The Impulse Design of Transformer Oil-Cellulose Structures

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 paths may be categorized as either “bulk” through oil volumes, “creep” along cellulose surfaces (paper or THE “cumulative stress” method is in industrial use for the pressboard) or some combination of the two. The design of composite (oil-paper) structures, particularly for prevailing electric field is computed along each chosen large transformers. It has evolved to provide a design tool for path, usually by the application of finite element flux use under alternating voltage conditions and is based on plotting software. Starting at the point of highest stress numerous experimental test results. The economic design of (which is usually at one end of the path, but not always complex liquid-solid dielectric structures in divergent electric so), the stress is calculated over a fixed increment in the fields is problematic since the electric stresses involved are direction which maximizes the stress. In a stepwise usually substantially non-uniform, may not change manner, the track is extended along the path by monotonically, and a plurality of materials and geometries are considering each successive increment and computing the prevalent. Furthermore, the problem is further complicated by largest cumulative stress i.e. the total voltage divided by the combined nature of many of the critical paths (i.e. part the corresponding portion of the path. The resulting creep, part bulk). Despite the semi-empirical nature of the profile (cumulative stress as a function of position on the method, there is a theoretical basis for the technique [1] based path) is then compared with design curves used by on known physics when applied for 50/60 Hz stresses. The individual industrial designers. An example taken from method has served the transformer industry well, and avoids Moser [2] is depicted in Figure 1 for bulk oil and creep establishing a withstand voltage simply on the basis of the paths under 50/60 Hz ac stresses. A detailed example of maximum prevailing electric field which is clearly an the method may be studied in [3] which describes the ineffective and uneconomic criterion. development of a computer-based algorithm to automate

the process A profile which is totally under the respective design 1.1 THE CUMULATIVE STRESS CRITERION curve is deemed to be a satisfactory design, and, In applying the cumulative stress technique, the structure is conversely, if any part of the profile lies above the curve, examined and paths thought to be critical are identified. Such the design (for that path) is considered unsafe. The

margin of safety can be assessed from the relative Manuscript received on 14 September 2005, in final form 14 November 2005 positions of the curves. It is important to recognize that

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 (a) 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 (b) method would not be likely to provide a valid basis for Electric Field (kV/cm) Field Electric

1 10 100 1000 impulse design. 0.10 1.00 10.00 100.00 Path Length (cm) 3 Figure 1. Power Frequency acrms design curves for (a) bulk 2.5 - Full Wave oil, (b) creep. 2.5 Impulse

2 1.7- Switching this is a design criterion and not a breakdown estimate. Impulse Statistical margin is already built into the design curves which 1.5 represent approximately a 1% failure probability. Figure 1 1 - Applied represents the two basic criteria for bulk and creep cases. DIL Factor 1 0.8 - Induced However, in practice, additional curves are sometimes used to 0.5

allow for gas content, electrode covering, non-continuous 0 operation, etc. An interesting feature of the bulk cumulative 1.E-06 1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 stress curve is that its power law relationship may be Time (s) expressed as:

–0.38 Figure 2. Design Insulation Levels (factors) for typical E = 75 d (1) ANSI dielectric tests.

Where d is the oil path length. It may also be shown that the Notwithstanding that, the transformer industry needs to volume effect [1,4] associated with oil breakdown may also be be able to account for impulse breakdown in the design in defined empirically as E ∝ v –0.137, where v is the volume order to insure that the structures meet the Basic within a 90% equigradient contour. This would imply that, for Insulation Level (BIL). One common method of design example, a plane parallel gap would exhibit an area which assessment is to use the power frequency criteria with a increased approximately as the square of the gap spacing. This factor to account for the surge conditions. The factor is is clearly erroneous unless the volume involved is not that varied according to the duration of the impulse applied. between the electrodes, but rather a hemispherical volume This factor is known as the “Design Insulation Level” surrounding each initiating event at the electrode. In these (DIL). A plot of the DIL versus the time duration of the circumstances the two representations are entirely compatible. applied voltage is given in Figure 2. However, the Such a description is also thus consistent with a weak link obvious differences in breakdown mechanism calls into theory of breakdown which can be represented by one of the question the use of a constant conversion factor for any asymptotic distributions of extreme values [5] as given in insulation system. Clearly, a comprehensive empirical Section 2.3. The nature of Figure 1 explains why liquids are study to document this relationship would be a formidable particularly weak when path lengths are long, and why undertaking. The results reported here provide a modest barriers are effective in improving dielectric integrity. start in the process of providing a better basis for the impulse design of composite structures. 1.2 IMPULSE FAILURE Under impulse conditions, it is clear that some of the 2 EXPERIMENTAL ARRANGEMENTS mechanisms known to influence power frequency breakdown are inoperative. Clearly, those agencies which require a 2.1 TEST STRUCRURES considerable period of time to operate such as In order to represent a number of different breakdown electrohydrodynamic motion producing flow-induced path configurations, eight different test structures cavitation, dielectrophoretic particle migration, large bubble (designated A – H) were developed and are described in formation etc. will effectively be frozen out leaving fast Table 1. These provide for breakdown paths which are processes like streamer propagation as likely mechanisms. Asa predominantly through bulk oil, along creep surfaces or result, many of the mechanisms which are known to trigger mixed configuration situations (i.e. failure paths where IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006 479

