K. Nelson and C. Shaw: The Impulse Design of Transformer Oil-Cellulose Structures
480
analysis with a maximum likelihood algorithm. The actual
tests usually consisted of 30 samples per structure to obtain a
statistically meaningful result. The 1% impulse value was then
determined by rearranging the Weibull cumulative distribution
function as follows:
Given,
( )
β
⎞⎟
P = 1 − exp⎛⎜ − x
α
⎝
⎠
(2)
then:
x = α (− ln(1 − P ) )
1
β
(with P = 0.01)
Descriptive statistics were gathered for each of the
structures considered and 90% confidence intervals
computed for the α and β parameters. On the basis of the
accumulated and processed data, Table 2 was established
which summarizes the data for the various structures
grouped according to their type.
There is a presumption that the data are represented by
a Weibull distribution. In order to determine the goodness
Table 2. Experimental impulse-to-ac ratios.
(3)
where x is the value of the breakdown voltage that gives
probability P, and α and β are the Weibull scale and shape
parameters, respectively.
Design curves similar to those in Figure 1 were used to
determine the 1% ac breakdown values for each of the eight
structures studied. This was done with the proper accounting
of the bulk and/or creep paths and the absence of electrode
covering where applicable. The prevailing electric fields were
Electrode ring
extension to create
composite path
3 RESULTS
Main disc
electrode
Cylinder
Figure 5. Flux plot of the composite path appropriate to Structure H.
determined by flux plots, such as that illustrated in Fig. 5 and
a program developed in FORTRAN that uses the output of a
finite element program to determine the cumulative stress and
associated margins [3]. Figure 5 depicts a combination (bulk
oil + surface creep) case in which the discharge path can be
partly across a surface and partly through series oil path(s).
The equipotential lines are asymmetrical as a result of the
grounded end of the test enclosure, which may make the
breakdown somewhat polarity dependent. The automatic
computation of cumulative stress was undertaken for the
critical paths for each particular structure and the voltage level
in the finite element analysis was adjusted until the margin
was zero for each structure. This voltage was taken as the 1%
ac breakdown value on which the design is (arbitrarily) based.
Structure
Calc. 1%
ac
Breakdown
Value (kV)
Exptl.
1% Neg.
Impulse
Breakdown
Value (kV)
Impulse
to ac
Ratio
Structures
with rings
A
157.5
346.0
2.19
G
212.5
526.5
2.48
H
Structures
w/o rings
187.5
495.0
2.49
B
137.5
400.0
2.71
C
F
E
177.5
135.0
92.5
506.0
460.0
195.0
2.84
3.34
2.00
D
162.5
341.0
1.94
of fit of the estimated parameters, a chi-squared
goodness-to-fit test [8] with six equiprobable bins was
applied to the data of each structure. Most fits yielded χ2
values of about 80% although, notably, structures B, D,
and G were significantly worse. However, all the
structures generated better fits to a Weibull distribution
than to a normal curve.
Not all the 30 samples of each structure failed in the
same way. There was usually a predominant mechanism
which has been summarized in Table 3. It is significant,
however, that those breakdowns which occur in a nonpredominant way also often have a breakdown voltage
which is anomalous. For example, Structure A usually
failed by creep exhibiting a characteristic value of 929
kV. However, 4 samples did exhibit punctures and these
had strengths as low as 380 kV which significantly
depress the ratios in Table 2.
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 13, No. 3; June 2006
Table 3. Summary of predominant failure modes.
Structure
A
Predominant Failure Mechanism
Outer surface
punctures
B
C
D
E
F
G
H
creep,
with
(b)
2
(c)
Figure 6. Physical evidence for creep and puncture failures. (a)
Outer cylinder creep (Structure A), (b) Inner cylinder creep (Structure
B), (c) Puncture (Structure A).
These failure modes may be further visualized by
undertaking a tear-down analysis and by examining the optical
records obtained during the experiment. As an example,
Figure 6a depicts external creep damage typical of Structure A
and Figure 7a shows the corresponding optical breakdown
image typical of the creep phenomenon for that structure.
However, Table 3 also indicates that a few of the failures of
Structure A also resulted in puncture of the cylinders. This is
depicted in Figure 6c. Similarly, the internal failure pattern is
(a)
(b)
shown in Figures 6b and 7c which corresponds to
Structures B and C.
