Converter Array Research Articles

Energy Maximisation and Power Management for a Wave-to-Wire Model of a Vibro-Impact Wave Energy Converter Array

This paper develops a wave-to-wire model of a vibro-impact wave energy converter array for stand-alone offshore applications. Nonlinear model predictive control is proposed for maximising the wave power capture of the array, and implemented by AC/DC converters and the space vector pulse width modulation technique. A hybrid energy storage system, consisting of batteries and supercapacitors, is placed parallel to the DC bus via buck-boost DC/DC converters to smooth the array power output, and a Lyapunov-based power management strategy is utilised to control the DC/DC converters for stabilising the DC bus voltage. Intensive numerical simulations are conducted; the results show that the proposed wave-to-wire model is capable to evaluate the performance of the vibro-impact wave energy converter array in various scenarios, and the proposed energy maximisation control and power management strategy can enhance wave power capture and stabilise the power output simultaneously.

Layout Optimization of Wave Energy Park Based on Multi-Objective Optimization Algorithm

Abstract In this paper, both semi-analytical method and numerical simulation is applied to investigate the hydrodynamic behavior of large arrays of point-absorber wave energy converters (WECs). To analyze wave interactions among multiple WECs within an array, a semi-analytical model is developed based on the potential flow theory and the matched eigen-function expansions method. The fluid domain is divided into two kinds of regions: interior regions underneath the cylinders and an exterior region surrounding all the cylinders. The matched eigenfunction expansions method is employed to solve the radiation potential problem in each domain, and the hydrodynamic coefficients and motion response of the cylinders in the array are evaluated. To validate the accuracy of the semi-analytical method, WAMIT is adopted to simulate the wave energy park numerically and compared with the results by the semi-analytical model. The hydrodynamic characteristics and power absorption performance of the WECs within the wave energy park are analyzed. The power performance of a wave energy park is studied as functions of layout geometry, incident wave direction and separation distance between WECs respectively. Finally, MOPSO based on a surrogate model is used to optimize the layout of wave energy array.

GWECS: An indicator to describe the energy absorption characteristics of wave energy converter arrays in real sea states

Grouping wave energy converters (WECs) into an array has become a trend to improve power production and achieve economies of scale. Therefore, the performance of a WEC array in real sea states is of vital importance. To intuitively reflect an array's frequency-based energy absorption characteristics instead of only the total extractable power in given irregular wave conditions, a new indicator of group wave energy capture spectrum (GWECS) is proposed by extending the concept of wave energy capture spectrum (WECS) to an array. A practical method to measure the indicator by estimating the absorbed wave surface from the array's power signal is also given. Simulations in two-dimensional conditions with a 2-cuboid WEC array and in three-dimensional conditions with a 2-cylinder WEC array are conducted to study the concept. The results examine the consistency in capture efficiency between the newly proposed indicator and conventional ones, and present the effect of various parameters, including linear power take-off (PTO) damping, buoy permutation, separation distance, and incident wave angle on the GWECS.

Synergistic Integration of Multiple Wave Energy Converters with Adaptive Resonance and Offshore Floating Wind Turbines through Bayesian Optimization

We developed a synergistic ocean renewable system where an array of Wave Energy Converters (WEC) with adaptive resonance was collocated with a Floating Offshore Wind Turbine (FOWT) such that the WECs, capturing wave energy through the resonance adapting to varying irregular waves, consequently reduced FOWFT loads and turbine motions. Combining Surface-Riding WECs (SR-WEC) individually designed to feasibly relocate their natural frequency at the peak of the wave excitation spectrum for each sea state, and to obtain the highest capture width ratio at one of the frequent sea states for annual average power in a tens of kilowatts scale with a 15 MW FOWT based on a semi-submersible, Bayesian Optimization is implemented to determine the arrangement of WECs that minimize the annual representation of FOWT’s wave excitation spectra. The time-domain simulation of the system in the optimized arrangement is performed, including two sets of interactions: one set is the wind turbine dynamics, mooring lines, and floating body dynamics for FOWT, and the other set is the nonlinear power-take-off dynamics, linear mooring, and individual WECs’ floating body dynamics. Those two sets of interactions are further coupled through the hydrodynamics of diffraction and radiation. For sea states comprising Annual Energy Production, we investigate the capture width ratio of WECs, wave excitation on FOWT, and nacelle acceleration of the turbine compared to their single unit operations. We find that the optimally arranged SR-WECs reduce the wave excitation spectral area of FOWT by up to 60% and lower the turbine’s peak nacelle acceleration by nearly 44% in highly occurring sea states, while multiple WECs often produce more than the single operation, achieving adaptive resonance with a larger wave excitation spectra for those sea states. The synergistic system improves the total Annual Energy Production (AEP) by 1440 MWh, and we address which costs of Levelized Cost Of Energy (LCOE) can be reduced by the collocation.

