Wave Energy Converter Research Articles

Optimal Control of Nonlinear, Nonautonomous, Energy Harvesting Systems Applied to Point Absorber Wave Energy Converters

Pursuing sustainable energy solutions has prompted researchers to focus on optimizing energy extraction from renewable sources. Control laws that optimize energy extraction require accurate modeling, often resulting in time-varying, nonlinear differential equations. An energy-maximizing optimal control law is derived for time-varying, nonlinear, second-order, energy harvesting systems. We demonstrate that sustaining periodic motion under this control law when subjected to periodic disturbances necessitates identifying appropriate initial conditions, inducing the system to follow a limit cycle. The general optimal solution is applied to two point absorber wave energy converter models: a linear model where the analytical derivation of initial conditions suffices and a nonlinear model demanding a numerical approach. A stable limit cycle is obtained for the latter when the initial conditions lie within an ellipse centered at the origin of the phase plane. This work advances energy-maximizing optimal control solutions for nonautonomous nonlinear systems with application to point absorbers. The results also shed light on the significance of initial conditions in achieving physically realizable periodic motion for periodic energy harvesting systems.

Real-time ocean wave prediction in time domain with autoregression and echo state networks

This study evaluates the potential of applying echo state networks (ESN) and autoregression (AR) for dynamic time series prediction of free surface elevation for use in wave energy converters (WECs). The performance of these models is evaluated on time series data at different water depths and wave conditions, including both measured and simulated data with a focus on real-time prediction of ocean waves at a given location without resolving for the surrounding ocean surface, in other words, short-time single-point forecasting. The work presented includes training the models on historical wave data and testing their ability to predict phase-resolved future surface wave patterns for short-time forecasts. Additionally, this study discusses the feasibility of deploying these models for extended time intervals. It provides valuable insights into the trade-offs between accuracy and practicality in the real-time implementation of predictive models for wave elevation, which are needed in wave energy converters to optimise the control algorithm.

Life cycle environmental impact assessment of the “Sindhuja-I” wave energy converter

The life cycle assessment (LCA) is an inevitable part of ocean wave energy systems. This paper presents an LCA of the Sindhuja-I ocean wave energy converter (WEC). The WEC is a point absorber type WEC tested at the Tuticorin port in India. This study utilized the ISO 14044 standard and SimaPro LCA software to assess the environmental impact of the WEC in comparison to a coal power plant, offshore wind, and tidal energy devices. The functional unit considered is the generation of 1 kWh of electricity. The WEC has a global warming potential of 174 gCO2-eq/kWh, showcasing an impressive 81.9% reduction in emissions compared to coal power plants. Stainless steel contributes significantly to emissions, accounting for 93.7%, 94.6%, 99.4%, and 94.1% of total CO2, NOx, SO2, and PM2.5 emissions, respectively. The paper emphasizes the potential environmental benefits of recycling WEC materials at the end of their lifespan. Furthermore, the study suggests that the longevity of a point absorber device can positively impact its overall environmental footprint, given its minimal moving parts and low maintenance requirements. The WEC has a promising environmental footprint of ocean wave energy conversion, particularly compared to traditional fossil fuel-based power generation.

A fully enclosed wave energy converter and effects of cable-based PTO on power absorption

Abstract Existing wave energy converters (WECs) are limited by high unit energy costs, narrow bandwidths and vulnerability to seawater corrosion, making it difficult for wave energy to compete with solar and wind energy. This paper presents a fully enclosed WEC based on cable-driven parallel mechanisms, which absorbs energy from multiple directions to enhance the total energy absorption efficiency and bandwidth. The configuration of the inner cable-parallel mechanism (CDPM) is the key to this improved absorption efficiency. A configuration synthesis method of cable-driven parallel mechanisms is proposed to generate more configurations for the fully enclosed WEC. The motion equation of the fully enclosed WEC is derived to evaluate the power absorption performance. Moreover, a configuration synthesis method for realizing n-DOF configurations in the fully constrained CDPMs is proposed, and the configurations of these n-DOF fully-constrained CDPMs with (n + 1) cables are acquired. Then, the power absorption performance under different PTO parameters and wave frequencies is calculated, and the effects of the CDPM configuration are investigated. The results indicate that the proposed WECs exhibit excellent performance in mean absorbed power and bandwidth. Several principles for configuration selection are provided to further improve the performance of the CDPM-based fully enclosed WEC.

