Analysis of Transformer Leakage Phenomena by High-Order Finite Elements

Transformer leakage reactances, short-circuit forces, and related quantities are derivable from the leakage flux distribution. Assuming axial symrimetry, flux is conveniently mapped by means of finite element techniques. Use of high-order elements permits reduction of approximating matrix order by a factor of 5-10, compared with the first-order elements previously employed. Typical flux patterns are shown. A new formulatiorn for the short-circuit forces, in terms of quantities related to the vector potential, is given, and it is shown that this formulation reduces the force calculation to a sequence of simple matrix multiplications; no numerical integration is necessary. A corresponding formulation for the leakage reactance is also given . It is coincluded that the use of few high-order elements, with direct solution of the resulting small matrix equations, is preferable to the iterative solution of large systems of equations resulting from large numbers of approximate first-order elements.