Electric field analytical formulas for single-circuit power lines with a horizontal arrangement of conductors

Analytical formulas are derived for the calculation of the electric field at any point in the vicinity of single-circuit power lines with a horizontal arrangement of conductors. The analytical formulas are appropriate for the assessment of public exposure as they allow direct calculation of the electric field. They are also suitable for assessing the dependence of the electric field on electric and geometric parameters. Initially, an accurate formula of the electric field is derived by using a proposed method. This method is based on the use of multipole expansions and double complex numbers for the representation of the electric field vector and symmetrical components analysis for the conductors' charges. Based on the accurate formula, a sensitivity analysis of the electric field is carried out with respect to the various parameters. Two simpler approximate formulas are finally developed, which provide the electric field with satisfactory accuracy in certain areas in the vicinity of the lines.