Vibration suppression analysis of iced transmission lines under axial time-delay velocity feedback strategy

To ensure the safety of power energy transmission channel and mitigate the harm caused by galloping of iced transmission lines, the axial time-delay velocity feedback strategy is adopted to suppress the galloping. The partial differential equation of galloping with axial time-delay velocity feedback strategy is established based on the variational principle for Hamiltonian. Then, the partial differential equation of galloping is transformed into ordinary differential equation based on normalization and the Galerkin method. The primary amplitude-frequency response equation, the first-order steady-state approximate solution, and the harmonic amplitude-frequency response equation are derived by the multiscale method. The impact of different parameters such as time-delay value, control coefficient, and amplitude of external excitation on the galloping response are analyzed. The amplitude under the primary resonance exhibits periodicity as time-delay value varies. The amplitude diminishes with increased control coefficient and increases with external excitation. Comprehensive consideration of various influences of parameters on vibration characteristics is crucial when employing the axial time-delay velocity feedback strategy to suppress galloping. Therefore, to achieve the best vibration suppression effect, it is crucial to adjust the time-delay parameter for modifying the range and amplitude of the resonance zone. The conclusions obtained by this study are expected to advance the refinement of active control techniques for iced transmission lines, and may provide valuable insights for practical engineering applications.