Optimization and Energy Maximizing Control Systems for Wave Energy Converters

A special issue of Journal of Marine Science and Engineering (ISSN 2077-1312). This special issue belongs to the section "Ocean Engineering".

Deadline for manuscript submissions: closed (14 November 2021) | Viewed by 35831

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Guest Editor
Marine Offshore Renewable Energy Lab (MOREnergy Lab), Department of Mechanical and Aerospace Engineering, Politecnico di Torino, 10129 Turin, Italy
Interests: marine energy; nonlinear hydrodynamics; wave–body interaction; energy-maximizing control systems; mooring systems; computational fluid dynamics; nonlinear dynamics; numerical modelling; optimization algorithms; numerical computing
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Guest Editor
Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Turin, Italy
Interests: marine energy; energy maximizing control systems; mooring systems; array optimization; resource assessment; stochastic analysis; numerical modelling; optimization algorithms; experimental tank testing; mechatronic systems

Special Issue Information

Dear Colleagues,

In recent years we are witnessing a great interest and activity in the field of wave energy converters (WECs) development, striving for competitiveness and economic viability via increasing power conversion while decreasing costs and ensuring survivability. In the community the consensus is that both optimization and control are sine qua non conditions for success, but many challenges, peculiar to WECs, need to be addressed. Unlike other traditional control applications, the control objective for WECs is to exaggerate the motion, potentially inducing strong nonlinearities in the system and stressing the power-conversion chain and mechanical structure. Therefore, it is crucial to include techno-economical constraints in both the optimization and control objective functions. Furthermore, although often considered as consecutive independent phases, optimization and control are mutually dependent and, ideally, should be considered together.

We would like to invite papers on the topic of “Optimization and Energy Maximizing Control Systems for Wave Energy Converters”. This includes, but is not limited to, holistic optimization algorithm, specific challenges of the WEC application case (large motions, estimation, forecasting, power take-off), theoretical and numerical development and implementation of novel control strategies for WECs, evaluation of their performance through high-fidelity numerical models or experiment, importance and representation of nonlinearities in the controlled device.

Dr. Giuseppe Giorgi
Dr. Sergej Antonello Sirigu
Guest Editors

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Keywords

  • Wave energy
  • Optimization
  • Energy maximizing control
  • Nonlinear hydrodynamics
  • Power take-off
  • Estimation
  • Forecasting

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Published Papers (12 papers)

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Editorial

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4 pages, 179 KiB  
Editorial
Optimization and Energy Maximizing Control Systems for Wave Energy Converters
by Giuseppe Giorgi and Sergej Antonello Sirigu
J. Mar. Sci. Eng. 2021, 9(12), 1436; https://doi.org/10.3390/jmse9121436 - 15 Dec 2021
Cited by 1 | Viewed by 2029
Abstract
In recent years, we have been witnessing great interest and activity in the field of wave energy converters’ (WECs) development, striving for competitiveness and economic viability via increasing power conversion while decreasing costs and ensuring survivability [...] Full article

