G. Lavidas
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Recent studies have demonstrated the merits of spectral-domain (SD) modeling in efficiently addressing nonlinear dynamic behvavior of stand-alone wave energy converters (WECs). However, the potential of the SD modeling approach deserves further exploitation by examining its applicability in simulating the entire wave-to-wire (W2W) process of WEC arrays. This article proposed and verified a SD W2W model of WEC arrays. The WEC arrays are considered as five same-sized heaving cylindrical point absorbers, and they are all equipped with linear Permanent Magnet (PM) generators. The established SD W2W model is verified by being compared with results of a nonlinear time-domain-based W2W model across a variety of operation conditions. The computational efficiency of the two simulation approaches in modeling WEC arrays is also identified and compared. The results suggest that the SD W2W model is associated with a relative error of less than 11 % to the nonlinear time-domain reference, with regard to the estimates of significant statistical performance indicators, such as WEC velocity, absorbed and electrical power of individual power, and total electrical power production of the WEC arrays. At the same time, the SD W2W model presents a high computational efficiency, being around 2000 times faster than the time-domain W2W model of WEC arrays.
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Recent studies have demonstrated the merits of spectral-domain (SD) modeling in efficiently addressing nonlinear dynamic behvavior of stand-alone wave energy converters (WECs). However, the potential of the SD modeling approach deserves further exploitation by examining its applicability in simulating the entire wave-to-wire (W2W) process of WEC arrays. This article proposed and verified a SD W2W model of WEC arrays. The WEC arrays are considered as five same-sized heaving cylindrical point absorbers, and they are all equipped with linear Permanent Magnet (PM) generators. The established SD W2W model is verified by being compared with results of a nonlinear time-domain-based W2W model across a variety of operation conditions. The computational efficiency of the two simulation approaches in modeling WEC arrays is also identified and compared. The results suggest that the SD W2W model is associated with a relative error of less than 11 % to the nonlinear time-domain reference, with regard to the estimates of significant statistical performance indicators, such as WEC velocity, absorbed and electrical power of individual power, and total electrical power production of the WEC arrays. At the same time, the SD W2W model presents a high computational efficiency, being around 2000 times faster than the time-domain W2W model of WEC arrays.
Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
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Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
Wave-to-Wire (W2W) modeling simulates the whole operation process of wave energy converters (WECs), which plays a pivotal role in the systematic design and optimization of WECs. Existing W2W models are predominantly constructed based on time-domain (TD) analysis to coherently incorporate relevant nonlinearities. However, TD models require a high computational cost, which hinders the design iterations of WECs. As a newly emerging alternative approach, spectral-domain (SD) modeling has demonstrated the applicability of describing the W2W process while efficiently covering nonlinear effects through statistical linearization. This study aims to develop an SD W2W modeling approach for WECs coupled with a gearbox and rotary generator. The application of the proposed model is exemplified in two case studies: (1) a point absorber with a rack-pinion system and a rotary generator; (2) a flap-type WEC with a revolving gearbox and a rotary generator. The simulation results obtained by the SD W2W model are compared against a higher-fidelity nonlinear TD W2W model to verify its accuracy across a variety of sea states. A good agreement between the two modeling approaches is observed, in which the maximum relative error is below 7 % with regard to the estimation of important system outputs. Meanwhile, the computational efficiency of the SD W2W model is thousands of times higher than the TD modeling approach.
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Wave-to-Wire (W2W) modeling simulates the whole operation process of wave energy converters (WECs), which plays a pivotal role in the systematic design and optimization of WECs. Existing W2W models are predominantly constructed based on time-domain (TD) analysis to coherently incorporate relevant nonlinearities. However, TD models require a high computational cost, which hinders the design iterations of WECs. As a newly emerging alternative approach, spectral-domain (SD) modeling has demonstrated the applicability of describing the W2W process while efficiently covering nonlinear effects through statistical linearization. This study aims to develop an SD W2W modeling approach for WECs coupled with a gearbox and rotary generator. The application of the proposed model is exemplified in two case studies: (1) a point absorber with a rack-pinion system and a rotary generator; (2) a flap-type WEC with a revolving gearbox and a rotary generator. The simulation results obtained by the SD W2W model are compared against a higher-fidelity nonlinear TD W2W model to verify its accuracy across a variety of sea states. A good agreement between the two modeling approaches is observed, in which the maximum relative error is below 7 % with regard to the estimation of important system outputs. Meanwhile, the computational efficiency of the SD W2W model is thousands of times higher than the TD modeling approach.
Obtaining the hydrodynamic pressure distribution on the wetted surface of floating structures is a critical step in structural analysis and is commonly achieved through pressure regeneration based on predicted global dynamic responses. Using derived hydrodynamic coefficients, various dynamic modeling approaches, including Cummins-equation-based nonlinear time-domain modeling, statistical linearization, and Lorentz linearization, can be applied to solve for the global dynamics of structures subjected to specific wave conditions. These dynamic modeling approaches differ in both computational efficiency and modeling fidelity. Despite their widespread use, a systematic comparison of these approaches, particularly between statistical and Lorentz linearization in predicting global dynamics and regenerated pressure fields, remains limited. This study addresses this gap by conducting a comparative study of linear-potential-flow-based dynamic modeling approaches using a generic cylindrical floater, incorporating a representative nonlinear external machinery effect through different modeling approaches. The resulting global responses are used to regenerate hydrodynamic pressure distributions, showing that all the dynamic modeling approaches agree well under low wave steepness. As wave steepness increases, the prediction performance of statistical linearization, Lorentz linearization, and a simplified Lorentz linearization, gradually decreases relative to the nonlinear time-domain model. Among these, the statistical linearization approach provides results closer to the nonlinear time-domain model than both Lorentz-based linearization methods, particularly in capturing global dynamics and reconstructing hydrodynamic pressure distributions under relatively high wave steepness. Given its high computational efficiency, the statistical linearization approach has the potential to be further developed as an efficient alternative modeling for estimating dynamic responses and hydrodynamic pressure distributions.