Nonlinear modelling of arrays of submerged wave energy converters

Studies of arrays of wave energy converters (WECs) with respect to power absorption and array interactions are often performed using linear models. However, nonlinear effects can be important and may change power estimates and optimal array designs. In this study, we have compared linear predictions of the behaviour of a shallowly submerged, buoyant point absorber with predictions from the nonlinear model SWASH with a WEC incorporated (WEC-SWASH). The latter was first comprehensively validated against 1:20 Froude scaled measured data from physical experiments. WEC-SWASH predictions of body motions and mean power absorption were generally in good agreement with measurements (absolute bias within 25%), although some discrepancies were observed in the body motions, especially when the device exhibited motion instabilities. The validated WEC-SWASH model was then compared with a linear frequency-domain model, as the latter is well-known and widely used because of its computational efficiency. Model comparisons were carried out for both an isolated WEC and small arrays (up to 5 devices). The mean power estimates from the linear model and WEC-SWASH for two representative wave farms showed good agreement for mild waves, with a difference of less than 5%. However, for larger waves, the disagreement increased to about 75 to 85% between the models (for the two wave farms tested). We found that array interactions for these arrays depend on wave amplitude and not just wave frequency. Furthermore, we discovered that the power take-off coefficients optimized using the linear model were not the optimum coefficients for the nonlinear model (WEC-SWASH).

Power absorption and dynamic response analysis of a hybrid system with a semi-submersible wind turbine and a Salter's duck wave energy converter array

A multi-energy system that integrates a floating offshore wind turbine (FOWT) with wave energy converters (WEC) is an effective way to commercialize new offshore energy and the levelized cost of energy in the future. This paper proposes a FOWT-WEC hybrid system concept consisting of a semi-submersible FOWT with a Salter's duck (SD) WEC array. A coupling framework is established based on OpenFAST and ANSYS-AQWA. A preliminary feasibility study is conducted on the power absorption and motion response of the hybrid system to evaluate the interaction between the SD WEC array and the FOWT. Systematic studies demonstrate that the SD WEC array significantly reduces the motion response of the hybrid system in terms of pitch and heave. An increase in the equilibrium position of the platform in the surge direction does not have a large effect on the stability of the system. The WEC array improves the stability of wind power output and can be used as an effective supplement to power generation. The effect of wave direction shows that the SD WEC has a high sensitivity to the angle of incident waves, and the diffraction and radiation from the platform have a large impact on the power absorption of the SD WEC array.

Experimental study of a WEC array-floating breakwater hybrid system in multiple-degree-of-freedom motion

Installing an array of wave energy converters (WECs) on an existing breakwater is viable to reduce the high cost and improve the reliability of wave energy applications. The interaction between WECs and floating breakwater under multi-degree-of-freedom motion is crucial but not well investigated, especially the impact of WECs on the mooring system of the breakwater. This article fills this gap by experimentally studying a hybrid system consisting of a rectangle floating breakwater and an array of oscillating body WECs. The interactions between the WEC and the breakwater, the effect of the WEC bottom shape on the hybrid system, and the performance of the hybrid system in waves with different nonlinearities are investigated. Results indicate that the wave amplification effect of the breakwater improves the wave energy conversion performance of the WEC by up to 324.6%. As the WEC absorbs wave energy, the mooring forces of the breakwater in the pitch and surge directions decrease by up to 19.8% and 47.4%, respectively. When the incident wave height increases, the energy extraction performance of the hybrid system improves while the wave attenuation performance decreases. This study provides a reference for the practical application of WEC-breakwater hybrid systems and test data for the validation of numerical methods.

Oscillating water column wave energy converter arrays coupled with a parabolic-wall energy concentrator in regular and irregular wave conditions

