- Open Access
Self-contained power optimization for wave energy conversion: A step change in generation
Phys. Rev. Research 8, 013075 – Published 23 January, 2026
DOI: https://doi.org/10.1103/f24b-9hkc
Abstract
Wave energy holds immense potential, yet to date progress has been hampered by substantial design challenges and perceived high levelized cost of electricity (LCoE). Control strategies could be vital for improving the economic viability of wave energy converters (WECs), yet practical implementations demonstrating performance remain limited. Here, we present, and implement experimentally for the first time, a self-sufficient control system requiring no external measurements. It is physically demonstrated for the complex hinged, Moored, MultiMode, Multifloat WEC, called M4. The controller operates within a linear noncausal framework to optimize generator torque, where excitation forces are estimated and predicted autoregressively. A real-time state-space hydrodynamic model, based on the Cummins-type linear diffraction-radiation formulation, enables operation based solely on motor-generator torque-speed data. In a first-of-its-kind wave basin experiment, the control strategy is shown to over double energy capture (up to a 125% increase) whilst also demonstrating performance in both unidirectional and directionally spread irregular wave conditions, mimicking real ocean complexity. Site-specific assessment across four European wave sites demonstrates substantial implications for system design and performance: The optimal device size is approximately less than that defined by the average peak period of a site, as often used, and with control implemented, the average power per unit mass (approximately proportional to the inverse of LCoE) increased by about across the four sites. This represents a step change toward the commercial viability of wave energy.
Physics Subject Headings (PhySH)
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References (62)
- D. Mollison, O. Buneman, and S. Salter, Wave power availability in the NE atlantic, Nature (London) 263, 223 (1976).
- A. Winter, The UK wave energy resource, Nature (London) 287, 826 (1980).
- I. Glendenning, Ocean wave power, Applied Energy 3, 197 (1977).
- K. Gunn and C. Stock-Williams, Quantifying the global wave power resource, Renew. Energy. 44, 296 (2012).
- R. A. Arinaga and K. F. Cheung, Atlas of global wave energy from 10 years of reanalysis and hindcast data, Renew. Energy. 39, 49 (2012).
- N. Gonzalez, P. Serna-Torre, P. A. Sánchez-Pérez, R. Davidson, B. Murray, M. Staadecker, J. Szinai, R. Wei, D. M. Kammen, D. A. Sunter et al., Offshore wind and wave energy can reduce total installed capacity required in zero-emissions grids, Nat. Commun. 15, 6826 (2024).
- A. W. Stahl, The utilization of the power of ocean waves, Trans. ASME 13, 438 (1892).
- S. H. Salter, Wave power, Nature (London) 249, 720 (1974).
- K. Budar and J. Falnes, A resonant point absorber of ocean-wave power, Nature (London) 256, 478 (1975).
- J. Falnes, A review of wave-energy extraction, Mar. Struct. 20, 185 (2007).
- R. Yemm, D. Pizer, C. Retzler, and R. Henderson, Pelamis: Experience from concept to connection, Philos. Trans. R. Soc. A 370, 365 (2012).
- T. Whittaker and M. Folley, Nearshore oscillating wave surge converters and the development of oyster, Philos. Trans. R. Soc. A 370, 345 (2012).
- E. Carpintero Moreno and P. Stansby, The 6-float wave energy converter M4: Ocean basin tests giving capture width, response and energy yield for several sites, Renewable Sustainable Energy Rev. 104, 307 (2019).
- H. Santo, P. H. Taylor, E. C. Moreno, P. Stansby, R. E. Taylor, L. Sun, and J. Zang, Extreme motion and response statistics for survival of the three-float wave energy converter M4 in intermediate water depth, J. Fluid Mech. 813, 175 (2017).
- S. Draycott, P. Stansby, and G. Li, Experimental measurements of two elastic taut-slack mooring configurations for the multi-float M4 WEC, International Marine Energy Journal 8, 119 (2025).
- P. Stansby, S. Draycott, G. Li, C. Zhao, E. C. Moreno, A. Pillai, and L. Johanning, Experimental study of mooring forces on the multi-float WEC M4 in large waves with buoy and elastic cables, Ocean Eng. 266, 113049 (2022).
- J. Apsley, X. Zhang, M. Iacchetti, I. E. Damian, Z. Liao, G. Li, P. Stansby, G. Li, H. Wolgamot, C. Gaudin, A. Kurniawan, X. Zhang, Z. Lin, N. Fernando, C. Shearer, and B. Saunders, Integrated hydrodynamic-electrical hardware model for wave energy conversion with M4 ocean demonstrator, Proc. EWTEC 15, (2024).
