Finite time-Lyapunov based approach for robust adaptive control of wind-induced oscillations in power transmission lines

• Finite time-Lyapunov based adaptive control of galloping vibrations in transmission lines.
• Modeling of transmission line as a continuous string under assumed piezoelectric actuators.
• Nonlinear quadratic and cubic terms are included in the derived linear ODEs.
• Design of appropriate adaptation and control laws for finite-time suppression of galloping.
• Robustness of proposed active control strategy in vibration suppression of uncertain models.

Large amplitude oscillation of the power transmission lines, which is also known as galloping phenomenon, has hazardous consequences such as short circuiting and failure of transmission line. In this article, to suppress the undesirable vibrations of the transmission lines, first the governing equations of transmission line are derived via mode summation technique. Then, due to the occurrence of large amplitude vibrations, nonlinear quadratic and cubic terms are included in the derived linear equations. To suppress the vibrations, arbitrary number of the piezoelectric actuators is assumed to exert the actuation forces. Afterwards, a Lyapunov based approach is proposed for the robust adaptive suppression of the undesirable vibrations in the finite time. To compensate the supposed parametric uncertainties with unknown bands, proper adaption laws are introduced. To avoid the vibration devastating consequences as quickly as possible, appropriate control laws are designed. The vibration suppression in the finite time with supposed adaption and control laws is mathematically proved via Lyapunov finite time stability theory. Finally, to illustrate and validate the efficiency and robustness of the proposed finite time control scheme, a parametric case study with three piezoelectric actuators is performed. It is observed that the proposed active control strategy is more efficient and robust than the passive control methods.