Wave Energy Converter Power Research Articles

Floating wave energy farms: How energy calculations shape economic feasibility?

The aim of this study is to use two different methodologies for calculating the energy produced by a total wave energy farm in the Cantabrian Sea (North of Spain). First method studies the energy produced by the farm taking into account the wave energy converter power matrix and the probability matrix of sea conditions for a particular location. On the other hand, second method is a more simplified methodology in which the wave energy converter power matrix is not taken into account, but it considers the density of the water, gravity, period and height of the wave, as well as the percentage of efficiency, among others. Finally, the energy generated by the farm and the economic parameters that allow calculating its economic feasibility are studied, such as Levelized Cost of Energy, Net Present Value and Internal Rate of Return. Results indicate the importance of using a particular method for calculating the energy produced by a wave energy farm in terms of the variation of its economic feasibility. In this sense, it is shown that despite the fact that the first method is more detailed, the variations between both methods are very small, therefore the simplest model can be used in the future studies, reducing the calculation process in the future.

Hydrodynamic Interactions and Enhanced Energy Harnessing amongst Many WEC Units in Large-Size Wave Parks

Interactions between wave energy converters (WECs) can significantly affect the overall energy-harnessing performance of a wave park. Although large-size wave parks with many WEC units are commonly considered in practical applications, it is challenging to simulate such parks due to huge computational costs. This paper presents a numerical model that uses the boundary element method (BEM) to simulate wave parks. Each wave energy converter (WEC) was modelled as a comprehensive system, including WEC buoys, power take-off, and mooring systems, with hydrodynamic interactions included. Two classical layouts for arranging 16 units were simulated using this numerical model. The energy-harnessing performance of these array layouts was analyzed for both regular waves and a selection of irregular sea state conditions with different wave directions, wave heights, wave periods and water depths. For each layout, three WEC separation distances were studied. An increase of up to 16% in the power performance of the WEC under regular waves was observed, which highlights the importance of interaction effects.

Wave Energy Converter Power Take-Off Modeling and Validation From Experimental Bench Tests

Wave Energy Converter Power Take-Off Modeling and Validation From Experimental Bench Tests

Experimental and numerical analysis of power take-off control effects on the dynamic performance of a floating wind-wave combined system

The integration of wave energy converters (WEC) into floating offshore wind turbines (FOWT) is regarded as a promising approach for comprehensively harnessing deep-sea energy and reducing the levelized cost of energy. This study aims to investigate the WEC power take-off (PTO) control effects on the dynamic performance of a floating wind-wave combined system, wherein three heaving-type WECs are integrated into a semi-submersible FOWT. In particular, the hydraulic PTO is modelled as a Coulomb damping system to enable a more realistic analysis. The aero-hydro-servo-elastic-mooring coupled numerical simulations and 1:50 wave basin experimental data demonstrate good agreement. It is observed that wave power production varies significantly with different control settings, potentially reaching 24.0 % of the overall hybrid energy production with proper control parameters. Furthermore, platform pitch oscillation generally shows a decreasing trend with increasing damping forces under below-rated and rated conditions, while showing minimal influence when above-rated. Conversely, tower base damage equivalent load (DEL) tends to initially decrease and subsequently increase across all examined conditions. This consistent convexity indicates the potential use of DEL as a performance index for optimising PTO control. In summary, power increment, motion reduction, and load mitigation could be achieved concurrently with appropriate control design. For instance, an extra 0.48 MW wave power could be produced under the rated condition, while a 10.4 % reduction in tower base DEL and a 6.57 % mitigation in platform pitch oscillation could also be achieved at the same time.

Enhancing the performance of hybrid wave-wind energy systems through a fast and adaptive chaotic multi-objective swarm optimisation method