4 DISCUSSION AND IMPLICATIONS
some
Inner surface creep
Inner surface creep
Inner surface creep + barrier creep
Short paths; very variable
Short paths; very variable
Bulk oil between rings
Bulk oil, but with some creep occurring
(a)
1
481
By establishing the characteristic impulse failure
voltages and comparing them with the equivalent power
frequency computations, estimates of the conversion
factors have been obtained for the 8 different
configurations studied based on a 1% failure probability
obtained from the Weibull statistics. Factors varied from
1.94 to 3.34 depending on the configuration. These limits
certainly encompass the factor (2.5) typically used for
1/50 µs surges (see Figure 2), but do indicate that it is by
no means certain that a common factor is appropriate to
all configurations.
Of particular interest are those structures which offer a
composite path where the discharge can take a variety of
trajectories. To assess the ability of the design criteria to
evaluate such configurations, cumulative stress analysis
based on the computed electric field distribution was
applied to Structure H (see Figure 3, right hand image,
and the associated flux plot of Figure 5) for several
composite paths with varying creep and bulk oil
components, typified by the broken lines. The paths
considered are represented in more detail in Figure 8 and
include: (1) a 10 cm creep path between the disc
electrodes, (2) a composite path consisting of the middle
6 cm of the creep surface and two 0.87 cm bulk oil paths
departing perpendicularly from the creep surface to the
ring electrodes, (3) a composite path consisting of the
middle 3 cm of the creep surface and two 1.44 cm bulk
oil paths departing at an angle from the creep surface to
(c)
Figure 7. Optical images of failure events. (a) dendritic outer
surface creep, (b) bulk oil breakdown, (c) inner surface creep
breakdown.
Figure 8. Schematic (not to scale) representation of the failure paths
considered for Structure H. [For description of numbered paths, see
text].
482
J.K. Nelson and C. Shaw: The Impulse Design of Transformer Oil-Cellulose Structures
the ring electrodes {such as the path shown in the flux plot of
Figure 5}, (4) a composite path consisting of the middle 1 cm
of the creep surface and two 2.25 cm bulk oil paths departing
at an angle from the creep surface to the ring electrodes, and
(5) a 4.6 cm bulk oil path between the ring electrodes. The
analysis showed that the first path became critical when the
potential difference between electrodes was 175 kV. The
second path became critical at 172.5 kV and was limited by
the creep component of the path. Likewise, the third path was
creep-limited at 207.5 kV. The fourth path, however, was oillimited at 260 kV and the oil path became critical at 187.5 kV.
The study suggests a minimum critical voltage for path (2).
However, the photographic breakdown evidence favored the
bulk oil path, path (4), with roughly 90% of the failures
occurring along this path. There is evidence, however, of 10%
creep failure as shown in Figure 6b giving rise to the mixed
failure mode given in Table 3 for Structure H. Noting this,
and the fact that the critical voltages of the two paths are only
10% different, it is plausible to conclude that the design
criteria can be used to evaluate the integrity of composite
paths with some measure of confidence.
When comparing Structures A, G, H it should be noted that
the creep curves used in these experiments assume paper
covered electrodes [2], while the oil curve applied to G and H
properly accounts for the fact that bare electrodes were used.
In light of this, it is expected that the 1% ac breakdown value
for Structure A, and for all creep structures, would be
somewhat lower. As a result, the corresponding ratios would
be higher. For example if the 1% ac values for the creep
structures are lowered [2] by 15% to account for bare
electrodes then the ratios for Structures A, B, and C become
2.58, 3.19, and 3.34, respectively. The results suggest that the
structures with rings have similar factors as do the structures
without rings excepting Structures E and D. The results also
indicate that there is a substantial difference between the two
values: roughly 2.5 for the structures with rings and 3.3 for the
structures without rings. This suggests that certain structures
are more susceptible to failure under steep front impulse
conditions than are others. If the discussion in [9] is viewed in
light of these results, it is conceivable that the failures
occurred along susceptible paths.
The factor of 2.5 for structures with rings is in-line with the
factor used for lightning impulses. However, published results
[8] show that the breakdown voltage for a 10 ns/2500 μs
impulse is only 78-93% of the lightning impulse value
depending on the insulating material tested. Some difference
can thus be expected since the front time used in these
experiments was 240 ns and the curve shown in Figure 2 may
not continue increasing for smaller impulse front times.
