WEC co-design

holistic design of wave energy converters

Based on findings with the WaveBot and FOSWEC, our team focused on a holistic design approach for wave energy converters, that could simultaneously factor in hydrodynamics, mechatronics, electronics, and control. Multi-port modeling constructs, which are popular in RF and electronics fields, provide excellent tools for understanding power flow and impedance matching in wave energy converters (Bacelli & Coe, 2021; Coe et al., 2025). These linear tools can be applied remarkably broadly when used properly (Tan et al., 2025) and provide invaluable insights. Along with nonlinear approaches that can more fully capture complex dynamics (Michelén Ströfer et al., 2023; Gaebele et al., 2023; Coe et al., 2024; Devin et al., 2024), these tools allow for a “control co-design” approach to be applied to wave energy converters. Our team has found immense value in applying these tools to a number of wave energy design problems (Keow et al., 2025; Keow et al., 2025; Forbush et al., 2025).

References

2025

Co-design of a wave energy converter through bi-conjugate impedance matching

Ryan G. Coe, Giorgio Bacelli, Daniel Gaebele, Alicia Keow, and Dominic Forbush

Mechatronics, Oct 2025

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As with other oscillatory power conversion systems, the design of wave energy converters can be understood as an impedance matching problem. By representing the wave energy converter as a multi-port network, two separate but related impedance matching conditions can be established. Satisfying these conditions maximizes power transfer to the load. In practice, these impedance matching conditions may be used to influence the design of the system (including the hull, power take-off, controller, mooring, etc.). To this end, this paper considers some example applications of wave energy converter design with the help of the impedance matching framework.
@article{Coe:2025ab, author = {Coe, Ryan G. and Bacelli, Giorgio and Gaebele, Daniel and Keow, Alicia and Forbush, Dominic}, bibtex_show = true, date-added = {2024-09-24 09:08:21 -0600}, date-modified = {2025-08-20 17:33:27 -0600}, doi = {10.1016/j.mechatronics.2025.103395}, issn = {0957-4158}, journal = {Mechatronics}, keywords = {Wave energy converter (WEC), Control co-design, Impedance matching}, pages = {103395}, title = {Co-design of a wave energy converter through bi-conjugate impedance matching}, url = {https://www.sciencedirect.com/science/article/pii/S0957415825001047}, volume = {111}, year = {2025}, bdsk-url-1 = {https://dx.doi.org/10.2139/ssrn.4996206} }
Benchmark of numerical modeling approaches on the systematic performance evaluation of wave energy converters

Jian Tan, Ryan G. Coe, and George Lavidas

Applied Ocean Research, Oct 2025

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Different numerical modeling methods have been developed and applied to evaluate a variety of performance indicators of wave energy converters (WECs), including the power performance, structural loads, levelized cost of energy, etc. Based on the modeling fidelity, the commonly used numerical modeling approaches can be classified as linear modeling, weakly nonlinear modeling and fully nonlinear modeling approaches. Each method differs in accuracy and computational efficiency, making them suitable for different stages of WEC design. However, the selection of modeling approach could significantly impact evaluation outcomes. For instance, simplified linear models may underestimate structural loads or overestimate energy production in some operational conditions, potentially leading to less cost-effective designs. Given the widespread utilization of these models, it is essential to understand the uncertainties brought by them in performance evaluations. This work is dedicated to benchmarking different linear-potential-flow-based numerical models for evaluating the systematic performance of WECs. Three representative numerical modeling approaches are considered in this work, including linear frequency-domain modeling, statistically linearized spectral-domain modeling and Cummins equation-based nonlinear time-domain modeling. A generic point absorber WEC is considered as the research reference in this work, and different sea sites are taken into account. The numerical models are utilized to predict critical performance indicators, including power performance, the annual energy production, the capacity factor, the levelized cost of energy and the PTO fatigue loads. By comparing the results, this work identifies the uncertainties associated with different modeling approaches in evaluating WEC performance.
@article{Tan:2025aa, author = {Tan, Jian and Coe, Ryan G. and Lavidas, George}, date-added = {2025-10-24 09:42:55 -0600}, date-modified = {2025-10-24 09:43:14 -0600}, doi = {10.1016/j.apor.2025.104725}, issn = {0141-1187}, journal = {Applied Ocean Research}, keywords = {Numerical modeling, Wave energy converter, Power, Fatigue, Levelized cost of energy}, pages = {104725}, title = {Benchmark of numerical modeling approaches on the systematic performance evaluation of wave energy converters}, url = {https://www.sciencedirect.com/science/article/pii/S0141118725003116}, volume = {162}, year = {2025}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0141118725003116}, bdsk-url-2 = {https://doi.org/10.1016/j.apor.2025.104725} }
Design Principles for Resonant Wave Energy Converters: Benchmarking Power Capture and Flow