Hybrid offshore renewable energy platforms have been proposed to optimise power production and reduce the levelised cost of energy by integrating or co-locating several renewable technologies. One example is a hybrid wave-wind energy system that combines offshore wind turbines with wave energy converters (WECs) on a single floating foundation. The design of such systems involves multiple parameters and performance measures, making it a complex, multi-modal, and expensive optimisation problem. This paper proposes a novel, robust and effective multi-objective swarm optimisation method (DMOGWA) to provide a design solution that best compromises between maximising WEC power output and minimising the effect on wind turbine nacelle acceleration. The proposed method uses a chaotic adaptive search strategy with a dynamic archive of non-dominated solutions based on diversity to speed up the convergence rate and enhance the Pareto front quality. Furthermore, a modified exploitation technique (Discretisation Strategy) is proposed to handle the large damping and spring coefficient of the Power Take-off (PTO) search space. To evaluate the efficiency of the proposed method, we compare the DMOGWA with four well-known multi-objective swarm intelligence methods (MOPSO, MALO, MODA, and MOGWA) and four popular evolutionary multi-objective algorithms (NSGA-II, MOEA/D, SPEA-II, and PESA-II) based on four potential deployment sites on the South Coast of Australia. The optimisation results demonstrate the dominance of the DMOGWA compared with the other eight methods in terms of convergence speed and quality of solutions proposed. Furthermore, adjusting the hybrid wave-wind model’s parameters (WEC design and PTO parameters) using the proposed method (DMOGWA) leads to a considerably improved power output (average proximate boost of 138.5%) and a notable decline in wind turbine nacelle acceleration (41%) throughout the entire operational spectrum compared with the other methods. This improvement could lead to millions of dollars in additional income per year over the lifespan of hybrid offshore renewable energy platforms.

Improving the OWC Wave Energy Converter Power Take-Off Efficiency throughout Experimental and Numerical Characterisation of an SCIG

The increasing interest in the use of renewable energy technologies is directing attention towards the potential contribution of marine energy technologies, especially ocean wave energy, to world energy demand. While open-sea demonstrations of full-scale devices have been carried out to validate several technologies, the focus now is shifting to optimising the components for efficiency and reliability. The efficiency of the electrical generator plays a crucial role in wave-to-wire numerical models for converting wave energy into usable electricity. It provides essential data that enables the industry to reduce technical risks and uncertainties. Wave-to-wire models typically simplify the generator’s efficiency through assuming a single curve based on the load. This curve is usually provided by the machine manufacturers for the nominal rotational speed. However, the rotational speed varies in the case of air turbines used in OWC devices. Therefore, to accurately estimate decision variables derived from these models, a comprehensive efficiency map is necessary. This map should demonstrate the performance at different rotational speeds and loads, as it directly influences the estimation of key parameters. The main objective of the present work is to improve the generator behaviour of an OWC for different generator operation regimes. For this purpose, a numerical model of the generator’s efficiency will be developed throughout the segregation of losses and validated experimentally. Finally, an optimal control law will be presented to maximise the electrical power output of the wave energy converter, considering the efficiency of both the generator and the turbine.

Evaluation of wave energy converters based on integrated ELECTRE approach

The demand for renewable energy sources is growing rapidly as a result of increasing energy consumption, fossil fuel depletion, climate change, and environmental degradation. The tide is one of the main sources of renewable energy in the ocean because of its huge potential to be harnessed. Wave-energy converters (WECs) are a potential alternative to present energy sources, with an emphasis on improving efficiency and increasing energy. With the goal of improving the uncertainty inherent in data representation, the literature gradually uses various fuzzy extensions that handle fuzzy information in subjective evaluations and decision-making processes. single-valued neutrosophic probabilistic hesitant fuzzy sets (SVNPHFS), a recent extension of neutrosophic fuzzy sets, address limitations associated with membership functions and the representation of hesitancy in multi-criteria decision-making (MCDM) approaches. In the decision-making process, uncertainty is successfully handled by SVNPHFS. The objective of this study is to investigate and select a potential converter for a WEC power plant using SVNPHFS. Seven criteria for WECs are selected as potential sites for establishing a wave-energy power plant. The paper proposes a novel hybrid MCDM methodology. Fuzzy SWARA (Stepwise Weighted Assessment Ratio Analysis) is utilized for assigning weights to the criteria for WEC selection, and fuzzy ELECTRE (Elimination and Choice Expressing Reality) is used to determine the most suitable alternative using these criteria weights. The proposed technique identifies the point absorber in the first rank for the best wave-to-energy converter power plant as it generates a high amount of electricity compared to other alternatives. The result shows that the proposed model is more robust compared to other approaches.