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Obtaining the hydrodynamic pressure distribution on the wetted surface of floating structures is a critical step in structural analysis and is commonly achieved through pressure regeneration based on predicted global dynamic responses. Using derived hydrodynamic coefficients, various dynamic modeling approaches, including Cummins-equation-based nonlinear time-domain modeling, statistical linearization, and Lorentz linearization, can be applied to solve for the global dynamics of structures subjected to specific wave conditions. These dynamic modeling approaches differ in both computational efficiency and modeling fidelity. Despite their widespread use, a systematic comparison of these approaches, particularly between statistical and Lorentz linearization in predicting global dynamics and regenerated pressure fields, remains limited. This study addresses this gap by conducting a comparative study of linear-potential-flow-based dynamic modeling approaches using a generic cylindrical floater, incorporating a representative nonlinear external machinery effect through different modeling approaches. The resulting global responses are used to regenerate hydrodynamic pressure distributions, showing that all the dynamic modeling approaches agree well under low wave steepness. As wave steepness increases, the prediction performance of statistical linearization, Lorentz linearization, and a simplified Lorentz linearization, gradually decreases relative to the nonlinear time-domain model. Among these, the statistical linearization approach provides results closer to the nonlinear time-domain model than both Lorentz-based linearization methods, particularly in capturing global dynamics and reconstructing hydrodynamic pressure distributions under relatively high wave steepness. Given its high computational efficiency, the statistical linearization approach has the potential to be further developed as an efficient alternative modeling for estimating dynamic responses and hydrodynamic pressure distributions.
Due to the complexity of the ocean environment and wave energy converter (WEC) system, it has been an effort-demanding work to assess either the power performance or fatigue loads of WECs. This work attempts to apply a data-driven approach to increase the efficiency of the collective prediction of the power and fatigue load of a point-absorber type WEC. Nonlinear time-domain modeling is first established to estimate the power and fatigue loads, which is considered the reference data in this work. To demonstrate the performance of the applied data-driven approach, two prevalent power take-off (PTO) mechanisms are implemented to represent different characteristics of WECs. A data-driven approach, active learning Kriging (AK), is adapted to predict power and fatigue loads collectively, and a new learning function is defined to select the enriched wave cases for the active learning process. Results show that the applied active learning approach can accurately and simultaneously predict power and fatigue loads in both PTO mechanisms. Compared to pure numerical simulation, the proposed method only requires 15 simulations of sea state, and the computational effort is reduced by more than 20 times. The maximum prediction error is less than 2%. The data-driven approach could be a powerful tool for WEC system optimization, considering both power performance and fatigue loads.
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Due to the complexity of the ocean environment and wave energy converter (WEC) system, it has been an effort-demanding work to assess either the power performance or fatigue loads of WECs. This work attempts to apply a data-driven approach to increase the efficiency of the collective prediction of the power and fatigue load of a point-absorber type WEC. Nonlinear time-domain modeling is first established to estimate the power and fatigue loads, which is considered the reference data in this work. To demonstrate the performance of the applied data-driven approach, two prevalent power take-off (PTO) mechanisms are implemented to represent different characteristics of WECs. A data-driven approach, active learning Kriging (AK), is adapted to predict power and fatigue loads collectively, and a new learning function is defined to select the enriched wave cases for the active learning process. Results show that the applied active learning approach can accurately and simultaneously predict power and fatigue loads in both PTO mechanisms. Compared to pure numerical simulation, the proposed method only requires 15 simulations of sea state, and the computational effort is reduced by more than 20 times. The maximum prediction error is less than 2%. The data-driven approach could be a powerful tool for WEC system optimization, considering both power performance and fatigue loads.
Wave power for e-fuels and e-chemicals production
Technical feasibility, economic viability, and regional opportunities
Journal article
(2026)
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Rasul Satymov, Dmitrii Bogdanov, George Lavidas, Shona Pennock, Sarah Kluge, Benjamin Lehner, Christian Breyer
The global energy transition necessitates the defossilisation of the energy-intensive industry and hard-to-abate transport sectors, where direct electrification falls short due to limitations in energy density. Electricity-based fuels and chemicals (e-fuels and e-chemicals) emerge as a viable alternative, offering high energy density and compatibility with existing infrastructure. However, their production hinges on access to vast amounts of low-cost renewable electricity, a challenge for regions with limited land. This study explores wave power as an underexplored source for e-fuel production, focusing on regions with exceptional wave energy: New Zealand, Chile, and Ireland. Using energyHub-LUT, a newly developed optimisation model, the research evaluates the techno-economics of wave power, alongside solar photovoltaics and wind power, for producing e-fuels and e-chemicals. The results show that wave power supplies more stable power for e-fuel production compared to onshore wind power and solar photovoltaics, cutting the need for batteries by 25-100%, depending on location. Chile produces the lowest cost e-fuels when wave power is integrated alongside solar photovoltaics and onshore wind power, thanks to over 7000 full load hours, but its higher capital expenditures render it less competitive than onshore renewable energy. The study concludes that wave power's economic viability is limited even in regions with very high full load hours but also highlights its potential as an alternative where land scarcity hinders large-scale renewable energy projects or in cases of near baseload direct electricity need.