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 Figure 3. Three of the 8 oil-cellulose structures. grounded enclosure insulated with Freon™-12 gas. The rig was controlled with a trigatron on the first stage Table 1. Descriptions of the structures. together with voltage control through N stack pressure Creep 2 adjustment. The negative-going applied voltage and A 4 cm x 10 cm cylinder with 2 cm waveform were determined by a 500 MHz digitizing standoffs holding the rings oscilloscope coupled through a matched 32,000:1 built-in B 2 cm cylinder cut to 5 cm in length divider. Where the impulse failure occurred on the 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. part is creep and part is through bulk liquid). Three typical Figure 4. Test enclosure mounted on the terminal of the 2.3 MV examples are depicted in Figure 3. The samples were Febetron™. primarily based on pressboard cylinders placed between contoured electrodes and vacuum oil impregnated to usual outside of the structure, a camera system (not shown in industrial standards. By using two different diameters of Figure 4) was able to document the breakdown path pressboard tube (4 cm and 2 cm), it was possible to provide a through the windows provided. It is recognized that the pure creep surface or a combination of bulk oil and surface impulse tests were not undertaken with a standard 1/50 µs creep (for the 2 cm cylinder where the pressboard was not in wave which would have been desirable. However the intimate contact with the doughnut-shaped metallic ring – see unique multi-MV impulse generator available was not Figure 3 right-hand image.). The structures were immersed in capable of front and tail time extended to the standard a standard transformer oil (Shell Diala B) with a moisture waveshape. The implications of the non-standard wave content of 7 ppm determined by a Karl Fischer electrometric are further discussed in Section 4. 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 2.3 PROCEDURES which the oil made multiple passes down plates in the vacuum To determine the impulse characteristics, samples were enclosure at 70°C. The known difficulties [6] of lapped paper tested according to the step up method [7], where the insulation on the electrodes prompted the use of bare actual breakdown voltage value was recorded. The electrodes in this study. However, proper allowance was made parameter estimates, were obtained from a Weibull 480 J.K. Nelson and C. Shaw: The Impulse Design of Transformer Oil-Cellulose Structures

analysis with a maximum likelihood algorithm. The actual 3 RESULTS tests usually consisted of 30 samples per structure to obtain a Descriptive statistics were gathered for each of the statistically meaningful result. The 1% impulse value was then structures considered and 90% confidence intervals determined by rearranging the Weibull cumulative distribution computed for the α and β parameters. On the basis of the function as follows: accumulated and processed data, Table 2 was established

which summarizes the data for the various structures Given, grouped according to their type. β P = 1− exp⎛− x ⎞ (2) There is a presumption that the data are represented by ⎜ ()α ⎟ ⎝ ⎠ a Weibull distribution. In order to determine the goodness then: 1 x = α()− ln(1− P) β (with P = 0.01) (3) Table 2. Experimental impulse-to-ac ratios. Exptl. Calc. 1% where x is the value of the breakdown voltage that gives 1% Neg. Impulse ac probability P, and α and β are the Weibull scale and shape Structure Impulse to ac Breakdown parameters, respectively. Breakdown Ratio Value (kV) Design curves similar to those in Figure 1 were used to Value (kV) determine the 1% ac breakdown values for each of the eight structures studied. This was done with the proper accounting Structures of the bulk and/or creep paths and the absence of electrode with rings covering where applicable. The prevailing electric fields were A 157.5 346.0 2.19 G 212.5 526.5 2.48 H 187.5 495.0 Electrode ring Main disc 2.49 extension to create electrode Structures composite path 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