Upsampling wave temporal resolution: Investigating wave parameters and the influence on WEC power performance

Power production of wave energy converters (WEC) predicted in the time domain utilize wave resource parameters and time-domain hydrodynamic model simulations of the WEC. While the hydrodynamic model provides high temporal resolution of power production (10’s of Hz), the wave resource parameters are often based on frequency-domain calculations with temporal resolution of 30 minutes to an hour. However, real ocean wave conditions vary on much shorter time scales. Relying on frequency-domain calculations will not be sufficient to capture the short-term variability and accurately predict WEC power production for a standardized methodology that follows power system requirements. These requirements need forecasted data with high sampling frequency for accurate energy predictions. Looking specifically at resource characterization, high temporal resolution datasets are not publicly available or do not exist for many coastal locations. Due to data availability, low temporal resolution datasets are being used in a majority of studies to generate representative wave conditions as inputs to numerical simulations. Representative wave conditions are used to generate wave spectrums. The issue with this practice is spectrums are then used to predict the efficiency of systems that will not accurately capture the variability of waves in short timeframes. Creating a standardized methodology to increase the temporal resolution of metaocean conditions to inform model development can provide better forecasting of power production. Random amplitude, Fourier coefficient methods have been suggested for WEC simulations of finite durations to improve the observed variability in wave heights and power production. Variability using this method does increase for finite durations compared to the commonly used deterministic amplitude method. In this paper we will investigate the influence of wave parameters (significant wave height, maximum wave height, and energy period) on the prediction of WEC power production. A better understanding of the influence of these parameters will provide a path towards future standardization methodology for resource inputs for time-domain modeling.

Power quality assessment of a wave energy converter using energy storage

Wave energy has been an immense area of interest in research and industry in our move towards a sustainable energy production society due to its high energy density and surface area. However, the grid connection of wave energy converters is still one of the major challenges due to the complexity of varying wave resources (amplitude and frequency). Wave energy converters grid integration can lead to several potential challenges, such as voltage fluctuations, harmonics and flicker. Using an energy storage system can help to mitigate few challenges by balancing the grid demand with the wave energy converter power supply. Hence, improving the power quality. This study assesses the power quality of wave energy converters equipped with energy storage against the scenario without any energy storage at different power levels. The power quality in this paper is investigated using total harmonic distortion (THD) of the grid current, dc-link voltage ripple and battery current ripple. The study shows that the addition of a hybrid energy storage system lowers the grid current THD at the point of common coupling (PCC), stabilizes the dc-link voltage ripple and reduces the stress of the battery.

Wave energy converter power take-off characterization: comparing dynamometer and field data

Through dynamometer testing of a wave energy converter’s (WEC’s) power take-off system (PTO), we characterize friction and establish a relationship between shaft speed and torque. This characterization is conducted through oscillation of the shaft with a velocity-controlled motor, yielding some key differences between lab tests and response of the system in the field. In this work, we develop an understanding of these differences, provide both linear and nonlinear representations of the PTO that can be used in hydrodynamic modeling, and assess how accurately these representations are reflected in data collected in the field. 
 
 The WEC used in this testing is the TigerRAY, built by CPower as part of a WEC-UUV (uncrewed underwater vehicle) system funded by the Naval Facilities Engineering Systems Command. The full device is a two-body point absorber with a subsurface heave plate that acts to hydrodynamically stabilize the system and serves as a docking and charging station for the UUV. The system is undergoing its second year of development and testing, which includes both at-sea trials and shore-side dynamometer experiments at the University of Washington Applied Physics Lab. The dynamometer system records torque at the WEC drive shaft, as well as motor shaft speed. Data acquisition on board the WEC simultaneously records key generator information, such as current, voltage, and angular shaft position. 
 
 Through comparison of lab and field data, we draw conclusions about the limits of a velocity-controlled dynamometer. Since this control scheme allows near-instantaneous changes in applied torque, it pushes the WEC through electrical system-induced torque spikes more quickly than is possible in the field. Reduction in the control gains of the dynamometer smooths the applied torque curve at the expense of added noise in the velocity profile. We weigh these tradeoffs using data obtained from field testing of the device in a real wave field. Additionally, we identify key characteristics in the dynamometer data and how they impact device performance in the field. Finally, we make recommendations about how to move forward with future dynamometer testing given these lessons learned.

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

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

ALK-PE: An efficient active learning Kriging approach for wave energy converter power matrix estimation

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%.

