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.

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.

The Energy Transition requires meticulous planning, taking into consideration economic, technical, social, and resource constraints. In Europe ambitious targets have been set for system electrification, however, integrating the potential of marine renewables have not been thoroughly investigated. This study extends the framework of PyPSA-Eur into PyPSA-Eur-MREL that for the first time incorporates all marine renewables, using high resolution datasets, that uncover the potential of marine renewables. Marine renewables are modelled in terms of power estimations, deployment strategies and revised packing density, and expected benefits for 2030, and 2050 across all European Countries are quantified. Higher spatio-temporal data have an immediate impact in estimates, and reduction of energy storage by 73%. Wind energy has a reduced installation capacity by 50%, but the higher fidelity of resource matches production to demand and reduces curtailments up to 60%. System costs with high resolution data are 40% reduced to 160 billion € for a 2030 100% renewable reliant system. The benefits of having more marine renewables are not limited to cost and more efficient demand matching, reduced energy storage, but it also with the area required to decarbonise the system. The results are encouraging and outline the importance and further need for marine renewable energies.

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.

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.

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.

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.

Ensuring safety and preventing accidents in waterway channels are critical challenges for networked marine surface vessel systems (NMSVs). This study introduces a regulation-aware decision-making system designed to minimize traffic conflicts and enhance navigational safety in inland waterway traffic separation schemes. The proposed framework integrates a hierarchical conditional state machine with chance-constrained model predictive control, allowing NMSVs to handle complex traffic situations while complying with safety regulations. The hierarchical conditional state machine effectively identifies vessel maneuver states, implementing safety constraints that proactively avoid collisions. Meanwhile, the chance-constrained model predictive control optimizes vessel trajectories, factoring in uncertainties and potential risks, while simultaneously enhancing operational efficiency. Simulation and experimental results demonstrate that the proposed system significantly reduces the likelihood of accidents and improves overall safety by efficiently managing vessel interactions. Compared to traditional methods, the regulation-aware approach ensures better collision avoidance, greater regulation compliance, and superior safety performance. This study confirms that the proposed decision-making system can be effectively implemented in real time, offering practical benefits for improving waterway safety and mitigating accident risks.

For manoeuvring surface target tracking in the presence of glint noise, Huber-based Kalman filters have been widely regarded as effective. However, when the proportion of outlier measurements is high, their numerical stability and estimation accuracy can deteriorate significantly. To address this issue, we propose a Robust Cubature Kalman Filter with the Current Statistical (RCKF_CS) model. Inspired by the Huber equivalent weight function, an adaptive factor incorporating a penalty strategy based on a smoothing approximation function is introduced to suppress the adverse effects of glint noise. The proposed method is then integrated into the Cubature Kalman Filter framework combined with the Current Statistical model. Unlike conventional Huber-based approaches, which process measurement residuals independently in each dimension, the proposed method evaluates the residuals jointly to improve robustness. Numerical stability analysis and extensive simulation experiments confirm that the proposed RCKF_CS achieves improved numerical robustness and filtering performance, even under strong glint noise conditions. Compared with existing Huber-based filters, the proposed method enhances filtering performance by 2.66% to 10.18% in manoeuvring surface target tracking tasks affected by glint noise.

The cooperative control of multiple autonomous surface vehicles (ASVs) is a critical area of research due to its significant applications in maritime operations, such as search and rescue and environmental monitoring. However, challenges such as communication delays and dynamic topologies often hinder stable cooperative control in practical scenarios. This study addresses these challenges by developing a formation control method based on consensus theory, focusing on both formation control and time delay. First, a simplified ASV characteristic model is established, and a basic consensus control algorithm is designed and analyzed for stability, considering different communication topologies. Then, to handle delays, the formation control method is extended, and the stability of the revised algorithm is rigorously proven using the Lyapunov function. Simulation results demonstrate that the proposed control strategy effectively maintains formations, even in the presence of communication delays. In the end, comparative simulations are carried out to demonstrate the effectiveness and robustness of the proposed controller. Simulation results demonstrate that the proposed control strategy effectively maintains formations, even in the presence of communication delays, with a convergence time of approximately 100 s and a formation error stabilizing at around 7 m. This research lays a foundation for more reliable cooperative control systems for ships, with potential applications in a variety of maritime and autonomous systems.

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.

A modified spectral-domain (SD) model is introduced in this study to address the nonlinear hydrostatic restoring force for heaving wave energy converters (WECs) with non-uniform cross-sectional areas. Distinguished from previous SD models, the modified SD model collectively includes the effects of incident wave elevation and buoy displacement, through the utilization of the multi-variate stochastic linearization method. The proposed SD model is verified against results obtained from a corresponding nonlinear time-domain (TD) model. Subsequently, a comprehensive comparison is carried out between the modified SD model, the other two existing SD models and the linear frequency-domain (FD) model. The nonlinear TD model is considered as the accuracy reference in this comparison. Various environmental and operational inputs, such as sea states, Power Take-Off (PTO) parameters, and buoy drafts, are systematically taken into account in the comparison. Additionally, the computational efficiency of each model is evaluated.

