Nonlinear optimal control of wind-excited oscillations of overhead transmission lines

Due to long length, relatively small weight and low structural damping of overhead transmission lines, they are vulnerable to external excitations such as strong wind or wind-rain. Among them, the low frequency and large amplitude galloping phenomenon is that serious consequences such as short circuiting and failure of the overhead transmission line.In this paper, to suppress the undesirable galloping vibrations, we first derive the governing equations of transmission line by applying the Hamilton’s principle and the quasi-static assumption, and then these equations are discretized by the Galerkin method. Then the application of nonlinear quadratic regulator (NLQR) theory is employed to design a closed-form feedback controller for suppressing undesirable vibration of the overhead transmission lines. To suppress galloping forced vibrations, an arbitrary number of piezoelectric actuators are assumed to apply control forces. Finally, by simulating a parametric case study with five piezoelectric actuators, validate the performance and robustness of the proposed control strategy is demonstrated. Numerical results show that the proposed active controller is more efficient and robust than the passive controllers.

Keywords:

Transmission lines , Galloping , Nonlinear control , Optimal control