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The global energy transition necessitates the defossilisation of the energy-intensive industry and hard-to-abate transport sectors, where direct electrification falls short due to limitations in energy density. Electricity-based fuels and chemicals (e-fuels and e-chemicals) emerge as a viable alternative, offering high energy density and compatibility with existing infrastructure. However, their production hinges on access to vast amounts of low-cost renewable electricity, a challenge for regions with limited land. This study explores wave power as an underexplored source for e-fuel production, focusing on regions with exceptional wave energy: New Zealand, Chile, and Ireland. Using energyHub-LUT, a newly developed optimisation model, the research evaluates the techno-economics of wave power, alongside solar photovoltaics and wind power, for producing e-fuels and e-chemicals. The results show that wave power supplies more stable power for e-fuel production compared to onshore wind power and solar photovoltaics, cutting the need for batteries by 25-100%, depending on location. Chile produces the lowest cost e-fuels when wave power is integrated alongside solar photovoltaics and onshore wind power, thanks to over 7000 full load hours, but its higher capital expenditures render it less competitive than onshore renewable energy. The study concludes that wave power's economic viability is limited even in regions with very high full load hours but also highlights its potential as an alternative where land scarcity hinders large-scale renewable energy projects or in cases of near baseload direct electricity need.
Marine resources such as wind and wave are expected to play an important role in decarbonising the UK’s energy network, as part of the global transition from fossil fuels to renewable energy. However, potential increases in global weather systems variability due to climate change cast doubt on the long-term sustainability of offshore renewable development and the ambitions of the UK government to rapidly expand current capacity. As such, growing interest in co-located wind–wave systems is being paid as a means of enhancing the climate resilience of the future energy network. This study investigates the impacts of climate change on wind and wave resources in the UK from 2015 to 2100, using available CMIP6 datasets and numerical wave modelling using SWAN. In doing so, an initial assessment of the potential for co-located infrastructure is undertaken to inform future research into its role in strengthening the climate resilience of ocean renewable generation. The results reveal gradual reductions in resource availability under a high emission scenario, with statistically significant annual trends detected across most of the study area. Reductions in average annual wind energy reach −16.0% in coastal areas of Northern Ireland towards the end of the century, while decreases in wave energy of more than 25% are projected in certain regions of the North Sea. These trends are primarily driven by seasonal reductions during summer months, with decreases in average wind power during these months as much as −29.0% and decreases in wave power of over −40%. In addition, increases in resource variability from the mid-century onwards suggest that climate change is likely to negatively affect the availability of the UK’s wind and wave energy resources in the long term.
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Marine resources such as wind and wave are expected to play an important role in decarbonising the UK’s energy network, as part of the global transition from fossil fuels to renewable energy. However, potential increases in global weather systems variability due to climate change cast doubt on the long-term sustainability of offshore renewable development and the ambitions of the UK government to rapidly expand current capacity. As such, growing interest in co-located wind–wave systems is being paid as a means of enhancing the climate resilience of the future energy network. This study investigates the impacts of climate change on wind and wave resources in the UK from 2015 to 2100, using available CMIP6 datasets and numerical wave modelling using SWAN. In doing so, an initial assessment of the potential for co-located infrastructure is undertaken to inform future research into its role in strengthening the climate resilience of ocean renewable generation. The results reveal gradual reductions in resource availability under a high emission scenario, with statistically significant annual trends detected across most of the study area. Reductions in average annual wind energy reach −16.0% in coastal areas of Northern Ireland towards the end of the century, while decreases in wave energy of more than 25% are projected in certain regions of the North Sea. These trends are primarily driven by seasonal reductions during summer months, with decreases in average wind power during these months as much as −29.0% and decreases in wave power of over −40%. In addition, increases in resource variability from the mid-century onwards suggest that climate change is likely to negatively affect the availability of the UK’s wind and wave energy resources in the long term.
Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
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Wave energy arrays are essential for reducing the Levelised Cost of Energy, yet the performance of traditional mono-device arrays is often limited by destructive hydrodynamic interactions and directional sensitivity. This work focuses on ”mixed arrays,” wherein different types and geometries of wave energy converters operating in different degrees of freedom (point Absorber and a flap) are deployed within the same array to exploit complementary device dynamics, whilst reducing spatial requirements. Using a weakly non-linear frequency-domain model utilising the solver HAMS-MREL, a systematic comparison is performed across 3360 cases considering varying array sizes, spacings, wave directions, and control strategies (active and passive). Comparison of array performance is based on the well known q-factor and a new geometry dependent metric (M-factor). The results demonstrate that mixed arrays can outperform mono-device arrays by leveraging favourable hydrodynamic cross-coupling and radiated wave-field alignment. For a 10-device staggered configuration, mixed arrays achieved a peak q-factor of 1.6 and an M-factor of 2.25 under regular waves, showing a 175% increase in point absorber heave response under displacement constraints and 34% increase in flap excitation forces. Performance is sensitive to the spacing-to-wavelength ratio, mixed arrays exhibit superior directional robustness, and reduced efficiency collapse compared to mono-flap arrays. The findings suggest that mixed-device configurations can provide a robust alternative for optimising energy capture, reducing spatial requirements, offering new collaboration opportunities and contributing to the viability of wave energy arrays.