Cost investigation of battery-supercapacitor hybrid energy storage system for grid-connected hourly dispatching wave energy converter power

This study demonstrates a successful application of a dispatching scheme for a slider-crank wave energy converter (WEC), utilizing a battery-supercapacitor hybrid energy storage system (HESS). The six sea states employed in the U.S. Department of Energy's Wave Energy Prize are incorporated to calculate the desired hourly grid reference power. The proposed architecture is responsible for fulfilling this grid demand in each dispatching period within an acceptable confidence level. A low pass filter is deployed to distribute the power between the supercapacitor and battery to exploit their benefits in the HESS configuration.Furthermore, several control techniques utilizing the supercapacitor state of charge (SOC) have been devised to predict the grid reference power accurately for each dispatching horizon. The techniques were applied to ensure that the energy storage system finishes each dispatching period with sufficient capacity for next-day operation (approximately 80 % SOC).The ESS life cycle expenditure is minimized based on three key factors: the best SOC algorithm, the best filter time constant, and the best depth of discharge (DOD) usage. The HESS was found to be the most cost-effective (2.6 ¢/kWh) for the WEC application under these conditions: a 100 ms filter time constant with a step-rules algorithm as a primary SOC controller, a 44 % DOD usage for the battery, and a 50 % DOD usage for the supercapacitor (SC). The HESS was also found to be less expensive than the battery-only (8.4 ¢/kWh) as well as the SC-only (2.8 ¢/kWh) cases. It is also noticeable that the SC calendar aging cost (61 %) and the battery cycling cost (96 %) contributed significantly to its overall HESS expenses for dispatching WEC power. Extensive MATLAB/Simulink simulations were performed to provide a realistic economic evaluation for WEC dispatching power.

Analysis of wave resource model spatial uncertainty and its effect on wave energy converter power performance

Analysis of wave resource model spatial uncertainty and its effect on wave energy converter power performance

An Efficient and Effective WEC Power Take-Off System

A numerical model for a hydraulic wave energy converter power take-off is developed in this study. The system architecture is described and the mathematical model for each component is presented. The accumulators are not used as energy storage devices. Instead, they are used to reduce the stiffness of the system, increase the response time, and improve the controllability. The numerical model was implemented using MATLAB/Simulink. The design variables selected for this study are the maximum displacement in the hydraulic motors, and the shaft inertia. The effect of these design variables on system performance is studied using latin-hypercube sampling to generate the cases to be simulated. The displacement in the hydraulic devices is used as a control input to adjust the pressure in the hydraulic cylinder and then change the force acting on the floating body. The desired force is calculated by a high level controller that estimates the force value to achieve impedance matching in the WEC. The torque in the electric generator is used to control the shaft speed. The system was designed to actively use reactive power flow to maximize the electric power output in the generator. The model developed in this study is a complete wave-to-wire model based on a co-design approach that considers the effect of all the different subsystems on the dynamic behavior of the whole WEC system. Twelve different wave conditions were tested. The most critical metric for this study is the electric power in the generator, which is the objective function of the optimization that was performed for all the wave conditions defined as case study. The wave-to-wire efficiency, which includes the complete wave energy to electrical energy conversion chain, is also calculated in this work.

Response power of floating three-body wave energy converter with different shapes

A study on the hydrodynamic characteristics of buoys in a floating three-body WEC (wave energy converter) has been conducted in this paper using STAR-CCM+, based on the linear wave conditions, by numerically analyzing the impacts of buoy geometry (cuboid, cylindroid, boat-like, and capsule) on the floating motions and capture energy. Hinge constraints and hydraulic damping are considered in the numerical model, and the effects of wave parameters on the captured power of WECs are analyzed. Numerical results show that with the increase of wave period, the capture power of each WEC first increases and then decreases, and the capsule-shaped WEC has the largest power capture capability with a capture width of 0.469λ. While the boat-like also has a considerable capture width (0.459λ), with a lower wave resistance (6657.5 N) and 16% less mass, so this novel WEC has more potential for practical applications.

