But as networks have become more sophisticated, the need was recognized to better distribute the electric field generated across a bushing – especially at higher voltages. Such simple bulk and solid type bushings are in fact still being applied at medium voltage levels. In their early years, bushings were little more than hollow porcelains filled with transformer oil or solid resin surrounding the conductor. Catastrophic bushing failure means expensive repairs or even total loss of transformer. Explosion of this OIP bushing in New Zealand launched porcelain shrapnel over wide adjoining residential area (dotted blue boundary). Certain types of bushings can threaten not only substation personnel but even nearby communities. While bushings account for only about 5% of the cost of a power transformer, their catastrophic failure can lead to total loss of the transformer and possibly other expensive equipment as well. Like a surge arrester, a bushing is a relatively low cost component ensuring the safe operation of a high value asset. Stanislaw Gubanski of Chalmers University of Technology in Sweden with excerpts from issues of INMR.
This edited overview combines an edited contribution to INMR by retired Prof. Moreover, a bushing must have the proper thermal design to avoid overheating of any of its components and prevent onset of ageing phenomena in its insulation – both at rated current and during short circuit events. Another key requirement is providing the mechanical strength needed to support the conductor as well as all external connections, including under short circuit and possible seismic forces. For example, bushings must provide reliable electrical insulation both internally (against breakdown) and externally (against flashover) of the conductor exposed to the rated voltage and also to periodic service overvoltages – even under contaminated conditions. An integral part of this function involves meeting all the electrical, thermal and mechanical requirements of the application. BLT neatly implement Conway's games and surreal numbers and a natural extension of BLT is definitionally equivalent with ZF.Bushings are devices that allow conductors to pass through the earthed walls of transformers, switchgear and substation structures. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. But we can rectify this, whilst retaining classical logic. The ordinary cumulative hierarchy dismisses this idea outright. On a very natural conception of sets, every set has an absolute complement. Moreover, if we assume that time is linear, the ensuing modal set theory is almost definitionally equivalent with non-modal set theories specifically, with Level Theory, as developed in Part 1. Using tensed language as an heuristic, the following bare-bones story introduces the idea of a potential hierarchy of sets: 'Always: for any sets that existed, there is a set whose members are exactly those sets there are no other sets.' Surprisingly, this story already guarantees well-foundedness and persistence. Potentialists think that the concept of set is importantly modal. I show this by presenting Level Theory, a simplifiation of set theories due to Scott, Montague, Derrick, and Potter. We find nothing else at S.' Surprisingly, this story already guarantees that the sets are arranged in well-ordered levels, and suffices for quasi-categoricity. At any stage S: for any sets found before S, we find a set whose members are exactly those sets. The following bare-bones story introduces the idea of a cumulative hierarchy of pure sets: 'Sets are arranged in stages. This document comprises Level Theory, parts 1-3.
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