The results suggest that the modified SD model demonstrates significantly enhanced accuracy in cases where hydrostatic force nonlinearity intensifies, compared to the existing SD models and the FD model. Throughout the entire domain of the simulation cases, the maximum relative error of the modified SD model to the nonlinear TD model is below 5 %, while it is 20 % for the FD model and approximately 15 % for the two existing SD models. Moreover, the modeling accuracy of the FD model and existing SD models could be strongly disturbed by the variation of the environmental and operational inputs. Comparatively, the modified SD model is associated with much more stable accuracy. Nevertheless, the modified SD model only requires a modest increase in computational load compared to the FD model and existing SD models and it is still thousands of times faster than the nonlinear TD model.

Wave-to-Wire models play an important role in the development of wave energy converters. They could provide insight into the complete operating process of wave energy converters, from the power absorption stage to the power conversion stage. In order to cover a set of relevant nonlinear effects, wave-to-wire models are predominately established in the time domain. However, the low computational efficiency of time-domain modeling is hindering the extensive application of wave-to-wire models, especially in early-stage design and optimization where a large number of iterations are required. To address this issue, a spectral-domain wave-to-wire model is proposed, and the nonlinear effects are incorporated by stochastic linearization. This model can significantly reduce the computational load and maintain good accuracy. The reference concept studied in this paper is defined as a heaving point absorber coupled with a linear permanent-magnet generator. Four representative nonlinear effects involved in both the hydrodynamic stage and the electrical stage of the concept are considered. The proposed model is verified against a corresponding nonlinear time-domain wave-to-wire model, and a good agreement is observed. The relative error of the proposed spectral-domain wave-to-wire model is around 2 % in typical operational regions and is still within 7 % for wave states with large significant wave heights, regarding the estimate of the power conversion efficiency. Meanwhile, the computational load of the spectral-domain wave-to-wire model is reduced by 2 to 3 orders of magnitudes compared with the conventional time-domain approach. Finally, a case study of tuning the PTO damping to maximize power production is conducted to demonstrate the performance of the proposed spectral-domain wave-to-wire model.

An adjustable draft point absorber was recently proposed as a novel approach to improve power absorption with constrained power take-off (PTO) capacities. The key feature of the novel wave energy converter (WEC) concept is to adjust the buoy draft by regulating the ballast water inside the buoy, which aims to enable variation of the natural frequency of the WEC. Although previous research has shown benefits for the energy absorption stage, the impact of the draft adjustment on the power conversion efficiency and overall performance has not been examined yet. Therefore, a wave-to-wire model is established to provide an in-depth insight into the systematic performance of the adjustable draft point absorber integrated with a linear permanent magnet generator. Both a nonlinear hydrodynamic model and an analytical generator model are derived, thus the complete process from the wave power input through the whole WEC system to the usable electricity is covered. Based on the established model, wave-to-wire responses of the novel concept are obtained and analyzed. The negative effects of the draft adjustment on the stroke and overlap between the stator and translator are demonstrated. Moreover, a comparison is made between this novel WEC and conventional fixed draft WEC, and both regular and irregular wave states are considered. The results show that the adjustable draft system could increase not only the absorbed power but also the generator conversion efficiency. In specific conditions, the delivered electrical power of the adjustable draft WEC was over 20 % and 10 % higher than a traditional fixed draft system for regular and irregular waves respectively.

Wave energy is considered one of the most potential renewable energy. In the last two decades, many wave energy converters (WECs) have been designed to harvest energy from the ocean. Different power take-off systems are developed to maximize the power generation of WECs. However, the estimation of the power matrix of the WECs and annual power generation on the different sites is much more complex. A lot of simulations or experiments are required to obtain the power matrix of one specific WEC. To solve this problem, this paper proposes an active learning Kriging approach to estimate the WEC power matrix with less computational cost or experiment test. The efficiency of the proposed approach is demonstrated by two analytic problems and a point absorber WEC. The results show the proposed approach can efficiently and accurately estimate the power matrix of the WECs. Using the proposed ALK-PE approach, less than one-fifth of simulations or experiments are required to construct the whole power matrix of WECs at all the sea states, and the mean absolute percentage error is around 1%.

A spectral domain model is established to analyze the performance of a recently proposed wave energy concept, namely the adjustable draft point absorber. The non-linear hydrostatic force is incorporated in the spectral domain model. To improve the accuracy of the proposed model, the incident wave elevation is considered in the statistic linearization of the non-linear term. The proposed model is verified by the results obtained by the non-linear time domain simulations. The results suggest that the proposed spectral domain model could include the non-linear hydrostatic force while maintaining a higher computational efficiency than the non-linear time domain model. Based on the proposed model, the power performance of the adjustable draft WEC is identified. Furthermore, a techno-economic analysis is performed to reveal the benefits of the adjustable draft WEC for a given European sea site. The results show that the adjustable draft WEC is associated with higher power absorption in powerful sea states compared with the conventional fixed draft WEC. In addition, the adjustable draft system could contribute to the improvement of the annual energy production as well as the reduction of the levelized cost of energy of WECs.

