Design, validation and application of wave-to-wire models for heaving point absorber wave energy converters

Ocean waves represent an untapped source of renewable energy which can significantly contribute to the energy transition towards a sustainable energy mix. Despite the significant potential of this energy source and the multiple solutions suggested for the extraction of energy from ocean waves, some of which have demonstrated to be technically viable, no commercial wave energy farm has yet been connected to the electricity grid. This means that none of the technologies suggested in the literature has achieved economic viability. In order to make wave energy converters economically viable, it is essential to accurately understand and evaluate the holistic behaviour and performance of wave energy converters, including all the different conversion stages from ocean waves to the electricity grid. This can be achieved through wave tank or open ocean testing campaigns, which are extremely expensive and, thus, can critically determine the financial sustainability of the developing organisation, due to the risk of such large investments. Therefore, precise mathematical models that consider all the important dynamics, losses and constraints of the different conversion stages (including wave-structure hydrodynamic interaction and power take-off system), known as wave-to-wire models, are crucial in the development of successful wave energy converters. Hence, a comprehensive literature review of the different mathematical approaches suggested for modelling the different conversion stages and existing wave-to-wire models is presented, defining the foundations of parsimonious wave-to-wire models and their potential applications. As opposed to other offshore applications, wave energy converters need to exaggerate their motion to maximise energy absorption from ocean waves, which breaks the assumption of small body motion upon which linear models are based. An extensive investigation on the suitability of linear models and the relevance of different nonlinear effects is carried out, where control conditions are shown to play an important role. Hence, a computationally efficient mathematical model that incorporates nonlinear Froude-Krylov forces and viscous effects is presented. In the case of the power take-off system, mathematical models for different hydraulic transmission system configurations and electric generator topologies are presented, where the main losses are included using specific loss models with parameters identified via manufacturers’ data. In order to gain confidence in the mathematical models, the models corresponding to the different conversion stages are validated separately against either high-fidelity well-established software or experimental results, showing very good agreement. The main objective of this thesis is the development of a comprehensive wave-to-wire model. This comprehensive wave-to-wire model is created by adequately combining the subsystems corresponding to the different components or conversion stages. However, time-step requirements vary significantly depending on the dynamics included in each subsystem. Hence, if the time-step required for capturing the fastest dynamics is used in all the subsystems, unnecessary computation is performed in the subsystems with slower dynamics. Therefore, a multi-rate time-integration scheme is implemented, meaning that each subsystem uses the sample period required to adequately capture the dynamics of the components included in that conversion stage, which significantly reduces the overall computational requirements. In addition, the relevance of using a high-fidelity comprehensive wave-to-wire model in accurately designing wave energy converters and assessing their capabilities is demonstrated. For example, energy maximising controllers based on excessively simplified mathematical models result in dramatic consequences, such as negative average generated power or situations where the device remains stuck at one of the end-stops of the power take-off system. Despite the reasonably high-fidelity of the results provided by this comprehensive wave-towire model, some applications require the highest possible fidelity level and have no limitation with respect to computational cost. Hence, the simulation platform HiFiWEC, which couples a numerical wave tank based on computational fluid dynamics to the high-fidelity power take-off model, is created. In contrast, low computational cost is the main requirement for other applications and, thus, a systematic complexity reduction approach is suggested in this thesis, significantly reducing the computational cost of the HiFiWEC platform, while retaining the adequate fidelity level for each application. Due to the relevance of the nonlinearity degree when evaluating the complexity of a mathematical model, two nonlinearity measures to quantify this nonlinearity degree are defined. Hence, wave-to-wire models specifically created for each application are generated via the systematic complexity reduction approach, which provide the adequate trade-off between computational cost and fidelity level required for each application

Improving Computational Efficiency in WEC Design: Spectral-Domain Modelling in Techno-Economic Optimization

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

EXPERIMENTAL EVALUATION AND SIMULATION OF TORQUE TRANSMISSIBILITY FREQUENCY RESPONSE FUNCTIONS OF VIBRATION ISOLATORS AND ABSORBERS FOR DRIVETRAIN APPLICATIONS

