PROXIMITY EFFECTS OF BUS BARS

Abstract

The present work is primarily an attempt to provide rigorous analytical basis for calculation of proximity effects of bus bars, viz. the induced currents and losses in enclosures of an isolated phase bus assembly. The results of studies have been reported in the form of curves which may be of help to design engineers in the field along the lines of the proposed guide to the design of isolated-phase bus assemblies. However, it may be pointed out that substantial modification of the recommendations ot the above committee have been proposed here for the cases of cylindrical enclosures of both continuous and discontinuous types, while the results for rectangular enclosures are entirely original. The case of a conductor sheet in the vicinity of a strip bus bar placed parallel or perpendicular to the sheet, has been studied. Expressions for field in different regions have been derived based on Maxwell's equations for time varying electromagnetic fields. This is the basic case in the simulation of a rectangular enclosure. Here,conductor sheet has infinite length and width but finite thickness. Source imptJance concept has been used to calculate losses in the conductor sheet in presence of a strip bus bar. An appropriate factor associated with the loss formulae for sheet of infinite width leads to loss occurring in a similar sheet of finite width. A -11- procedure is suggested for calculating this modifying factor in individual cases. These results have been extended to calculate the losses in a rectangular enclo sure with a rectangular bus bar which can be considered to be formed by four such strips. An important conclusion has been drawn about the thickness of the conductor sheet theoretically and this has been verified on an experimental set up. It is found that there is an optimum thickness of the sheet for which the loss is a minimum. The loss has been measured in a novel way by application of potentiometric technique instead of calorimetric method generally used in such cases. This method gives more accurate results in comparison with calorimetric method where deter mination of convective coefficient entails uncertainties. The next subject taken up for study is an investi gation of cylindrical bus bars with cylindrical enclosures : of continuous type. The study consists of two parts*, an analytical investigation and an experimental study. The basic field problem is formulated in a cylindrical co-ordinate system and the bus bar is represented as a current sheet. This results in anone-dimensicnal Bessel' s equation. Direct numerical solutions of this can be obtained but have not been attempted here; instead, an approximation is used to obtain *2 modified solution. It is shown that this modified solution is similar to the results (12) of the other workers, thus obtaining an indication as to the amount of approximation involved in these results. -in- More accurate values can be obtained by direct calculat ions, if such accuracy is desired. A modification introduced here over previous recommendations of the IEEE Sub-Committee on the subject lies in the procedure to be followed in calculating the a.c. resistance of the enclosure. It is recommended here that the inner diameter of the enclosure be used rather than the outer one, as stated in the above committee report. Two non-dimensional parameters called the loss factor and optimization factor have been introduced to facilitate the design of the enclosure. These factors have been reported in the form of curves forre^dy us?.. An optimum thickness of the enclosure has been calculated which minimizes the losses, and has been shown to be the same as in the case of the rect angular enclosure. These results are substantiated by an experimental study. The set up used has features similar to those of the rectangular enclosure, especially with regard to the potentiometric method of measurement* For ths thermal analysis of forced air cooled busenclosure assembly in a set up with cylindrical bus bar and cylindrical enclosure, energy balance technique has been applied. Temperature distribution in different regions of the assembly has been plotted. In this study, optimum mass flow rate of coolant fluid has been deter mined, in an assembly having enclosure of optimum thick ness as predicted in preceding analysis. This optimum mass flow rate is based on the constraint that temperature -ivrise in all the regions should be within their respective permissible limits. Though the present work is primarily devoted to a study of continuous enclosures, the results have been • obtained for a cylindrical discontinuous enclosure also. The expression for the losses in such enclosures given by previous workers , has been modified. The modifica tion consists of an extra term, which arises due to currents flowing in the bus bar within the enclosure, a factor neglected by previous authors. It has been shown that this term is independent of the losses arising due to all outside currents and that the two effects can be calculated separately and added to give the total loss.