G. Lavidas
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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.
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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 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.
Conference paper
(2026)
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Ardemia Acampora, Harishankar Sivaprasad, George Lavidas, Apostolos Tsouvalas
The deployment of floating offshore wind turbines requires the installation of anchoring systems in deep-water environments, where pile driving operations may be performed using fully submerged impact hammers. While underwater noise from offshore pile driving has been widely studied, most existing approaches assume impacts occurring in air and may not entirely capture these emerging installation configurations. Furthermore, current assessment frameworks are primarily based on pressure-related acoustic metrics and do not explicitly account for particle motion. This study investigates the vibro-acoustic response of a driven pile under submerged impact conditions, with particular focus on particle motion in both the water column and the seabed. A physics-based modelling approach is adopted to analyse the coupled pile–soil–fluid system, capturing both the radiated acoustic field in the water and the vibration field transmitted through the seabed. The response is described in terms of particle velocity, enabling a consistent representation across both media. The results provide insight into the mechanisms governing energy transmission into the seabed, supporting a more comprehensive assessment of environmental effects in deep-water pile installation.
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The deployment of floating offshore wind turbines requires the installation of anchoring systems in deep-water environments, where pile driving operations may be performed using fully submerged impact hammers. While underwater noise from offshore pile driving has been widely studied, most existing approaches assume impacts occurring in air and may not entirely capture these emerging installation configurations. Furthermore, current assessment frameworks are primarily based on pressure-related acoustic metrics and do not explicitly account for particle motion. This study investigates the vibro-acoustic response of a driven pile under submerged impact conditions, with particular focus on particle motion in both the water column and the seabed. A physics-based modelling approach is adopted to analyse the coupled pile–soil–fluid system, capturing both the radiated acoustic field in the water and the vibration field transmitted through the seabed. The response is described in terms of particle velocity, enabling a consistent representation across both media. The results provide insight into the mechanisms governing energy transmission into the seabed, supporting a more comprehensive assessment of environmental effects in deep-water pile installation.
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.
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-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.
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 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.
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.
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.
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.
This article investigates the methodology and applicability of the statistical linearization (SL) method to incorporating multi-variate non-differentiable nonlinearities, with a focus on floating renewable energy devices. The SL method serves as a highly competitive approach for analyzing floating renewable energy structures, such as wave energy converters (WECs) and floating wind energy turbines, because it inherently combines adequate accuracy and high computational efficiency. The origin of high accuracy comes from its incorporation of nonlinear effects through statistically linearized representations. Yet, the statistically linearized solutions have only been derived and verified for a limited number of nonlinearities of floating renewable energy devices, mostly simply-formed and differentiable in their mathematical expressions. However, floating renewable energy devices usually exhibit a complex dynamic mechanism, in which the relevant nonlinear effects could appear to be highly complex for linearization process to describe. These nonlinear effects could make a significant impact on the system dynamics, exemplified by external machinery force saturation and nonlinear hydrostatics of floaters with a non-uniform geometry. To push forward the boundary of the SL method, it is crucial to demonstrate how it applies to nonlinearities of different features. In this paper, the existing SL method is extended to address the nonlinear effects expressed as multi-variate non-differentiable functions. Several case studies are carried out to exemplify the application of the extended SL approach to the concerned nonlinearities in floating renewable energy devices. The accuracy and computational efficiency of the extended SL approach are evaluated by verifying against the corresponding nonlinear time-domain (TD) and linear frequency-domain (FD) models. Despite the complexity of the given nonlinearities, the relative errors of the SL approach are no more than 6 % while its computational time is comparable to the FD model, being thousands of times faster than the TD model. Comparatively, the FD model leads to a relative error of over 70% in some cases.
