Leakage field of a transformer under conventional and superconducting condition

The purpose of this work is to determine the leakage field in a transformer and the current density distribution in its windings. These are of concrete height and concrete thickness and are assumed not to be in proximity to the yokes. Also the conductivity of the conductive material is taken into account. The primary winding is formed by many layers of round conductors with negligible cross-section. The secondary winding consists of two layers of rectangular conductors. Using Maxwell’s differential equations and introducing the vector potential, general equations result for the components of the magnetic induction in two-dimensional field space. The formulae of these components are converted into Fourier series, so that boundary conditions can be applied for determining the integrating constants of the general solutions. The leakage inductance results from the calculation of the magnetic energy. Since its expression depends on the conductivity, so depends on the temperature too. In the superconducting condition in the region of the windings, the leakage inductance becomes equal to 0.