scholarly journals Extending Complex Conjugate Control to Nonlinear Wave Energy Converters

2020 ◽  
Vol 8 (2) ◽  
pp. 84
Author(s):  
David G. Wilson ◽  
Rush D. Robinett ◽  
Giorgio Bacelli ◽  
Ossama Abdelkhalik ◽  
Ryan G. Coe
Keyword(s):  
Energy Harvesting ◽  
Limit Cycle ◽  
Wave Energy ◽  
Limit Cycles ◽  
Reactive Power ◽  
Complex Conjugate ◽  
Linear Wave ◽  
Wave Energy Converters ◽  
Linear Limit ◽  
Energy Converters

This paper extends the concept of Complex Conjugate Control (CCC) of linear wave energy converters (WECs) to nonlinear WECs by designing optimal limit cycles with Hamiltonian Surface Shaping and Power Flow Control (HSSPFC). It will be shown that CCC for a regular wave is equivalent to a power factor of one in electrical power networks, equivalent to mechanical resonance in a mass-spring-damper (MSD) system, and equivalent to a linear limit cycle constrained to a Hamiltonian surface defined in HSSPFC. Specifically, the optimal linear limit cycle is defined as a second-order center in the phase plane projection of the constant energy orbit across the Hamiltonian surface. This concept of CCC described by a linear limit cycle constrained to a Hamiltonian surface will be extended to nonlinear limit cycles constrained to a Hamiltonian surface for maximum energy harvesting by the nonlinear WEC. The case studies presented confirm increased energy harvesting which utilizes nonlinear geometry realization for reactive power generation.

scholarly journals Excitation Forces Estimation for Non-linear Wave Energy Converters: A Neural Network Approach

2020 ◽  
Vol 53 (2) ◽  
pp. 12334-12339
Author(s):  
M. Bonfanti ◽  
F. Carapellese ◽  
S.A. Sirigu ◽  
G. Bracco ◽  
G. Mattiazzo
Keyword(s):  
Neural Network ◽  
Wave Energy ◽  
Linear Wave ◽  
Network Approach ◽  
Neural Network Approach ◽  
Wave Energy Converters ◽  
Non Linear ◽  
Energy Converters

scholarly journals Revisiting Theoretical Limits for One-Degree-of-Freedom Wave Energy Converters

2020 ◽  
pp. 1-11
Author(s):  
Nathan Tom
Keyword(s):  
Power Generation ◽  
Wave Energy ◽  
Degree Of Freedom ◽  
Upper And Lower Bounds ◽  
Complex Conjugate ◽  
Hydrodynamic Coefficients ◽  
Damping Coefficients ◽  
Wave Energy Converters ◽  
Heave Motion ◽  
Energy Converters

Abstract This work revisits the theoretical limits of one-degree-of-freedom wave energy converters (WECs). This paper considers the floating sphere used in the OES Task 10 WEC modeling and verification effort for analysis. Analytical equations are derived to determine bounds on displacement amplitude, time-averaged power (TAP), and power-take-off (PTO) force. A unique result found shows that the TAP absorbed by a WEC can be defined solely by the inertial properties and radiation hydrodynamic coefficients. In addition, a unique expression for the PTO force was derived that provides upper and lower bounds when resistive control is used to maximize power generation. For complex conjugate control, this same expression only provides a lower bound, as there is theoretically no upper bound. These bounds assist in comparing the performance of the floating sphere if it were to extract energy using surge or heave motion. The analysis shows because of differences in hydrodynamic coefficients for each oscillating mode, there are different frequency ranges that provide better power capture efficiency. The influence of a motion constraint on TAP while utilizing a nonideal power take-off is examined and found to reduce the losses associated with bidirectional energy flow. The expression to calculate TAP with a nonideal PTO is modified by the mechanical-to-electrical efficiency and the ratio of the PTO spring and damping coefficients. The PTO spring and damping coefficients were separated in the expression, allowing for limits to be set on the PTO coefficients to ensure net power generation.