A Comparison of the Capture Width and Interaction Factors of WEC Arrays That Are Co-Located with Semi-Submersible-, Spar- and Barge-Supported Floating Offshore Wind Turbines

This research paper explores an approach to enhancing the economic viability of the heaving wave energy converters (WECs) of both cylinder-shaped and torus-shaped devices, by integrating them with four established, floating offshore wind turbines (FOWTs). Specifically, the approach focused on the wave power performance matrix. This integration of WECs and FOWTs not only offers the potential for shared construction and maintenance costs but also presents synergistic advantages in terms of power generation and platform stability. The study began by conducting a comprehensive review of the current State-of-the-Art in co-locating different types of WECs with various foundation platforms for FOWTs, taking into consideration the semi-submersible, spar and barge platforms commonly employed in the offshore wind industry. The research took a unified approach to investigate more and new WEC arrays, totaling 20 configurations across four distinct FOWTs. The scope of this study’s assumption primarily focused on the hydrodynamic wave power performance matrix, without the inclusion of aerodynamic loads. It then compared their outcomes to determine which array demonstrated superior wave energy under the key metrics of total absorbed power, capture width, and interaction factor. Additionally, the investigation could serve to reinforce the ongoing research and development efforts in the allocation of renewable energy resources.

Effects of mooring failure on the dynamic behavior of the power capture platforms

In recent years, for enhancing the ocean energy capture, it has been prevail to combine multiple wave energy converters (WECs) with the floating platforms. A power capture platform concepts is proposed in this paper based on the point-absorber WEC array and the SPIC semi-submersible platform. The present study conducts the time-domain dynamic analysis on the performance of the power capture platforms with mooring failure. After the validation of the numerical models, ANSYS-AQWA is employed to investigate the platform motion response, the remaining mooring lines' tension response, and the WEC array's power output. The results show that the platform motion and the remaining mooring lines' tension appear significant transient overshoots after mooring failure. The mean motion response of the platform increases because of the reduction of mooring stiffness. Meanwhile, the energy distribution of the platform slow-drift and roll motions at the low-frequency region increases as well. Moreover, the mooring line tension adjacent to the failed mooring line increases significantly, while that of other mooring lines decreases. Notably, mooring failure has slight effects on the WEC array's energy conversion performance, and the total absorbed power among Model 2 is more than that among Model 1. These important findings provide some insights into the design of power capture platforms. Moreover, to ensure the floating system stable and reliable, the effects of mooring failure and the resulting changes should be evaluated in advance.

Numerical Analysis and Validation of Horizontal and Vertical Displacements of a Floating Body for Different Wave Periods

This study concentrates on numerically evaluating the behavior of a floating body with a box format. Although research on floating objects has been conducted, the numerical modeling of Wave Energy Converter (WEC) devices, considering the effects of fluctuations, remains underexplored. Therefore, this research intends to facilitate the analysis of floating devices. First, the experimental data served as a benchmark for evaluating the motion paths of the floating box’s centroid. Second, the effects of various wave periods and heights on the floating body’s movement were analyzed. The Volume of Fluid (VOF) multiphase model was applied to simulate the interactions between phases. The computational model involved solving governing equations of mass conservation, volumetric fraction transport, and momentum, employing the Finite Volume Method (FVM). The validation demonstrated that the Normalized Root Mean Square Error (NRMSE) for the x/h ratio was 3.3% for a wave height of 0.04 m and 4.4% for a wave height of 0.1 m. Moreover, the NRMSE for the z-coordinate to the depth of water (z/h) was higher, at 5% for a wave height of 0.04 m and 5.8% for a wave height of 0.1 m. The overall NRMSE remained within acceptable ranges, indicating the reliability of the numerical solutions. Additionally, the analysis of horizontal and vertical velocities at different wave periods and heights showed that for H = 0.04 m, the wave periods had a minimal impact on the amplitude, but the oscillation frequency varied. At H = 0.1 m, both velocities exhibited significantly larger amplitudes, especially for T = 1.2 s and T = 2.0 s, indicating stronger motion with higher wave heights.