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This article investigates the methodology and applicability of the statistical linearization (SL) method to incorporating multi-variate non-differentiable nonlinearities, with a focus on floating renewable energy devices. The SL method serves as a highly competitive approach for analyzing floating renewable energy structures, such as wave energy converters (WECs) and floating wind energy turbines, because it inherently combines adequate accuracy and high computational efficiency. The origin of high accuracy comes from its incorporation of nonlinear effects through statistically linearized representations. Yet, the statistically linearized solutions have only been derived and verified for a limited number of nonlinearities of floating renewable energy devices, mostly simply-formed and differentiable in their mathematical expressions. However, floating renewable energy devices usually exhibit a complex dynamic mechanism, in which the relevant nonlinear effects could appear to be highly complex for linearization process to describe. These nonlinear effects could make a significant impact on the system dynamics, exemplified by external machinery force saturation and nonlinear hydrostatics of floaters with a non-uniform geometry. To push forward the boundary of the SL method, it is crucial to demonstrate how it applies to nonlinearities of different features. In this paper, the existing SL method is extended to address the nonlinear effects expressed as multi-variate non-differentiable functions. Several case studies are carried out to exemplify the application of the extended SL approach to the concerned nonlinearities in floating renewable energy devices. The accuracy and computational efficiency of the extended SL approach are evaluated by verifying against the corresponding nonlinear time-domain (TD) and linear frequency-domain (FD) models. Despite the complexity of the given nonlinearities, the relative errors of the SL approach are no more than 6 % while its computational time is comparable to the FD model, being thousands of times faster than the TD model. Comparatively, the FD model leads to a relative error of over 70% in some cases.
Journal article
(2025)
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Andreas T. Asiikkis, Vaibhav Raghavan, Dimokratis G.E. Grigoriadis, Andrei V. Metrikine, George Lavidas, Antonis I. Vakis
The accurate modelling of hydrodynamic interactions in dense arrays of Wave Energy Converters (WECs) is critical for optimizing design and predicting energy capture efficiency. This study presents the first time-domain experimental validation of the Boundary Element Method (BEM) multi body solver HAMS-MREL, for WEC arrays. The validation involves a comparative assessment of wave excitation forces from numerical predictions and physical measurements for an array of 5 floaters. Results exhibit good overall agreement, with Normalized Root Mean Square Error (NRMSE) values typically below 10 %, though with some exceptions. The results highlight solver limitations that vary with wave steepness and floater positioning within the array. Additionally, this study presents the first integration of HAMS-MREL with WEC-Sim for time-domain simulations, evaluating the linear HAMS-MREL and the weakly nonlinear WEC-Sim hydrodynamic models across various wave conditions. The comparative study conducted with the Ocean Grazer 4.0 case, a dense array of 18 floaters around a monopile, reveals the conditions under which linear modelling remains valid and when nonlinear approaches become necessary. Despite significant wave excitation force differences at wave steepness above 2 %, power output estimates remain within acceptable limits (∼10 %). These findings offer critical insights into appropriate model selection for different wave conditions.
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The accurate modelling of hydrodynamic interactions in dense arrays of Wave Energy Converters (WECs) is critical for optimizing design and predicting energy capture efficiency. This study presents the first time-domain experimental validation of the Boundary Element Method (BEM) multi body solver HAMS-MREL, for WEC arrays. The validation involves a comparative assessment of wave excitation forces from numerical predictions and physical measurements for an array of 5 floaters. Results exhibit good overall agreement, with Normalized Root Mean Square Error (NRMSE) values typically below 10 %, though with some exceptions. The results highlight solver limitations that vary with wave steepness and floater positioning within the array. Additionally, this study presents the first integration of HAMS-MREL with WEC-Sim for time-domain simulations, evaluating the linear HAMS-MREL and the weakly nonlinear WEC-Sim hydrodynamic models across various wave conditions. The comparative study conducted with the Ocean Grazer 4.0 case, a dense array of 18 floaters around a monopile, reveals the conditions under which linear modelling remains valid and when nonlinear approaches become necessary. Despite significant wave excitation force differences at wave steepness above 2 %, power output estimates remain within acceptable limits (∼10 %). These findings offer critical insights into appropriate model selection for different wave conditions.