Emulation and Control Methods for Direct Drive Linear Wave Energy Converters

2013 ◽  
Vol 9 (2) ◽  
pp. 790-798 ◽  
Author(s):  
Zanxiang Nie ◽  
Xi Xiao ◽  
Richard McMahon ◽  
Peter Clifton ◽  
Yunxiang Wu ◽  
...  
Keyword(s):  
Wave Energy ◽  
Linear Wave ◽  
Control Methods ◽  
Direct Drive ◽  
Wave Energy Converters ◽  
And Control ◽  
Energy Converters

An Efficient Convex Formulation for Model-Predictive Control on Wave-Energy Converters

2017 ◽  
Author(s):  
Qian Zhong ◽  
Ronald W. Yeung
Keyword(s):  
Model Predictive Control ◽  
Predictive Control ◽  
Wave Energy ◽  
Optimization Problem ◽  
Reactive Power ◽  
Tuning Parameter ◽  
Primary Concern ◽  
Penalty Term ◽  
Wave Energy Converters ◽  
Energy Converters

Model-Predictive Control (MPC) has shown its strong potential in maximizing energy extraction for Wave-Energy Converters (WECs) while handling hard constraints. As MPC can solve the optimization problem on-line, it can better account for state changes and reject disturbances from the harsh sea environment. Interests have arisen in applying MPC to an array of WECs, since researchers found that multiple small-size WECs are more economically viable than a single large-size WEC. However, the computational demand is known to be a primary concern for applying MPC in real-time, which can determine the feasibility of such a controller, particularly when it comes to controlling an array of absorbers. In this paper, we construct a cost function and cast the problem into a Quadratic Programming (QP) with the machinery force being the “optimizer,” for which the convexity can be guaranteed by introducing a penalty term on the slew rate of the machinery force. The optimization problem can then be solved efficiently, and a feasible solution will be assured as the global optima. Constraints on the motion of the WEC and the machinery force will be taken into account. The current MPC will be compared to others existing in literature, including a nonlinear MPC [1] which has been applied in wave-tank tests. The effects of constraints on the control law and the absorbed power are investigated. Performances of the WEC are shown for both regular and irregular wave conditions. The current MPC is found to have good energy-capture capability and is able to broaden the band-width for capturing wave energy. The reactive power required by the PTO system is presented. The additional penalty term provides a tuning parameter, of which the effects on the MPC performance and the reactive power requirement are discussed.

Genetic Optimization of Shape and Control of Non-Linear Wave Energy Converters

2020 ◽  
Author(s):  
Jiajun Song ◽  
Ossama Abdelkhalik ◽  
Shangyan Zou
Keyword(s):  
Wave Energy ◽  
Time Domain ◽  
Optimization Approach ◽  
Linear Wave ◽  
Variable Size ◽  
Wave Energy Converters ◽  
Hydrostatic Force ◽  
Non Linear ◽  
The Time Domain ◽  
Energy Converters

Abstract This paper presents an optimization approach to design ax-isymmetric wave energy converters (WECs) based on a nonlinear hydrodynamic model. This paper shows optimal nonlinear shapes of buoy can be generated by combing basic shapes in an optimal sense. The time domain non-linear Froude-Krylov force can be computed for a complex buoy shape, by adopting analytical formulas of its basic shape components. The time domain Forude-Krylov force is decomposed into its dynamic and static components, and then contribute to the calculation of the excitation force and the hydrostatic force. A non-linear control is assumed in the form of the combination of linear and nonlinear damping terms. A variable size genetic algorithm (GA) optimization tool is developed to search for the optimal buoy shape along with the optimal control coefficients simultaneously. Chromosome of the GA tool is designed to improve computational efficiency and to leverage variable size genes to search for the optimal non-linear buoy shape. Different criteria of wave energy conversion can be implemented by the variable size GA tool. Simulation results presented in this paper show that it is possible to find non-linear buoy shapes and non-linear controllers that take advantage of non-linear hydrodynamics to improve energy harvesting efficiency with out adding reactive terms to the system.