Research

Jump to: Editorial

16 pages, 3734 KiB  
Article
Sliding Mode Control of a Nonlinear Wave Energy Converter Model
by Tania Demonte Gonzalez, Gordon G. Parker, Enrico Anderlini and Wayne W. Weaver
J. Mar. Sci. Eng. 2021, 9(9), 951; https://doi.org/10.3390/jmse9090951 - 1 Sep 2021
Cited by 11 | Viewed by 3203
Abstract
The most accurate wave energy converter models for heaving point absorbers include nonlinearities, which increase as resonance is achieved to maximize the energy capture. Over the power production spectrum and within the physical limits of the devices, the efficiency of wave energy converters [...] Read more.
The most accurate wave energy converter models for heaving point absorbers include nonlinearities, which increase as resonance is achieved to maximize the energy capture. Over the power production spectrum and within the physical limits of the devices, the efficiency of wave energy converters can be enhanced by employing a control scheme that accounts for these nonlinearities. This paper proposes a sliding mode control for a heaving point absorber that includes the nonlinear effects of the dynamic and static Froude-Krylov forces. The sliding mode controller tracks a reference velocity that matches the phase of the excitation force to ensure higher energy absorption. This control algorithm is tested in regular linear waves and is compared to a complex-conjugate control and a nonlinear variation of the complex-conjugate control. The results show that the sliding mode control successfully tracks the reference and keeps the device displacement bounded while absorbing more energy than the other control strategies. Furthermore, due to the robustness of the control law, it can also accommodate disturbances and uncertainties in the dynamic model of the wave energy converter. Full article
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19 pages, 62076 KiB  
Article
Real-Time Nonlinear Model Predictive Controller for Multiple Degrees of Freedom Wave Energy Converters with Non-Ideal Power Take-Off
by Ali S. Haider, Ted K. A. Brekken and Alan McCall
J. Mar. Sci. Eng. 2021, 9(8), 890; https://doi.org/10.3390/jmse9080890 - 18 Aug 2021
Cited by 13 | Viewed by 2719
Abstract
An increase in wave energy converter (WEC) efficiency requires not only consideration of the nonlinear effects in the WEC dynamics and the power take-off (PTO) mechanisms, but also more integrated treatment of the whole system, i.e., the buoy dynamics, the PTO system, and [...] Read more.
An increase in wave energy converter (WEC) efficiency requires not only consideration of the nonlinear effects in the WEC dynamics and the power take-off (PTO) mechanisms, but also more integrated treatment of the whole system, i.e., the buoy dynamics, the PTO system, and the control strategy. It results in an optimization formulation that has a nonquadratic and nonstandard cost functional. This article presents the application of real-time nonlinear model predictive controller (NMPC) to two degrees of freedom point absorber type WEC with highly nonlinear PTO characteristics. The nonlinear effects, such as the fluid viscous drag, are also included in the plant dynamics. The controller is implemented on a real-time target machine, and the WEC device is emulated in real-time using the WECSIM toolbox. The results for the successful performance of the design are presented for irregular waves under linear and nonlinear hydrodynamic conditions. Full article
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22 pages, 43785 KiB  
Article
A Comparative Study of Model Predictive Control and Optimal Causal Control for Heaving Point Absorbers
by Mirko Previsic, Anantha Karthikeyan and Jeff Scruggs
J. Mar. Sci. Eng. 2021, 9(8), 805; https://doi.org/10.3390/jmse9080805 - 27 Jul 2021
Cited by 4 | Viewed by 1811
Abstract
Efforts by various researchers in recent years to design simple causal control laws that can be applied to WEC devices suggest that these controllers can yield similar levels of energy output as those of more complex non-causal controllers. However, most studies were established [...] Read more.
Efforts by various researchers in recent years to design simple causal control laws that can be applied to WEC devices suggest that these controllers can yield similar levels of energy output as those of more complex non-causal controllers. However, most studies were established without adequately considering device and power conversion system constraints which are relevant design drivers from a cost and economic point of view. It is therefore imperative to understand the benefits of MPC compared to causal control from a performance and constraint handling perspective. In this paper, we compare linear MPC to a casual controller that incorporates constraint handling to benchmark its performance on a one DoF heaving point absorber in a range of wave conditions. Our analysis demonstrates that MPC provides significant performance advantages compared to an optimized causal controller, particularly if significant constraints on device motion and/or forces are imposed. We further demonstrate that distinct control performance regions can be established that correlate well with classical point absorber and volumetric limits of the wave energy conversion device. Full article
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25 pages, 5660 KiB  
Article
The Influence of Sizing of Wave Energy Converters on the Techno-Economic Performance
by Jian Tan, Henk Polinder, Antonio Jarquin Laguna, Peter Wellens and Sape A. Miedema
J. Mar. Sci. Eng. 2021, 9(1), 52; https://doi.org/10.3390/jmse9010052 - 5 Jan 2021