Wave energy as a renewable resource has been shown to have immense potential. Up to date research has predominately focused on sector focused approaches, with devices being explored in small applications, or solely on their own merit. However, when discussing the integration to energy systems with high share of renewable energies, large levels of electrical interconnectivity and grid balancing infrastructure, the role of wave energy is often “lost”. This work further refines the approach of integrating wave energy in the European and UK energy system, highlighting potential future pathways to improve wave energy considerations.
This study assesses the input source of climate data for evaluation of wave energy production and economics. The comparison of ERA5 and a high-fidelity wave dataset across all Europe, the ECHOWAVE database, show a clear benefit for wave energy. When ERA5 is utilised to assess the potential of wave energy, the usefulness and integration of wave energy is not reflected in the system. This works shows that a proper representation of wave energy in terms of climate, power production methodologies and economic considerations. ...
This study assesses the input source of climate data for evaluation of wave energy production and economics. The comparison of ERA5 and a high-fidelity wave dataset across all Europe, the ECHOWAVE database, show a clear benefit for wave energy. When ERA5 is utilised to assess the potential of wave energy, the usefulness and integration of wave energy is not reflected in the system. This works shows that a proper representation of wave energy in terms of climate, power production methodologies and economic considerations. ...
Wave energy as a renewable resource has been shown to have immense potential. Up to date research has predominately focused on sector focused approaches, with devices being explored in small applications, or solely on their own merit. However, when discussing the integration to energy systems with high share of renewable energies, large levels of electrical interconnectivity and grid balancing infrastructure, the role of wave energy is often “lost”. This work further refines the approach of integrating wave energy in the European and UK energy system, highlighting potential future pathways to improve wave energy considerations.
This study assesses the input source of climate data for evaluation of wave energy production and economics. The comparison of ERA5 and a high-fidelity wave dataset across all Europe, the ECHOWAVE database, show a clear benefit for wave energy. When ERA5 is utilised to assess the potential of wave energy, the usefulness and integration of wave energy is not reflected in the system. This works shows that a proper representation of wave energy in terms of climate, power production methodologies and economic considerations.
This study assesses the input source of climate data for evaluation of wave energy production and economics. The comparison of ERA5 and a high-fidelity wave dataset across all Europe, the ECHOWAVE database, show a clear benefit for wave energy. When ERA5 is utilised to assess the potential of wave energy, the usefulness and integration of wave energy is not reflected in the system. This works shows that a proper representation of wave energy in terms of climate, power production methodologies and economic considerations.
Wave energy converter (WEC) arrays should be designed to ensure consistent and optimal power production over long operational periods. This requires an understanding of stochastic wave variability, interactive effects among devices and their mutual dependence. In this work, a computationally efficient surrogate modelling framework was developed using data-driven polynomial chaos expansion (PCE) to analyze the performance of WEC arrays under realistic sea state conditions spanning 30 years. For this purpose, using Latin hypercube sampling scheme on a joint probability distribution derived from the ECHOWAVE hindcast dataset, resulting $10^6$ combinations of significant wave height (Hs), wave period (Tp), and WEC radius (R) for two array configurations—interacting and non-interacting cases were evaluated. The surrogate model was set up to evaluate the performance of WEC arrays by means of global sensitivity analysis using Sobol indices. The results conclude that the interactive effects significantly alter the contribution of design parameters (like geometry and spatial configurations) to power output, emphasizing the inadequacy of single-device analysis for array optimization. The findings highlight the importance of tailored WEC design within arrays and offer a robust approach for long-term performance prediction and optimization of wave energy farms.
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Wave energy converter (WEC) arrays should be designed to ensure consistent and optimal power production over long operational periods. This requires an understanding of stochastic wave variability, interactive effects among devices and their mutual dependence. In this work, a computationally efficient surrogate modelling framework was developed using data-driven polynomial chaos expansion (PCE) to analyze the performance of WEC arrays under realistic sea state conditions spanning 30 years. For this purpose, using Latin hypercube sampling scheme on a joint probability distribution derived from the ECHOWAVE hindcast dataset, resulting $10^6$ combinations of significant wave height (Hs), wave period (Tp), and WEC radius (R) for two array configurations—interacting and non-interacting cases were evaluated. The surrogate model was set up to evaluate the performance of WEC arrays by means of global sensitivity analysis using Sobol indices. The results conclude that the interactive effects significantly alter the contribution of design parameters (like geometry and spatial configurations) to power output, emphasizing the inadequacy of single-device analysis for array optimization. The findings highlight the importance of tailored WEC design within arrays and offer a robust approach for long-term performance prediction and optimization of wave energy farms.
To accelerate the energy transition, offshore renewable energy is increasingly moving toward array deployment. This shift demands accurate, reliable analysis of hydrodynamics and array interactions at low computational cost. Frequency-domain tools, especially those based on the Boundary Integral Equation Method (BIEM), have thus become widely adopted in the renewables community. Hydrodynamic Analysis of Marine Structures-Marine Renewable Energies Lab (HAMS-MREL) is a recently developed open-source multi-body BIEM solver that computes diffraction and radiation problems, yielding hydrodynamic coefficients and excitation forces on structures. The solver has been validated across a range of geometries using experiments, semi-analytical solutions, and cross-model comparisons, demonstrating high accuracy. This study extends HAMS-MREL with several new features—including wave field calculations (free-surface elevation and pressure), global symmetry, irregular frequency suppression, and generalized (dry) modes—all of which have been validated for accuracy and computational efficiency. OpenMP parallelization has been integrated into each feature, delivering significant computational speed-ups ranging from 13.5 to 47.2.