Alicia Keow, Jantzen Lee, Giorgio Bacelli, and Ryan G. Coe

IEEE Transactions on Energy Conversion, Oct 2025

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Control co-design (CCD) in Wave Energy Converters (WECs) integrates the controller, power take-off (PTO), and buoy models during system design to optimize power output. Using the bi-conjugate impedance matching principle, this study models the PTO as a two-port network, revealing impedance matching conditions at the input and output ports as a function of the buoy, PTO, and controller. This study examines the pairing of a flywheel-type pitch resonator PTO within a given buoy constrained by limited space and ballast capacity. The results show that physical constraints imposed by the buoy affect PTO performance. While controller tuning achieves optimal output impedance matching and flywheel inertia is maximized within the buoy’s limitations, the PTO’s input impedance remains smaller than the complex conjugate of the buoy’s intrinsic impedance. This mismatch limits the PTO’s ability to generate sufficient reaction torque, particularly outside the resonance frequency, resulting in narrow-band power transfer. The findings emphasize the need for PTO design modifications to improve input power transfer. Pendulum-based PTO mechanisms are proposed as alternatives to couple with multiple buoy motion modes and improve wave-to-wire efficiency while respecting system constraints.
@article{Keow:2025aa, author = {Keow, Alicia and Lee, Jantzen and Bacelli, Giorgio and Coe, Ryan G.}, bibtex_show = true, date-added = {2024-11-11 11:22:20 -0700}, date-modified = {2025-08-20 17:55:39 -0600}, doi = {10.1109/TEC.2025.3593152}, issn = {1558-0059}, journal = {IEEE Transactions on Energy Conversion}, keywords = {Impedance;Impedance matching;Torque;Generators;Energy exchange;Seaports;Flywheels;Charge coupled devices;Wave energy conversion;Angular velocity;Wave Energy Converter;Power Take-off Design;Design Methodology;Wave-to-Wire Efficiency;Impedance Matching;Control Co-Design;Energy Conversion}, pages = {1-12}, title = {Design Principles for Resonant Wave Energy Converters: Benchmarking Power Capture and Flow}, year = {2025}, bdsk-url-1 = {https://doi.org/10.1109/TEC.2025.3593152} }

Comparative Analysis of Pendulum and Flywheel Power Take-Off Mechanisms for Wave Energy Conversion

Alicia Keow, Jantzen Lee, Giorgio Bacelli, and Ryan G. Coe

IEEE Transactions on Energy Conversion (under review), Oct 2025

Bib

@article{Keow:2025ab,
  author = {Keow, Alicia and Lee, Jantzen and Bacelli, Giorgio and Coe, Ryan G.},
  bibtex_show = true,
  date-added = {2025-07-19 16:14:13 -0600},
  date-modified = {2025-07-19 16:15:09 -0600},
  journal = {IEEE Transactions on Energy Conversion (under review)},
  status = review,
  title = {Comparative Analysis of Pendulum and Flywheel Power Take-Off Mechanisms for Wave Energy Conversion},
  year = {2025}
}

Towards an intuitive application of WEC control co-design

Dominic D. Forbush, Ryan G. Coe, Giorgio Bacelli, Daniel T. Gaebele, and Alicia Keow