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.
The increasing global demand for wind power underscores the importance of understanding and characterizing extreme ramp events, which are significant fluctuations in wind power generation over short periods that pose challenges for grid integration. This study focuses on modeling frontal low-level jets (FLLJs) and associated extreme ramp-down events, particularly their impact on wind power production at Belgium offshore wind farms. Using the Weather Research and Forecasting (WRF) model, we analyzed five cases of extreme wind power ramp-down events, including in-depth analysis of two cases and generalization of three additional cases. We assessed the sensitivity of various model configurations, including initial and boundary condition (IC/BC) datasets (ERA5 and CERRA), the activation of Fitch wind farm parameterization (WFP), planetary boundary layer (PBL) schemes, and single- versus nested-domain configuration. Our findings indicate that CERRA IC/BCs provide a superior representation of atmospheric flow compared to ERA5, resulting in more accurate predictions of ramp timing, intensity, and FLLJ characteristics. The WFP significantly impacts wind power output by modeling turbine interactions and wake effects, leading to slightly lower wind speeds. The scale-aware Shin and Hong PBL scheme yielded a stronger FLLJ core at higher altitudes with a more pronounced jet nose, although wind speeds below 200 m were lower compared to the Mellor–Yamada–Nakanishi–Niino 2.5 scheme. Single-domain configuration proved more effective in simulating wind power ramps but had higher core heights and higher wind speeds below 200 m, resulting in a diffused jet profile. Our analysis highlights that reliable simulation of extreme ramps associated with FLLJs using a single-domain configuration could reduce computational costs. Further, the FLLJs and associated extreme ramps can be predicted 1 d in advance, offering substantial benefits for operational efficiency in wind energy management.
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The increasing global demand for wind power underscores the importance of understanding and characterizing extreme ramp events, which are significant fluctuations in wind power generation over short periods that pose challenges for grid integration. This study focuses on modeling frontal low-level jets (FLLJs) and associated extreme ramp-down events, particularly their impact on wind power production at Belgium offshore wind farms. Using the Weather Research and Forecasting (WRF) model, we analyzed five cases of extreme wind power ramp-down events, including in-depth analysis of two cases and generalization of three additional cases. We assessed the sensitivity of various model configurations, including initial and boundary condition (IC/BC) datasets (ERA5 and CERRA), the activation of Fitch wind farm parameterization (WFP), planetary boundary layer (PBL) schemes, and single- versus nested-domain configuration. Our findings indicate that CERRA IC/BCs provide a superior representation of atmospheric flow compared to ERA5, resulting in more accurate predictions of ramp timing, intensity, and FLLJ characteristics. The WFP significantly impacts wind power output by modeling turbine interactions and wake effects, leading to slightly lower wind speeds. The scale-aware Shin and Hong PBL scheme yielded a stronger FLLJ core at higher altitudes with a more pronounced jet nose, although wind speeds below 200 m were lower compared to the Mellor–Yamada–Nakanishi–Niino 2.5 scheme. Single-domain configuration proved more effective in simulating wind power ramps but had higher core heights and higher wind speeds below 200 m, resulting in a diffused jet profile. Our analysis highlights that reliable simulation of extreme ramps associated with FLLJs using a single-domain configuration could reduce computational costs. Further, the FLLJs and associated extreme ramps can be predicted 1 d in advance, offering substantial benefits for operational efficiency in wind energy management.