Cylinder 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 Figure 5. Flux plot of the composite path appropriate to Structure H. values of about 80% although, notably, structures B, D, determined by flux plots, such as that illustrated in Fig. 5 and and G were significantly worse. However, all the a program developed in FORTRAN that uses the output of a structures generated better fits to a Weibull distribution finite element program to determine the cumulative stress and than to a normal curve. associated margins [3]. Figure 5 depicts a combination (bulk Not all the 30 samples of each structure failed in the oil + surface creep) case in which the discharge path can be same way. There was usually a predominant mechanism partly across a surface and partly through series oil path(s). which has been summarized in Table 3. It is significant, The equipotential lines are asymmetrical as a result of the however, that those breakdowns which occur in a non- grounded end of the test enclosure, which may make the predominant way also often have a breakdown voltage breakdown somewhat polarity dependent. The automatic which is anomalous. For example, Structure A usually computation of cumulative stress was undertaken for the failed by creep exhibiting a characteristic value of 929 critical paths for each particular structure and the voltage level kV. However, 4 samples did exhibit punctures and these in the finite element analysis was adjusted until the margin had strengths as low as 380 kV which significantly was zero for each structure. This voltage was taken as the 1% depress the ratios in Table 2. ac breakdown value on which the design is (arbitrarily) based. IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006 481

Table 3. Summary of predominant failure modes. shown in Figures 6b and 7c which corresponds to Structures B and C. Structure Predominant Failure Mechanism 4 DISCUSSION AND IMPLICATIONS A Outer surface creep, with some punctures By establishing the characteristic impulse failure B Inner surface creep voltages and comparing them with the equivalent power C Inner surface creep frequency computations, estimates of the conversion D Inner surface creep + barrier creep factors have been obtained for the 8 different configurations studied based on a 1% failure probability E Short paths; very variable obtained from the Weibull statistics. Factors varied from F Short paths; very variable 1.94 to 3.34 depending on the configuration. These limits G Bulk oil between rings certainly encompass the factor (2.5) typically used for H Bulk oil, but with some creep occurring 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 (a)12 (b) (c) considered are represented in more detail in Figure 8 and include: (1) a 10 cm creep path between the disc Figure 6. Physical evidence for creep and puncture failures. (a) electrodes, (2) a composite path consisting of the middle Outer cylinder creep (Structure A), (b) Inner cylinder creep (Structure B), (c) Puncture (Structure A). 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 These failure modes may be further visualized by middle 3 cm of the creep surface and two 1.44 cm bulk undertaking a tear-down analysis and by examining the optical oil paths departing at an angle from the creep surface to 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) (c)

