Automatic Control of Optimal Pumping Cycles in Airborne Wind Energy

MS Theseus with SkySails system. 54

Michael Erhard Research & Development

SkySails GmbH Luisenweg 40 20537 Hamburg Germany michael.erhard@skysails.de www.skysails.info

Automatic Control of Optimal Pumping Cycles in Airborne Wind Energy

1_{SkySails GmbH}

2_{Systems Control and Optimization Laboratory, University of Freiburg}

The development of airborne wind energy plants de-mands for control setups, which allow for fully au-tonomous power generation cycles. Further, in order to achieve an economic operation, optimisation of the aver-age power output is a crucial design goal. This contribu-tion presents optimisacontribu-tions based on an experimentally verified model. The results aim at being directly imple-mented to the small-scale prototype in the near future.

0

0 40 80 120 160

Power [arb. units]

Time [s] -10 -5 0 5 10 15 4950 5000 5050 5100 5150 Power Pmech [kW] Time [s] e_x = wind direction 2. Transfer Phase 1. Power Phase 3. Return Phase

Three-dimensional flight trajectories and corresponding time se-ries of mechanical power. Experimental data from autonomous flight operation [1] (left), optimisation result based on this data as initial guess (right).

The first part deals with a simple model for the teth-ered kite flight dynamics [1], which will be used for both controller design and cycle optimisation. The validity of the model will be discussed by presenting experimental flight results from the SkySails 55 kW small-scale func-tional prototype [2]. Further, the autonomous opera-tion of pumping cycles based on flight control for pat-tern eight-down and winch operation algorithms will be briefly summarised. The second part aims at optimisa-tion of the average power output, which is computed by integrating the mechanical energy given as product of tether reeling speed and tether force. The optimisation of complete pumping cycles is implemented as optimal feedforward control problem using the CasADi package [3]. The focus of simulations is clearly put on improve-ment and further developimprove-ment of operational flight algo-rithms applicable to the small-scale functional prototype.

References:

[1] Erhard M., Strauch H.: Theory and experimental validation of a simple comprehensible model of tethered kite dynamics used for controller design. In: Airborne Wind Energy. Springer (2013) [2] Erhard M., Strauch H.: Flight control of tethered kites in au-tonomous pumping cycles for airborne wind energy. Control Engi-neering Practice, Vol. 40, pp. 13–26 (2015)

[3] Andersson J., Akesson J., Diehl M.: CasADi: A symbolic pack-age for automatic differentiation and optimal control. In: Recent Advances in Algorithmic Differentiation. Lecture Notes in Compu-tational Science and Engineering, Vol. 87, pp. 297–307. Springer (2012)