Four studies involving torsional vibration isolation performance of automotive drivetrain components, make up this dissertation. One study features a prototype planetary torsional vibration absorber, a unique device that targets low frequency torsion modes in automotive drivetrains. Two studies feature experiments on several torque converters, clutch locked and open, to validate models of the hardware. The last study details experiments on a centrifugal pendulum absorber in a torque converter, to characterize the viscous friction while submerged in automatic transmission fluid (ATF). The enclosed studies improve the state of the art of drivetrain vibration absorbers and isolators, by introducing a new vibration absorber concept and increasing understanding of the underlying physics of torque converters, lock-up clutch dampers, and centrifugal pendulum absorbers. The design and test of the planetary torsional vibration absorber concept demonstrated the utility of a gear reduction in increasing the apparent inertia of the absorber. By increasing its apparent inertia, the device successfully attenuated a ~20 Hz mode of vibration, and used less packaging volume and mass than a traditional torsional vibration absorber of equivalent performance. Various lockup clutch designs were characterized with torque transmissibility frequency response function (TTFRF) measurements while spinning at simulated vehicle operating conditions. This in situ testing lent itself useful in characterizing the speed dependent friction in a lockup clutch damper, while also confirming other damper parameters—like stiffness and damping. The torque converters were also tested in open mode (lockup clutch not engaged). The open mode testing revealed that the hydrodynamic torque converter transmits enough torsional vibration to excite the damper mode for the turbine damper architectures. The open clutch testing contributes a complete data set—encompassing a wide range of speed ratios—to verify torque converter models with. When comparing the test TTFRFs to model TTFRFs, a discrepancy in the damper mode’s natural frequency was revealed, and it was hypothesized that this error resulted from a reflected inertia effect of the ATF undergoing toroidal flow. The locked clutch testing provoked some questions about the centrifugal pendulum absorber (CPA)—a component of one of the tested torque converter clutch dampers. To validate an existing CPA model, and to characterize the equivalent viscous damping of the CPA mechanism, TTFRFs of custom made torque converters were measured. The custom hardware included: pinned damper (CPA active), pinned CPA (damper active), and pinned straight spring (CPA and arc spring active). The torques due to friction and viscous damping of the damper were effectively eliminated from the CPA, and the equivalent viscous damping of the CPA characterized

Modelling and control for the oscillating water column

xxii, 219 p.Renewable energies are definitely part of the equation to limit our dependence to fossil fuels. Within this sector, ocean energies, and especially wave energy, represent a huge potential but is still a growing area. And like any new field, it is synonym to a high cost of energy production. Increasing the energy production, while keeping the costs controlled, has the leverage to drop down the cost of energy produced by wave energy converters (WECs). The main objective of this thesis is to make progress on the understanding of the effect of advanced control algorithms in the improvement of the power produced by wave energy devices. For that purpose, several control strategies are designed, compared, and assessed. To support this analysis, numerical models representing the overall energy conversion chain of WECs are developed. The Basque Country in Spain is fortunate enough to host the development and operation of two devices based on the Oscillating Water Column (OWC) principle. One is the Mutriku OWC plant, and the second is the floating buoy Marmok-A from Oceantec/IDOM, both devices were made available for sea trials. Several control algorithms were then implemented to be tested in real environments. Among them was a non-linear predictive control algorithm. Its test in real conditions represent a world first in the area of control for OWC systems, and maybe for the whole WEC sector if comparing with publicly available information. An outstanding results of the thesis is undoubtedly to move forward the predictive control algorithm from TRL3 to TRL6 after successful implementation and operation in both devices under real environmental conditions

[Report of] Specialist Committee V.4: ocean, wind and wave energy utilization

The committee's mandate was :Concern for structural design of ocean energy utilization devices, such as offshore wind turbines, support structures and fixed or floating wave and tidal energy converters. Attention shall be given to the interaction between the load and the structural response and shall include due consideration of the stochastic nature of the waves, current and wind

A harmonic balance framework for the numerical simulation of non-linear wave energy converter models in random seas

Numerical simulation is essential, to assist in the development of wave energy technology. In particular, tasks such as power assessment, optimisation and structural design require a large number of numerical simulations to calculate the wave energy converter (WEC) outputs of interest, over a variety of wave conditions or physical parameters. Such challenges involve a sound understanding of the statistical properties of ocean waves, which constitute the forcing inputs to the wave energy device, and computationally efficient numerical techniques for the speedy calculation of WEC outputs. This thesis studies the statistical characterisation, and numerical generation, of ocean waves, and proposes a novel technique for the numerical simulation of non-linear WEC models. The theoretical foundations, the range of validity, and the importance of the statistical representation of ocean waves are first examined. Under relatively mild assumptions, ocean waves can be best described as a stationary Gaussian process, which is entirely characterised by its spectral density function (SDF). Various wave superposition techniques are discussed and rigorously compared, for the numerical generation of Gaussian wave elevation time series from a given SDF. In particular, the harmonic random amplitude (HRA) approach can simulate the target statistical properties with perfect realism. In contrast, the harmonic deterministic amplitude (HDA) approach is statistically inconsistent (because the generated time-series are non-Gaussian, and under-represent the short-term statistical variability of real ocean waves), but can be advantageous in the context of WEC simulations since, if it can be verified that HDA results are unbiased, the HDA method requires a smaller number of random realisations than the HRA method, to obtain accurate WEC power estimates. When either HDA or HRA are used for the generation of wave inputs, the forcing terms of WEC mathematical models are periodic. Relying on a Fourier representation of the system inputs and variables, the harmonic balance (HB) method, which is a special case of spectral methods, is a suitable mathematical technique to numerically calculate the steady-state response of a non-linear system, under a periodic input. The applicability of the method to WEC simulation is demonstrated for those WEC models which are described by means of a non-linear integro-differential equation. In the proposed simulation framework, the WEC output, in a given sea state, is assessed by means of many, relatively short, simulations, each of which is efficiently solved using the HB method. A range of four case studies is considered, comprising a flap-type WEC, a spherical heaving point-absorber, an array of four cylindrical heaving point-absorbers, and a pitching device. For each case, it is shown how the HB settings (simulation duration and cut-off frequency) can be calibrated. The accuracy of the HB method is assessed through a comparison with a second-order Runge-Kutta (RK2) time-domain integration scheme, with various time steps. RK2 results converge to the HB solution, as the RK2 time step tends to zero. Furthermore, in a Matlab implementation, the HB method is between one and three orders of magnitude faster than the RK2 method, depending on the RK2 time step, and on the method chosen for the calculation of the radiation memory terms in RK2 simulations. The HB formalism also provides an interesting framework, for studying the sensitivity of the WEC dynamics to system parameter variations, which can be utilised within a gradient-based parametric optimisation algorithm. An example of WEC gradientbased parametric optimisation, carried out within the HB framework, is provided