Comparison of Structure A (which is a creep configuration)
with Structure H (which is the same structure with two oil
gaps inserted to form a mixed path) would indicate that the
provision of the series oil paths creates over a 40%
improvement for impulse conditions, but less than 20% is
predicted for ac with the attendant change in ratio from
2.19 (A) to 2.49 (H). The reasons for this probably lie in
the small oil gap formed by the curvature of the ring
where it meets the cylinder. This gap is readily discharged
by the impulse voltage with the resulting precipitation of
complete failure. Further evidence for this may be found
in the comparison of Structures B and D which are again
similar with the exception of the central disc barrier in
Structure D designed to break up the creep path. While
this barrier is seen to be effective for ac withstand, it is
actually counter-productive for surge stresses yielding a
very low ratio. This probably results again from initiating
discharges in the inevitable interstitial oil gaps at the
discontinuities – shown arrowed in Figure 3.
5 CONCLUSION
This limited study would suggest that the use of a
universal equivalence between ac and impulse design
criteria for oil/cellulose structures was not always
appropriate. The nature of the structure will cause
anomalies. However, the cumulative stress methodology
used for ac would appear to provide some basis for the
assessment of composite impulse breakdown paths
despite the obvious physical differences.
ACKNOWLEDGEMENTS
The authors are grateful to the sponsors of the Philip
Sporn Chair at Rensselaer for the support of this activity,
and to EHV-Weidmann Industries for the fabrication of
the numerous test samples involved.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
J.K. Nelson, “An assessment of the physical basis for the
application of design criteria to dielectric structures”, Trans. IEEE,
Vol. 24, pp. 835-847, 1989.
H.P. Moser, Transformerboard, Scientia Electrica, 1979.
A. Tahani, J.K. Nelson and S.J. Salon, "Automated dielectric
design of oil/cellulose structures - a computer implementation",
Proc. 10th Conf. on the Computation of Electromagnetic Fields,
Berlin, Germany, 1995.
W.R. Wilson, “A fundamental factor controlling the unit dielectric
strength of oil”, Trans. AIEE, Vol.72, pp. 68-74, 1953.
E.J. Gumbel, Statistics of Extremes, Columbia Press, 1967.
P.B. McGrath and J.K. Nelson, “Events leading to failure of
transformer oil duct spacers”, Conf. Elect. Ins. & Diel. Phen.,
NAS, pp. 249, 1976.
H. Hirose, “More accurate breakdown voltage estimation for the
new step-up test method in the Weibull model,” IEEE Trans.
Dielectr. Electr. Insul. Vol. 11, pp. 418-423, 2004.
E. Kreyszig, Ädvanced Engineering Mathematics, Wiley, 1983.
M. Vandermaar, M. Wang, J.B. Neilson and K.D. Srivastava, “The
Electrical breakdown characteristics of oil-paper insulation under
steep front impulse voltages”, IEEE Trans. Power Del., Vol. 9, pp.
1926-1933, 1994.
IEEE Transactions on Dielectrics and Electrical Insulation
Vol. 13, No. 3; June 2006
J. Keith Nelson (F’90) was born in Oldham,
UK and received his B.Sc.(Eng.) and Ph.D.
degrees from the University of London, UK.
He is currently Philip Sporn Chair of Electric
Power Engineering at the Rensselaer
Polytechnic
Institute.
Prior
to
his
appointment at Rensselaer, he was manager
of Electric Field Technology Programs at the
General Electric R & D Center in
Schenectady, NY. He has held numerous
IEEE appointments including that of the Presidency of the Dielectrics &
Electrical Insulation Society, 1995-6. He is a chartered electrical
engineer, a Fellow of the IEE and the recipient of the IEEE Millennium
Medal.
483
Cory Shaw’s interest in electricity started
when he was working with his father as an
electrician. He studied at the University of
Utah and graduated with a Bachelors of
Science in Electrical Engineering. He
continued his studies at Rensselaer
Polytechnic Institute where he completed
his Masters in Electric Power Engineering.
He currently works for Northeast Utilities
as a Distribution Engineer.