This study examines the potential contribution of marine renewable generators in Greece, in order to achieve a 100% renewable energy system by 2050. Using PyPSA-Eur, a cost-optimization model of the European energy system, possible energy transition pathways are explored, across five-year intervals from 2030 to 2050. For each five-year target, a new cost assumption dataset is used, one that follows estimated cost reduction learning rates. This version of the model is called PyPSA-Eur-MREL, and is modified to include marine power generators, i.e. floating wind, wave, tidal and floating solar, but also high fidelity climate data, in the scale of 5.5 km
2 for wind and 4 km
2 for wave resources. Three different approaches were employed in this investigation: greenfield, generator constrained, and a high-load scenario inspired by Greece's National Energy and Climate Plan (NECP). The analysis focused on generator capacity and performance, the levels of utilization and availability of each energy carrier and the land-use impact of onshore and offshore generators. While the first two scenarios exhibit similar overall system capacities, they differ in land-use requirements, with the constrained case installing more bottom-fixed wind turbines (1.2 GW), thereby reducing land occupation. The high-load scenario introduces floating wind turbines (4.5 GW), however, the scale of onshore installations remains substantial, covering nearly one-third of Greece's total land area.
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This study examines the potential contribution of marine renewable generators in Greece, in order to achieve a 100% renewable energy system by 2050. Using PyPSA-Eur, a cost-optimization model of the European energy system, possible energy transition pathways are explored, across five-year intervals from 2030 to 2050. For each five-year target, a new cost assumption dataset is used, one that follows estimated cost reduction learning rates. This version of the model is called PyPSA-Eur-MREL, and is modified to include marine power generators, i.e. floating wind, wave, tidal and floating solar, but also high fidelity climate data, in the scale of 5.5 km 2 for wind and 4 km 2 for wave resources. Three different approaches were employed in this investigation: greenfield, generator constrained, and a high-load scenario inspired by Greece's National Energy and Climate Plan (NECP). The analysis focused on generator capacity and performance, the levels of utilization and availability of each energy carrier and the land-use impact of onshore and offshore generators. While the first two scenarios exhibit similar overall system capacities, they differ in land-use requirements, with the constrained case installing more bottom-fixed wind turbines (1.2 GW), thereby reducing land occupation. The high-load scenario introduces floating wind turbines (4.5 GW), however, the scale of onshore installations remains substantial, covering nearly one-third of Greece's total land area.
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.
In line with the global shift to transition away from fossil fuels to sustainable energy sources, tidal stream energy has emerged as a promising renewable option. This study investigates the tidal stream energy resources along the Dutch coast and focuses on the impact of Mean Sea Level (MSL) rise on the future resource potential. A THETIS high-resolution unstructured model is used. The model is validated against sea surface elevations, and the Dutch tidal stream resource uncertainties are well defined. The validated model is used to evaluate the tidal stream energy potential of the Netherlands, regions in the Wadden Sea and Westerschelde in Zeeland display noteworthy potential, evidenced by maximum average flow velocities of 1.3 m/s and maximum average energy densities of 1600 W/m2 for the Wadden Sea and maximum average flow velocities of 0.75 m/s and maximum average energy densities of 300 W/m2 for the Westerschelde. Forecasting the 2050 tidal stream resource, considering a projected 118 mm MSL rise, results indicate persistent energy characteristics, with minimal fluctuations in average velocities and average energy density when compared to the 2016 model. In the Wadden Sea and Zeeland, respectively, only marginal changes of +25 W/m2, and +8 W/m2 are observed in average energy density for those same locations. Furthermore, the inclusion of long-term constituents has negligible effects on the 2050 results, emphasising the stability of the tidal stream energy source. Tidal stream energy in the Netherlands stands out as a reliable and resilient energy source, demonstrating consistency in the face of projected MSL rise. Such predictability has the potential to contribute significantly to fostering a sustainable and secure energy system in the Netherlands, while aligning with global efforts to combat climate change.