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To accelerate the energy transition, offshore renewable energy is increasingly moving toward array deployment. This shift demands accurate, reliable analysis of hydrodynamics and array interactions at low computational cost. Frequency-domain tools, especially those based on the Boundary Integral Equation Method (BIEM), have thus become widely adopted in the renewables community. Hydrodynamic Analysis of Marine Structures-Marine Renewable Energies Lab (HAMS-MREL) is a recently developed open-source multi-body BIEM solver that computes diffraction and radiation problems, yielding hydrodynamic coefficients and excitation forces on structures. The solver has been validated across a range of geometries using experiments, semi-analytical solutions, and cross-model comparisons, demonstrating high accuracy. This study extends HAMS-MREL with several new features—including wave field calculations (free-surface elevation and pressure), global symmetry, irregular frequency suppression, and generalized (dry) modes—all of which have been validated for accuracy and computational efficiency. OpenMP parallelization has been integrated into each feature, delivering significant computational speed-ups ranging from 13.5 to 47.2.
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.
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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.
Understanding the effects of arrays of Wave Energy Converters (WEC) on the wave fields is still an ongoing effort. Many publications have proposed different approaches to incorporate WEC farms in wave models to assess sea state changes in the near and far field. In the present study, a practical iterative method is proposed to incorporate the spectral response of a WEC obtained from the HAMS-MREL Boundary Element Model (BEM) in the SWAN spectral wave model. This allows to change the transmission and reflection properties of the WEC, represented in the model as an obstacle, at each time step. Since the response of a WEC simulated in the BEM model is defined in the frequency domain, it is possible to relate the absorbed power, at each discrete frequency, to the transmission coefficient applied at each frequency used to discretize the wave spectrum in SWAN. In this case, the method is applied to a single point-absorber type device since its response is independent of the waves’ directions. Validation of the method is done comparing the omnidirectional spectrum obtained downwave of the WEC in SWAN, with the spectrum reconstructed using the regular wave fields information (for each frequency) obtained in HAMS-MREL.
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Understanding the effects of arrays of Wave Energy Converters (WEC) on the wave fields is still an ongoing effort. Many publications have proposed different approaches to incorporate WEC farms in wave models to assess sea state changes in the near and far field. In the present study, a practical iterative method is proposed to incorporate the spectral response of a WEC obtained from the HAMS-MREL Boundary Element Model (BEM) in the SWAN spectral wave model. This allows to change the transmission and reflection properties of the WEC, represented in the model as an obstacle, at each time step. Since the response of a WEC simulated in the BEM model is defined in the frequency domain, it is possible to relate the absorbed power, at each discrete frequency, to the transmission coefficient applied at each frequency used to discretize the wave spectrum in SWAN. In this case, the method is applied to a single point-absorber type device since its response is independent of the waves’ directions. Validation of the method is done comparing the omnidirectional spectrum obtained downwave of the WEC in SWAN, with the spectrum reconstructed using the regular wave fields information (for each frequency) obtained in HAMS-MREL.
As the necessity for the decarbonisation of the global electricity market increases, a range of renewable energy technologies will be implemented, one of which is wave energy. A key step in this process is the thorough quantification of both the power resource at locations of interest, and the impacts of these devices on the natural environment. The present work streamlines these 2 processes into one methodology by investigating the long-term impacts of an array of 20 WECs on the nearshore Dutch wave climate, while also calculating the potential power resource at the site considering intra-array wake effects. Simulations of 10 year duration were conducted in the baseline scenario (no farm present) and with 2 array configurations, using the spectral wave model SWAN on an unstructured mesh. It was demonstrated that the power production of the farm during this period, when wake effects are considered, is calculated to be up to 1.8% less than traditional methods. The presence of the farm is shown to reduce significant wave height and wave power in its lee, with the effects being largely attenuated at the coast. It was shown that the magnitude of the change is dependent on both the period and height of the waves at the farm, and notably the magnitude of the reduction does not increase consistently with the wave height, contradicting the sentiment that wave farms are effective protection mechanisms against damaging high-energy conditions. Furthermore, the present work suggests that changes to the nearshore breaker index may impact longshore currents that are essential for nutrient and sediment transport, the effect of which on the ecosystem is not yet well quantified.
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As the necessity for the decarbonisation of the global electricity market increases, a range of renewable energy technologies will be implemented, one of which is wave energy. A key step in this process is the thorough quantification of both the power resource at locations of interest, and the impacts of these devices on the natural environment. The present work streamlines these 2 processes into one methodology by investigating the long-term impacts of an array of 20 WECs on the nearshore Dutch wave climate, while also calculating the potential power resource at the site considering intra-array wake effects. Simulations of 10 year duration were conducted in the baseline scenario (no farm present) and with 2 array configurations, using the spectral wave model SWAN on an unstructured mesh. It was demonstrated that the power production of the farm during this period, when wake effects are considered, is calculated to be up to 1.8% less than traditional methods. The presence of the farm is shown to reduce significant wave height and wave power in its lee, with the effects being largely attenuated at the coast. It was shown that the magnitude of the change is dependent on both the period and height of the waves at the farm, and notably the magnitude of the reduction does not increase consistently with the wave height, contradicting the sentiment that wave farms are effective protection mechanisms against damaging high-energy conditions. Furthermore, the present work suggests that changes to the nearshore breaker index may impact longshore currents that are essential for nutrient and sediment transport, the effect of which on the ecosystem is not yet well quantified.