Linear transverse flux generator for wave energy conversion: design optimization and analysis

Abstract The electric power industry impacts each state’s economy significantly, driven by increasing electricity consumption that necessitates expanding power plants and finding alternative energy sources. Among alternative energy sources, ocean and sea wave energy converters can be distinguished as a separate class. Wave energy converters transform wave energy into mechanical and then electrical energy. The purpose of the study is to analyze and optimize the magnetic system of a transverse flux machine (TFM) linear generator and to determine the influence of the distance between the stator cores on the efficiency of the generator. This research included conducting 3D modeling and analysis to identify this rational distance. The methods for investigating the magnetic system and calculating the magnetic field pattern are divided into analytical and numerical. Thanks to advanced software for solving such tasks, numerical calculation methods based on the finite element method play a decisive role. Meanwhile, analytical calculations of the magnetic circuit are performed using Kirchhoff’s second law for preliminary analysis. The article discusses a two-phase linear TFM generator with a U-shaped core and permanent magnets. The results of numerical modeling show that the distance between the stator cores should have a specific size and requires detailed selection when designing the magnetic system in each particular case. In the design studied, it was calculated that 6 mm between the stator cores increases the machine’s performance. 3D modeling is necessary for accurate analysis, considering the axial magnetic flux to minimize stray fields and their mutual demagnetization. Future research will explore an E-shaped core TFM design.

Analytical method for an excitation adaptive bistable wave energy converter

Analytical method for an excitation adaptive bistable wave energy converter

Understanding the Uncertainty in the Technical Performance Level Assessment for Wave Energy

The design of wave energy converters (WECs) has been explored with interest, with varying design concepts emerging across both research and industry. One critical element that governs the speed of adoption is the performance of a WEC concept. WEC performance has been assessed using the Technology Performance Level (TPL) assessment, which provides designers with a quantitative score, situating a grid-scale WEC concept on a scale from 1-9. The TPL assessment is designed to be used during design iteration, when a WEC concept is fully ideated, to enable designers to consider potential means of improving the downstream performance of the concept. One concern that may be slowing developers’ adoption of TPL is the inherent uncertainty in the assessment, and how uncertainty in the individual questions may contribute to the final score. In this work, we quantify the uncertainty present in the assessment using both traditional mathematical operations and a Monte Carlo simulation. Results show areas of improvement of the TPL assessment, enabling TPL practitioners and users to understand with more accuracy those design elements that can be improved to impact device performance.

Simple Method to Introduce Artificial Damping in Oscillating Surge Wave Energy Converters under Regular Waves Considering Viscous Effects

Simple Method to Introduce Artificial Damping in Oscillating Surge Wave Energy Converters under Regular Waves Considering Viscous Effects

Feasibility Assessment of Using Wavestar Energy Converter in a Grid-Connected Hybrid Renewable Energy System (a case study)

