A mathematical treatment of the dynamic behaviour of a power-transformer winding under axial short-circuit forces

Abstract
The paper gives the mathematical formulation, and indicates the mathematical solution, of the problem of the dynamic behaviour of a transformer winding under axial short-circuit forces, certain basic physical assumptions being made initially. Various practical tapping arrangements are considered so that there may be either magnetic balance or unbalance between the winding and an adjacent winding of constant length.Two methods of solution are discussed. In the classical method, it is explained how a system of ordinary linear differential equations with constant coefficients may be solved. This method can be used only when the stiffnesses of the winding insulation and end insulation remain virtually constant. When these stiffnesses vary, the coefficients are no longer constant and the classical method is impracticable, and the second method of adapting the mathematical formulation of the problem for solution with a digital computer is used. The system of ordinary linear differential equations is replaced by an approximately equivalent system of linear difference equations with constant time step-length. Assuming that some empirical law or data are known for the variation of stiffness in the insulation elements, these difference equations can then be programmed for the digital computer.Attention is drawn to the advantages of using a digital computer, even with constant insulation stiffnesses, because the work in the classical method may be tedious and involved. Finally, two sets of results from the digital computer are compared with test measurements with a fair measure of agreement.

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