Based upon previous research on a single, high-efficiency Oscillating Water Column (OWC) wave energy capture system (Mayon et al., 2021), this work further extends the numerical investigation to the layout design and performance of the wave energy convertor (WEC) array coupled with a parabolic, energy concentrating wall in both regular and irregular incident wave conditions. A heuristic method to identify the optimal siting of the component, cylindrical OWC WECs in the array, installed in the concave opening of the wall is presented. The most advantageous location of the chambers is found to lie on a parabolic curvature line which is inset from the wall. Two separate arrays composed of three and five component OWCs are investigated in a range of regular wave conditions. The hydrodynamic power and efficiency of each chamber in each of the arrays is determined, and subsequently the aggregated array performance is established. It is found that the primary OWC chamber in the array configuration can attain approximately the same hydrodynamic power output as a single, isolated OWC chamber located the parabolic wall focus, albeit with a narrower energy capture bandwidth. The secondary and tertiary component chambers in the arrays contribute a lesser, yet still considerable quantity of hydrodynamic power to the consolidated system. The cumulative hydrodynamic efficiency of the collective arrays is less than the hydrodynamic efficiency of a single OWC chamber at the wall focus, but more efficient than an isolated OWC chamber positioned in open-sea conditions. Moreover, the hydrodynamic efficiency of the arrays exhibits better stability across the range of incident wave periods investigated, denoting that the individual component chambers in the array are efficacious at different incident wave conditions. The five chamber array is comprehensively analysed in irregular incident wave conditions. The array system is demonstrated to maintain a high power output and efficient behaviour in irregular incident wave conditions-an effect attributable to the reflecting wall influence. In summary, the five-chamber array configuration yields a higher power output and improved stability in terms of efficiency performance when compared with the three-chamber array configuration in regular waves. The array maintains this exceptional performance in irregular incident wave conditions.

Hydrokinetic tidal energy resource assessment following international electrotechnical commission guidelines

Energetic tidal streams are an especially attractive source of clean energy due to the daily occurrence of high tidal flows. However, before any deployment of tidal turbine farms, it is essential to perform a resource assessment depending on the scope and scale of the project. The International Electrotechnical Commission has developed a technical specification for assessing the tidal stream resource “IEC TS 62600-201” to aid in this effort: determine a particular site’s feasibility and design the project layout. In this study, we implemented and validated a three-dimensional numerical model and provided results following the specification for a ‘Stage 2’ project layout design in a highly energetic tidal channel: Tacoma Narrows of Puget Sound, in the State of Washington, USA. Implementation of the numerical model based on the specification has helped estimate the annual energy production with higher model accuracy. We also used the same setup to evaluate the undisturbed theoretical and technical resources, where the latter included energy extraction from the flow field arranging a hypothetical tidal energy converter array. Ultimately, this work has shown the important role of the technical specification in larger project layout design, which can simultaneously act as a benchmark for other ‘Stage 2’ theoretical and technical resource assessment studies worldwide.

Wave energy converter arrays: A methodology to assess performance considering the disturbed wave field

Wave Energy Converters (WECs) often face power fluctuations due to wave variability, making grid integration costly. To mitigate this, placing multiple WECs in an array can reduce both power variability and expenses. Prior research has limited consideration of the impact of individual WECs on the disturbed wave field. Therefore, a novel simulation framework is proposed which is capable of evaluating the disturbed wave field by coupling a time domain hydrodynamics solver (ProteusDS) and a spectral wave field propagation model (Simulating WAves Nearshore (SWAN)).Numerical simulations are conducted for three different WEC archetypes (RM3, RM5, and Triton) under four representative sea states. The framework is compared with two lower-fidelity models to highlight key array effects. Results show that (a) placing WECs in an array significantly improves power quality (e.g., Triton reduces CoV by up to 37%); (b) WECs notably impact the wave field (e.g., RM3 up to 14%, RM5 up to 39%, Triton up to 29% diffraction); (c) Wave refraction, alongside attenuation, is crucial, or array power may be underpredicted (e.g., RM5 by 40% and Triton by 26%); (d) Constructive array effects can be found (e.g., Triton Q-factor up to 1.07) even without optimization, emphasizing the potential for further improvements.

A high‐power and high‐efficiency low‐profile aperture converter array

AbstractFor a phased‐array antenna system, position mismatches in spacing distances between source's output and antenna arrays’ input ports are common. At present, flexible radiofrequency cables are always utilized to electrically connect those two parts, which will result in the reduced integration. To tackle this problem, a low‐profile aperture converter array (ACA) is first proposed, which is applied between a microwave source and antenna arrays. Each stripline‐structured channel of the ACA is composed of the signal lines with different routing shapes to achieve nearly the same phase shift. In this study, a high‐power and high‐efficiency 16‐channel ACA is designed, fabricated and measured at X‐band. Experimental results show that it meets the requirement of 5‐kW pulse wave input, and the power transfer efficiency of each channel is more than 93.8%. Furthermore, its profile is only 0.42 at 9 GHz, which is favorable to transforming the integration of the whole system.

