The study presents a calculation method of the voltage induced by power-line sagged conductor in an inductively coupled overhead circuit of arbitrary configuration isolated from ground. The method bases on the solution utilizing the magnetic vector potential for modeling 3D magnetic fields produced by sagging conductors of catenary electric power lines. It is assumed that the equation of the catenary exactly describes the line sag and the influence of currents induced in the earth on the distribution of power line magnetic field is neglected. The method derived is illustrated by exemplary calculations and the results obtained are partially compared with results computed by optional approach.

Electromagnetic forces generated by the short circuit current and leakage flux in low- and high-voltage windings of distribution transformers as well as amorphous core transformers will cause the translation, destruction, and explosion of the windings. Thus, the investigation of these forces plays a significant role for researchers and manufacturers. Many authors have recently used the finite element method to analyze electromagnetic forces. In this paper, an analytic model is first developed for magnetic vector potential formulations to compute the electromagnetic forces (i.e., axial and radial forces) acting on the low- and high-voltage windings of an amorphous core transformer. The finite element technique is then presented to validate the results obtained from the analytical model. The developed model is applied to an actual problem.

The article presents a closed-form formula for solving a weakly singular surface integral with a linear current source distribution associated with the SIE-MoM formulation used for solving electromagnetic (EM) problems. The analytical formula was obtained by transforming the surface integral over a triangular domain into a double integral, and then directly determining formulas for the inner and outer integrals. The solution obtained is marked by high computational efficiency, high accuracy, and very simple implementation. The derived formula, in contrast to the currently available formulas, consists of quantities that have a clear and simple geometric interpretation, related to the geometry of the computational domain.