Power Take-off System Research Articles

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.

Analytical study on an oscillating buoy integrated with a perforated structure with a quadratic pressure drop condition: A case study on a WEC-perforated breakwater integration system

A general analytical method for solving the linear wave interactions with the integration systems comprising an oscillating buoy and perforated structure is presented, with a quadratic pressure drop condition on the perforated surface. Using the method of variable separation and eigenfunction expansion, the motion response of the buoy and total velocity potential can be solved using a two-loop iterative method. The method is validated against the published results. The integration system with a heaving WEC arranged inside a perforated breakwater was investigated particularly. Under the quadratic pressure drop condition, the symmetry of the hydrodynamic coefficients and Haskind relation, are found no longer satisfied, and the dissipation through the perforated wall also contribute to the damping coefficient. Effects of the damping of the power take-off system, front wall porosity, wave amplitude, and position of the WEC are investigated in particular. It was found that the horizontal and vertical wave forces on the WEC increase significantly as wave amplitude increases; however, the hydrodynamic efficiency decreases. When the WEC is near the solid rear wall, the horizontal wave forces on the WEC and solid rear wall increase significantly at the frequencies of piston mode gap resonance and heave motion resonance.

Sea trials of Sigma wave energy converter – Power and efficiency

Sigma Energy has performed its foremost prototype tests of a scaled wave energy converter (WEC) in a real sea environment. The prototype was a point absorber with a circular buoy, a mechanical power take-off (PTO) system and a counterweight, moored to the seabed as a tension leg platform with three equal tendons. In these extensive experiments, numerous device characteristics were measured and analysed. The paper presents these sea trials, focusing on the power and efficiency of the device. The power has been calculated from the data recorded at 6 locations along the PTO system. In that way, a decay of capture width ratio (CWR) from the one absorbed from the waves to the one delivered to the electrical network was found and analysed. Also, losses of the main elements of the PTO system were defined, calculated and ranked. Optimal sea and loading conditions were indicated, giving the maximal values of the efficiencies. These optimal conditions are physically explained, and the challenges in their prediction are discussed. In addition to the results of numerous 20-min tests, the paper presents the long-term average values of the efficiencies, covering all the tests performed, and accounting for the probabilities of different sea conditions.

Performance characteristics and parameter analysis of a multi-DOF wave energy converter with hybrid power take-off systems

A multi-degree-of-freedom (multi-DOF) wave energy converter (WEC) with hybrid power take-off (PTO) systems may capture more wave energy than a traditional single-DOF WEC, which usually obtains energy from pitch or heave. Compared with the existing WECs with a single PTO, this paper presents the concept design of a multi-DOF WEC with hybrid PTOs named PUWEC, which has prismatic pairs in the hydraulic cylinder and universal pairs in the gear transmission system. Two corresponding PTOs are matched to the motion of the buoy in heave and pitch to enhance wave energy conversion. This work focuses on establishing a time-domain numerical model to simulate the coupled dynamics and power capture performance of the proposed PUWEC. The model tests are carried out in a wave tank to verify the validity of the numerical model. The results show that the numerical model is efficient in predicting the dynamic performance of the PUWEC. Regular and irregular wave conditions are considered in the numerical simulations to explore the performance characteristics of the devices. It is found that the maximum improvement of the captured power of PUWEC is 49.8 % compared with single-DOF PWEC under the regular wave frequency 0.42 Hz, and the capture width ratio of PUWEC is close to 30 % under three wave conditions. In addition, the motion trajectory of the center of gravity of the buoy is analyzed. With the increase in U-PTO damping, the trajectory of the float changes from horizontal bowl-shaped irregular path to inclined regular hollow elliptical orbit. The trajectory coefficient is introduced to provide insights into how the PUWEC improves the energy conversion. The actual working space of the PUWEC is then calculated, which is less than the design working space, indicating that the actual performance of the PUWEC is fully developed. The proposed PUWEC and constructed numerical model which considers the coupled dynamic performance of dual PTOs, can provide valid reference for the design of other multi-DOF WECs with hybrid PTOs.

Sea trials of Sigma wave energy converter – slacking and snapping of TLP mooring lines

Sigma Energy has performed its foremost prototype tests of scaled wave energy converter in a real sea environment. The prototype was a point absorber with a cylindrical buoy, a mechanical power take-off system with a counterweight, moored to the seabed as a tension leg platform (TLP) with three equal tendons. In these extensive experiments, numerous device characteristics were measured and analysed. The present paper focuses on the dynamic forces in the mooring lines, and some unexpected and rare data obtained. It is well known that TLP tendons are prone to a brief loss of tension (the slacking) and that, after such events, high snapping forces of short duration can arise. Partly by intention, and partly due to underestimation of the dynamical forces, several such slacking-snapping incidents were recorded during the experiments. In some severe storms, the snapping forces were up to six times higher than the tendon pretension. The paper presents several recordings of dynamic forces and platform motion during these critical events. It analysis them, and gives a typical scenario under which they occur. It gives also some theoretical explanations, and numerical predictions of dynamical tendon forces, with their comparison to the experimental results.

