Control co-design for cyclorotor wave energy conversion

The European Commission's Offshore Renewable Energy Strategy [1], published in November 2020, sets ambitious targets for ocean energy deployment: 1 GW of capacity, including wave and tidal energy, by 2030, and 40 GW by 2050. However, conventional wave energy converters (WECs) that rely on buoyancy or diffraction forces face challenges in achieving commercial viability due to their high levelized cost of energy (LCoE) [2]. In contrast, lift-based cyclorotor WECs have emerged as a promising alternative. Analytical and experimental studies from the Horizon 2020 LiftWEC project [3] and the Atargis Wave Energy Corporation [4] suggest these devices exhibit enhanced power absorption potential, especially when advanced control strategies are implemented [5]. Despite these promising findings, the optimal design parameters, such as cyclorotor radius and submergence depth, remain unexplored for various wave climates and control strategies. This study addresses this gap by employing a control co-design methodology to investigate a cyclorotor WEC operated with a non-linear model predictive control (NMPC) strategy. The system hydrodynamic behavior in waves is simulated using a mathematical, control-oriented, point vortex model [5] [6]. Device performance is evaluated through the Capture Width Ratio (CWR) [7], with all simulations performed in MATLAB. Three separate control approaches—velocity-only control, pitch-only control, and combined control [5, 8]—are analyzed and compared, as part of the co-design exercise focusing on cyclorotors of different radii. By way of example, selected results, summarized in the table below, showcase the performance of cyclorotor WECs with varying radii operating under pitch-only control in an irregular sea state characterized by a peak period Tp =10s and a significant wave height Hs=2m. Radius [m] 3 4 5 6 7 8 CWR [%] 16.08 26.88 39.58 53.74 68.99 85.07 References [1] European Commission, An EU Strategy to Harness the Potential of Offshore Renewable Energy for a Climate Neutral Future. European Commission, Belgium, 2020 [2] C. Guo, W. Sheng, D. G. De Silva, and G. Aggidis, “A review of the levelized cost of wave energy based on a techno-economic model,” Energies, vol. 16, no. 5, 2023 [3] LiftWEC, available: https://cordis.europa.eu/project/id/851885/results [Accessed: 7-Dec-2024] [4] S. G. Siegel, “Numerical benchmarking study of a cycloidal wave energy converter,” Renewable Energy, vol. 134, pp. 390–405, 2019 [5] A. Ermakov, A. Marie, and J. V. Ringwood, “Optimal control of pitch and rotational velocity for a cyclorotor wave energy device,” IEEE Transactions on Sustainable Energy, vol. 13, no. 3, 2022 [6] A. Ermakov and J. V. Ringwood, “A control-orientated analytical model for a cyclorotor wave energy device with N hydrofoils,” Journal of Ocean Engineering and Marine Energy, vol. 7, pp. 201–210, 2021. [7] A. Babarit, “A database of capture width ratio of wave energy converters,” Renewable Energy, vol. 80, pp. 610–628, 2015. [8] J. V. Ringwood and A. Ermakov, “Energy-maximising control philosophy for a cyclorotor wave energy device,” in 41st International Conference on Ocean, Offshore & Arctic Engineering (OMAE), Hamburg, no. 80990. American Society of Mechanical Engineers, 2022