WecOptTool

WEC design optimization

While immense insight can be gain from linear analysis tools, such as those developed within the WEC co-design project, there is also value in the ability to fully consider the nonlinear behavior of a real system. To that end, WecOptTool utilizes a pseudo-spectral to efficiently perform simulation/optimization of wave energy converters (WECs). The tool was first conceptualized in Giorgio Bacelli’s PhD thesis (Bacelli, 2014; Bacelli & Ringwood, 2014), and then developed as an open-source tool by Sandia (Coe et al., 2020). WecOptTool has been applied extensively to support external developers (Gaebele et al., 2023) and research projects including the Pioneer WEC (Devin et al., 2024; Coe et al., 2024), the WaveBot (Grasberger et al., 2023; Michelén Ströfer et al., 2023), and the LUPA (Michelén Ströfer et al., 2023)

References

2024

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} }

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

Abs DOI Bib HTML

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}
}

2023

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

Abs DOI Bib HTML Slides

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} }

Maximizing Wave Energy Converter Power Extraction by Utilizing a Variable Negative Stiffness Magnetic Spring

Jeff T. Grasberger, Ryan G. Coe, Jonathan Bird, Giorgio Bacelli, Alex Hagmüller, and Carlos Michelén Ströfer

In Proceedings of the 15th European Wave and Tidal Energy Conference (EWTEC2023), Sep 2023

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Complex conjugate impedance matching is a key concept for wave energy converter design. Matching the impedance of the power take-off (PTO) system to the complex conjugate of the wave energy converter’s (WEC) impedance ensures efficient transfer of energy from the WEC body motion to electrical power. In low frequency waves, impedance matching often requires a negative PTO stiffness. In this paper, an adjustable stiffness magnetic torsion spring will be presented and modeled to understand its potential to improve WEC performance. The spring has the ability to provide a negative stiffness, allowing the PTO impedance to more closely match the complex conjugate of the WEC impedance at low frequencies. The spring also supports an adjustable stiffness value, meaning it can be tuned according to the incoming wave conditions. The spring’s tunability may put less stress on the rest of the PTO system in wave conditions outside its normal operation zone without sacrificing electrical power output. The adjustable magnetic spring’s effects are modeled and explored in this paper by examining the resultant average annual electrical power and capacity factor. The study suggests that the tunable magnetic spring has the potential to significantly improve capacity factor while maintaining a high average electrical power.

@inproceedings{Grasberger:2023aa,
  abstractnote = {&amp;lt;p&amp;gt;Complex conjugate impedance matching is a key concept for wave energy converter design. Matching the impedance of the power take-off (PTO) system to the complex conjugate of the wave energy converter's (WEC) impedance ensures efficient transfer of energy from the WEC body motion to electrical power. In low frequency waves, impedance matching often requires a negative PTO stiffness. In this paper, an adjustable stiffness magnetic torsion spring will be presented and modeled to understand its potential to improve WEC performance. The spring has the ability to provide a negative stiffness, allowing the PTO impedance to more closely match the complex conjugate of the WEC impedance at low frequencies. The spring also supports an adjustable stiffness value, meaning it can be tuned according to the incoming wave conditions. The spring's tunability may put less stress on the rest of the PTO system in wave conditions outside its normal operation zone without sacrificing electrical power output. The adjustable magnetic spring's effects are modeled and explored in this paper by examining the resultant average annual electrical power and capacity factor. The study suggests that the tunable magnetic spring has the potential to significantly improve capacity factor while maintaining a high average electrical power.&amp;lt;/p&amp;gt;},
  address = {Bilbao, Spain},
  author = {Grasberger, Jeff T. and Coe, Ryan G. and Bird, Jonathan and Bacelli, Giorgio and Hagm{\"u}ller, Alex and {Michel{\'e}n Str{\"o}fer}, Carlos},
  bibtex_show = true,
  booktitle = {Proceedings of the 15th European Wave and Tidal Energy Conference (EWTEC2023)},
  date-added = {2023-02-22 13:15:35 -0700},
  date-modified = {2025-08-20 10:39:07 -0600},
  doi = {10.36688/ewtec-2023-510},
  journal = {Proceedings of the European Wave and Tidal Energy Conference},
  month = sep,
  title = {Maximizing Wave Energy Converter Power Extraction by Utilizing a Variable Negative Stiffness Magnetic Spring},
  url = {https://doi.org/10.36688/ewtec-2023-510},
  volume = {15},
  year = {2023},
  bdsk-url-1 = {https://doi.org/10.36688/ewtec-2023-510}
}