Energy harvesting for marine based sensors

This work examines powering marine based sensors (MBSs) by harvesting energy from their local environment. MBSs intrinsically operate in remote locations, traditionally requiring expensive maintenance expeditions for battery replacement and data download. Nowadays, modern wireless communication allows real-time data access, but adds a significant energy drain, necessitating frequent battery replacement. Harvesting renewable energy to recharge the MBSs battery, introduces the possibility of autonomous MBS operation, reducing maintenance costs and increasing their applicability. The thesis seeks to answer if an unobtrusive energy harvesting device can be incorporated into the MBS deployment to generate 1 Watt of average power. Two candidate renewable energy resources are identified for investigation, ocean waves and the thermal gradient across the air/water interface. Wave energy conversion has drawn considerable research in recent years, due to the large consistent energy flux of ocean waves compared to other conventional energy sources such as solar or wind, but focussing on large scale systems permanently deployed at sites targeted for their favourable wave climates. Although a small amount of research exists on using wave energy for distributed power generation, the device sizes and power outputs of these systems are still one to two orders of magnitude larger than that targeted in this thesis. The present work aims for an unobtrusive device that is easily deployable/retrievable with a mass less than 50kg and which can function at any deployment location regardless of the local wave climate. Additionally, this research differs from previous work, by also seeking to minimise the wave induced pitch motion of the MBS buoy, which negatively affects the data transmission of the MBS due to tilting and misalignment of the RF antenna. Thermal energy harvesting has previously been investigated for terrestrial based sensors, utilising the temperature difference between the soil and ambient air. In this thesis, the temperature difference between the water and ambient air is utilised, to present the first investigation of this thermal energy harvesting concept in the marine environment. A prototype wave energy converter (WEC) was proposed, consisting of a heaving cylindrical buoy with an internal permanent magnet linear generator. A mathematical model of the prototype WEC is derived by coupling a hydrodynamic model for the motion of the buoy with a vibration energy harvester model for the generator. The wave energy resource is assessed, using established mathematical descriptions of ocean wave spectra and by analysing measured wave data from the coast of Queensland, resulting in characteristic wave spectra that are input to the mathematical model of the WEC. The parameters of the WEC system are optimised, to maximise the power output while minimising the pitch motion. A prototype thermal energy harvesting device is proposed, consisting of a thermoelectric device sandwiched between airside and waterside heat exchangers. A mathematical model is derived to assess the power output of the thermal energy harvester using different environmental datasets as input. A physical prototype is built and a number of experiments performed to assess its performance. The results indicate that the prototype WEC should target the high frequency tail of ocean wave spectra, diverging from traditional philosophy of larger scale WECs which target the peak frequency of the input wave spectrum. The analysis showed that the prototype WEC was unable to provide the required power output whilst remaining below 100kg and obeying a 40 degrees pitch angle constraint to ensure robust data transmission. However, a proposed modification to the WECs cylindrical geometry, to improve its hydrodynamic coupling to the input waves, was shown to enable the WEC to provide the required 1W output power whilst obeying the pitch constraints and having a mass below 50kg. The thermal energy harvester results reveal that the thermal gradient across the air/water interface alone is not a suitable energy resource, requiring a device with a cross-sectional area in excess of 100m² to power a MBS. However, including a solar thermal energy collector to increase the airside temperature, greatly improves the performance and enables a thermal energy harvester with a cross-sectional area on the order of 1m² to provide 1W of output power. The findings in this thesis suggest that a well hydrodynamically designed buoy can provide two major benefits for a MBS deployment: enabling efficient wave energy absorption by the MBS buoy, and minimising the wave induced pitch motion which negatively affects the data transmission