ABSTRACT
Transformers must be designed to withstand the large forces which occur during fault conditions. Fault currents for the shndard fault types such as single line to ground, line to line, double line to ground, and all three lines to ground must be calculated. Since these faults can occur during any part of the ac cycle, the worst case transient overcurrent must be used to determine the forces. This can be calculated and is specified in the standards as an asymmetry factor which multiplies the rms steady state currents. It is given by [IEE93]
where ,+ = tan-'(&) and x/r is the ratio of the effective ac reactance to resistance. They are part of the total impedance which limits the fault current in the transformer when the short circuit occurs. Using this factor, the resulting currents are used to obtain the magnetic field (leakage field) surrounding the coils and, in turn, the resulting forces on the windings. Analytic methods such as Rabins' method [Rab56] as
discussed in Chapter 5 or finite element methods can be used to calculate the magnetic field. An example of such a leakage field is shown in Fig. 6.1 which was generated by the finite element program ~axwel l@ EM2D Field Simulator [Ansoft]. Since this is a 2D program, the figure is cylindrically symmetrical about the core center line and only the bottom half of the windings and core are shown because of assumed symmetry about a horizontal center plane. Although details such as clamps and shields can be included in the calculation using a finite element approach, they are not part of Rabins' analytical approach which assumes a simpler ideal id geometry. However, calculations show that the magnetic field in the windings and hence the forces are nearly identical in the two cases.
