**5. Conclusions**

This paper describes a frequency domain method to compute transient voltage and current profiles along nonuniform multiconductor transmission lines, where the nonuniformities along the line are introduced in the model by means of the cascaded connection of chain matrices. The method can incorporate nonlinear and time-dependent elements by using the superposition principle. The profiles obtained provide useful information to locate possible overvoltages at interior points along the transmission line, in contrast to traditional methods that only provide information at the line's ends. This information can be used as a helpful instrument in the insulation coordination design of transmission lines, as well as an educational tool in electrical engineering courses.

The results computed with the described method were compared with time-domain simulations using the well-known software ATP. In all of the comparisons, a high level of agreemen<sup>t</sup> was observed, demonstrating that the proposed method has a high level of accuracy.

It is worth mentioning that, although the results from both methods were very similar, the ATP simulations required substantially more time samples (10 to 50 times more samples) to achieve such results, which can result in a large computational burden. Additionally, in order to obtain measurements at interior points of the transmission line and to include nonuniformities along the transmission line in the ATP simulations, it is necessary to subdivide the line into many line segments, which can be a time-consuming process and can lead to error accumulation. Because of these issues, the proposed frequency domain method is a superior alternative to analyze the transient behavior of a transmission line when the voltage at interior points of the line is of interest.

The relevance of the proposed method lies in its strong potential for application in the accurate fault location and insulation coordination of transmission systems with prominent nonuniformities, which are commonly encountered in many power systems around the world.

**Author Contributions:** Conceptualization, R.N.-G. and F.P.E.C.; investigation, P.G. and F.P.E.C.; methodology, R.N.-G.; funding acquisition, P.G. and C.T.M.; software, R.N.-G.; validation, R.N.-G. and F.P.E.C.; visualization, C.T.M.; writing—original draft, R.N.-G.; writing—review & editing, R.N.-G., F.P.E.C. and P.G.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
