High-Altitude Wind Energy

Airborne wind energy systems (AWE systems) are systems that utilize the wind above the reach of conventional wind turbines by using an airborne device (aircraft) instead of turbine blades and ropes instead of a turbine-carrying tower, thereby providing access to stronger and steadier high-altitude winds and requiring less construction material per unit of produced energy. The basic classification of AWE systems is to those with on-board generators (OBG) and those with ground-based generators (GBG), where both types have theoretically identical energy production potential.

The GBG AWE system called HAWE (High Altitude Wind Energy; developed through EU FP7 project HAWE) consists of an airborne module (ABM), including a rotating cylindrical balloon subject to the Magnus effect, connected by a single rope (tether) to the winch-generator system (Fig. 1a). Wind produces the Magnus effect-based aerodynamic lift on the rotating cylinder, driving the generator in an ascending-descending pumping mode. Each operating cycle includes a power production phase, when the ABM ascends and drives the generator, and a power consumption phase, when the electric machine operates as a motor, pulling the ABM back down (Fig. 1b). The cylinder is rotated by an electric drive, with the rope serving as both the mechanical and the electrical link with the ground. The intended planar motion of the ABM, produced by forces shown in Fig. 1c, is contained in a vertical plane aligned with the wind (plane xz). The main research objectives include modelling of system dynamics, conducting a control strategy optimization study, synthesis of the control system and the simulation analysis of the proposed control strategy.

Dynamics modelling includes: (i) the ABM using the Magnus effect (Fig. 1c), (ii) the rope that introduces effects of elasticity, inertia and aerodynamic drag (Fig. 2), and (iii) winch and generator. In particular, Fig. 2 shows the three developed dynamic rope models, along with the rope aerodynamic drag modelling approach. Their corresponding mathematical models are presented in the publications listed below. The comparison of the three models in a simulation of one ascending-descending cycle that includes a gust of wind (Fig. 3) shows that the multi-mass model is most capable of accurately describing the catenary form of the rope, as well as predicting a complex form of system vibrations and conveniently introducing the effect of aerodynamic drag force. For fast, control-oriented simulations, one of the simpler models can provide a favourable trade-off between modelling accuracy and computational efficiency.

The overall control system structure (Fig. 4) comprises low-level winch speed and cylinder speed controllers coordinated by the high-level supervisory control strategy. The two controlled variables are the rope unwinding speed v_r (obtained from winch speed ω_w) and the cylinder speed ω_cyl. The basic supervisory control strategy controls v_r so that its maximum magnitudes are maintained during ascending and descending, which may not be optimal. The numerical control strategy optimization should, therefore, find control variables’ time-responses that maximize energy production.

The optimization problem formulation is gradually refined in different characteristic ways, as presented in the provided publications, and it is solved numerically using the TOMLAB/PROPT software tool. The main goal is to maximize the energy production during a continuously repeatable operating cycle comprising ABM ascending and descending phases. The optimization results with the cylinder speed limited to 200 rpm (matching simulation results) are shown in Fig. 5 along with the simulation results for basic control strategy. There are three important observations: (i) optimal trajectory is almost vertical for the given horizontal direction of the wind, suggesting that the ABM should fly in the crosswind direction, (ii) the trajectory position in the xz-plane is as far as possible from the winch for the given rope length limit, and (iii) the average mechanical power produced is increased by 122% compared to basic control strategy. However, a model-based feasibility analysis has shown that the vertical trajectory can be achieved in the limited area in the xz-plane, because it requires that the rope pulls on the ABM at a suitable angle, whereas the actual rope angle cannot be freely chosen, as it is determined by the ABM position.

To achieve optimal-like, vertical ABM motion (i.e. v_x = 0), the rope speed reference v_rR (Fig. 4a), which is generally v_rR = v_xRcosβ + v_zsinβ, is changed to v_rR = v_zsinβ in the nominal, unsaturated (i.e. lower than limit value) speed case. This reference can approach zero during winding-in at unfavourable ABM positions, so it is refined by developing a PI controller of unsaturated rope unwinding speed reference. The comparison of basic and improved vertical operation strategy is shown in Fig. 6, while Table 1 compares optimization results with simulation ones using idealized winch and cylinder control (as used during optimization). At high speed limits, the vertical operation strategy approaches and even exceeds optimization in terms of average produced power P_avg (optimization algorithm most likely found local optimums there).

Table 1. Comparison between optimization and vertical operation strategy simulation power production.

Vertical operation performance strongly depends on the chosen position in the xz-plane. Therefore, simulations of the basic and the vertical control strategy are conducted at different positions, where two ways of defining the available rope length during an operating cycle are used: (i) setting the maximum length of the rope to l_r,max = 800 m, and (ii) disregarding the initial length and setting the length of the active rope (the part cyclically wound out and wound in) to l_r,act = 100 m. Figures 7a and 7b show the average power vs. initial ABM position for vertical and basic control strategies when maximum rope length is prescribed. The vertical operation is more productive far from the winch, but not sustainable near the winch, and its power gain over basic strategy does not exceed 7.3%. Outside the approximate feasible region of vertical lift for v_r = 4 m/s (see Fig. 7c), the produced power is significantly diminished. Fig. 7d shows that the basic control strategies’ trajectories also become increasingly vertical for ABM positions farther from the winch (i.e. for small active rope lengths; cf. Fig. 5). Figures 8a and 8b show the control strategies’ power production comparison when the active rope length is prescribed. The productive area for the vertical operation is now much larger (cf. Fig. 7a), because smaller active rope length keeps the ABM near the area of feasible vertical lift (cf. Fig. 8c and Fig. 7c). However, the vertical strategy’s average power increase over basic strategy is no more than 9.7%, while the basic control strategy remains more robust and simpler to implement. The basic strategy performance is rather insensitive to the initial ABM position (Fig. 8b), as the trajectories cluster on a line and become nearly vertical when active rope length is small (Fig. 8d).