In this paper, self inductance for a conductor with rectangular cross section is investigated. Using the three-dimensional Fredholm's integral equation of the second kind with weakly singular kernel we obtain an equation for the complex voltage drop in the conductor. Self impedance appearing in the equation is expressed in the form of integral relation for any current density distribution. The imaginary part of this impedance divided by angular frequency is the self inductance of a conductor of any shape and finite length. In the case of direct current (DC), low frequency (LF) or thin strip conductor of rectangular cross section the formulae for the self inductances are given for any length and for length much greater than the other dimensions.

This paper describes an analytical-numerical method for the skin and proximity effects in a system of two parallel conductors of circular cross section—a system very frequently encountered in various applications. The magnetic field generated by the current applied on each conductor is expressed by means of vector magnetic potential and expanded into Fourier series. Using the Laplace and Helmholtz equations, as well as the classical boundary conditions, the current density induced due to the proximity and skin effect is determined in each conductor. The resulting current density is expressed as a series of successive reactions. The results obtained are compared with those obtained via finite elements. Although the paper is theoretical, the considered problem has a practical significance, because transmission lines with round conductors are universally used. Besides, the results can be used to estimate errors when only the first reaction is taken into account, which gives relatively simple formulas.

No abstract

Abstract-In this paper, a new numerical method of calculating rectangular busbar impedance is proposed. This method is based on integral equation method and partial inductance theory. In particular, impedances of shielded and unshielded three-phase systems with rectangular phase and neutral busbars, conductive enclosure, and use of the method are described. Results for resistances and reactances for these systems of multiple rectangular conductors have been obtained, and skin and proximity effects have also been taken into consideration. The impact of the enclosure on impedances is also presented. Finally, two applications to three-phase shielded and unshielded systems busbars are described. The validation of the proposed method is carried out through FEM and laboratory measurements, and a reasonable level of accuracy is demonstrated.