Journal article
(2025)
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Chen Xi, Jian Tan, George Lavidas, Hongyi Jiang, Shengjie Rui, Yujie Jiang, Zhen Guo
A critical challenge to the practical deployment of wave energy converters (WECs) is their vulnerability to extreme wave loads. This study proposes a novel design for an oscillating body-WEC, called adjustable draft WEC (ADWEC), which aims to enhance resilience under extreme wave conditions while maintain extraction efficiency at normal sea states. The present numerical simulations focus on the interaction between regular extreme waves and ADWEC in both fixed and dynamic conditions. It is found that the excitation force is highly sensitive to wave nonlinearities, appearing as an asymmetric excitation force in the horizontal direction and a double-peak phenomenon in the vertical direction. Increasing the draft can significantly reduce vertical loads and heave motion, thereby enhancing survivability by mitigating impact forces and buoyancy fluctuations. A shallower draft allows for greater heave amplitude and higher energy conversion, particularly under short-period conditions. The present findings reveal that the draft of the ADWEC has significant effects on the wave loads, hydrodynamic performance and energy extraction, which provides guidance to the practical design of WECs for survivability.
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A critical challenge to the practical deployment of wave energy converters (WECs) is their vulnerability to extreme wave loads. This study proposes a novel design for an oscillating body-WEC, called adjustable draft WEC (ADWEC), which aims to enhance resilience under extreme wave conditions while maintain extraction efficiency at normal sea states. The present numerical simulations focus on the interaction between regular extreme waves and ADWEC in both fixed and dynamic conditions. It is found that the excitation force is highly sensitive to wave nonlinearities, appearing as an asymmetric excitation force in the horizontal direction and a double-peak phenomenon in the vertical direction. Increasing the draft can significantly reduce vertical loads and heave motion, thereby enhancing survivability by mitigating impact forces and buoyancy fluctuations. A shallower draft allows for greater heave amplitude and higher energy conversion, particularly under short-period conditions. The present findings reveal that the draft of the ADWEC has significant effects on the wave loads, hydrodynamic performance and energy extraction, which provides guidance to the practical design of WECs for survivability.
The proper design of wave energy converters (WECs) is crucial for ensuring robustness in harsh wave climates without incurring the additional expense of unnecessary overdesign. The power take-off (PTO) mechanism, serving as a vital link between the moving body and the electric generator, is a key component in the design load analysis of WECs. However, the setting of PTO system parameters significantly impacts the dynamic behavior of the entire WEC system, leading to alterations in estimated loads. This work is dedicated to studying the influence of PTO control strategies on the identification of extreme loads of a heaving point absorber WEC. A nonlinear time-domain model is established to estimate the dynamic responses and loads of the WEC. Both PTO loads and end-stop loads under extreme conditions are examined, considering the wave climate of a realistic sea site. The results suggest that the PTO setting strategies significantly impact the extreme load exerted on both the PTO system and the end-stop system. Varying the PTO damping within a certain range could lead to a difference of 57% and 63% in short-term extreme loads for the PTO system and the end-stop system, respectively. Furthermore, the impacts of the PTO control strategy appear to be specific to each WEC component. The PTO parameters selected for reducing the extreme PTO loads might increase the extreme end-stop loads. A holistic examination is therefore recommended for estimating the extreme loads of WECs.
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The proper design of wave energy converters (WECs) is crucial for ensuring robustness in harsh wave climates without incurring the additional expense of unnecessary overdesign. The power take-off (PTO) mechanism, serving as a vital link between the moving body and the electric generator, is a key component in the design load analysis of WECs. However, the setting of PTO system parameters significantly impacts the dynamic behavior of the entire WEC system, leading to alterations in estimated loads. This work is dedicated to studying the influence of PTO control strategies on the identification of extreme loads of a heaving point absorber WEC. A nonlinear time-domain model is established to estimate the dynamic responses and loads of the WEC. Both PTO loads and end-stop loads under extreme conditions are examined, considering the wave climate of a realistic sea site. The results suggest that the PTO setting strategies significantly impact the extreme load exerted on both the PTO system and the end-stop system. Varying the PTO damping within a certain range could lead to a difference of 57% and 63% in short-term extreme loads for the PTO system and the end-stop system, respectively. Furthermore, the impacts of the PTO control strategy appear to be specific to each WEC component. The PTO parameters selected for reducing the extreme PTO loads might increase the extreme end-stop loads. A holistic examination is therefore recommended for estimating the extreme loads of WECs.
The deployment of marine renewables (MRE) is important for transitioning to a low-carbon energy system. However, their performance is highly dependent on the deployment location, making the selection of feasible sites critical for large-scale implementation. To contribute meaningfully to Europe’s renewable energy strategy and support a carbon-neutral energy system by 2050, the environmental performance of MREs must be taken into account in site selection, beyond the typical economic and technical aspects. Therefore, this study presents a geospatial analysis of the climate change mitigation potential of two wave energy converters, floating offshore photovoltaics, and floating wind turbines in northern European coastal waters. By combining a detailed life cycle assessment model of the four MREs with spatial data, the distribution of their life cycle global warming impact and carbon payback periods is assessed across multiple regions. The results show significantly varying impact levels of the different MREs, with carbon-neutral deployment not guaranteed at every location. Wave energy converters only partially reach carbon neutrality, while floating photovoltaics fail to do so across the entire study area. Floating wind turbines can be considered carbon-neutral nearly across their entire theoretical application area. The findings highlight the importance of taking into account site-specific environmental performance of MREs in order to ensure a positive contribution to climate change mitigation. By providing spatially explicit maps of MREs’ global warming impacts and carbon payback periods, this study enables as the first of its kind the inclusion of climate change mitigation considerations in the site selection process for MREs.