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In line with the global shift to transition away from fossil fuels to sustainable energy sources, tidal stream energy has emerged as a promising renewable option. This study investigates the tidal stream energy resources along the Dutch coast and focuses on the impact of Mean Sea Level (MSL) rise on the future resource potential. A THETIS high-resolution unstructured model is used. The model is validated against sea surface elevations, and the Dutch tidal stream resource uncertainties are well defined. The validated model is used to evaluate the tidal stream energy potential of the Netherlands, regions in the Wadden Sea and Westerschelde in Zeeland display noteworthy potential, evidenced by maximum average flow velocities of 1.3 m/s and maximum average energy densities of 1600 W/m2 for the Wadden Sea and maximum average flow velocities of 0.75 m/s and maximum average energy densities of 300 W/m2 for the Westerschelde. Forecasting the 2050 tidal stream resource, considering a projected 118 mm MSL rise, results indicate persistent energy characteristics, with minimal fluctuations in average velocities and average energy density when compared to the 2016 model. In the Wadden Sea and Zeeland, respectively, only marginal changes of +25 W/m2, and +8 W/m2 are observed in average energy density for those same locations. Furthermore, the inclusion of long-term constituents has negligible effects on the 2050 results, emphasising the stability of the tidal stream energy source. Tidal stream energy in the Netherlands stands out as a reliable and resilient energy source, demonstrating consistency in the face of projected MSL rise. Such predictability has the potential to contribute significantly to fostering a sustainable and secure energy system in the Netherlands, while aligning with global efforts to combat climate change.
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.
To date the use of the JONSWAP parametric spectrum is still widely accepted in many engineering applications, including the wave energy sector. Nevertheless, in the last 15 years many studies have progressively shown the necessity to implement more detailed and realistic spectral information in order to reduce the errors (or differences) introduced when the JONSWAP spectrum fails to describe more complex sea states. In the present study, the changes in produced power estimations, related to different spectral representations, are analysed. All power production estimates are obtained through 30 years simulations of point-absorber Wave Energy Converter (WEC) arrays, using the HAMS-MREL Boundary Element Method (BEM) solver. To assess the effects of the wave energy distribution on power production, 3 different spectral forcing are considered. Two based on the JONSWAP spectrum, and 1 using spectra time series from the ECHOWAVE hindcast specially developed for wave energy applications. For comparison purposes, the hindcast spectra is used as reference, since it can accurately represent the sea states evolution in time including the occurrence of multimodal conditions, which are not considered by the JONSWAP formulation. Additionally, 3 locations with different wave climates are analysed within European coastal waters. Recent results, focused on the response of a single (point-absorber) WEC, show that the differences in the mean yearly production can be > 12% when compared to reference hindcast data. The generalised analysis presented here, including the hydrodynamic interactions between multiple WECs within an array, is an important step forward in the understanding and quantification of the uncertainties present in power production assessments.
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To date the use of the JONSWAP parametric spectrum is still widely accepted in many engineering applications, including the wave energy sector. Nevertheless, in the last 15 years many studies have progressively shown the necessity to implement more detailed and realistic spectral information in order to reduce the errors (or differences) introduced when the JONSWAP spectrum fails to describe more complex sea states. In the present study, the changes in produced power estimations, related to different spectral representations, are analysed. All power production estimates are obtained through 30 years simulations of point-absorber Wave Energy Converter (WEC) arrays, using the HAMS-MREL Boundary Element Method (BEM) solver. To assess the effects of the wave energy distribution on power production, 3 different spectral forcing are considered. Two based on the JONSWAP spectrum, and 1 using spectra time series from the ECHOWAVE hindcast specially developed for wave energy applications. For comparison purposes, the hindcast spectra is used as reference, since it can accurately represent the sea states evolution in time including the occurrence of multimodal conditions, which are not considered by the JONSWAP formulation. Additionally, 3 locations with different wave climates are analysed within European coastal waters. Recent results, focused on the response of a single (point-absorber) WEC, show that the differences in the mean yearly production can be > 12% when compared to reference hindcast data. The generalised analysis presented here, including the hydrodynamic interactions between multiple WECs within an array, is an important step forward in the understanding and quantification of the uncertainties present in power production assessments.