A study on mathematical model, calculation and physical mechanism of transmission lines with mutual inductance

Conventionally, when discussing the parameters of transmission lines, we suppose that the parameters of each sequence (positive, negative and zero) are mutually independent whether they are involved in a single circuit or double-circuit. Thus both the sequence based impedance matrix of single circuit lines and the sequence based mutual impedance matrix of double-circuit lines are diagonal. What´s more, on the assumption that the parameters of 3-phase lines are all equal, only the zero sequence mutual inductance between the two circuits is of concern. While, in practice, the hypotheses discussed above are not feasible, the spatial unsymmetry of lines leads to the temporal unsymmetry of the total magnetic flux which couples with the circuit composed of each line and its mirror image. Thus, a certain sequence current may induce a different sequence voltage, sequence parameters are not independent, and the impedance matrices discussed above are not diagonal. It is evident that we must calculate 9 elements to describe the character of a single circuit or two circuits with magnetic coupling. This paper discusses the relationship between coupled impedance. Based on the electromagnetic theory, a more reasonable method is applied to calculate them. Comparing the results from different methods using two examples from practical detection, shows this method is correct in theoretical analysis.