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The deployment of marine renewables (MRE) is important for transitioning to a low-carbon energy system. However, their performance is highly dependent on the deployment location, making the selection of feasible sites critical for large-scale implementation. To contribute meaningfully to Europe’s renewable energy strategy and support a carbon-neutral energy system by 2050, the environmental performance of MREs must be taken into account in site selection, beyond the typical economic and technical aspects. Therefore, this study presents a geospatial analysis of the climate change mitigation potential of two wave energy converters, floating offshore photovoltaics, and floating wind turbines in northern European coastal waters. By combining a detailed life cycle assessment model of the four MREs with spatial data, the distribution of their life cycle global warming impact and carbon payback periods is assessed across multiple regions. The results show significantly varying impact levels of the different MREs, with carbon-neutral deployment not guaranteed at every location. Wave energy converters only partially reach carbon neutrality, while floating photovoltaics fail to do so across the entire study area. Floating wind turbines can be considered carbon-neutral nearly across their entire theoretical application area. The findings highlight the importance of taking into account site-specific environmental performance of MREs in order to ensure a positive contribution to climate change mitigation. By providing spatially explicit maps of MREs’ global warming impacts and carbon payback periods, this study enables as the first of its kind the inclusion of climate change mitigation considerations in the site selection process for MREs.
This study presents a first long term (30 years) assessment to quantify the effects of both, the wave spectrum representation, and occurrences of multi-modal sea states, on power production estimations from a point-absorber Wave Energy Converter (WEC). Analysis in 3 different offshore locations (Portugal, Ireland and The Netherlands) is included to ensure robustness of results. In general, traditional methods based on the use of the JONSWAP spectrum, with an adequate gamma shape value, can lead to mean overestimation in yearly power production >12% when compared to reference hindcast spectral data. This can be partially reduced when capping is applied to power production, but still can be close to 10%. An alternative method is proposed to modulate the JONSWAP spectrum at each time step which helps to reduce differences, but leads to slight yearly underestimations (−2.5 to −5% in average). Although in all analyzed sites the occurrences of multi-modal spectra is >30%, contribution to errors due to misrepresentation of these sea states are estimated to be of about 2.5%. These findings provide valuable insights on the uncertainties introduced in power production estimations, related to wave conditions characterization, that can have important economic impact when planning for large scale deployments.
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This study presents a first long term (30 years) assessment to quantify the effects of both, the wave spectrum representation, and occurrences of multi-modal sea states, on power production estimations from a point-absorber Wave Energy Converter (WEC). Analysis in 3 different offshore locations (Portugal, Ireland and The Netherlands) is included to ensure robustness of results. In general, traditional methods based on the use of the JONSWAP spectrum, with an adequate gamma shape value, can lead to mean overestimation in yearly power production >12% when compared to reference hindcast spectral data. This can be partially reduced when capping is applied to power production, but still can be close to 10%. An alternative method is proposed to modulate the JONSWAP spectrum at each time step which helps to reduce differences, but leads to slight yearly underestimations (−2.5 to −5% in average). Although in all analyzed sites the occurrences of multi-modal spectra is >30%, contribution to errors due to misrepresentation of these sea states are estimated to be of about 2.5%. These findings provide valuable insights on the uncertainties introduced in power production estimations, related to wave conditions characterization, that can have important economic impact when planning for large scale deployments.
Wave energy holds substantial promise as a renewable resource, but its commercial deployment remains limited. Research primarily focuses on individual wave energy converter (WEC) devices, while the interactions within WEC arrays have received less attention. Optimizing these interactions is essential for maximizing energy capture and minimizing operational costs. However, due to the variability of wave conditions, it is unlikely that a single WEC configuration will be effective across all scenarios. Therefore, to optimize performance, a large number of simulations are required, which is computationally expensive with traditional high-fidelity numerical methods. This paper addresses this challenge by utilizing a surrogate model based on polynomial chaos expansion (PCE), which efficiently captures the behavior of a WEC array over a 30-year probabilistic based on a high-fidelity wave dataset. The surrogate model is compared to a frequency domain model, demonstrating a high efficiency. The surrogate model is used to simulate the performance of an array of five point absorber WECs under varying wave conditions. The study highlights the following requirements for optimal array performance: the spatial configuration of WECs must consistently produce optimal power throughout the operational period and must adapt to the high variability of wave parameters. The results reveal that the fixed array configuration under study, produces power that is inconsistent over varying sea conditions, showing suboptimal energy production under most wave conditions, and higher power output only under less probable wave scenarios. These findings provide insights into the physical interactions influencing WEC array performance and can inform future design methodologies for wave energy farms. The proposed surrogate modeling framework offers a highly efficient tool for conducting large-scale probabilistic analyses of WEC arrays, significantly reducing computational effort while enabling more accurate performance predictions.