Cited by 22 | Viewed by 3091
Abstract
Currently, the techno-economic performance of Wave Energy Converters (WECs) is not competitive with other renewable technologies. Size optimization could make a difference. However, the impact of sizing on the techno-economic performance of WECs still remains unclear, especially when sizing of the buoy and [...] Read more.
Currently, the techno-economic performance of Wave Energy Converters (WECs) is not competitive with other renewable technologies. Size optimization could make a difference. However, the impact of sizing on the techno-economic performance of WECs still remains unclear, especially when sizing of the buoy and Power Take-Off (PTO) are considered collectively. In this paper, an optimization method for the buoy and PTO sizing is proposed for a generic heaving point absorber to reduce the Levelized Cost Of Energy (LCOE). Frequency domain modeling is used to calculate the power absorption of WECs with different buoy and PTO sizes. Force constraints are used to represent the effects of PTO sizing on the absorbed power, in which the passive and reactive control strategy are considered, respectively. A preliminary economic model is established to calculate the cost of WECs. The proposed method is implemented for three realistic sea sites, and the dependence of the optimal size of WECs on wave resources and control strategies is analyzed. The results show that PTO sizing has a limited effect on the buoy size determination, while it can reduce the LCOE by 24% to 31%. Besides, the higher mean wave power density of wave resources does not necessarily correspond to the larger optimal buoy or PTO sizes, but it contributes to the lower LCOE. In addition, the optimal PTO force limit converges at around 0.4 to 0.5 times the maximum required PTO force for the corresponding sea sites. Compared with other methods, this proposed method shows a better potential in sizing and reducing LCOE. Full article
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15 pages, 1491 KiB  
Article
Spectral Control of Wave Energy Converters with Non-Ideal Power Take-off Systems
by Alexis Mérigaud and Paolino Tona
J. Mar. Sci. Eng. 2020, 8(11), 851; https://doi.org/10.3390/jmse8110851 - 28 Oct 2020
Cited by 8 | Viewed by 1628
Abstract
Spectral control is an accurate and computationally efficient approach to power-maximising control of wave energy converters (WECs). This work investigates spectral control calculations with explicit derivative computation, applied to WECs with non-ideal power take-off (PTO) systems characterised by an efficiency factor smaller than [...] Read more.
Spectral control is an accurate and computationally efficient approach to power-maximising control of wave energy converters (WECs). This work investigates spectral control calculations with explicit derivative computation, applied to WECs with non-ideal power take-off (PTO) systems characterised by an efficiency factor smaller than unity. To ensure the computational efficiency of the spectral control approach, it is proposed in this work to approximate the discontinuous efficiency function by means of a smooth function. A non-ideal efficiency function implies that the cost function is non-quadratic, which requires a slight generalisation of the derivative-based spectral control approach, initially introduced for quadratic cost functions. This generalisation is derived here in some detail given its practical interest. Two application case studies are considered: the Wavestar scale model, employed for the WEC control competition (WECCCOMP), and the 3rd reference model (RM3) two-body heaving point absorber. In both cases, with the approximate efficiency function, the spectral approach calculates WEC trajectory and control force solutions, for which the mean electrical power is shown to lie within a few percent of the true optimal electrical power. Regarding the effect of a non-ideal PTO efficiency upon achievable power production, and concerning heaving point-absorbers, the results obtained are significantly less pessimistic than those of previous studies: the power achieved lies within 80–95% of that obtained by simply applying the efficiency factor to the optimal power with ideal PTO. Full article
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16 pages, 985 KiB  
Article
Towards Real-Time Reinforcement Learning Control of a Wave Energy Converter
by Enrico Anderlini, Salman Husain, Gordon G. Parker, Mohammad Abusara and Giles Thomas
J. Mar. Sci. Eng. 2020, 8(11), 845; https://doi.org/10.3390/jmse8110845 - 28 Oct 2020
Cited by 35 | Viewed by 3940
Abstract
The levellised cost of energy of wave energy converters (WECs) is not competitive with fossil fuel-powered stations yet. To improve the feasibility of wave energy, it is necessary to develop effective control strategies that maximise energy absorption in mild sea states, whilst limiting [...] Read more.
The levellised cost of energy of wave energy converters (WECs) is not competitive with fossil fuel-powered stations yet. To improve the feasibility of wave energy, it is necessary to develop effective control strategies that maximise energy absorption in mild sea states, whilst limiting motions in high waves. Due to their model-based nature, state-of-the-art control schemes struggle to deal with model uncertainties, adapt to changes in the system dynamics with time, and provide real-time centralised control for large arrays of WECs. Here, an alternative solution is introduced to address these challenges, applying deep reinforcement learning (DRL) to the control of WECs for the first time. A DRL agent is initialised from data collected in multiple sea states under linear model predictive control in a linear simulation environment. The agent outperforms model predictive control for high wave heights and periods, but suffers close to the resonant period of the WEC. The computational cost at deployment time of DRL is also much lower by diverting the computational effort from deployment time to training. This provides confidence in the application of DRL to large arrays of WECs, enabling economies of scale. Additionally, model-free reinforcement learning can autonomously adapt to changes in the system dynamics, enabling fault-tolerant control. Full article
