FEM-Aided Modeling and Control of a Tethered Hydrokinetic Energy Kite

In this paper, a six-degree-of-freedom tethered rigid kite with a kite-mounted turbine is modeled using Newtonian and Lagrangian formulations supplemented with corresponding kinematic analysis and an Euler-angle representation. In addition, to capture the coupled effects of kite and tether dynamics, the Euler-Bernoulli bending equations are taken into their weak form to be spatially discretized into N-segments utilizing a Galerkin Finite Element Method (FEM) strategy. Consequently, the infinite-dimensional beam governing equations become a finite set of 5(N+1) ordinary time differential equations. The kite and tether dynamics are placed into their state-space form and their interactions are characterized by the force balance at the tip of the tether at which the kite is attached. The formulations obtained in this work provide a baseline for the study of the effect of the tether loads on the energy generation of the kite.