IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006

1070-9878/06/$20.00 © 2006 IEEE

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

J.K. Nelson and C. Shaw: The Impulse Design of Transformer Oil-Cellulose Structures 478

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

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.

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

Figure 1. Power Frequency acrms design curves for (a) bulk oil, (b) creep.

110

100

1000

0.10 1.00 10.00 100.00

Path Length (cm)

Elec

tric

Fiel

d (k

V/cm

)

(a)

(b)

Figure 2. Design Insulation Levels (factors) for typical ANSI dielectric tests.

0.8 - Induced

1 - Applied

1.7- Switching Impulse

2.5 - Full Wave Impulse

0

0.5

1

1.5

2

2.5

3

1.E-06 1.E-04 1.E-02 1.E+00 1.E+02 1.E+04

Time (s)D

IL F

acto

r

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006

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

for that [2] when applying the design criteria as discussed in Section 4.

2.2 PULSE SOURCE The structures were accommodated in a sealed oil-

filled 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

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

Creep A 4 cm x 10 cm cylinder with 2 cm

standoffs holding the rings B 2 cm cylinder cut to 5 cm in length

between disc electrodes C 2 cm cylinder cut to 8 cm between

disc electrodes D 2-2x2.7 cm cylinders separated by

6 mm x 3 cm pressboard disc between disc electrodes

Bulk Oil E 1.59 cm oil gap between disc

electrodes F 2.86 cm oil gap between disc

electrodes Combination G 2 cm x 10 cm cylinder with 1 cm

standoffs holding the rings H 2 cm x 10 cm cylinder with 2 cm

standoffs holding the rings.

Figure 4. Test enclosure mounted on the terminal of the 2.3 MV Febetron™.

Figure 3. Three of the 8 oil-cellulose structures.

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Table 1. Descriptions of the structures.

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

αxP exp1 (2)

then:

( ) βα1

)1ln( Px −−= (with P = 0.01) (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

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.

3 RESULTS 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

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 non-predominant 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.

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 187.5 495.0 2.49 Structures

w/o rings

B 137.5 400.0 2.71 C 177.5 506.0 2.84 F 135.0 460.0 3.34 E 92.5 195.0 2.00 D 162.5 341.0 1.94

Table 2. Experimental impulse-to-ac ratios.

Figure 5. Flux plot of the composite path appropriate to Structure H.

Main disc electrode

Electrode ring extension to create composite path

Cylinder

IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006

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

shown in Figures 6b and 7c which corresponds to Structures B and C.

4 DISCUSSION AND IMPLICATIONS 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

Structure Predominant Failure Mechanism

A Outer surface creep, with some punctures

B Inner surface creep C Inner surface creep D Inner surface creep + barrier creep E Short paths; very variable F Short paths; very variable G Bulk oil between rings H Bulk oil, but with some creep occurring

Table 3. Summary of predominant failure modes.

(a) (b) (c) Figure 7. Optical images of failure events. (a) dendritic outer surface creep, (b) bulk oil breakdown, (c) inner surface creep breakdown.

(a) (b) (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).

1 2

Figure 8. Schematic (not to scale) representation of the failure paths considered for Structure H. [For description of numbered paths, see text].

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J.K. Nelson and C. Shaw: The Impulse Design of Transformer Oil-Cellulose Structures 482

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 oil-limited 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] 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.

[2] H.P. Moser, Transformerboard, Scientia Electrica, 1979. [3] 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.

[4] W.R. Wilson, “A fundamental factor controlling the unit dielectric strength of oil”, Trans. AIEE, Vol.72, pp. 68-74, 1953.

[5] E.J. Gumbel, Statistics of Extremes, Columbia Press, 1967. [6] 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.

[7] 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.

[8] E. Kreyszig, Ädvanced Engineering Mathematics, Wiley, 1983. [9] 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.

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.

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