Quasi-Steady Model Enhancements of Airborne Wind Energy Systems

Abstract

The quasi-steady model (QSM) was developed to calculate the power output of a soft-wing airborne wind energy (AWE) system operated in pumping cycles. The comparison with experimental data shows that the original formulation of the model underestimates the power output. The model does not take inertial forces into account and highly simplifies the reel-out flight path. In this work, these assumptions are critically reviewed and their impact on the simulation results assessed.

The effect of inertial forces is analytically described for a helical flight path with fixed turning radius around the downwind axis. The derived analytical solution for this flight path verifies the formulation of inertial forces in spherical coordinates proposed in earlier studies. The proposed equations are modified and added to the QSM. Both, the analytically developed set of equations and the QSM with added inertia are compared for the helical flight case. It is observed that at larger cone angles where the tether length is rather short, but the turning radius is large, the inertial effect increases the tether force and the power output. With small cone angles this effect reverses. Based on the example case, the impact of the inertial effects on the output power computed with the QSM is limited to 1-2% for lightweight soft kites.

In the original formulation of the QSM the figure-of-eight maneuvers are not resolved. Instead, the tether is reeled out at representative constant values for the elevation, azimuth and course angles. QSM output based on real flight path coordinates is used as a benchmark to calculate the accuracy of reel-out path simplifications. The power output error of resolving reel-out flight with constant angles is on average 4.1% when compared to the reference simulations. An alternative flight path representation is developed, fitting a known figure-of-eight, lemniscate, to measured asymmetric reel-out flight paths. By flying the fitted figure in the QSM, the output power error caused by this path representation is estimated to be only 1.7% in comparison to the reference simulations. It is recommended to use this fitting method based on a class function/shape function transformation technique (CST), to parametrize the reel-out flight path, despite the added complexity.

The study has shown that the accuracy improvement by including the inertial effects in the QSM is marginal if the model is limited to lightweight soft wing simulation. As a follow-up study the inertial effects should be tested with bigger kites and heavier rigid-wing systems. The adjusted CST fitting method together with the inertial equations enable these maneuvering flight simulations in the QSM.