Ocean Engineering, Oct 2025

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A simple co-design example in a reduced parameter space is presented for an oscillating flap device. Initially, the WEC geometry and mass properties are considered along with drivetrain gear ratio, inertia, motor constant and stiffness under both PI and optimal control. This parameter space is reduced to those to which performance is most sensitive for a fixed geometry. The gear ratio, drivetrain stiffness, and flap mass are found to be the most impactful design criteria as they can create orders of magnitude variations in power performance. The performance of the optimized system is compared with several sub-optimal variants in terms of electrical and mechanical power capture, transmission coefficients, and transducer power gain. Notably, though substantial power capture improvements are demonstrated when an optimal controller is employed, this power capture remains sensitive to appropriate selections of drivetrain and flap design parameters, implying that control co-design procedures remain necessary for high-performing WECs. A number of practical caveats and extensions to the presented co-design methodology are suggested, including the characterization of system static friction, especially in the presence of high gear ratios.
@article{Forbush:2025ab, author = {Forbush, Dominic D. and Coe, Ryan G. and Bacelli, Giorgio and Gaebele, Daniel T. and Keow, Alicia}, bibtex_show = true, date-added = {2025-07-19 16:16:25 -0600}, date-modified = {2025-10-02 07:43:37 -0600}, doi = {10.1016/j.oceaneng.2025.122762}, issn = {0029-8018}, journal = {Ocean Engineering}, keywords = {Wave energy converter (WEC), Control co-design, Impedance matching}, pages = {122762}, title = {Towards an intuitive application of {WEC} control co-design}, url = {https://www.sciencedirect.com/science/article/pii/S002980182502445X}, volume = {341}, year = {2025}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S002980182502445X}, bdsk-url-2 = {https://doi.org/10.1016/j.oceaneng.2025.122762} }

2024

Co-design of a wave energy converter for autonomous power

Ryan G. Coe, Michael C. Devin, Carlos A. Michelén Ströfer, Jantzen Lee, Giorgio Bacelli, Alicia Keow, Daniel T. Gaebele, Jeff Grasberger, Steven J. Spencer, Johannes Spinneken, Vincent S. Neary, and Brek Meuris

In 15th IFAC Conference on Control Applications in Marine Systems, Robotics and Vehicles (IFAC-CAMS), Sep 2024

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A “bolt-on” wave energy converter is designed to provide power for sensors on an existing oceanographic buoy. The narrow-banded pitch/roll response of the target oceanographic buoy lends itself to a tuned-resonator design, for which we suggest a novel “pitch resonator” wave energy converter concept. Using a pseudo-spectral method, the performance of the proposed wave energy converter is modeled in the range of sea states expected to be present at the target deployment location to study the effect of flywheel inertia on performance. The results show that the system can marginally meet the desired power demands, but suggest that related design concepts may be worth consideration.

@inproceedings{Coe:2024aa,
  address = {Blacksburg, VA},
  author = {Coe, Ryan G. and Devin, Michael C. and {Michel{\'e}n Str{\"o}fer}, Carlos A. and Lee, Jantzen and Bacelli, Giorgio and Keow, Alicia and Gaebele, Daniel T. and Grasberger, Jeff and Spencer, Steven J. and Spinneken, Johannes and Neary, Vincent S. and Meuris, Brek},
  bibtex_show = true,
  booktitle = {15th IFAC Conference on Control Applications in Marine Systems, Robotics and Vehicles (IFAC-CAMS)},
  date-added = {2024-01-29 14:01:55 -0700},
  date-modified = {2024-10-30 08:52:43 -0600},
  doi = {10.1016/j.ifacol.2024.10.094},
  issn = {2405-8963},
  keywords = {pseudo-spectral method, autonomous power, wave energy converter (WEC)},
  month = sep,
  number = {20},
  organization = {IFAC},
  pages = {446-451},
  title = {Co-design of a wave energy converter for autonomous power},
  url = {https://www.sciencedirect.com/science/article/pii/S2405896324018494},
  volume = {58},
  year = {2024},
  bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S2405896324018494},
  bdsk-url-2 = {https://doi.org/10.1016/j.ifacol.2024.10.094}
}

High-dimensional control co-design of a wave energy converter with a novel pitch resonator power takeoff system

Michael C. Devin, Daniel T. Gaebele, Carlos A. Michelén Ströfer, Jeff T. Grasberger, Jantzen Lee, Ryan G. Coe, and Giorgio Bacelli

