Galloping of a single iced conductor based on curved-beam theory

• We develop a finite element model of iced conductors to account for the nonlinearity and coupling of movements.
• We put forward a nonlinear iteration algorithm to successfully solve for the equilibrium position.
• We deduce the linearized movement equations of galloping and discuss the stability and galloping in the sub-space.
• An example of galloping of the iced C-shaped conductors shows the validity and discrepancies from three models.

Based on the displacement interpolations and curvature–displacement relationship of spatial curved beam theory, a finite element model of iced conductor galloping is presented, which involves 3 translational degrees of freedom (DOF) and 3 rotational DOF. The nonlinearity and coupling of translational and torsional movement can be taken into account in this model. A nonlinear iteration algorithm is employed to solve for the equilibrium position under eccentric gravity loads and the quasi-steady aerodynamic forces. The linearized movement equations are derived and the stability of the equations is judged according to the initial equilibrium solution (IES). Time integration is also performed in the sub-space. An example of three thicknesses of iced C-shaped conductors shows that the update of aerodynamic forces will greatly affect the initial equilibrium position, which will result in different critical wind speeds and galloping amplitudes of an iced transmission line. Different types of galloping, such as one-loop or two-loop, will occur at different wind attack angles.