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

Abs DOI Bib HTML

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} }

Control co-design and uncertainty analysis of the LUPA’s PTO using WecOptTool

Carlos Michelén Ströfer, Ryan Coe, Daniel Gaebele, Courtney Beringer, Bret Bosma, Bryson Robertson, Giorgio Bacelli, and Michael Devin

In Proceedings of the 15th European Wave and Tidal Energy Conference (EWTEC2023), Sep 2023

Abs DOI Bib HTML

Control co-design has been shown to significantly improve the performance of wave energy converters (WEC). By considering the control and WEC design concurrently, the space searched by the optimization routine is greatly expanded which results in better performing devices. Recently, an open-source WEC co-design code, WecOptTool, was released to perform control co-design research and facilitate its adoption in the community. In this study, we use WecOptTool to perform control co-optimization and uncertainty analysis of the LUPA device. The Laboratory Upgrade Point Absorber (LUPA) is a new open-source laboratory-scale WEC that provides a platform for testing new concepts, innovating control schemes, and validating numerical models. The LUPA can be adjusted to different configurations, including changing the number of bodies, the degrees of freedom (DOF), the float and spar geometry, and the diameter of the drive sprocket pulley in the power take off (PTO) system, as well as providing different control algorithms and input waves. The drive sprocket diameter influences the torque vs speed of the generator, which allows for more flexibility in operating under different wave conditions or with different control schemes. In this study we optimize the drive sprocket diameter, while considering the optimal control algorithm for each potential design, to identify the optimal diameter for electric power production at the PacWave South WEC test site. This case study demonstrates several new capabilities of WecOptTool including a multi-body multi-DOF system and multi-directional irregular waves. The PTO dynamics are modeled using first principle methods for a parametrized model of the mechanical subcomponents in combination with generator model obtained using a power-invariant Park transform. The case-study will be made available to serve as a design tool along the LUPA hardware. Users can readily use this model to perform their own design optimization prior to testing with the physical LUPA device. Finally, we use the automatic differentiation capability of WecOptTool to perform a sensitivity and uncertainty analysis of the LUPA device.

@inproceedings{Michelen-Strofer:2023ab,
  abstractnote = {&amp;lt;p class=&amp;quot;FirstParagraph&amp;quot;&amp;gt;Control co-design has been shown to significantly improve the performance of wave energy converters (WEC). By considering the control and WEC design concurrently, the space searched by the optimization routine is greatly expanded which results in better performing devices. Recently, an open-source WEC co-design code, WecOptTool, was released to perform control co-design research and facilitate its adoption in the community. In this study, we use WecOptTool to perform control co-optimization and uncertainty analysis of the LUPA device. The Laboratory Upgrade Point Absorber (LUPA) is a new open-source laboratory-scale WEC that provides a platform for testing new concepts, innovating control schemes, and validating numerical models. The LUPA can be adjusted to different configurations, including changing the number of bodies, the degrees of freedom (DOF), the float and spar geometry, and the diameter of the drive sprocket pulley in the power take off (PTO) system, as well as providing different control algorithms and input waves. The drive sprocket diameter influences the torque vs speed of the generator, which allows for more flexibility in operating under different wave conditions or with different control schemes. In this study we optimize the drive sprocket diameter, while considering the optimal control algorithm for each potential design, to identify the optimal diameter for electric power production at the PacWave South WEC test site. This case study demonstrates several new capabilities of WecOptTool including a multi-body multi-DOF system and multi-directional irregular waves. The PTO dynamics are modeled using first principle methods for a parametrized model of the mechanical subcomponents in combination with generator model obtained using a power-invariant Park transform. The case-study will be made available to serve as a design tool along the LUPA hardware. Users can readily use this model to perform their own design optimization prior to testing with the physical LUPA device. Finally, we use the automatic differentiation capability of WecOptTool to perform a sensitivity and uncertainty analysis of the LUPA device.&amp;lt;/p&amp;gt;},
  address = {Bilbao, Spain},
  author = {{Michel{\'e}n Str{\"o}fer}, Carlos and Coe, Ryan and Gaebele, Daniel and Beringer, Courtney and Bosma, Bret and Robertson, Bryson and Bacelli, Giorgio and Devin, Michael},
  bibtex_show = true,
  booktitle = {Proceedings of the 15th European Wave and Tidal Energy Conference (EWTEC2023)},
  date-added = {2023-02-09 07:51:06 -0700},
  date-modified = {2025-08-20 10:39:59 -0600},
  doi = {10.36688/ewtec-2023-288},
  journal = {Proceedings of the European Wave and Tidal Energy Conference},
  month = sep,
  title = {Control co-design and uncertainty analysis of the {LUPA}'s {PTO} using {WecOptTool}},
  url = {https://doi.org/10.36688/ewtec-2023-288},
  volume = {15},
  year = {2023},
  bdsk-url-1 = {https://doi.org/10.36688/ewtec-2023-288}
}

