A Method for Calculating the Minimum Modal Torsional Stiffness of Bundle Conductors Based on Dynamic Eigenvalue Analysis

As ultra-high voltage transmission technology advances, bundle conductors are increasingly used, and their torsional stiffness significantly influence the stability problems of galloping and overturning. Existing studies on torsional stiffness rely on static models depending on torque application position and distribution, and existing analytical models are further limited to uniform spacer arrangements and zero height differences between line ends. To address these limitations, this paper proposes a dynamic eigenvalue-based method to calculate the minimum modal torsional stiffness of bundle conductors, providing a clear physical interpretation. The proposed method is independent of torque application position and distribution, flexibly adapting to various conditions. The minimum modal torsional stiffness effectively characterizes the torsional resistance of bundle conductors under dynamic loads. Results indicate that the minimum modal torsional stiffness consistently corresponds to the half-wave vibration mode. Increasing initial tension results in an increasing-then-decreasing minimum modal torsional stiffness. Uniform annular ice coating enhances minimum modal torsional stiffness; however sudden ice shedding may cause abrupt stiffness changes and negatively affect torsional stability. Additionally, increasing height differences and span length reduce torsional stiffness and weaken torsional resistance. The method overcomes the limitations of static models, providing valuable support in the design and optimization of transmission lines.