Fast analytical computation of power-line magnetic fields by complex vector method

The electromagnetic environment related to electric power installations is typically evaluated by numerical integration methods. Numerical techniques, although powerful, are not well suited for assessing the dependence of the field strength on electric and geometric parameters. In this paper, a fast procedure to analytically evaluate power-line magnetic fields, based on complex vectors, is proposed. The use of complex algebra greatly simplifies analytical calculations compared to other approaches proposed in literature, allowing also complex conductor arrangements to be taken into account. A general formula for the magnetic-field intensity of any multiphase single-circuit line configuration is obtained. An expression for practical three-phase line configurations is simply derived as a particular case of the general formula. The proposed approach is then extended successfully to double-circuit lines, taking the load differences between circuits into account. Approximate formulas are validated by comparing magnetic flux density values with those computed from the general expression.