Ocean Engineering, Sep 2024

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Researchers are exploring adding wave energy converters to existing oceanographic buoys to provide a predictable source of renewable power. A ”pitch resonator” power take-off system has been developed that generates power using a geared flywheel system designed to match resonance with the pitching motion of the buoy. However, the novelty of the concept leaves researchers uncertain about various design aspects of the system. This work presents a novel design study of a pitch resonator to inform design decisions for an upcoming deployment of the system. The assessment uses control co-design via WecOptTool to optimize control trajectories for maximal electrical power production while varying five design parameters of the pitch resonator. Given the large search space of the problem, the control trajectories are optimized within a Monte Carlo analysis to identify optimal designs, followed by parameter sweeps around the optimum to identify trends between the design parameters. The gear ratio between the pitch resonator spring and flywheel are found to be the most sensitive design variables to power performance. The assessment also finds similar power generation for various sizes of resonator components, suggesting that correctly designing for optimal control trajectories at resonance is more critical to the design than component sizing.
@article{Devin:2024aa, author = {Devin, Michael C. and Gaebele, Daniel T. and Str{\"o}fer, Carlos A. Michel{\'e}n and Grasberger, Jeff T. and Lee, Jantzen and Coe, Ryan G. and Bacelli, Giorgio}, bibtex_show = true, date-added = {2024-02-07 13:37:15 -0700}, date-modified = {2024-11-11 11:18:47 -0700}, doi = {10.1016/j.oceaneng.2024.119124}, issn = {0029-8018}, journal = {Ocean Engineering}, keywords = {Wave energy converter, Control co-design, Optimization, Power take-off, Central Pioneer Array, WecOptTool}, month = sep, pages = {119124}, title = {High-dimensional control co-design of a wave energy converter with a novel pitch resonator power takeoff system}, url = {https://www.sciencedirect.com/science/article/pii/S0029801824024624}, volume = {312}, year = {2024}, bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/S0029801824024624}, bdsk-url-2 = {https://doi.org/10.1016/j.oceaneng.2024.119124} }

2023

Control Co-Design of Power Take-off Systems for Wave Energy Converters using WecOptTool

Carlos A. Michelén Ströfer, Daniel T. Gaebele, Ryan G. Coe, and Giorgio Bacelli

IEEE Transactions on Sustainable Energy, Sep 2023

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Improved power take-off (PTO) controller design for wave energy converters is considered a critical component for reducing the cost of energy production. However, the device and control design process often remains sequential, with the space of possible final designs largely reduced before the controller has been considered. Control co-design, whereby the device and control design are considered concurrently, has resulted in improved designs in many industries, but remains rare in the wave energy community. In this paper we demonstrate the use of a new open-source code, WecOptTool, for control co-design of wave energy converters, with the aim to make the co-design approach more accessible and accelerate its adoption. Additionally, we highlight the importance of designing a wave energy converter to maximize electrical power, rather than mechanical power, and demonstrate the co-design process while modeling the PTO’s components (i.e., drive-train and generator, and their dynamics). We also consider the design and optimization of causal fixed-structure controllers. The demonstration presented here considers the PTO design problem and finds the optimal PTO drive-train that maximizes annual electrical power production. The results show a 22% improvement in the optimal controller and drive-train co-design over the optimal controller for the nominal, as built, device design.
@article{Michelen-Strofer:2023aa, author = {{Michel{\'e}n Str{\"o}fer}, Carlos A. and Gaebele, Daniel T. and Coe, Ryan G. and Bacelli, Giorgio}, bibtex_show = true, date-added = {2022-08-24 15:57:28 -0600}, date-modified = {2025-06-25 12:01:07 -0600}, doi = {10.1109/TSTE.2023.3272868}, journal = {IEEE Transactions on Sustainable Energy}, number = {4}, pages = {2157-2167}, title = {Control Co-Design of Power Take-off Systems for Wave Energy Converters using {WecOptTool}}, url = {https://ieeexplore.ieee.org/document/10114969}, volume = {14}, year = {2023}, bdsk-url-1 = {https://ieeexplore.ieee.org/document/10114969}, bdsk-url-2 = {https://doi.org/10.1109/TSTE.2023.3272868} }
Incorporating Empirical Nonlinear Efficiency Into Control Co-Optimization of a Real World Heaving Point Absorber Using WecOptTool

Daniel T. Gaebele, Carlos A. Michelén Ströfer, Michael C. Devin, Jeff T. Grasberger, Ryan G. Coe, and Giorgio Bacelli

In Proceedings of the ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering (OMAE2023), Jun 2023

