New simplified expressions for ionized electric fields and corona losses of HVDC monopolar transmission lines

New analytical expressions for ionized electric field, current density and corona losses of HVDC unipolar lines are derived under Deutsch's assumption by expanding charge and current densities on the emitter wire into a two-harmonics Fourier series. Simplified expressions are presented for the practical case, wherein the radius of the wire is small with respect to its height above the ground plane. Voltage-current characteristics, electric field and current density distributions at the ground are computed for unipolar configurations. A comparison of the profiles thereby obtained with already known experimental or computational results shows the accuracy of the proposed analytical approach.