Layout optimisation of the two-body heaving wave energy converter array

As the two-body heaving wave energy converter (TBH-WEC) moves toward more commercial and large-scale applications, it usually has to be deployed in the form of arrays to reduce costs and achieve better performance. However, hydrodynamic interactions in TBH-WEC arrays are highly complex and difficult to evaluate. The effect of array configuration on the performance and interactions of TBH-WECs within the array has not been fully investigated. To address this gap, the power output time-domain modeling of TBH-WEC arrays is first established using the enhanced MATLAB-APDL-AQWA unified simulation system. Based on this system, this work investigates the internal relationship between incident wave frequency, array size, array layout, and Power Take-Off (PTO) system, and array interaction factors in both unidirectional regular and irregular waves, as well as multidirectional real-wave scenarios. The energy redistribution properties of the array wavefield are then analyzed, as is the correlation between array layout and the disturbance wavefield of the devices. Results show that array layout optimisation and PTO configuration optimisation are relatively independent from each other, and that better array layouts can be quickly obtained by iteratively adding clusters or devices in the amplified region of the existing array disturbance wavefield.

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.

GA-optimized inverse fuzzy model control of OWC wave power plants

Oscillating water columns (OWCs) are widely regarded as the simplest and most reliable type of wave energy converter. An economically viable OWC wave power plant requires maximizing the performance of the power take-off system, composed of an air turbine coupled to an electrical generator. Besides, the OWC power plant’s inherent nonlinearities and modeling uncertainties must be dealt with. One solution is the use of fuzzy controllers since they capture both nonlinearities and uncertainties of the system, which can largely contribute to improving the overall efficiency. This paper shows how an inverse fuzzy model optimized by a genetic algorithm (GA) can improve the control of an OWC and, consequently, its performance. As a case study, the Mutriku power plant with a biradial turbine was addressed, considering 11 different sea states of the characteristic wave climate. Two optimization objectives were considered: maximizing turbine and generator output average powers. Compared with a well-known baseline control strategy, the GA-fuzzy control did not significantly contribute to increasing average turbine power. However, when maximizing generator yearly-accumulated power, there were improvements of over 9%. Ultimately, these research findings may play an essential role in control strategies for wave power plants.

An Improved Hydraulic Energy Storage Wave Power-Generation System Based on QPR Control

According to the inherent characteristics of the hydraulic power take-off (PTO) system, the output power of a generator tends to be intermittent when the wave is random. Therefore, this paper aims to improve the effective utilization of wave energy and reduce power intermittency by constructing a topology with two branches to transmit electrical energy. Firstly, the wave-to-wire (W2W) model of the system is constructed. Secondly, the W2W model is simulated by using synovial and quasi-proportional resonance (QPR) control with regular and irregular incident waves, and the results of PI control are compared. Then, the control strategy in simulation is verified by experiments. The simulation and experimental results show that the control strategy has better performance, and the stability of the system output power is greatly improved.

Multi-Objective Model-Predictive Control for Dielectric Elastomer Wave Harvesters

This contribution deals with multi-objective model-predictive control (MPC) of a wave energy converter (WEC) device concept, which can harvest energy from sea waves using a dielectric elastomer generator (DEG) power take-off system. We aim to maximise the extracted energy through control while minimising the accumulated damage to the DEG. With reference to system operation in stochastic waves, we first generate ground truth solutions by solving an optimal control problem, comparing it to the performance of MPC to determine a prediction horizon that trades off accuracy and efficiency for computation. Fixed weights in the MPC scheme can produce unpredictable costs for variable sea conditions, meaning the average rate of cost accumulation can vary vastly. To steer this cost growth, we propose a heuristic to adapt the algorithm by changing the weighting of the cost functions for fulfilling the long-time goal of accumulating a small enough damage in a fixed time. A simulated case-study is presented in order to evaluate the performance of the proposed MPC framework and the weight-adaptation algorithm. The proposed heuristic proves to be able to limit the amount of accumulated damage while improving the energy yield obtained with a comparable fixed-weight MPC.

Is the Velocity Always in Phase with the Wave Excitation Force in Constrained Optimal Control of Wave Energy Converters?