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The open-source WecOptTool was developed to make wave energy converter (WEC) control co-design accessible. WecOptTool is based on the pseudo-spectral method which is capable of efficiently dealing with any linear or nonlinear constraints and nonlinear dynamics by solving the WEC optimal control problem in the time domain using a gradient based optimization algorithm. This work1 presents a control co-optimization study of the AquaHarmonics Inc. heaving point absorber WEC sized for ocean deployment to solve practical industry design problems. Components such as the specific type of generator, the hull shape, and the displaced volume are pre-determined. We co-optimize the WEC’s mass versus mooring line pretension in conjunction with the controller. The optimization is subject to the power-take-off (PTO) dynamics and the rated constraints of the components. In particular, the continuous torque rating is implemented as an explicit constraint, a novel approach for WEC optimization. The PTO dynamics are incorporated into the optimization algorithm via a combination of first principle methods (linear drivetrain model) and empirical efficiency maps (electrical generator) represented as a power loss map. This is a practical method applicable to a variety of PTO architectures and transferable to other WECs. A discussion between using an efficiency coefficient versus a power loss map and their implication for the optimization method is presented. This application of WecOptTool represents a real world WEC by combining simplified models with empirical efficiency data. The WEC, as a dynamically coupled, oscillatory system, requires consideration of the time trajectory dependent power loss for optimizing the average electrical power. This objective function, the modelling approach, and the realistic loss terms makes the common practice of artificially penalizing the reactive power needless.
@inproceedings{Gaebele:2023wf, address = {Melbourne, Australia}, author = {Gaebele, Daniel T. and {Michel{\'e}n Str{\"o}fer}, Carlos A. and Devin, Michael C. and Grasberger, Jeff T. and Coe, Ryan G. and Bacelli, Giorgio}, bibtex_show = true, booktitle = {Proceedings of the ASME 2023 42nd International Conference on Ocean, Offshore and Arctic Engineering (OMAE2023)}, date-added = {2023-01-12 14:02:25 -0700}, date-modified = {2025-10-02 07:46:49 -0600}, doi = {10.1115/OMAE2023-103899}, month = jun, pages = {V008T09A067}, title = {{Incorporating Empirical Nonlinear Efficiency Into Control Co-Optimization of a Real World Heaving Point Absorber Using WecOptTool}}, url = {https://asmedigitalcollection.asme.org/OMAE/proceedings-abstract/OMAE2023/86908/V008T09A067/1167388}, volume = {8: Ocean Renewable Energy}, year = {2023}, bdsk-url-1 = {https://doi.org/10.1115/OMAE2023-103899} }

2021

Comments on control of wave energy converters

Giorgio Bacelli, and Ryan G. Coe

IEEE Transactions on Control Systems Technology, Jan 2021

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The main objective of this letter is to consolidate the knowledge about the dynamics and control of oscillating-body wave energy converters (WECs). A number of studies have shown that control systems strongly affect power absorption; however, there remains a need for a concise and integrated explanation of the theoretical and practical implications that control can have on both performance and the broader WEC design process. This short letter attempts to fill this gap by presenting a discussion on the key practical aspects concerning the dynamics and control of oscillating-body WEC. In particular, the focus is on the choice of control models and a simple causal control scheme suitable for real-time implementation. Finally, consideration is given to the effect of the power takeoff (PTO) on the maximization of electrical power, thus leading to the derivation of useful conditions for the control co-design of the PTO system.
@article{Bacelli:2021aa, author = {Bacelli, Giorgio and Coe, Ryan G.}, bibtex_show = true, date-added = {2020-10-07 12:37:21 -0600}, date-modified = {2025-06-25 12:01:07 -0600}, doi = {10.1109/TCST.2020.2965916}, groups = {AdvWecCntrls Pubs}, journal = {IEEE Transactions on Control Systems Technology}, keywords = {Impedance;Frequency control;Control systems;Force;Absorption;Biological system modeling;Impedance matching;Control co-design;impedance matching;wave energy converter (WEC)}, month = jan, number = {1}, pages = {478-481}, title = {Comments on control of wave energy converters}, url = {https://ieeexplore.ieee.org/document/9005201}, volume = {29}, year = {2021}, bdsk-url-1 = {https://ieeexplore.ieee.org/document/9005201}, bdsk-url-2 = {https://doi.org/10.1109/TCST.2020.2965916} }