Wave excitation force prediction for arrays of wave energy converters in directional waves

The implementation of advanced control strategies is an effective means of maximizing the energy production of wave energy converters (WECs), and most of them require future wave excitation forces to determine the optimal control sequence. The WECs deployed in arrays can enable a significant reduction in the cost of wave energy and improve prediction performance by incorporating excitation forces from the array. In this paper, a critical comparison of the excitation prediction methods, including the time series, machine learning, and neural network, for a two-body heaving point absorber WEC is presented. Considering the symmetry of the WEC and arrays, the directional spectrum is utilized to determine the reference measurement of wave excitation. The prediction methods are applied to isolated WEC and different array layouts. Moreover, additional sensitivity analyses are performed to evaluate the performance. The results show that the autoregressive with extra input (ARX) model has the best performance in short-term wave excitation force prediction. In most cases, the ARX model is weakly influenced by the sampling period and can adapt well to changes in the directional distribution and sea states of irregular waves, and the ARX model requires the least amount of computational time in the simulations.

Control co-design for wave energy farms: Optimisation of array layout and mooring configuration in a realistic wave climate

This paper presents a novel Control Co-Design (CCD) methodology aimed at economically optimising the layout of wave energy converter (WEC) arrays. CCD ensures the synergy of optimised WEC and array parameters with the final control strategy, resulting in a comprehensive and efficient design of the array. By integrating a spectral-based control strategy into the array layout design, this study pursues the twin objectives of maximising energy absorption while reducing costs. To prove the performance of the proposed CCD methodology, an application case is proposed where the inter-device distance, alignment, and mooring configuration of a five-device array, considering realistic wave scenarios, are optimised. Energy capture and system cost evaluations are conducted, with results emphasising the significance of incorporating advanced control strategies in the design phase to improve energy absorption and reduce costs. With the application case, the study demonstrates that the optimal layout of a WEC array considering economic factors may differ from the optimal from purely technical factors, such as energy absorption, in the analysed case.

Hydrodynamic and power conversion performance for linear and triangular dual-buoy wave energy converter array

Hydrodynamic and power conversion performance for linear and triangular dual-buoy wave energy converter array

Extracted power optimization of hybrid wind-wave energy converters array layout via enhanced snake optimizer

In recent years, wind energy and wave energy are widely concerned as highly developmental clean energy alternatives to traditional energy sources. From the perspective of cost reduction and power output enhancement, in this study, a V27-225 kW wind turbine and wave energy converter are combined to construct a hybrid wind-wave energy converters (HWWEC), which greatly improves the power generation and operation stability. The optimization of wind-wave energy layout that involves strategically placing wave energy devices can directly influence the energy output of the whole system. To enhance the overall power generation efficiency, the optimal array configuration becomes a challenging but also promising solution regarding this concern. To optimize the array configuration that is composed of multiple HWWECS, this study develops an enhanced snake optimizer (ESO) based optimization scheme including chaotic initialization, asynchronous learning factors, and levy flight, which shows strong optimum searching ability while avoiding falling into local optimums. Simulation results under various case studies of three-line WECs consisting of three, six, and twelve buoys indicate that the ESO achieves the highest absorption power compared to other algorithms, particularly, the output power achieved by ESO is 144.337 kW higher than that obtained by the original SO.

A 3D BEM-Coupled Mode Model for the Performance Analysis of Wave Energy Converter Parks in Nearshore-Coastal Regions

Estimation on the production capacity of wave energy converter arrays (WECs) of the type of simple floaters deployed in nearshore locations highly depends on the evaluation of their performance. The latter also depends on various factors, including the dimensions and inertial characteristics of the devices, their relevant positioning, and the power take-off (PTO) system characteristics. Studying the system operation, based on the prevailing sea conditions in the region considered for deployment, can ensure that such WEC farms are sized and designed in an effective way. Furthermore, the wavelength and propagation direction of incoming wave fields can be significantly impacted by wave-seabed interactions in coastal areas, which can alter the WECs’ response pattern and ultimately the array’s power output. In this work, a 3D BEM hydrodynamic model is proposed aiming to assess the energy-capturing capacity of WEC arrays, accounting for the hydrodynamic interactions between various identical floating devices, as well as the local seabed topography. The model is supplemented by a Coupled Mode System (CMS) to calculate the incident wave field propagating over variable bathymetry, in order to simulate realistic nearshore environments. Finally, a case study is performed for an indicative geographical area, north of the coast of the island of Ikaria, located in the Eastern Aegean Sea region, where the wave potential is high, using long-term data. The latter study highlights the applicability of the proposed method and suggests its usage as a tool to support optimal WEC park design.