Renewable energies, as a sustainable alternative to fossil fuels, confront a twofold challenge characterized by intermittency and the imperative to enhance reliability. Hybrid energy systems (HES) emerge as a pragmatic solution with the potential to mitigate carbon emissions and foster self-sufficiency within local communities. This investigation primarily seeks to ascertain the optimal configuration of a HES integrated with Wavestar wave energy converter, considering economic, technical, and environmental factors, tailored to meet the electricity demands of two cities in Iran including Chabahar and Anzali alongside of the Caspian sea and Oman sea, respectively. For this purpose, HOMER software is used for modeling and optimization the energy systems. In both locations, the optimal system includes photovoltaic (PV), wind turbine (WT), Wavestar wave energy converter (WEC), diesel generator (DG), and batteries which results in cost of energy (COE) of 0.136 and 0.109 in Chabahar and Anzali, respectively. Sensitivity analysis reveals that wind speed significantly impacts COE and reliability, also grid electricity purchases play a vital role. Economic uncertainty highlights varying importance between capital costs for PV and WT in Anzali and Chabahar. Furthermore, this study delves into the limitations posed by the fuel dependency of diesel generators. Finally, by conducting a thorough assessment of solar energy potential by GIS software, the research identifies a favorable location for the establishment of a solar power plant, contributing to the overall feasibility of the proposed hybrid energy systems.

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.

Dynamic response and power performance of a combined semi-submersible floating wind turbine and point absorber wave energy converter array

Dynamic response and power performance of a combined semi-submersible floating wind turbine and point absorber wave energy converter array

Marine spatial planning techniques with a case study on wave-powered offshore aquaculture farms

As emerging marine technologies lead to the development of new infrastructure across the ocean, they enter an environment that existing ecosystems and industries already rely on. Although necessary to provide sustainable sources of energy and food, careful planning will be important to make informed decisions and avoid conflicts. This paper examines several techniques used for marine spatial planning, an approach for analyzing and planning the use of marine resources. Using open-source software including QGIS and Python, the potential for developing offshore aquaculture farms powered by a reference model wave energy converter from the Sandia National Labs, the RM3, along the Northeast coast of the United States is assessed and several feasible sites are identified. The optimal site, located at 43.7°N 68.9°W along the coast of Maine, has a total cost for a 5-pen farm of $56.8M, annual fish yield of 676 tonnes, and a levelized cost of fish of $9.23 per kilogram. Overall trends indicate that the cost greatly decreases with distance to shore due to the greater availability of wave energy and that conflicts and environmental constraints significantly limit the number of feasible sites in this region.

A Multi-Stage Design Approach for Optimizing a PMSG-Based Grid-Connected Ocean Wave Energy Conversion System

A Multi-Stage Design Approach for Optimizing a PMSG-Based Grid-Connected Ocean Wave Energy Conversion System

The effect of a 120 kg pontoon mass on the wave energy converter device due to heaving

The environment is negatively impacted by the use of fossil fuels as a source of electricity. Using sustainable ocean wave energy is one way to replace fossil fuels and maximize the usage of natural energy. Electrical energy is produced from mechanical energy by ocean waves. An apparatus for converting wave energy from the ocean is needed to absorb it. The wave energy converter uses the up-and-down action of a chain on a pontoon to rotate a generator, producing electrical energy. The mass of the pontoon and the force of the ocean waves that excite it both have an impact on its vertical movement. Thus, the impact of pontoon mass on the wave energy converter is examined in this research. Both a planetary gear system and one without were used in the investigation. The voltage and current obtained at a wave height of 35 cm were 2.28 Volts and 0.160 A, respectively, without the planetary gear and 160.41 Volts and 13.95 A, with the planetary gear. Furthermore, an evaluation of the wave energy converter machine's performance was carried out. Using a planetary gear and a wave height of 13 cm, the second experiment's minimum power production was 212.63 Watts, while the sixth experiment's maximum power output was 2237.72 Watts with a wave height of 35 cm. In the second experiment, the generator without a planetary gear produced 0.0327 watts of power with the same wave height, and in the sixth trial, the generator produced a maximum of 0.3648 watts with a 35 cm wave height. As a result, utilizing a generator with a planetary gear is preferable to using one without one

