Overhead transmission lines in mountainous regions are highly susceptible to ice accretion and subsequent ice-shedding. The violent jumping vibration of conductors triggered by ice-shedding may result in severe hazards, including inter-phase flashover, hardware damage, or even conductor breakage. The extant literature principally utilizes numerical simulations to model the ice-shedding process and employs empirical formulas to predict the maximum jump height. However, these approaches are limited in their ability to reveal the underlying mechanisms and evolution laws of the physical quantities as theoretical models do. Furthermore, the maximum jump height alone is insufficient to meet the requirements of engineering risk assessment. To address these limitations, this study proposes a nonlinear theoretical model for a multi-span transmission line-insulator coupled system. This model can systematically predict both static and dynamic responses during the ice-shedding process. The model is expected to provide an efficient and reliable computational tool for forecasting and safety evaluation of transmission line ice-shedding hazards.

A multi-span transmission line with equal span lengths and no elevation differences was selected as the object of study. Bundled conductors were simplified as single conductors, and the most unfavorable condition was considered by assuming that the entire middle span undergoes simultaneous ice-shedding. The process of ice-shedding by multi-span transmission lines comprises three fundamental static equilibrium stages: the initial equilibrium state, the static equilibrium state following icing, and the static equilibrium state after ice-shedding. The profile of the initial equilibrium state can be expeditiously obtained based on suspension theory. The integration of supplementary ice elements within the static equilibrium equations facilitates the derivation of tension and displacement distributions after icing. After the shedding of ice by the middle span, the system undergoes free vibration under the combined effects of the conductor and the ice self-weight, eventually reaching a new stable equilibrium. The incorporation of deformation compatibility conditions between conductors and suspension insulators facilitates the determination of tension and displacement distributions at the static equilibrium state following ice-shedding. The initial condition for the subsequent analysis was the static equilibrium state following the occurrence of icing. This was expanded to include the static equilibrium state after ice-shedding. The nonlinear coupled free vibration equations for all spans and insulator strings were established and solved simultaneously with the compatibility conditions. This approach enabled the determination of the complete time-history response of ice-shedding. The accuracy and efficiency of the proposed model were validated through comparisons with finite element simulations and existing static theoretical methods under various span numbers and ice thicknesses.

The comparative results demonstrated that, for ice thicknesses ranging from 5 to 25 mm and for 3-7 span configurations, the time-history responses predicted by the proposed model exhibited strong agreement with finite element results, with deviations in maximum jump height controlled within ±10%. Concurrently, the computational efficiency of the proposed method was notably superior to that of finite element methods. A thorough parametric analysis revealed that both the jump amplitude and the inter-span unbalanced tension exhibited an increase with greater ice thickness and span number. However, these variables tended to stabilize once the span number exceeded five. Furthermore, the displacement of suspension insulators facilitated the redistribution of local unbalanced tension across a greater number of spans. In addition, the magnitude of interspan unbalanced tension underwent rapid decay as the distance from the de-iced span increased.

This introduces the nonlinear static and dynamic theories of flexible suspension cables into the study of transmission lines. It systematically develops a unified theoretical model for multi-span transmission line-insulator coupled systems. This model covers the static equilibrium state after icing, the static equilibrium state after ice-shedding, and the dynamic response process. The proposed method combines accuracy with efficiency, thereby enabling effective prediction of conductor jump responses induced by ice-shedding. In addition, it provides theoretical support for the refinement of anti-icing design formulas.