The resonance condition for maximum absorption of the energy carried by ocean waves incident to an oscillating wave energy converter (WEC) is one of the most well known results of the WEC control research. It was shown that the maximum occurs when the WEC velocity is in phase with the wave excitation force. The condition was obtained with the assumption that the WEC frees to oscillate with whatever amplitude was necessary, and that the power take-off (PTO) system can deliver the unlimited force. In practical WEC implementations, this assumption does not hold. The purpose of this paper is twofold. First, to obtain the frequency response of the closed-loop WEC motion, and of the optimal control law in terms of the hydrodynamic coefficients with limited PTO force and limited motion amplitudes. Secondly, the obtained results are used to investigate the resonance condition of the WEC velocity with the incoming wave in the presence of constraints.

Dynamical modeling and parametric analysis of an electret-based wave energy converter

Carbon neutrality and the Internet of Underwater Things have injected new impetus into the development of wave energy converters (WECs) albeit most of WEC projects have ended in failure due to low cost-effectiveness. Hereupon we present the dynamical modeling and parametric analysis of a novel electret-based WEC that has a distinct power take-off system compared to the conventional ones and has exhibited high power density in our previous study. Linear wave theory and Morison equation are applied for wave field and forces, respectively. WEC motions parallel with incident waves are modeled, and the electrical subsystem of the generator is treated as a current source and a capacitor. With these simplifications, the governing equations of the nonlinear and non-smooth electromechanical system are obtained and then numerically solved using an event-driven algorithm. The new power take-off system is experimentally validated. We find that the power output varies nonlinearly with wave parameters under regular wave excitation but linearly under irregular ones, and that superharmonic resonance can significantly enhance energy conversion performance at relatively low frequencies, based on which the optimum parameters are obtained. A peak average power of around 2 mW (at a matched load resistance) is generated from each generator encapsulated in the WEC of a diameter of 15 cm. The findings shed light on the characteristics of electret-based WECs and provide support for the development of wave energy farm; moreover, the methodologies of modeling and analysis can be extended to the design and optimization of the scaleups of the proposed electret-based WEC.

Oscillating-water-column wave energy converters: A critical review of numerical modelling and control

Wave energy is a significant untapped renewable energy source which can be harnessed by wave energy converters (WECs). The oscillating water column (OWC) is one of the most promising WECs, due to its relative simplicity of operation and relatively small number of moving parts, all located above the water level. OWC power take-off systems also have lower levels of mechanical stress and more easily dissipate excess wave power, compared to other types of WECs, helping to increase the capacity factor. To improve the economic viability of OWC WECs, the performance of the associated energy-maximising control system is a major determining factor. However, energy maximisation alone does not necessarily imply that the economic return is maximised, since: (i) capital and operational costs of the OWC system should be considered and (ii) the additional goals of power quality and device integrity are also important. Indeed, to maximise return on investment, the optimisation pathway should ideally minimise the levelised cost of energy (LCoE). This critical review aims to: (i) provide a comprehensive analysis of the OWC control problem, (ii) offer an exhaustive review of available control strategies for OWCs, (iii) identify unexplored control and optimisation possibilities, and (iv) suggest future directions for OWC control. Ultimately, this review highlights that, to date, OWC control mainly focuses on turbine control, especially due to the importance of operating the turbine around its maximum efficiency point. However, comprehensive control strategies should maximise the overall, or wave-to-wire (W2W), efficiency of the device. To this end, control-oriented (complete and computationally simple) W2W OWC models should be considered in model-based control strategies. Finally, control co-design techniques should be adopted to guarantee optimal control-informed WEC design and to take into account cost-related aspects.

Influence of Hydraulic PTO Parameters on Power Capture and Motion Response of a Floating Wind-Wave Hybrid System

Hybrid systems that integrate wave energy converters (WECs) with floating offshore wind turbines (FOWTs) are considered to be key equipment to deeply exploit marine renewable energy. The power take-off (PTO) system is an important component of the hybrid system, whose parameters also have a significant impact on the hybrid system’s performance. In this paper, a wind-wave hybrid system using hydraulic PTO systems is proposed. A numerical simulation framework based on the linear wave theory and basic equations of hydraulic components is built and verified. The influence of six critical hydraulic parameters on the wave energy capture and motion response performance of the hybrid system is investigated. Specifically, the parameters of piston area, motor displacement, and equivalent generator damping affect the performance of the hybrid system similar to changing the damping term of the PTO system. The parameters of the initial gas volume and the pre-charged pressure of the accumulator affect the wave power capture only for short wave periods, while the motion response of the hybrid system increases with the increase of these two parameters. The parameter of orifice area of the throttle valve affects the performance of the hybrid system slightly only when it is small. The optimal value of partial hydraulic parameters and their corresponding peak performance are also discussed.

