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Computationally fast and accurate mathematical models are essential for effective design, optimization, and control of wave energy converters. However, the energy-maximising control strategy, essential for reaching economic viability, inevitably leads to the violation of linearising assumptions, so the common linear models become unreliable and potentially unrealistic. Partially nonlinear models based on the computation of Froude–Krylov forces with respect to the instantaneous wetted surface are promising and popular alternatives, but they are still too slow when floaters of arbitrary complexity are considered; in fact, mesh-based spatial discretisation, required by such geometries, becomes the computational bottle-neck, leading to simulations 2 orders of magnitude slower than real-time, unaffordable for extensive iterative optimizations. This paper proposes an alternative analytical approach for the subset of prismatic floating platforms, common in the wave energy field, ensuring computations 2 orders of magnitude faster than real-time, hence 4 orders of magnitude faster than state-of-the-art mesh-based approaches. The nonlinear Froude–Krylov model is used to investigate the nonlinear hydrodynamics of the floater of a pitching wave energy converter, extracting energy either from pitch or from an inertially coupled internal degree of freedom, especially highlighting the impact of state constraints, controlled/uncontrolled conditions, and impact on control parameters’ optimization, sensitivity and effectiveness.

In the field of renewable technologies, the possibility to obtain energy exploiting seas and oceans’ wave motion has been known for a long time. Devices that transform wave energy into electric energy exploiting wave motion are called Wave Energy Converters (WEC). Following the design studies carried out in recent years, the research now proceeds towards the development of useful processes for the optimization of these devices. In this work we develop a preliminary robust optimal design process for the WEC system devices, in order to increase their reliability and robustness. Robust optimal design is a probabilistic optimization method for realistic optimization problems, in which, the uncertainty that occurs between real-world implementations and their ideal project value is taken into account. This method studies these parameters and finds suitable solutions to avoid unsatisfactory system performances and designs which can compromise their performances. Therefore, the process final purpose is to obtain a robust optimum instead of a global optimum. In this work, we developed the robust design optimization strategy for the design of a pitching wave energy converter, able to minimize its Levelized Cost of Energy (LCoE). This is done exploiting information given by two selected robustness indexes.

Numerical models are essential in all the development stages of a Wave Energy Converter. The results accuracy, the capacity to model the (main) WEC non-linearities and the computational burden associated to a numerical simulation make up the focus of many academic researchers. This paper pursues the development of a spectral-domain model of a gyroscopic wave energy converter, called ISWEC, equipped with a hydraulic PTO system. Due to its ability to model the ISWEC non-linearities and the low computational time required for a single wave simulation, the spectral-domain model represents a valid solution to perform the design of the ISWEC system, at least to accomplish its first draft in which million of single wave simulation are required. The major outcomes of this work are the detailed derivation of the spectral-domain model together with a first evaluation of the model accuracy and computational effort required.

Wave energy converter (WEC) optimization often underlines incremental and iterative approaches that result in suboptimal solutions, since all the elements that concur with a techno-economical evaluation are optimized separately due to computation constraints. A design process should rely on precise WEC models to ensure high result accuracy while minimizing the computational demand. These conflicting objectives can be addressed with non-linear time-domain models, known to be numerically accurate, and frequency-domain models due to their high computational efficiency. This work pursues the development of an all-encompassing optimization tool for a gyroscopic-type WEC called ISWEC that applies a new modelling technique named spectral-domain technique as a substitution to the complex time-domain model previously employed. In particular, the spectral-domain technique provides accurate and fast performance predictions of the ISWEC system and offers the possibility to model a hydraulic power take-off, not representable in the frequency domain. The article illustrates techno-economic trends associated with an early-stage design of the ISWEC in high-energy sea-sites, where the low-speed and high-torque profiles call for the use of hydraulic transmissions as opposed to the old electro-mechanical transmissions. The design tool proposed could facilitate the development of WEC technologies via efficient and accurate power assessment and via the possibility of carrying out advanced techno-economic optimisation that goes beyond linear models.

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.

In this paper we compare the heave, surge, and pitch dynamics of a submerged cylindrical point absorber, simulated using potential flow and fully-resolved computational fluid dynamics (CFD) models. The potential flow model is based on the time-domain Cummins equation, whereas the CFD model uses the fictitious domain Brinkman penalization (FD/BP) technique. The submerged cylinder is tethered to the seabed using a power take-off (PTO) unit which restrains the heave, surge, and pitch motions of the converter, and absorbs energy from all three modes. It is demonstrated that the potential theory over-predicts the amplitudes of heave and surge motions, whereas it results in an insignificant pitch for a fully-submerged axisymmetric converter. It also under-estimates the slow drift of the buoy, which the CFD model is able to capture reliably. Further, we use fully-resolved CFD simulations to study the performance of a three degrees of freedom (DOF) cylindrical buoy under varying PTO coefficients, mass density of the buoy, and incoming wave heights. It is demonstrated that the PTO coefficients predicted by the linear potential theory are sub-optimal for waves of moderate and high steepness. The wave absorption efficiency improves significantly when higher than the predicted value of the PTO damping is selected. Simulations with different mass densities of the buoy show that converters with low mass densities have an increased tension in their PTO and mooring lines. Moreover, the mass density also influences the range of resonance periods of the device. Finally, simulations with different wave heights show that at higher heights, the wave absorption efficiency of the converter decreases and a large portion of available wave power remains unabsorbed., Final published version

Investigating optimal control algorithms is a continuing concern within the Wave Energy field. A considerable amount of literature has been published on optimal control architectures applied to Wave Energy Converter (WEC) devices. However, most of them requires the knowledge of the wave excitation forces acting on the WEC body. In practice such forces are unknown and an estimate must be used. In this work a methodology to estimate the wave excitation forces of a non-linear WEC along with the achievable accuracy, is discussed. A feedforward Neural Network (NN) is applied to address the estimation problem. Such a method aims to map the WEC dynamics to the wave excitation forces by training the network through a supervised learning algorithm. The most challenging aspects of these techniques are the ability of the network to estimate data not considered in the training process and their accuracy in presence of model uncertanities. Numerical simulations under different irregular sea conditions demonstrate accurate estimation results of the NN approach as well as a small sensitivity to changes in the plant parameters relative to the case study presented.

