52 Ioannis Lymperopoulos Automatic Control Laboratory EPFL LA EPFL, STI IGM LA3, Station 9 Bâtiment ME Lausanne - 1015 Switzerland ioannis.lymperopoulos@epfl.ch la.epfl.ch
Optimal Altitude Estimation for Power Generating Kites
in an Uncertain Wind-Field
Ioannis Lymperopoulos and Colin Jones
Automatic Control Laboratory, EPFL
Building on previous knowledge for the correlation structure of wind forecast uncertainties in spacetime and using measure-ments both from the ground and onboard the flying kite, we are able to provide filtering estimates for the wind speed. We fil-ter for the full span of altitudes of infil-terest, with varying confi-dence, depending on the availability of measurements at each height. We proceed to calculate the potential power that can be extracted at different altitudes and force the kite to grad-ually move towards the region with the maximum available power. During this process, the incoming measurements are continuously employed to improve on the previous filtering es-timates and a new optimal altitude may arise. Simulation re-sults show that even using such a simple method, power ex-tracted could improve with a factor of more than 20% in the case of fixed tether length and considerably more in the case of variable length.
The flying kite is experiencing a wind-field that varies in space and time. We assume that the wind is comprised of two com-ponents, the forecast (nominal part) and the forecast error (sto-chastic part). The nominal part is available to the operator while the stochastic part is modelled as a random field, with a zero mean multivariate Gaussian distribution [2]. For the length and time spans considered here (few km, 100s of seconds), both horizontal and time correlations are very strong, while cor-relation with altitude fades quickly. Simple kinematic equa-tions are used to simulate the trajectory of the kite since we are mostly interested in finding the optimal flying altitude rath-er than estimating the actual optimal orbit. We assume that power (P) is proportional to the cube of the wind speed (vw) but is also strongly affected by the inclination (Ø) of the cable to the horizontal level (a trade-off to cross-wind conditions), and
slightly affected by the decrease of air-density (ρ) with altitude (h), as in [1], namely
Our system is comprised of two wind speed sensors, one po-sitioned 10 m above the ground and another mounted to the kite (the kite is not allowed to operate below a certain height). We assume drag mode operation, therefore fixed line-length. Each time a new set of measurements arrives, we appropriate-ly condition the multivariate distribution to incorporate them in-to the correlation structure of the wind forecast error. This pro-vides an update to the forecast error mean and covariance of the wind speed across all altitudes. We use the mean to calcu-late the optimal altitude at each time step and force the mean flying altitude of the kite towards this direction with a verti-cal speed vh. If a new optimum is found while transversing the wind-field the kite will be again directed towards it.
Simulations of the described setup exhibit encouraging results. The method is able to improve performance by more than 20% on a scenario to scenario basis for a fixed tether length. If we vary the tether length two-fold (in order to be able to exploit higher altitudes, without being significantly penalised for de-viation from cross-wind conditions) this performance increas-es considerably. Finally, it is worth noting that the margin from the case where the real wind optimal altitude is available is considerably small.
References
[1] I Argatov, P Rautakorpi, and R Silvennoinen. Estimation of the mechanical en-ergy output of the kite wind generator. Renewable Enen-ergy, 34(6):1525–1532, 2009. [2] RE Cole, C Richard, S Kim, and D Bailey. An Assessment of the 60 km Rapid Up-date Cycle (RUC) with Near Real-Time Aircraft Reports. Technical Report NASA/A-1, MIT Lincoln Laboratory, 1998.