- Opening wave energy data to the world, Nature news, 2025, https://www.nature.com/articles/d42473-024-00484-7.
- W. Hugh, G. Christophe, S. Peter, A. Kurniawan, E. Wiebke, and P. Irene, The M4 Wave Energy Demonstration Project: Overview, impact and insight Proc. EWTEC 16 (2025).
- B. Sørensen, Commercial hurdles to wave power, Nature (London) 543, 491 (2017).
- J. Portilla-Yandún, F. Barbariol, A. Benetazzo, and L. Cavaleri, On the statistical analysis of ocean wave directional spectra, Ocean Eng. 189, 106361 (2019).
- P. Stansby and S. Draycott, M4 wec development and wave basin Froude testing, Eur. J. Mech. B Fluids 104, 182 (2024).
- S. Draycott, P. K. Stansby, and G. Li, An experimental assessment of the effect of directional spreading on mooring line loads for the multi-float M4 WEC, in ISOPE International Ocean and Polar Engineering Conference (ISOPE, 2023), pp. ISOPE–I.
- U. A. Korde and J. Ringwood, Hydrodynamic Control of Wave Energy Devices (Cambridge University Press, Cambridge, 2016).
- P. Nebel, Maximizing the efficiency of wave-energy plant using complex-conjugate control, Proc. Inst. Mech. Eng., Part I 206, 225 (1992).
- A. Babarit and A. Clément, Optimal latching control of a wave energy device in regular and irregular waves, Appl. Ocean Res. 28, 77 (2006).
- M. Lopes, J. Hals, R. Gomes, T. Moan, L. Gato, and A. O. Falcão, Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter, Ocean Eng. 36, 386 (2009).
- U. A. Korde, Preliminary consideration of energy storage requirements for sub-optimal reactive control of axisymmetric wave energy devices, Annu. Rev. Control 40, 93 (2015).
- A. Mérigaud, B. Thiria, and R. Godoy-Diana, Geometrical framework for hydrodynamics and control of wave energy converters, PRX Energy 2, 023003 (2023).
- J. Falnes, Ocean Waves and Oscillating Systems: Linear Interactions Including Wave-energy Extraction (Cambridge University Press, Cambridge, 2002).
- J. V. Ringwood, G. Bacelli, and F. Fusco, Energy-maximizing control of wave-energy converters: The development of control system technology to optimize their operation, IEEE Control Syst. Mag. 34, 30 (2014).
- G. Li, G. Weiss, M. Mueller, S. Townley, and M. R. Belmont, Wave energy converter control by wave prediction and dynamic programming, Renew. Energy. 48, 392 (2012).
- S. Zhan and G. Li, Linear optimal noncausal control of wave energy converters, IEEE Trans. on Control Sys. Tech. 27(4), 1526 (2019).
- Z. Liao, N. Gai, P. Stansby, and G. Li, Linear non-causal optimal control of an attenuator type wave energy converter M4, IEEE Trans. Sustainable Energy 11, 1278 (2020).
- Z. Liao, P. Stansby, and G. Li, A generic linear non-causal optimal control framework integrated with wave excitation force prediction for multi-mode wave energy converters with application to M4, Appl. Ocean Res. 97, 102056 (2020).
- Z. Liao, P. Stansby, G. Li, and E. C. Moreno, High-capacity wave energy conversion by multi-float, multi-pto, control and prediction: Generalized state-space modelling with linear optimal control and arbitrary headings, IEEE Trans. Sustainable Energy 12, 2123 (2021).
- P. Stansby, E. Carpintero Moreno, and T. Stallard, Large capacity multi-float configurations for the wave energy converter M4 using a time-domain linear diffraction model, Appl. Ocean Res. 68, 53 (2017).
- J. V. Ringwood, S. Zhan, and N. Faedo, Empowering wave energy with control technology: Possibilities and pitfalls, Annu. Rev. Control 55, 18 (2023).
- Zhijing and Tao, Modelling and control tank testing validation for attenuator type wave energy converter, Part I: Experimental setup and control-oriented modelling, IEEE Trans. Sustainable Energy 14, 1747 (2023).
- Z. Liao, T. Sun, M. Al-Ani, L.-B. Jordan, G. Li, Z. Wang, M. Belmont, C. Edwards, and S. Zhan, Modelling and control tank testing validation for attenuator type wave energy converter–Part II: Linear noncausal optimal control and deterministic sea wave prediction tank testing, IEEE Trans. Sustainable Energy 14, 1758 (2023).
