Trajectory Optimization of a Tethered Underwater Kite

Abstract

This dissertation addresses the challenge of optimizing the motion trajectory of a tethered marine hydrokinetic energy harvesting kite in order to maximize its average electric power output. The dissertation focuses specifically on the “pumping” kite configuration, where the kite is periodically reeled out from a floating base station at high tension, then reeled in at low tension. This work is motivated by the significant potential for sustainable electricity generation from marine currents such as the Gulf Stream. Tethered systems can increase their energy harvesting potential significantly through cross-current motion. Such motion increases apparent flow speed, which is valuable because the instantaneous maximum power that can be harvested is proportional to the cube of this apparent speed. This makes it possible for tethered systems to achieve potentially very attractive power densities and levelized costs of electricity compared to stationary turbines. However, this also necessitates the use of trajectory optimization and active control in order to eke out the maximum energy harvesting capabilities of these systems.

The problem of optimizing the trajectories of these kites is highly non-linear and thus challenging to solve. In this dissertation we make key simplifications to both the modeling and the structure of the optimal solution which allows us to learn valuable insights in the nature of the power maximizing trajectory. We first do this analysis to maximize the average mechanical power of the kite, then we expand it to take into account system losses. Finally, we design and fabricate an experimental setup to both parametrize our model and validate our trajectories.

In summary, the goal of this research is to furnish model-based algorithms for the online optimal flight control of a tethered marine hydrokinetic system. The intellectual merit of this work stems from the degree to which it will tackle the difficulty of solving this co-optimization problem taking into account overall system efficiency and the full range of possible system motion trajectories. From a broader societal perspective, this work represents a step towards experimentally validating the potential of pumped underwater kite systems to serve as renewable energy harvesters in promising environments such as the Gulf Stream.