Optimization of Pumping Cycles for Power Kites

The main contribution of this chapter is the formulation of an optimization problem to find the set of parameters of two decentralized control schemes—one for the wing flight and another for the ground winch—that maximizes the cycle power of a pumping kite. The pumping cycle consists of two phases, traction (reel-out) and retraction (reel-in), with predefined trajectories. The optimization takes into account constraints of reel speed saturation and minimum angle of attack, and can be applied to any wing with de-powering capability and given aerodynamic curves. The solution is computed through an iterative algorithm that uses a model of massless kite in dynamic equilibrium for the traction phase, and a dynamic 2D point mass model for the retraction phase. Other contributions are a discussion on the influence of the tether drag on the optimal angle of attack, and how the base angle of attack affects the average angle of attack. All results are validated by simulations with a dynamic 3D point mass kite model.