2020

Initial conceptual demonstration of control co-design for WEC optimization

Ryan G. Coe, Giorgio Bacelli, Sterling Olson, Vincent S. Neary, and Matthew B. R. Topper

Journal of Ocean Engineering and Marine Energy, Sep 2020

Abs DOI Bib HTML

While some engineering fields have benefited from systematic design optimization studies, wave energy converters have yet to successfully incorporate such analyses into practical engineering workflows. The current iterative approach to wave energy converter design leads to sub-optimal solutions. This short paper presents an open-source MATLAB toolbox for performing design optimization studies on wave energy converters where power take-off behavior and realistic constraints can be easily included. This tool incorporates an adaptable control co-design approach, in that a constrained optimal controller is used to simulate device dynamics and populate an arbitrary objective function of the user’s choosing. A brief explanation of the tool’s structure and underlying theory is presented. To demonstrate the capabilities of the tool, verify its functionality, and begin to explore some basic wave energy converter design relationships, three conceptual case studies are presented. In particular, the importance of considering (and constraining) the magnitudes of device motion and forces in design optimization is shown.
@article{Coe:2020aa, author = {Coe, Ryan G. and Bacelli, Giorgio and Olson, Sterling and Neary, Vincent S. and Topper, Matthew B. R.}, bibtex_show = true, da = {2020/11/07}, date = {2020-07-07}, date-added = {2020-10-07 12:35:05 -0600}, date-modified = {2025-06-25 12:01:07 -0600}, doi = {10.1007/s40722-020-00181-9}, id = {Coe2020}, isbn = {2198-6452}, journal = {Journal of Ocean Engineering and Marine Energy}, number = {4}, pages = {441--449}, title = {Initial conceptual demonstration of control co-design for {WEC} optimization}, ty = {JOUR}, url = {https://doi.org/10.1007/s40722-020-00181-9}, volume = {6}, year = {2020}, bdsk-url-1 = {https://www.techrxiv.org/articles/preprint/Initial_conceptual_demonstration_of_control_co-design_for_WEC_optimization/12928898}, bdsk-url-2 = {https://doi.org/10.36227/techrxiv.12928898.v1}, bdsk-url-3 = {https://doi.org/10.1007/s40722-020-00181-9} }

2014

Optimal control of wave energy converters

Giorgio Bacelli

Sep 2014

Bib HTML

@phdthesis{Bacelli:2014aa,
  address = {Maynooth, Ireland},
  author = {Bacelli, Giorgio},
  date-added = {2021-12-07 13:18:13 -0700},
  date-modified = {2021-12-07 14:15:30 -0700},
  school = {National University of Ireland, Maynooth},
  title = {Optimal control of wave energy converters},
  type = {{PhD}},
  url = {http://mural.maynoothuniversity.ie/6753/},
  mine = {false},
  year = {2014}
}

Numerical optimal control of wave energy converters

Giorgio Bacelli , and John V Ringwood

IEEE Transactions on Sustainable Energy, Sep 2014

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Energy maximizing control for wave energy converters (WECs) is a nonstandard optimal control problem. While the constrained optimal control problem for WECs has been addressed by model-predictive control strategies, such strategies need to employ cost function modifications due to convexity problems and the algorithms are computationally complex, making real-time implementation difficult. The recently developed family of direct transcription methods offer a promising alternative, since they are computationally efficient and a convex problem results. Moreover, constraints on both the device displacement and velocity, and power take off force, are easily incorporated. Both single-body and multibody device models can be used, as well as arrays of single-body or multibody devices.
@article{Bacelli:2014ab, author = {Bacelli, Giorgio and Ringwood, John V}, date-modified = {2021-12-07 13:16:10 -0700}, doi = {10.1109/TSTE.2014.2371536}, journal = {IEEE Transactions on Sustainable Energy}, number = {2}, pages = {294--302}, publisher = {IEEE}, title = {Numerical optimal control of wave energy converters}, volume = {6}, year = {2014}, url = {https://ieeexplore.ieee.org/document/6987295}, mine = {false} }