During the last years, considerable progress has been reached in energy research field focused on the renewable energy extraction technologies. In particular wave energy is one of the most important branches. Among the possibility, the Inertial Sea Wave Energy Converter (ISWEC) is one of the most promising technology. This work was divided in two parts: firstly, the ISWEC model was created in order to predict the behavior of the system with accuracy to assure the correct functionality of the plant; then ISWEC model was applied to develop the Model Predictive control algorithm (MPC). All the work was developed for a three degrees of freedom system, considering the correlation between the horizontal movement, the vertical movement and the rotation, called surge, heave and pitch respectively. This correlation was important to improve the power extraction. The aim of this work is to design a controller that allow the automatic set the control value with the aim to extract the maximum power without an external prediction of the wave forces and regarding the input constraints due to components mechanical limits.

We introduce and discuss the principles of a new technology to increase the efficiency of oscillating wave energy converters: the Pitch Resonance Tuning Tanks (PRTT). This new technology is based on purposely sized U-tanks of naval derivation. The novelty of the proposed solution is the integration of the water U-shaped tanks on pitching/rocking Wave Energy Converter in order to tune the pitch resonance frequency as a function of the prevalent incoming wave period, hence increasing the energy harvesting efficiency. We demonstrate the capability of the proposed solution, in a case study, where the PRTT technology is integrated in the IOwec (gyroscopic PTO) pitching device. A numerical time domain wave-to-PTO model is developed and used to evaluate the energy performance enhancement of the integrated system with and without the PRTT technology.

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.

The wave energy sector is experiencing lively years of conceptual innovation and technological advances. Among the great variety of candidates, only a few are going to be able to reach maturity and, eventually, industrial feasibility and competitiveness. The essential requisite for success is the continuous innovation in response to the incremental experience gained during the design and prototyping stages. In particular, the ability to generate detailed mathematical models, representative of every phenomenon involved in the system, is crucial for informing the design and control stages, allowing to maximize productivity while minimizing costs, and inspiring technological breakthrough and innovation. This papers considers the case of the ISWEC (Inertial Sea Wave Energy Converter), where a technological leap is tightly linked with the modelling of aerodynamic losses around its spinning flywheel, the core of the energy conversion chain. Two mathematical models of increasing complexity are considered, one semi-empiric and one based on computational fluid dynamics, which are successfully validated against experimental data. Such models are used to quantify the benefits of a technological innovation consisting of enclosing the flywheel in a sealed container, allowing pressure regulation to reduce aerodynamic friction. Compared to the free configuration, power losses with the enclosed configuration are about half already at atmospheric pressure, and about one third at half the atmospheric pressure.

This paper presents a method to estimate the sea state PSD (Power Spectral Density) of the current wave climate, by using the measured floater motion and the body hydrodynamic response. The knowledge of PSD and the sea state synthetic parameters derivable from the PSD, such as the Significant Wave Height and the Energy Period, is fundamental for the navigation and operation in naval field and also for the control strategies of the Wave Energy Converters (WEC). The ISWEC (Inertial Sea Wave Energy Converter) is used as case study for the validation of the sea state estimation method. ISWEC is a floating device using the inertial effects of a gyroscopic system to convert a floater motion into electric energy. Sea state parameters are used in the control of the device to tune gyroscope speed and the generator torque law to achieve maximum power absorption. The heave measurements are used to estimate the PSD of the incoming wave and it is compared with the wave PSD measured by a wave measurement system. The method is studied and validated for three different sea state cases. At this stage the method presents satisfying results, with an accuracy under the 10% of the estimated parameters. Such accuracy is comparable with the short term (1-3h) wave forecast produced by ECMWF.

Friction is a complicated phenomenon that plays a central role in a wide variety of physical systems. An accurate modeling of the friction forces is required in the model-based design approach, especially when the efficiency optimization and system controllability are the core of the design. In this work, a gyroscopic unit is considered as case study: the flywheel rotation is affected by different friction sources that needs to be compensated by the flywheel motor. An accurate modeling of the dissipations can be useful for the system efficiency optimization. According to the inertial sea wave energy converter (ISWEC) gyroscope layout, friction forces are modeled and their dependency with respect to the various physical quantities involved is examined. The mathematical model of friction forces is validated against the experimental data acquired during the laboratory testing of the ISWEC gyroscope. Moreover, in the wave energy field, it is common to work with scale prototypes during the full-scale device development. For this reason, the scale effect on dissipations has been correlated based on the Froude scaling law, which is commonly used for wave energy converter scaling. Moreover, a mixed Froude–Reynolds scaling law is taken into account, in order to maintain the scale of the fluid-dynamic losses due to flywheel rotation. The analytical study is accompanied by a series of simulations based on the properties of the ISWEC full-scale gyroscope.