Analytical calculation of the electric field produced by single-circuit power lines

The electric field produced by overhead power lines is usually calculated with the use of numerical methods through a computer. However, the analytical calculation offers the advantage that leads to a mathematical expression, which allows the direct calculation of the electric field. A method to derive analytical formulas of the intensity of the electric field produced by single-circuit power lines is developed in this paper. This method is based on the analysis of the intensity of the electric field into the sum of two multipole expansions and in the use of double complex numbers for the simplification of the mathematical expressions. Due to the asymmetry of conductors' charges, they are analyzed in their symmetrical components. Using this method, the accurate analytical formula of the intensity of the electric field for single-circuit power lines with conductors in triangular arrangement is given, which is valid at any point in the vicinity of these lines. Apart from the accurate formula, simpler approximate formulas are presented, which provide the electric field with known precision.