Qualitative Properties of Nonlinear Neutral Transmission Line Models and Their Applications

Neutral transmission line models are essential for analyzing stability and periodicity in systems influenced by nonlinear and delayed dynamics, particularly in modern smart grids. This study utilizes Krasnoselskii’s fixed-point theorem to establish sufficient conditions for the existence and asymptotic stability of periodic solutions, eliminating the need for differentiability in delay terms and coefficients. The results extend existing findings and are validated through a single test example, demonstrating the theoretical applicability of the proposed approach. These findings provide a mathematical framework for understanding the behavior of power distribution systems under nonlinear and delayed influences.