BIE formulation for skin and proximity effect problems of parallel conductors

The boundary integral equation (BIE) is used to determine the current distribution in the cross sections of a group of parallel conductors. Magnetic vector potentials at conductor surfaces are calculated by using the boundary element technique. The known current in each conductor is used as a constraint in the formulation. A source component (Å^s) is introduced for the magnetic vector potential in order to maintain the balance between unknowns and equations and to transform Helmholtz´s equation into a homogeneous equation. The choice of A^s is preferred over any other choice because it has physical meaning and its simplifies the calculation of various quantities such as voltage drop along the conductor, power loss, and line impedance