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30 pages, 3750 KiB  
Article
Real-Time Wave Excitation Forces Estimation: An Application on the ISWEC Device
by Mauro Bonfanti, Andrew Hillis, Sergej Antonello Sirigu, Panagiotis Dafnakis, Giovanni Bracco, Giuliana Mattiazzo and Andrew Plummer
J. Mar. Sci. Eng. 2020, 8(10), 825; https://doi.org/10.3390/jmse8100825 - 21 Oct 2020
Cited by 19 | Viewed by 4035
Abstract
Optimal control strategies represent a widespread solution to increase the extracted energy of a Wave Energy Converter (WEC). The aim is to bring the WEC into resonance enhancing the produced power without compromising its reliability and durability. Most of the control algorithms proposed [...] Read more.
Optimal control strategies represent a widespread solution to increase the extracted energy of a Wave Energy Converter (WEC). The aim is to bring the WEC into resonance enhancing the produced power without compromising its reliability and durability. Most of the control algorithms proposed in literature require for the knowledge of the Wave Excitation Force (WEF) generated from the incoming wave field. In practice, WEFs are unknown, and an estimate must be used. This paper investigates the WEF estimation of a non-linear WEC. A model-based and a model-free approach are proposed. First, a Kalman Filter (KF) is implemented considering the WEC linear model and the WEF modelled as an unknown state to be estimated. Second, a feedforward Neural Network (NN) is applied to map the WEC dynamics to the WEF by training the network through a supervised learning algorithm. Both methods are tested for a wide range of irregular sea-states showing promising results in terms of estimation accuracy. Sensitivity and robustness analyses are performed to investigate the estimation error in presence of un-modelled phenomena, model errors and measurement noise. Full article
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23 pages, 5194 KiB  
Article
A Real-Time Detection System for the Onset of Parametric Resonance in Wave Energy Converters
by Josh Davidson and Tamás Kalmár-Nagy
J. Mar. Sci. Eng. 2020, 8(10), 819; https://doi.org/10.3390/jmse8100819 - 20 Oct 2020
Cited by 9 | Viewed by 2405
Abstract
Parametric resonance is a dynamic instability due to the internal transfer of energy between degrees of freedom. Parametric resonance is known to cause large unstable pitch and/or roll motions in floating bodies, and has been observed in wave energy converters (WECs). The occurrence [...] Read more.
Parametric resonance is a dynamic instability due to the internal transfer of energy between degrees of freedom. Parametric resonance is known to cause large unstable pitch and/or roll motions in floating bodies, and has been observed in wave energy converters (WECs). The occurrence of parametric resonance can be highly detrimental to the performance of a WEC, since the energy in the primary mode of motion is parasitically transferred into other modes, reducing the available energy for conversion. In addition, the large unstable oscillations produce increased loading on the WEC structure and mooring system, accelerating fatigue and damage to the system. To remedy the negative effects of parametric resonance on WECs, control systems can be designed to mitigate the onset of parametric resonance. A key element of such a control system is a real-time detection system, which can provide an early warning of the likely occurrence of parametric resonance, enabling the control system sufficient time to respond and take action to avert the impending exponential increase in oscillation amplitude. This paper presents the first application of a real-time detection system for the onset of parametric resonance in WECs. The method is based on periodically assessing the stability of a mathematical model for the WEC dynamics, whose parameters are adapted online, via a recursive least squares algorithm, based on online measurements of the WEC motion. The performance of the detection system is demonstrated through a case study, considering a generic cylinder type spar-buoy, a representative of a heaving point absorber WEC, in both monochromatic and polychromatic sea states. The detection system achieved 95% accuracy across nearly 7000 sea states, producing 0.4% false negatives and 4.6% false positives. For the monochromatic waves more than 99% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude, whereas for the polychromatic waves 63% of the detections occurred while the pitch amplitude was less than 1/6 of its maximum amplitude and 91% while it was less than 1/3 of its maximum amplitude. Full article
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30 pages, 1125 KiB  
Article
Simple Controllers for Wave Energy Devices Compared
by Demián García-Violini, Nicolás Faedo, Fernando Jaramillo-Lopez and John V. Ringwood
J. Mar. Sci. Eng. 2020, 8(10), 793; https://doi.org/10.3390/jmse8100793 - 13 Oct 2020
Cited by 32 | Viewed by 2565
Abstract