A Comparison of Selected Strategies for Adaptive Control of Wave Energy Converters

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Jørgen Hals ◽  
Johannes Falnes ◽  
Torgeir Moan
Keyword(s):  
Wave Energy ◽  
Reactive Power ◽  
Average Power ◽  
Volume Ratio ◽  
External Input ◽  
Irregular Waves ◽  
Optimal Velocity ◽  
Wave Energy Converters ◽  
Absorbed Power ◽  
Energy Converters

Wave-energy converters of the point-absorbing type (i.e., having small extension compared with the wavelength) are promising for achieving cost reductions and design improvements because of a high power-to-volume ratio and better possibilities for mass production of components and devices as compared with larger converter units. However, their frequency response tends to be narrow banded, which means that the performance in real seas (irregular waves) will be poor unless their motion is actively controlled. Only then the invested equipment can be fully exploited, bringing down the overall energy cost. In this work various control methods for point-absorbing devices are reviewed, and a representative selection of methods is investigated by numerical simulation in irregular waves, based on an idealized example of a heaving semisubmerged sphere. Methods include velocity-proportional control, approximate complex conjugated control, approximate optimal velocity tracking, phase control by latching and clutching, and model-predictive control, all assuming a wave pressure measurement as the only external input to the controller. The methods are applied for a single-degree-of-freedom heaving buoy. Suggestions are given on how to implement the controllers, including how to tune control parameters and handle amplitude constraints. Based on simulation results, comparisons are made on absorbed power, reactive power flow, peak-to-average power ratios, and implementation complexity. Identified strengths and weaknesses of each method are highlighted and explored. It is found that overall improvements in average absorbed power of about 100–330% are achieved for the investigated controllers as compared with a control strategy with velocity-proportional machinery force. One interesting finding is the low peak-to-average ratios resulting from clutching control for wave periods about 1.5 times the resonance period and above.

scholarly journals Designing and Testing Composite Energy Storage Systems for Regulating the Outputs of Linear Wave Energy Converters

Energies ◽  
2017 ◽  
Vol 10 (1) ◽  
pp. 114 ◽  
Author(s):  
Zanxiang Nie ◽  
Xi Xiao ◽  
Pritesh Hiralal ◽  
Xuanrui Huang ◽  
Richard McMahon ◽  
...  
Keyword(s):  
Energy Storage ◽  
Wave Energy ◽  
Storage Systems ◽  
Linear Wave ◽  
Energy Storage Systems ◽  
Wave Energy Converters ◽  
Composite Energy ◽  
Energy Converters

scholarly journals A Coupled Methodology for Wave-Body Interactions at the Scale of a Farm of Wave Energy Converters Including Irregular Bathymetry

2014 ◽  
Author(s):  
François Charrayre ◽  
Christophe Peyrard ◽  
Michel Benoit ◽  
Aurélien Babarit
Keyword(s):  
Wave Energy ◽  
Diffraction Problem ◽  
Wave Theory ◽  
Field Approximation ◽  
Coupling Scheme ◽  
Linear Wave ◽  
Wave Energy Converters ◽  
Mild Slope Equation ◽  
Wave Farm ◽  
Energy Converters

Knowledge of the wave perturbation caused by an array of Wave Energy Converters (WEC) is of great concern, in particular for estimating the interaction effects between the various WECs and determining the modification of the wave field at the scale of the array, as well as possible influence on the hydrodynamic conditions in the surroundings. A better knowledge of these interactions will also allow a more efficient layout for future WEC farms. The present work focuses on the interactions of waves with several WECs in an array. Within linear wave theory and in frequency domain, we propose a methodology based on the use of a BEM (Boundary Element Method) model (namely Aquaplus) to solve the radiation-diffraction problem locally around each WEC, and to combine it with a model based on the mild slope equation at the scale of the array. The latter model (ARTEMIS software) solves the Berkhoff’s equation in 2DH domains (2 dimensional code with a z-dependence), considering irregular bathymetries. In fact, the Kochin function (a far field approximation) is used to propagate the perturbations computed by Aquaplus into Artemis, which is well adapted for a circular wave representing the perturbation of an oscillating body. This approximation implies that the method is only suitable for well separated devices. A main advantage of this coupling technique is that Artemis can deal with variable bathymetry. It is important when the wave farm is in shallow water or in nearshore areas. The methodology used for coupling the two models, with the underlying assumptions is detailed first. Validations test-cases are then carried out with simple bodies (namely heaving vertical cylinders) to assess the accuracy and efficiency of the coupling scheme. These tests also allow to analyze and to quantify the magnitude of the interactions between the WECs inside the array.

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