Design and experiment of a direct-drive wave energy converter using a variable stiffness mechanism

This paper proposes a new method to achieve the resonant behavior of a point absorber floating buoy type of Wave Energy Converter using direct drive power take-off system. The system has four main components: a frame; a buoy with a guiding shaft; a supplementary mass coupled with a linear generator and a variable stiffness structure. Firstly, the motion in the vertical direction of the buoy in the sea is converted to an oscillating motion of the supplementary mass. Next, the mass is coupled with a copper coil. The coil motion inside a magnetic wall induces an electrical current in the coil as a linear generator. Besides, a pair of pre-tension springs creates a negative stiffness phenomenon that acts on the motion of the mass and increases the performance of the system. Finally, a variable stiffness structure is installed to control the trajectory of the mass, it can increase the velocity of the mass motion thus the performance of the system is improved. Configuration and working principles of WEC were introduced, studied and analyzed. The mathematical model was presented to explain system behavior. The numerical simulation had been carried out to evaluate the operation of the system. The experimental test rig had been set up and implemented to verify the effectiveness of the proposed structure.

Optimisation of Control Algorithm for Hydraulic Power Take-Off System in Wave Energy Converter

Wave energy converters are still a maturing technology and, as such, still face a series of challenges before they can compete with already-established technologies. One of these challenges is optimising the amount of energy extracted from the waves and delivered to the power grid. This study investigates the possibility of increasing the energy output of the existing hydraulic power take-off system of a wave energy converter made by Floating Power Plant during small-scale testing of their hybrid wind and wave energy platform. This system consists of a floater arm that rotates an axle when displaced by the waves. When the axle rotates, two hydraulic cylinders are actuated, displacing oil to run through a hydraulic motor driving an electric generator. The energy extraction is controlled by implementing a control algorithm on a series of on/off valves, which decouples the two hydraulic cylinders driving the hydraulic motor, and by varying the applied torque from the generator to match the wave conditions. Finally, it is investigated whether adding high-pressure pathways to the cylinder pressure chambers is beneficial for maximum power point tracking with reactive control. The analysis is conducted through a numerical model developed in Simulink and verified by comparison to the experimental setup supplied by Floating Power Plant. The study finds that a continuous valve switching strategy is optimal compared to end-point switching and reactive control with high-pressure pathways.

Downsizing the Linear PM Generator in Wave Energy Conversion for Improved Economic Feasibility

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.

Wave power extraction from a floating elastic disk-shaped wave energy converter

In this paper, a concept of a floating elastic wave energy converter consisting of a disk-shaped elastic plate is proposed. The floating plate is moored to the seabed through a series of power take-off (PTO) units. A theoretical model based on the linear potential flow theory and eigenfunction matching method is developed to study the hydroelastic characteristics and evaluate wave power absorption of the device. The PTO system is simulated as a discrete PTO, and moreover, it is also modelled as a continuum PTO to represent the case when the PTO system is composed of a large number of PTO units. The continuum PTO approximation is tested against the discrete PTO simulation for accuracy. Two methods are proposed to predict the wave power absorption of the device. After running convergence analysis and model validation, the present model is employed to do a multiparameter impact analysis. The device adopting a continuum PTO system is found to capture wave power efficiently in an extensive range of wave frequencies. For the continuum PTO system, it is theoretically possible to adopt optimised PTO damper and stiffness/mass to guarantee the absorption of 100 % of the energy flux available in one circular component of the plane incident wave.

Power Take-off System for Electric Commercial Vehicles

Power Take-off System for Electric Commercial Vehicles

Development of the control system for taking off the maximum power of an autonomous wind plant with a synchronous magnetoelectric generator

The object of this study is electromechanical processes in an autonomous wind power plant with a magnetoelectrical generator. Under actual conditions, the wind speed is constantly changing. The wind turbine works as efficiently as possible only at the rated value of wind speed. When the wind speed changes, the efficiency of converting mechanical wind energy into electrical energy decreases. Controlling the power of the electric generator when the wind speed changes is a relevant scientific and technical task. A maximum power selection control system based on the parameters of an experimental sample of a synchronous magnetoelectric generator has been designed and investigated. A feature of the synthesized control system is that it was developed on the basis of the concept of inverse dynamics problems in combination with minimization of local functionals of instantaneous energy values. The control law provides weak sensitivity to parametric perturbations of the object and carries out dynamic decomposition of the interdependent nonlinear system, which predetermines its practical implementation. Transient processes of the power, voltage, and current of the stator, as well as the voltage and excitation current were established when the wind speed changes from 3 to 8 m/s, as well as when the active electrical resistance of the load changes. The results of this study confirm the effectiveness of the maximum power take-off control system when wind speed and load change. When the wind speed changes within 3–8 m/s and the load by 50 %, the efficiency of converting mechanical wind energy into electrical energy increases by 15–40 % compared to the traditional magnetoelectric system. The findings of the current study are recommended for practical use in autonomous power plants based on wind turbines with generators with permanent magnets.