Penalba, Markel
(2018)
Design, validation and application of
wavetowire models for heaving point absorber
wave energy converters.
PhD thesis, National University of Ireland Maynooth.
Abstract
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 wavestructure
hydrodynamic interaction and power takeoff system), known as wavetowire 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 wavetowire models is presented, defining the foundations of parsimonious
wavetowire 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 FroudeKrylov forces and viscous effects is presented. In the case
of the power takeoff 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 manufacturersâ€™ data. In order to gain
confidence in the mathematical models, the models corresponding to the different conversion stages
are validated separately against either highfidelity wellestablished software or experimental
results, showing very good agreement.
The main objective of this thesis is the development of a comprehensive wavetowire model.
This comprehensive wavetowire model is created by adequately combining the subsystems corresponding
to the different components or conversion stages. However, timestep requirements
vary significantly depending on the dynamics included in each subsystem. Hence, if the timestep
required for capturing the fastest dynamics is used in all the subsystems, unnecessary computation
is performed in the subsystems with slower dynamics. Therefore, a multirate timeintegration
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 highfidelity
comprehensive wavetowire 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 endstops of the power
takeoff system.
Despite the reasonably highfidelity of the results provided by this comprehensive wavetowire
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 highfidelity power takeoff
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, wavetowire models specifically created for each application are generated
via the systematic complexity reduction approach, which provide the adequate tradeoff
between computational cost and fidelity level required for each application.
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