Dynamic modeling and stability analysis of parafoil traction cable for high altitude wind power generation

In high altitude wind parafoil power generation (HAWPG), parafoil traction cable plays an important role. The cable, which is stretched by the parafoil, is prone to excite vibration even under small disturbances, which affects the stability of the entire HAWPG system. In view of this problem, this paper establishes parafoil traction cable dynamic model and analyzes the unstable regions of the cable parametrically excited vibration. The cable dynamic model, which has axial time-varying velocity and tension, is established based on Hamilton principle. Based on the cable ordinary differential equation, a second-order cable Mathieu–Hill differential equation can be obtained. Then, solve the vibration instability regions caused by changing parameters, the boundaries of different regions on the parameter plane can be directly determined by constructing the periodic solution. Finally, numerical examples and phase portraits are provided to verify the proposed method. The parameters, which includes the cable material properties, length and axial velocity, determined the boundedness of cable vibration. Therefore, the parafoil traction force on the cable should be set appropriately when determining the cable material properties to avoid the unstable vibration.