For basic studies of power transmission lines, in steady state, any line is usually modeled through a single-line pi-circuit, which intrinsically represents all the conductors of the three phases, as well as the grounding wires, and thus, allows analytical approaches that facilitate the understanding of the theoretical fundamentals of the operation of any transmission line. However, for practical applications, when any unavoidable degree of unbalance is present, this method does not give accurate results and thus alternative and more complex methods of analysis are naturally used. On the other hand, although most of the usual alternative methods are quite effective in the analysis of the behavior of the line, they require the obvious use of computer tools and calculations that make difficult any of the important analytical approaches. Thus, based on these concerns and with the aim of giving emphasis on allowing the analytical approach, this article proposes a new analytical method for the analysis of the behavior of a power transmission line, in a steady state, based on the application of the Laplace transform. To illustrate the proposed method, it is introduced and validated through an actual case in the Swedish transmission grid with a basis on real data of phasor measurement units (PMU) systems. The accuracy of the proposed method is evidenced by the comparison with actual data from PMU measurements along with the prediction of the voltage and current profile for each phase, over the line length.