Figure 7. Optical images of failure events. (a) dendritic outer Figure 8. Schematic (not to scale) representation of the failure paths surface creep, (b) bulk oil breakdown, (c) inner surface creep considered for Structure H. [For description of numbered paths, see breakdown. 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 provision of the series oil paths creates over a 40% Figure 5}, (4) a composite path consisting of the middle 1 cm improvement for impulse conditions, but less than 20% is of the creep surface and two 2.25 cm bulk oil paths departing predicted for ac with the attendant change in ratio from at an angle from the creep surface to the ring electrodes, and 2.19 (A) to 2.49 (H). The reasons for this probably lie in (5) a 4.6 cm bulk oil path between the ring electrodes. The the small oil gap formed by the curvature of the ring analysis showed that the first path became critical when the where it meets the cylinder. This gap is readily discharged potential difference between electrodes was 175 kV. The by the impulse voltage with the resulting precipitation of second path became critical at 172.5 kV and was limited by complete failure. Further evidence for this may be found the creep component of the path. Likewise, the third path was in the comparison of Structures B and D which are again creep-limited at 207.5 kV. The fourth path, however, was oil- similar with the exception of the central disc barrier in limited at 260 kV and the oil path became critical at 187.5 kV. Structure D designed to break up the creep path. While The study suggests a minimum critical voltage for path (2). this barrier is seen to be effective for ac withstand, it is However, the photographic breakdown evidence favored the actually counter-productive for surge stresses yielding a bulk oil path, path (4), with roughly 90% of the failures very low ratio. This probably results again from initiating occurring along this path. There is evidence, however, of 10% discharges in the inevitable interstitial oil gaps at the creep failure as shown in Figure 6b giving rise to the mixed discontinuities – shown arrowed in Figure 3. failure mode given in Table 3 for Structure H. Noting this, and the fact that the critical voltages of the two paths are only 5 CONCLUSION 10% different, it is plausible to conclude that the design This limited study would suggest that the use of a criteria can be used to evaluate the integrity of composite universal equivalence between ac and impulse design paths with some measure of confidence. criteria for oil/cellulose structures was not always When comparing Structures A, G, H it should be noted that appropriate. The nature of the structure will cause the creep curves used in these experiments assume paper anomalies. However, the cumulative stress methodology covered electrodes [2], while the oil curve applied to G and H used for ac would appear to provide some basis for the properly accounts for the fact that bare electrodes were used. assessment of composite impulse breakdown paths In light of this, it is expected that the 1% ac breakdown value despite the obvious physical differences. 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 ACKNOWLEDGEMENTS structures are lowered [2] by 15% to account for bare The authors are grateful to the sponsors of the Philip electrodes then the ratios for Structures A, B, and C become Sporn Chair at Rensselaer for the support of this activity, 2.58, 3.19, and 3.34, respectively. The results suggest that the and to EHV-Weidmann Industries for the fabrication of structures with rings have similar factors as do the structures the numerous test samples involved. without rings excepting Structures E and D. The results also indicate that there is a substantial difference between the two REFERENCES values: roughly 2.5 for the structures with rings and 3.3 for the [1] J.K. Nelson, “An assessment of the physical basis for the structures without rings. This suggests that certain structures application of design criteria to dielectric structures”, Trans. IEEE, are more susceptible to failure under steep front impulse Vol. 24, pp. 835-847, 1989. [2] H.P. Moser, Transformerboard, Scientia Electrica, 1979. conditions than are others. If the discussion in [9] is viewed in [3] A. Tahani, J.K. Nelson and S.J. Salon, "Automated dielectric light of these results, it is conceivable that the failures design of oil/cellulose structures - a computer implementation", occurred along susceptible paths. Proc. 10th Conf. on the Computation of Electromagnetic Fields, Berlin, Germany, 1995. The factor of 2.5 for structures with rings is in-line with the [4] W.R. Wilson, “A fundamental factor controlling the unit dielectric factor used for lightning impulses. However, published results strength of oil”, Trans. AIEE, Vol.72, pp. 68-74, 1953. [8] show that the breakdown voltage for a 10 ns/2500 μs [5] E.J. Gumbel, Statistics of Extremes, Columbia Press, 1967. impulse is only 78-93% of the lightning impulse value [6] P.B. McGrath and J.K. Nelson, “Events leading to failure of transformer oil duct spacers”, Conf. Elect. Ins. & Diel. Phen., depending on the insulating material tested. Some difference NAS, pp. 249, 1976. can thus be expected since the front time used in these [7] H. Hirose, “More accurate breakdown voltage estimation for the experiments was 240 ns and the curve shown in Figure 2 may new step-up test method in the Weibull model,” IEEE Trans. Dielectr. Electr. Insul. Vol. 11, pp. 418-423, 2004. not continue increasing for smaller impulse front times. [8] E. Kreyszig, Ädvanced Engineering Mathematics, Wiley, 1983. Comparison of Structure A (which is a creep configuration) [9] M. Vandermaar, M. Wang, J.B. Neilson and K.D. Srivastava, “The with Structure H (which is the same structure with two oil Electrical breakdown characteristics of oil-paper insulation under steep front impulse voltages”, IEEE Trans. Power Del., Vol. 9, pp. gaps inserted to form a mixed path) would indicate that the 1926-1933, 1994. IEEE Transactions on Dielectrics and Electrical Insulation Vol. 13, No. 3; June 2006 483

J. Keith Nelson (F’90) was born in Oldham, Cory Shaw’s interest in electricity started UK and received his B.Sc.(Eng.) and Ph.D. when he was working with his father as an degrees from the University of London, UK. electrician. He studied at the University of He is currently Philip Sporn Chair of Electric Utah and graduated with a Bachelors of Power Engineering at the Rensselaer Science in Electrical Engineering. He Polytechnic Institute. Prior to his continued his studies at Rensselaer appointment at Rensselaer, he was manager Polytechnic Institute where he completed of Electric Field Technology Programs at the his Masters in Electric Power Engineering. General Electric R & D Center in He currently works for Northeast Utilities Schenectady, NY. He has held numerous as a Distribution Engineer. 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.