Singular Value Decomposition-Based Saturated Control Scheme for a Multi-DOF Wave Energy Converter

This paper proposes a singular value decomposition-based velocity tracking control system for the multi-degree of freedom wave energy converter (WEC) to address the velocity tracking problem. Compared with our previous work presented at the conference, the detailed hydrodynamics of WEC is analyzed. In order to estimate the wave excitation force and optimal reference velocity, a linear extended state observer is employed in this control scheme. Considering that the output torque of power take-off (PTO) is limited, a novel saturated sliding mode controller is proposed to ensure that the output control torque of PTO will not exceed what the actuators can supply. With the attempt to enhance the performance of LESO, a new fuzzy logic rule is introduced into this control scheme to make the observer achieve self-tune. Based on the proposed control scheme, the power take-off system can generate appropriate control input to drive the WEC's buoy to operate at the specified speed to maximize the performance benefit of the WEC's power generation.

Power Performance and Response Analysis of a Semi-Submersible Wind Turbine Combined With Flap-Type and Torus Wave Energy Converters

Abstract An integrated offshore wind and wave energy system is an attractive concept in areas with abundant wind and wave energy resources. The sharing of supporting platform and facilities, e.g., mooring systems, offers significant cost savings. This will effectively lower the levelized cost of energy (LCOE). In the present study, a conceptual design consisting of a braceless semi-submersible floating horizontal axis wind turbine (FHAWT), three flap-type wave energy converters (WECs), as well as a torus (donut-shaped) point absorber-type WEC is proposed. The flap-type WECs harvest wave energy through the flap motion caused by oscillating wave surge, while the torus WEC absorbs wave energy generated from its heaving motion. The absorbed mechanical power of the power take-off (PTO) systems is calculated based on linear damping forces and the motions of the WECs relative to the supporting platform. Hydrodynamic interaction between the WECs and the supporting platform is considered by including the coupling terms in the added mass and potential damping coefficient matrices. A fully coupled aero-servo-hydro-elastic numerical model of the concept is constructed. The feasibility study of the concept is carried out using time-domain simulations. Only operational environmental conditions are simulated based on simultaneous wind and wave hindcast data of a selected offshore site. The effects of the WECs on the wind turbine, platform motions, and WEC power take-off are examined. Based on the power performance of WECs, recommendations are also provided for optimum power absorption.

Control-oriented wave surface elevation forecasting strategies: Experimental validation and comparison*

Optimal control strategies are a key development step towards commercialization of wave energy converters (WECs). Most of these rely on optimization routines to find a suitable control action to maximize WEC power production. Nevertheless, most of these solutions make use of device dynamical models, with the free-surface elevation as the external (uncontrollable) input, effectively representing the incoming wave field. Consequently, predictive strategies, such as model predictive control, strongly depend on the availability of future wave information, and hence suitable forecasters are commonly used to ‘restore’ the causality of the optimization problem. Motivated by the intrinsic requirement of suitable forecasting strategies within optimal WEC control, this study provides a validation and comparison of different algorithms, including adaptive and non-adaptive techniques, based on experimental data. The paper focuses on the adaptability of each algorithm, which must be capable to fit properly each wave surface elevation signal, thus not affecting the optimality condition by providing poor prediction results.

Dynamic Load Effects and Power Performance of an Integrated Wind–Wave Energy System Utilizing an Optimum Torus Wave Energy Converter

To increase the utilization of wave and other renewable energy resources, an integrated system consisting of an offshore wind turbine and a wave energy converter (WEC) could be used to harvest the potential energy. In this study, a dimensionless optimization method is developed for shape optimization of a hollow cylindrical WEC, and an optimal shape is obtained using a differential evolution (DE) algorithm. The frequency domain response characteristics of the WEC with different geometric shapes and viscous damping loads are studied. The numerical model of the wind-wave integrated system, which consists of a semisubmersible platform and the WEC, is developed and used. The dynamic responses of the integrated system with and without using the WEC optimum section are compared. The results show that the dimensionless optimization method utilized in this paper is very applicable for hollow cylindrical WECs. A smaller inner radius and larger draft increase the heave RAO amplitude of the WEC significantly. In addition, optimization of the WEC shape and power take-off (PTO) damping coefficient can significantly improve the energy capture of the integrated system, which increases by 32.03%. The research results of this paper provide guidance for achieving the optimum design of offshore wind-wave energy integrated systems and quantify the benefits of using optimum designs in the produced wave energy power. In addition, the proposed dimensionless optimization method is generic and can be widely applied to different types of WECs.