#
Airborne Wind Energy - to fly or not to fly?
Doktorsavhandling, 2020

To estimate the AWES power production, the thesis provides a dynamic system model that serves as the basis for all the work. The model describes the flight dynamics of a rigid wing that is exposed to tether and aerodynamic forces controlled by flight control surfaces. Index-3 Differential Algebraic Equations (DAEs) based on Lagrangian mechanics describe the dynamics.

This model is validated by fitting it to real flight measurements obtained with a pumping-mode AWES, the prototype AP2 by Ampyx Power. The optimal power production of an AWES depends on complex trade-offs; this motivates formulating the power production computation as an Optimal Control Problem (OCP). The thesis presents the numerical methods needed to discretize the OCP and solve the resulting Nonlinear Program (NLP).

Large-scale implementation of AWESs raises challenges related to variability in power production on the time scale of minutes to weeks. For the former, we investigate the periodic fluctuations in the power output of a single AWES. These fluctuations can be severe when operating a wind farm and have to be considered and reduced for an acceptable grid integration. We analyse the option of controlling the flight trajectories of the individual systems in a farm so that the total power output of the farm is smoothed. This controlled operation fixes the system's trajectory, reducing the ability to maximize the power output of individual AWESs to local wind conditions. We quantify the lost power production if the systems are controlled such that the total farm power output is smoothed. Results show that the power difference between the optimal and fixed trajectory does not exceed 4% for the systems modelled in the study.

The variations in AWESs power production on the timescale of hours to weeks are particularly relevant to the interaction between AWE and other power generation technologies. Investigating AWESs in an electricity system context requires power-generation profiles with high spatio-temporal resolution, which means solving a large number of OCPs. In order to efficiently solve these numerous OCPs in a sequential manner, this thesis presents a homotopy-path-following method combined with modifications to the NLP solver. The implementation shows a 20-fold reduction in computation time compared to the original method for solving the NLP for AWES power optimization. For large wind-data sets, a random forest regression model is trained to a high accuracy, providing an even faster computation.

The annual generation profiles for the modelled systems are computed using ERA5 wind data for several locations and compared to the generation profile for a traditional wind turbine. The results show that the profiles are strongly correlated in time, which is a sobering fact in terms of technology competition. However, the correlation is weaker in locations with high wind shear.

The potential role of AWESs in the future electricity system is further investigated. This thesis implements annual AWE-farm generation profiles into a cost-optimizing electricity system model. We find that AWE is most valuable to the electricity system if installed at sites with low wind speed within a region. At greater shares of the electricity system, even if AWESs could demonstrate lower costs compared to wind turbines, AWE would merely substitute for them instead of increasing the total share of wind energy in the system. This implies that the economic value of an AWES is limited by its cost relative to traditional wind turbines.

## Författare

### Elena Malz

Chalmers, Elektroteknik, System- och reglerteknik

### Drag-mode airborne wind energy vs. wind turbines: An analysis of power production, variability and geography

Energy,; Vol. 193(2020)

**Artikel i vetenskaplig tidskrift**

### A reference model for airborne wind energy systems for optimization and control

Renewable Energy,; Vol. 140(2019)p. 1004-1011

**Artikel i vetenskaplig tidskrift**

### A Quantification of the Performance Loss of Power Averaging in Airborne Wind Energy Farms

2018 European Control Conference, ECC 2018,; (2018)p. 58-63

**Paper i proceeding**

### E.C. Malz, V. Verendel, S. Gros, “Computing the power profiles for an airborne wind energy system based on large-scale wind data”, in press in Renewable Energy, 2020.

### E.C. Malz, V. Walter, L. Go ̈ransson, S. Gros, “The value of AWE systems in the future electricity system”, submitted to Wind Energy, Wiley, 2020.

Nowadays, traditional wind power systems are well established in the power system. The expected capacity is increasing and so are the height of the tower and the length of the turbine blades. The concept of an AWE system replaces the heavy, material-intensive tower with a tether. Instead of a nacelle with three blades, a wing harvests high-altitude wind energy. Due to the reduced material intensity and an expected higher energy yield from operating higher altitudes, AWE is expected to have economic advantages compared to the known wind power technology.

As of today, no commercial system is available, and the actual power production potential is yet unknown. Thus, in order to create the right incentives, research on AWE power generation and how it relates to already well-established renewable energy systems is essential.

This thesis formulates a mathematical model of an AWE system in order to simulate and optimize the power generation given external wind conditions. The model is used to investigate the power fluctuations within a sub-minute scale as well as the hourly power variations over a year.

The results identify important factors that influence the level and the variability of power generation, and the related economic value of AWE systems.

### Styrkeområden

Energi

### Ämneskategorier

Energisystem

Reglerteknik

### ISBN

978-91-7905-373-4

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 4840

### Utgivare

Chalmers