The design of controllers for wave energy devices has evolved from early monochromatic impedance-matching methods to complex numerical algorithms that can handle panchromatic seas, constraints, and nonlinearity. However, the potential high performance of such numerical controller comes at a computational cost, with some [...] Read more.
The design of controllers for wave energy devices has evolved from early monochromatic impedance-matching methods to complex numerical algorithms that can handle panchromatic seas, constraints, and nonlinearity. However, the potential high performance of such numerical controller comes at a computational cost, with some algorithms struggling to implement in real-time, and issues surround convergence of numerical optimisers. Within the broader area of control engineering, practitioners have always displayed a fondness for simple and intuitive controllers, as evidenced by the continued popularity of the ubiquitous PID controller. Recently, a number of energy-maximising wave energy controllers have been developed based on relatively simple strategies, stemming from the fundamentals behind impedance-matching. This paper documents this set of (5) controllers, which have been developed over the period 2010–2020, and compares and contrasts their characteristics, in terms of energy-maximising performance, the handling of physical constraints, and computational complexity. The comparison is carried out both analytically and numerically, including a detailed case study, when considering a state-of-the-art CorPower-like device. Full article
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23 pages, 94365 KiB  
Article
Comparison of Wave Energy Park Layouts by Experimental and Numerical Methods
by Marianna Giassi, Jens Engström, Jan Isberg and Malin Göteman
J. Mar. Sci. Eng. 2020, 8(10), 750; https://doi.org/10.3390/jmse8100750 - 26 Sep 2020
Cited by 12 | Viewed by 2227
Abstract
An experimental campaign of arrays with direct-driven wave energy converters of point-absorbing type is presented. The arrays consist of six identical floats, moving in six degrees of freedom, and six rotating power take-off systems, based on the design developed at Uppsala University. The [...] Read more.
An experimental campaign of arrays with direct-driven wave energy converters of point-absorbing type is presented. The arrays consist of six identical floats, moving in six degrees of freedom, and six rotating power take-off systems, based on the design developed at Uppsala University. The goals of the work were to study and compare the performances of three different array layouts under several regular and irregular long-crested waves, and in addition, to determine whether the numerical predictions of the best performing array layouts were confirmed by experimental data. The simulations were executed with a frequency domain model restricted to heave, which is a computationally fast approach that was merged into a genetic algorithm optimization routine and used to find optimal array configurations. The results show that good agreement between experiments and simulations is achieved when the test conditions do not induce phenomena of parametric resonance, slack line and wave breaking. Specific non-linear dynamics or extensive sway motion are not captured by the used model, and in such cases the simulation predictions are not accurate, but can nevertheless be used to get an estimate of the power output. Full article
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30 pages, 3391 KiB  
Article
Techno-Economic Optimisation for a Wave Energy Converter via Genetic Algorithm
by Sergej Antonello Sirigu, Ludovico Foglietta, Giuseppe Giorgi, Mauro Bonfanti, Giulia Cervelli, Giovanni Bracco and Giuliana Mattiazzo
J. Mar. Sci. Eng. 2020, 8(7), 482; https://doi.org/10.3390/jmse8070482 - 30 Jun 2020
Cited by 59 | Viewed by 3896
Abstract
Although sea and ocean waves have been widely acknowledged to have the potential of providing sustainable and renewable energy, the emergence of a self-sufficient and mature industry is still lacking. An essential condition for reaching economic viability is to minimise the cost of [...] Read more.
Although sea and ocean waves have been widely acknowledged to have the potential of providing sustainable and renewable energy, the emergence of a self-sufficient and mature industry is still lacking. An essential condition for reaching economic viability is to minimise the cost of electricity, as opposed to simply maximising the converted energy at the early design stages. One of the tools empowering developers to follow such a virtuous design pathway is the techno-economic optimisation. The purpose of this paper is to perform a holistic optimisation of the PeWEC (pendulum wave energy converter), which is a pitching platform converting energy from the oscillation of a pendulum contained in a sealed hull. Optimised parameters comprise shape; dimensions; mass properties and ballast; power take-off control torque and constraints; number and characteristics of the pendulum; and other subcomponents. Cost functions are included and the objective function is the ratio between the delivered power and the capital expenditure. Due to its ability to effectively deal with a large multi-dimensional design space, a genetic algorithm is implemented, with a specific modification to handle unfeasible design candidate and improve convergence. Results show that the device minimising the cost of energy and the one maximising the capture width ratio are substantially different, so the economically-oriented metric should be preferred. Full article
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