Three-Dimensional Analytical Modeling and an Improved Ice-Shedding Motion-Range Envelope for Wind-Deflected Multi-Span Transmission Lines

Wind-induced deflection makes the ice-shedding trajectory of the conductor spatially coupled and more difficult to predict. To accurately and efficiently predict the dynamic response of the multi-span transmission line-insulator system (MSTLIS) following entire-span ice shedding under steady mean crosswind, this study develops a three-dimensional nonlinear analytical framework that couples the vertical-transverse conductor motion, inter-span compatibility, and the spatial boundary conditions of suspension insulator strings. Comparisons with nonlinear finite element method (FEM) analyses show close agreement in key dynamic response time histories under the stated modeling assumptions and an approximately 14-fold computational speedup. Based on five-span analyses, a total uplift height referenced to the corresponding no-wind iced equilibrium state is proposed to account for both windinduced static uplift and the subsequent dynamic jump, providing a more representative measure of the vertical clearance demand under wind-induced deflection than the conventional maximum jump height. Furthermore, an improved positioning method is developed for the conventional upright-andinverted triangular motion-range envelope to better encompass the spatial ice-shedding trajectories in the investigated cases. Within the investigated parameter range and model assumptions, the proposed analytical framework and motion-range assessment method support efficient ice-shedding response prediction and preliminary interphase-clearance assessment.