The Impulse Design of Transformer Oil-Cellulose Structures
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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 1070-9878/06/$20.00 © 2006 IEEE 478 J.K. Nelson and C. Shaw: The Impulse Design of Transformer Oil-Cellulose Structures 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.