Analytical study on dynamic performance of a hybrid system in real sea states

A mathematical model is developed to investigate the performance of a hybrid system comprising semi-submersible floating offshore wind turbines (FOWT) coupled to an array of point-absorbing wave energy converters (WECs) under irregular waves and dynamic winds. In this study, the hydrodynamic interaction of the hybrid system is conducted by applying the matching-method of eigenfunctions to solve the diffraction and radiation velocity potentials. Non-linearities of the hybrid system are taken into account in the Cummins framework, covering aerodynamic, catenary mooring, PTO system, fluid viscosity modeling, and frequency–time domain transformation of hydrodynamic coefficients. After running the convergence analysis and model validation, the present model is employed to perform a multiparameter effect analysis. Case studies are presented to clarify the effects of WEC parameters (including radius, draft, PTO damping, and layout) on the performance of a hybrid system. Nevertheless, a significant aspect of this work revolves around the development of a precise and efficient mathematical model, capable of accurately computing hydrodynamic coefficients for specific marine structures and evaluating the motion response of the interconnected floaters. Additionally, the study offers valuable insights into the preliminary design of hybrid systems and lays a mathematical foundation along with corresponding code for hybrid system projects.

Optimal Constrained Control of Arrays of Wave Energy Converters

Wave Energy Converters (WECs) are designed to be deployed in arrays, usually in a limited space, to minimize the cost of installation, mooring, and maintenance. Control methods that attempt to maximize the harvested power often lead to power flow from the WEC to the ocean, at times, to maximize the overall harvested power from the ocean over a longer period. The Power Take-Off (PTO) units that can provide power to the ocean (reactive power) are usually more expensive and complex. In this work, an optimal control formulation is presented using Pontryagin’s minimum principle that aims to maximize the harvested energy subject to constraints on the maximum PTO force and power flow direction. An analytical formulation is presented for the optimal control of an array of WECs, assuming irregular wave input. Three variations of the developed control are tested: a formulation without power constraints, a formulation that only allows for positive power, and finally, a formulation that allows for finite reactive power. The control is compared with optimally tuned damping and bang–bang control.

Hydrodynamic responses and layout optimization of wave energy converter arrays consisting of five-degree-of-freedom truncated cylinders in front of a vertical wall

The hydrodynamic responses and layout optimization of a group of cylindrical wave energy conversion devices (WEC) in front of a fully reflecting vertical wall are investigated. Each truncated floating cylinder can oscillate with five degrees of freedom, i.e., surge, sway, heave, roll, and pitch. Based on the linear water wave theory, an analytical solution is developed for the hydrodynamic problem. The results of specific parameter studies suggest that the wall reflection effect significantly improves the energy extraction performance of the WEC array with the appropriate parameter conditions. A multi-level optimization method based on a genetic algorithm is developed. This paper investigates the optimal layout of the six WEC arrays, composed of 2–7 buoys, respectively. Additionally, the impact of other degrees of freedom (DOFs), besides the heave mode, on the hydrodynamic performance of the array is investigated. For β ≤ π/12, there is no need to consider the impact of other DOFs on the energy extraction in heave mode. The dimensionless amplitudes of other DOFs gradually decrease as the equivalent constraint stiffness increases. For k0a > 1.0, the heave amplitude and energy capture performance of the WEC array are significantly smaller. However, the amplitudes of other DOFs still have considerable magnitudes for k0a > 1.0. Therefore, for the sea area with high-frequency incident waves (k0a > 1.0), setting up a power takeoff system on other DOFs of each buoy to extract energy is a feasible solution to improve the performance of the WEC array.

Cost-Effective Optimization of an Array of Wave Energy Converters in Front of a Vertical Seawall

The present paper focuses on investigating the cost-effective configuration of an array of wave energy converters (WECs) composed of vertical cylinders situated in front of a vertical seawall in irregular waves. First, the hydrodynamic calculations are performed using a WAMIT commercial code based on linear potential theory, where the influence of the vertical wall is incorporated using the method of image. The viscous damping experienced by the oscillating cylinder is considered through CFD simulations of a free decay test. A variety of parameters, including WEC diameter, number of WECs, and the spacing between them, are considered to determine an economically efficient WEC configuration. The design of the WEC configuration is aided by a cost indicator, defined as the ratio of the total submerged volume of the WEC to overall power capture. The cost-effective configuration of WECs is achieved when WECs are positioned in front of a vertical wall and the distance between them is kept short. It can be explained that the trapped waves formed between adjacent WECs as well as the standing waves in front of a seawall significantly intensify wave fields around WECs and consequently amplify the heave motion of each WEC. A cost-effective design strategy of WEC deployment enhances the wave energy greatly and, consequently, contributes to constructing the wave energy farm.