Study on the effect of pitching on wave energy converter devices due to a spring constant of 980 N/M

Having enough energy is crucial to living a healthy and fulfilling life. Energy is necessary for many of the actions and tasks that individuals carry out regularly. To increase national resilience and enhance the welfare of its citizens, Indonesia is thought to be a good place to use renewable energy through the development of its natural resources. The Wave Energy Converter is one of the energy producers (WEC). The Wave Energy Converter is a machine that uses the up-and-down motion of a chain through a pontoon to drive the rotation of a solenoid in a generator to produce electrical energy. The component that produces energy is the vertical movement of waves. Thus, the impact of the spring constant on ocean waves is examined in this work. Both planetary and non-planetary approaches were used in this study. Based on the research objectives and the experimental results on the pitching motion performance of the Wave Energy Converter machine, it can be concluded that the power without planetary gear in the analysis of potential energy and sea data identification is 0.43 Volts, and the highest is 4.2 Volts. The RPM range is 78.18 RPM at the minimum and 91.45 RPM at the maximum. 0.021 amps is the minimum and 0.043 amps is the maximum current value. The power range for planetary gear potential energy analysis and sea data identification is 58.5 volts to 168.36 volts. The RPM range is 78.18 RPM at the minimum and 91.45 RPM at the maximum. 1.93 amps is the least current value, and 14.01 amps is the maximum

Analysis of the effect of a spring constant of 980 N/m on a wave energy converter device due to heaving

Indonesia is a country with a larger sea area compared to its land area. Therefore, utilizing ocean current or wave energy as a renewable energy source, specifically for generating electricity through Wave Energy Converters (WEC), is a suitable solution. Wave Energy Converters (WEC) work on the basic principle of converting wave energy into linear motion or rotation to drive a generator and then convert it into electricity. The rotation is generated by the up-and-down movement of the pontoon affected by the pontoon's spring constant, which originates from sea waves. Hence, this study aims to analyze the effect of the spring constant on the pontoon due to heaving motion in response to sea waves. The study uses a spring constant of 980 N/m and is conducted with and without a planetary gear system. The highest voltage and current were achieved at a wave height of 0.35 m, producing a voltage of 84.5 V with a current of 8.26 A and a power of 698 Watts for the generator with the planetary system. For the generator without the planetary system, it produced a voltage of 1.73 V with a current of 0.046 A and a power of 0.0795 Watts with a gearbox shaft rotation of 37.32 RPM. The lowest voltage and current were observed at a wave height of 0.15 m, producing a voltage of 39.6 V with a current of 3.58 A and a power of 141.8 Watts for the generator with the planetary system. For the generator without the planetary system, it produced a voltage of 0.53 V with a current of 0.021 A and a power of 0.0111 Watts with a gearbox shaft rotation of 21.62 RPM

Multi-objective optimal control of a hybrid offshore wind turbine platform integrated with multi-float wave energy converters

Offshore floating wind turbines will play a pivotal role in achieving net-zero emissions. This study explores a hybrid platform combining an offshore floating wind turbine with wave energy converters (WECs) from an active control perspective to mitigate turbine damage risk while maximizing wave energy conversion. Initially, the control-oriented state-space modelling of the hybrid platform and the validation of the time-domain Cummins-type models of different orders are performed by the Eulerian-Lagrangian method with model linearization and downscaling. Then, a multi-objective non-causal optimal controller is introduced, balancing wave energy capture and penalizing the nacelle acceleration. When wave energy capture maximization is set as the control target, the proposed optimal controller can improve energy output by 184% as compared against a well-tuned passive damper across all peak periods tested. However this causes peak hub acceleration to increase marginally beyond the desirable limits of 3–4 m/s2 for wind turbine operation. When hub acceleration is penalized, the multi-objective optimal controller can reduce peak values below limits by between 40% and 61% with trivial loss of wave energy capture.