Ocean wave energy has a huge potential to make a contribution to global energy transition. However, the high Levelized Cost of Energy (LCOE) is currently a big hurdle to the development of wave energy converters (WECs). This thesis is motivated to improve the techno-economic competitiveness of WECs. It focuses on the effects of systematic sizing of WECs. "Systematic sizing" is reflected in this thesis by considering the effects of sizing on the two main components of WECs, namely the buoy and PTO system. The main body of this thesis starts with a literature review. First, it is intended to provide an overview of current wave energy technologies and the application of power take-off (PTO) systems. Secondly, the studies relevant to sizing of WECs are reviewed, and sizing methods used in the context are discussed and compared. It indicates that the existing studies mainly focus on the effects of buoy sizing and there is a lack of consideration of PTO sizing. In addition, the sizing methods based on the Budal diagram and Froude scaling can only be used to conduct sizing of buoy but the influence of PTO sizing cannot be covered. Numerical simulation can be applied to take into account both effects of buoy sizing and PTO sizing, but it is usually associated with low computational-efficiency. As sizing can be regarded as a kind of optimization which normally requires a number of iterations, an efficient method is beneficial for accelerating the design process of WECs. Followed up by the literature review, Chapter 3 to Chapter 7 of this thesis are dedicated to accomplishing two main research objectives...

The Power Take-Off (PTO) rating of Wave Energy Converters (WECs) is generally much higher than the average extracted power. Scientific literature has indicated that downsizing the PTO capacity to a suitable level is beneficial for improving the techno-economic competitiveness. In this paper, a novel design, namely the adjustable draft system, is proposed for point absorbers to implement PTO downsizing. A frequency domain model is established to calculate the performance of the proposed device. From frequency domain analysis, two potential advantages are identified by installing the adjustable draft system. Firstly, the excitation force can be controlled by adjusting the buoy draft, which could be utilized to reduce the required PTO force. This is helpful for downsizing the PTO capacity. Secondly, the relevant natural frequency of the point absorber can be adapted to the operating wave states by varying the buoy draft, which improves the power absorption. A nonlinear approach is adopted specifically for the spherical buoy to include the nonlinear Froude–Krylov force and viscous drag force. The results show that the nonlinear forces have a significant influence on the power absorption when operating close to resonance regions. However, the advantages resulting from the proposed system still can be observed while considering the nonlinear forces. The power absorption can be improved by 27% and 12% in particular cases of regular and irregular wave states respectively.

A crucial part of wave energy converters (WECs) is the power take-off (PTO) mechanism, and PTO sizing has been shown to have a considerable impact on the levelized cost of energy (LCOE). However, as a dominating type of PTO system in WECs, previous research pertinent to PTO sizing did not take modeling and optimization of the linear permanent magnet (PM) generator into consideration. To fill this gap, this paper provides an insight into how PTO sizing affects the performance of linear permanent magnet (PM) generators, and further the techno-economic performance of WECs. To thoroughly reveal the power production of the WEC, both hydrodynamic modeling and generator modeling are incorporated. In addition, three different methods for sizing the linear generator are applied and compared. The effect of the selection of the sizing method on the techno-economic performance of the WEC is identified. Furthermore, to realistically reflect the relevance of PTO sizing, wave resources from three European sea sites are considered in the techno-economic analysis. The dependence of PTO sizing on wave resources is demonstrated.

The power take-off (PTO) system is a main component in wave energy converters (WECs), and it accounts for a notable proportion in the total cost. Sizing the PTO capacity has been proven to be significant to the cost-effectiveness of WECs. In the numerical modeling, the PTO size is normally represented by a force constraint. Therefore, to accurately evaluate the power performance of WECs with various PTO sizes, it is necessary to take the PTO force limitation, a nonlinear effect, into consideration. In this paper, a computationally-efficient spectral domain model of the PTO force saturation is developed for a heaving point absorber, and the nonlinear term is included by statistical linearization. For comparison, a frequency domain and nonlinear time domain model are implemented, and the developed spectral model is verified with the results of the nonlinear time domain model. Compared with the frequency domain model, the spectral domain model remarkably reduces the relative errors in predicting the power performance of WECs with force constraints, while the computational demand is much lower than the nonlinear time domain model. Furthermore, a case study is conducted to size the PTO capacity for reducing the levelized cost of energy (LCOE) in a chosen wave site. Three different numerical models are applied respectively. The frequency domain model could lead to a misestimate of the optimal PTO capacity, with a maximum relative error on the prediction of the annual energy production (AEP) of 24%. In contrast, the spectral domain model indicates the same optimal PTO size with the time domain modeling, and its relative errors on the prediction of the AEP are within 4.3%.