- T. Sun, Z. Liao, M. Al-Ani, L.-B. Jordan, G. Li, S. Zhan, M. Belmont, and C. Edwards, Modelling and control tank testing validation for attenuator type wave energy converter–Part III: Model predictive control and robustness validation, IEEE Trans. Sustainable Energy 14, 1737 (2023).
- M. L. McAllister, S. Draycott, T. Adcock, P. Taylor, and T. Van Den Bremer, Laboratory recreation of the Draupner wave and the role of breaking in crossing seas, J. Fluid Mech. 860, 767 (2019).
- M. McAllister, S. Draycott, R. Calvert, T. Davey, F. Dias, and T. van den Bremer, Three-dimensional wave breaking, Nature (London) 633, 601 (2024).
- M. Garcia-Abril, F. Paparella, and J. Ringwood, Excitation force estimation and forecasting for wave energy applications, IFAC-PapersOnLine 50, 14692 (2017).
- Y. Peña-Sanchez, A. Mérigaud, and J. V. Ringwood, Short-term forecasting of sea surface elevation for wave energy applications: The autoregressive model revisited, IEEE J. Oceanic Eng. 45, 462 (2020).
- W. Cummins, The impulse response function and ship motions, Schiffstechnik 9, 101 (1962).
- G. Li and P. Stansby, Software framework to accelerate bem linear wave load program using Openmp (OREGEN-BEM), in ISOPE International Ocean and Polar Engineering Conference (ISOPE, 2023), pp. ISOPE–I.
- C. Lee and J. Newman, Wamit user manual, version 7.0, WAMIT Inc, Chestnut Hill, Massachusetts, 2013.
- K. Hasselmann, T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. Ewing, A. Gienapp, D. Hasselmann, P. Kruseman et al., Measurements of wind-wave growth and swell decay during the joint north sea wave project (JONSWAP), Ergaenzungsheft zur Deutschen Hydrographischen Zeitschrift, Reihe A A8, 1 (1973).
- M. Latheef, C. Swan, and J. Spinneken, A laboratory study of nonlinear changes in the directionality of extreme seas, Proc. R. Soc. A 473, 20160290 (2017).
- P. Stansby, E. C. Moreno, S. Draycott, and T. Stallard, Total wave power absorption by a multi-float wave energy converter and a semi-submersible wind platform with a fast far field model for arrays, J. Ocean Eng. Mar. Energy 8, 43 (2022).
- R. A. Dalrymple, Directional wavemaker theory with sidewall reflection, J. Hydraul. Res. 27, 23 (1989).
- J. Zelt and J. E. Skjelbreia, Estimating incident and reflected wave fields using an arbitrary number of wave gauges, in Proceedings of the 23rd International Conference on Coastal Engineering (1993), pp. 777–789.
- S. Draycott, J. Steynor, T. Davey, and D. M. Ingram, Isolating incident and reflected wave spectra in the presence of current, Coastal Eng. J. 60, 39 (2018).
- G. Dalton, R. Alcorn, and T. Lewis, Case study feasibility analysis of the Pelamis wave energy convertor in Ireland, Portugal and North America, Renew. Energy. 35, 443 (2010).
- J. C. van Nieuwkoop, H. C. Smith, G. H. Smith, and L. Johanning, Wave resource assessment along the Cornish coast (UK) from a 23-year hindcast dataset validated against buoy measurements, Renew. Energy. 58, 1 (2013).
- A. Pecher, Experimental testing and evaluation of wecs, in Handbook of Ocean Wave Energy, edited by A. Pecher and J. P. Kofoed (Springer International Publishing, Cham, 2017), pp. 221–260.
- M. Penalba and J. V. Ringwood, A review of wave-to-wire models for wave energy converters, Energies 9, 506 (2016).
- J.-C. Gilloteaux and J. Ringwood, Control-informed geometric optimisation of wave energy converters, IFAC Proc. Vol. 43, 366 (2010).
- D. T. Gaebele, M. L. Anderson, A. L. Roach, D. D. Forbush, J. D. Roberts, and J. Weber, From TPL assessment to design optimization: Wave energy converter control co-design applied to the RM3, Renew. Energy. 241, 122338 (2025).
- Z. Liao and G. Li, Model predictive control of a wave-to-wire wave energy converter system with non-linear dynamics and non-linear constraints using a tailored pseudo-spectral method, Energy 304, 132060 (2024).
- Z. Liao, X. Zhang, J. Apsley, M. F. Iacchetti, P. Stansby, and G. Li, A sea-state-dependent control strategy for wave energy converters: Power limiting in large wave conditions and energy maximising in moderate wave conditions, IEEE Trans. Sustainable Energy 15, 1743 (2024).