ANEXO: RESUMEN DE LA U.D
III. ANÁLISIS DE LA DIMENSIÓN ‘RECURSOS VIRTUALES’
As an alternative to the above empirical method, the author and his colleagues have investigated a so-called semi-empirical breakdown estimation method, based on streamer theory of gas breakdown [1]. For air, the criterion for minimum break-down voltage was given by Pederson [47, 48] as
lnaxþðx
0
adx ¼ ln a þ ax ð3:3Þ
Table 3.5 Breakdown data for hemispherically ended rod/plate arrangement (r¼ 12.7 mm) [42]
Gap g (Mm) Breakdown voltage at relative density (kV)
3 5 7
Experimental 100 158 210
Empiricala 20 102 158 214
Semi-empirical 103 162 220
Experimental 127 200 259
Empiricala 40 126 197 267
Semi-empirical 129 203 276
Experimental 144 227 288
Empiricala 80 143 222 301
Semi-empirical 142 227 310
aEstimate using (3.1), together with equation of form rE¼ K1prþ K2derived from concentric sphere hemisphere data.
whereaxis the numerical value ofa, Townsend’s first ionisation coefficient, at the head of the avalanche, of length x, at which the critical ion number is reached in an electron avalanche; in a non-uniform field, streamers are formed, resulting in cor-ona or breakdown.
The left-hand side of (3.3) is evaluated from the electrostatic field distribution, obtained using a general field analysis program for practical arrangements or from precise equations for standard geometries [41, 42]. The right-hand side of (3.3) is computed from existing empirical breakdown potential gradient data for uniform fields of gap x. The values of a used in both sides of (3.3) for the examples dis-cussed in previous studies [41, 42] have been published by earlier workers [1, 42].
This semi-empirical approach was extended to SF6using a modified form of (3.3), namely
ðx
0
ða hÞdx ¼ k ¼ 18 ð3:4Þ
wherea and h are Townsend’s first ionisation coefficient and attachment coefficient, respectively, in SF6. An essential prerequisite of Pederson’s semi-empirical approach for any particular set of conditions is information concerning the following parameters:
1. uniform field breakdown potential gradients 2. a and h values
3. potential-gradient distribution across the non-uniform gap
General purpose digital computer programs have been developed, which are capable of solving equations of the form of (3.3) to predict, with acceptable accuracy, the minimum breakdown voltage, V, for a wide range of standard and practical electrode arrangements in air, N2and SF6, for pressures in the range 1–5 atmospheres [41, 42, 44] and for air at high temperatures.
Similarity and Paschen’s law type relationships were also studied. For example with uniform field gaps of 0.5–2.0 cm and temperatures 20–1,100 C, Powell and Ryan obtained results for the DC (static breakdown) voltage, kV, of air, which fitted a relationship of the form
Vs¼ 24:49ð@gÞ þ6:61ffiffiffi p@
g ðkVÞ to within þ5% and 2%
Here, the same constants were selected as given by Boyd et al. from their earlier study at standard atmospheric conditions, where the relative air density @ ¼ 1.0, pressure p¼ 1,013 mbar and T ¼ 293 K (20C).
An example of these techniques is given in Table 3.5, which compares experimental and estimated breakdown voltages in air, at relative air densities (d) of 3, 5 and 7, respectively, for a hemispherically ended rod/plate arrangement [radius r¼ 12.7 mm]. It is clearly seen that both these estimation methods are capable of predicting breakdown voltage levels to within5% over the range of gaps and air pressures considered.
Applications of gaseous insulants to switchgear 147
3.6 Summary
This chapter has provided a general introduction to the application of gaseous insu-lation systems. Although it has only been possible to touch very briefly on some major aspects, important strategic issues will be further developed in other chapters focusing on special areas. An indication has been given in this chapter of numerical field techniques, which have found widespread application in the insulation design of GIS and other switchgear for many years. The simple breakdown estimation methods (empirical and semi-empirical) by Ryan et al., which are extensions of the work by Schwaiger (1954) and Pederson (1967) [47, 48] together with an available experi-mental database obtained from extensive Paschen’s Law/similarity type studies in gaseous insulants, have been thoroughly developed to such a degree that minimum breakdown voltages of practical GIS design layouts (as well as a host of gas-gap arrangements; see References 1 and 5) can be estimated to within a few per cent, at the design stage, often without recourse to expensive development testing. Such derived voltages are generally the minimal withstand levels attainable under practical conditions. Undoubtedly, there is still considerable scope in the future to predict dielectric performance by utilising advanced planning simulation tools incorporating genetic algorithms and artificial intelligence techniques, linked to various ‘extensive databases’ relating to breakdown characteristics of gaseous insulation, including equipment service performance data (e.g. from surveys similar to Reference 34).
Again, it should be emphasised that the outstanding strategic developments in switchgear designs reducing from 4 to 1 breaks/phase at this time, as discussed in this chapter, were due to the complementary skills of the switchgear designers and development team, together with the dielectric contribution and importantly the excellent collaboration with Professor G.R. Jones and his team at the Centre for Intelligent Monitoring Systems, Department of Electrical Engineering and Elec-tronics, University of Liverpool, UK.
Finally, it is anticipated that the continuing, and growing, environmental concerns will influence the development of the next generation of gas-insulated switchgear but a commercial replacement for 100% SF6gas, for interruption pur-poses at the higher ratings, still seems very remote!
Acknowledgements
The author wishes to thank the Directors of NEI Reyrolle Ltd and later VA TECH REYROLLE, before Reyrolle became an ‘affiliate’ to other large international companies for permission to publish, earlier papers, which have been extensively referred to in the studies reported in this chapter. He also gratefully acknowledges the assistance given by many of his former colleagues and for their contributions and generous support over the years.
For about two decades, the IET, High Voltage Engineering and Testing, HVET, International Summer School was held in Newcastle upon Tyne, UK, during a period of major company changes within the UK Power industry. The
ongoing generosity of Reyrolle and sequentially, the ‘various changing company ownership affiliations’ over the years, e.g. Rolls Royce, The Bushing Company, Siemens (-the last Clothier laboratory operator being NaREC-) all continued with strong support of the IET, HVET School series, by making the Clothier laboratory and factory resources available for visits by International HVET School delegates from more than 20 countries, which was greatly appreciated by all.
This author and the HVET Series Organising Committee again acknowledge their sincere thanks to the facility owners for this ongoing generosity and support.
Undoubtedly, these industrial visits to the Clothier laboratory/adjacent industrial complex contributed greatly to ‘delegate empowerment’ and to the great success of this highly rated course series over the years.
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