Abstract
This article addresses the problem of optimizing electrical power generation using kite power systems (KPSs). KPSs are airborne wind energy systems that aim to harvest the power of strong and steady high-altitude winds. With the aim of maximizing the total energy produced in a given time interval, we numerically solve an optimal control problem and thereby obtain trajectories and controls for kites. Efficiently solving these optimal control problems is crucial when the results are used in real-time control schemes, such as model predictive control. For this highly nonlinear problem, we derive continuous-time models—in 2D and 3D—and implement an adaptive time-mesh refinement algorithm. By solving the optimal control problem with such an adaptive refinement strategy, we generate a block-structured adapted mesh which gives results as accurate as those computed using fine mesh, yet with much less computing effort and high savings in memory and computing time.
Highlights
In the last few years we have seen a fast increase in installed wind power capacity
A simplified problem in two dimensions was solved with the adaptive mesh refinement (AMR) 29 times faster than with an equidistant mesh leading to the same level of accuracy
The airborne wind energy systems (AWES) considered in the paper is a kite generator system (KGS) involving a controlled kite module (CKM) connected to a ground generator module (GGM) by a single tether
Summary
In the last few years we have seen a fast increase in installed wind power capacity. The installed cumulative power grew by 12.6% in 2016, reaching a total of 486.8 GW [1]. We consider the optimal control problem with a continuous-time model of the kite power system, further developing the work reported in [10,11]. The solution to this problem provides the trajectory of the kite and the corresponding control laws that maximize the total energy produced in a given time interval. The efficient solution of optimal control problems is necessary so that the results may be used in a real-time control schemes such as model predictive control (see e.g., [12,13,14,15]) We solve this problem in a time-mesh that is adaptively refined to achieve a desired level of accuracy. The complete 3D problem was successfully solved using the AMR strategy, while when using an equidistant mesh leading to the same level of accuracy, the maximum number of iterations of the nonlinear optimization solver was exceeded
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