Analysis of Magnetic Field for Power Transmission Line With Multiple AC Singular Currents by Coupling of Fourier Series Expansion and FEM

The central characteristic of line current problems with AC power transmission lines and overhead trolley lines are that the source region of conductors is extremely small compared with the entire analytical region. This is a problem with singular point sources in two-dimensional space that creates computational difficulties whit the standard finite element method. This paper proposes an accurate and efficient method for magnetic field calculations for such electric lines, which couples the analytical method and finite element formulation. The analytical solution is expressed as a Fourier series. Unknowns of finite elements at the boundary between the current and finite element regions are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a three-phase two-circuit transmission line. The results are compared with the measured one.