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Wave energy holds substantial promise as a renewable resource, but its commercial deployment remains limited. Research primarily focuses on individual wave energy converter (WEC) devices, while the interactions within WEC arrays have received less attention. Optimizing these interactions is essential for maximizing energy capture and minimizing operational costs. However, due to the variability of wave conditions, it is unlikely that a single WEC configuration will be effective across all scenarios. Therefore, to optimize performance, a large number of simulations are required, which is computationally expensive with traditional high-fidelity numerical methods. This paper addresses this challenge by utilizing a surrogate model based on polynomial chaos expansion (PCE), which efficiently captures the behavior of a WEC array over a 30-year probabilistic based on a high-fidelity wave dataset. The surrogate model is compared to a frequency domain model, demonstrating a high efficiency. The surrogate model is used to simulate the performance of an array of five point absorber WECs under varying wave conditions. The study highlights the following requirements for optimal array performance: the spatial configuration of WECs must consistently produce optimal power throughout the operational period and must adapt to the high variability of wave parameters. The results reveal that the fixed array configuration under study, produces power that is inconsistent over varying sea conditions, showing suboptimal energy production under most wave conditions, and higher power output only under less probable wave scenarios. These findings provide insights into the physical interactions influencing WEC array performance and can inform future design methodologies for wave energy farms. The proposed surrogate modeling framework offers a highly efficient tool for conducting large-scale probabilistic analyses of WEC arrays, significantly reducing computational effort while enabling more accurate performance predictions.
Numerical modelling plays a pivotal role in the design and optimization of wave energy converters. Spectral-domain (SD) modelling has recently received significant research interest as a newly emerging numerical tool. SD modelling is commonly characterized as an extension of frequency-domain (FD) modelling but can incorporate nonlinearities. Thereby, it combines high computational efficiency and adequate accuracy. Previous studies have demonstrated the applicability of SD modelling to a variety of nonlinear hydrostatic/hydrodynamic effects, including viscous drag force, nonlinear hydrostatic force, nonlinear mooring force, etc. However, there also exist influential nonlinear effects in the power generation phase in wave energy conversion. For instance, previous studies have demonstrated that the current limit of the electrical generator could impact the PTO force and the dynamics of the whole system. Therefore, it is necessary to further develop the SD modelling to cover the entire wave-to-wire process in WECs.
In this paper, a SD model is derived to simulate the wave-to-wire process of a point absorber WEC. A mechanical PTO system coupled with a rotary permanent-magnet generator is considered for the WEC. Representative nonlinear effects of the wave-to-wire process are incorporated, including viscous drag force, nonlinear PTO force, and the current limit of the generator. A nonlinear time-domain (TD) wave-to-wire model is established correspondingly to serve as the accuracy reference because it is inherently associated with higher modelling fidelity. The dynamic response and the power performance of the proposed SD model are verified against those of the nonlinear TD wave-to-wire model. Additionally, the computational efficiency of the proposed SD model and the TD model is identified and compared. ...
In this paper, a SD model is derived to simulate the wave-to-wire process of a point absorber WEC. A mechanical PTO system coupled with a rotary permanent-magnet generator is considered for the WEC. Representative nonlinear effects of the wave-to-wire process are incorporated, including viscous drag force, nonlinear PTO force, and the current limit of the generator. A nonlinear time-domain (TD) wave-to-wire model is established correspondingly to serve as the accuracy reference because it is inherently associated with higher modelling fidelity. The dynamic response and the power performance of the proposed SD model are verified against those of the nonlinear TD wave-to-wire model. Additionally, the computational efficiency of the proposed SD model and the TD model is identified and compared. ...
Numerical modelling plays a pivotal role in the design and optimization of wave energy converters. Spectral-domain (SD) modelling has recently received significant research interest as a newly emerging numerical tool. SD modelling is commonly characterized as an extension of frequency-domain (FD) modelling but can incorporate nonlinearities. Thereby, it combines high computational efficiency and adequate accuracy. Previous studies have demonstrated the applicability of SD modelling to a variety of nonlinear hydrostatic/hydrodynamic effects, including viscous drag force, nonlinear hydrostatic force, nonlinear mooring force, etc. However, there also exist influential nonlinear effects in the power generation phase in wave energy conversion. For instance, previous studies have demonstrated that the current limit of the electrical generator could impact the PTO force and the dynamics of the whole system. Therefore, it is necessary to further develop the SD modelling to cover the entire wave-to-wire process in WECs.
In this paper, a SD model is derived to simulate the wave-to-wire process of a point absorber WEC. A mechanical PTO system coupled with a rotary permanent-magnet generator is considered for the WEC. Representative nonlinear effects of the wave-to-wire process are incorporated, including viscous drag force, nonlinear PTO force, and the current limit of the generator. A nonlinear time-domain (TD) wave-to-wire model is established correspondingly to serve as the accuracy reference because it is inherently associated with higher modelling fidelity. The dynamic response and the power performance of the proposed SD model are verified against those of the nonlinear TD wave-to-wire model. Additionally, the computational efficiency of the proposed SD model and the TD model is identified and compared.
In this paper, a SD model is derived to simulate the wave-to-wire process of a point absorber WEC. A mechanical PTO system coupled with a rotary permanent-magnet generator is considered for the WEC. Representative nonlinear effects of the wave-to-wire process are incorporated, including viscous drag force, nonlinear PTO force, and the current limit of the generator. A nonlinear time-domain (TD) wave-to-wire model is established correspondingly to serve as the accuracy reference because it is inherently associated with higher modelling fidelity. The dynamic response and the power performance of the proposed SD model are verified against those of the nonlinear TD wave-to-wire model. Additionally, the computational efficiency of the proposed SD model and the TD model is identified and compared.