51 research outputs found
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
Optimal trajectories, nonlinear models and constraints in wave energy device control
The optimal control problem for a generic, one-degree of freedom Wave Energy Converter (WEC) with dynamical nonlinearities is formulated in the frequency-domain. Previous research, concerning more specifically a heaving point-absorber with nonlinear restoring force, shows that the unconstrained optimal velocity trajectory is influenced neither by the linear inertial terms, nor by the linear or nonlinear static forces. Further to this result, in this paper, we examine the influence of velocity-dependent nonlinear forces on the optimal trajectory, as well as the effect of physical system constraints. In particular, we show that, under state constraints (e.g. position and velocity limitations), the optimal velocity trajectory remains uninfluenced by static forces; but this is no longer true for constraints involving the control force, such as force limitation and passivity constraints. In addition, unlike static terms and linear inertial terms, the velocity-dependent forces, such as viscous drag, significantly influence the optimal velocity trajectory, regardless of constraints, and must be carefully modelled at the control design stage. In any case, even when the optimal velocity trajectory is not affected by some of the forces considered, the optimal control force required to achieve it depends on all the model dynamics (inertial terms, velocity-dependent and static forces). Numerical simulations, in the specific case of a heaving point absorber, are used to validate and illustrate the theoretical results
A nonlinear extension for linear boundary element methods in wave energy device modelling
To date, mathematical models for wave energy devices typically
follow Cummins equation, with hydrodynamic parameters
determined using boundary element methods. The resulting models
are, for the vast majority of cases, linear, which has advantages
for ease of computation and a basis for control design to
maximise energy capture. While these linear models have attractive
properties, the assumptions under which linearity is valid
are restrictive. In particular, the assumption of small movements
about an equilibrium point, so that higher order terms are not
significant, needs some scrutiny. While this assumption is reasonable
in many applications, in wave energy the main objective
is to exaggerate the movement of the device through resonance,
so that energy capture can be maximised. This paper examines
the value of adding specific nonlinear terms to hydrodynamic
models for wave energy devices, to improve the validity of such
models across the full operational spectrum
A nonlinear extension for linear boundary element methods in wave energy device modelling
To date, mathematical models for wave energy devices typically
follow Cummins equation, with hydrodynamic parameters
determined using boundary element methods. The resulting models
are, for the vast majority of cases, linear, which has advantages
for ease of computation and a basis for control design to
maximise energy capture. While these linear models have attractive
properties, the assumptions under which linearity is valid
are restrictive. In particular, the assumption of small movements
about an equilibrium point, so that higher order terms are not
significant, needs some scrutiny. While this assumption is reasonable
in many applications, in wave energy the main objective
is to exaggerate the movement of the device through resonance,
so that energy capture can be maximised. This paper examines
the value of adding specific nonlinear terms to hydrodynamic
models for wave energy devices, to improve the validity of such
models across the full operational spectrum
Ocean forecasting for wave energy production
There are a variety of requirements for future forecasts in relation to optimizing the production of
wave energy. Daily forecasts are required to plan maintenance activities and allow power producers
to accurately bid on wholesale energy markets, hourly forecasts are needed to warn of impending
inclement conditions, possibly placing devices in survival mode, while wave-by-wave forecasts are
required to optimize the real-time loading of the device so that maximum power is extracted from the
waves over all sea conditions. In addition, related hindcasts over a long time scale may be performed to
assess the power production capability of a specific wave site. This paper addresses the full spectrum
of the aforementioned wave modeling activities, covering the variety of time scales and detailing
modeling methods appropriate to the various time scales, and the causal inputs, where appropriate,
which drive these models. Some models are based on a physical description of the system, including
bathymetry, for example (e.g., in assessing power production capability), while others simply use
measured data to form time series models (e.g., in wave-to-wave forecasting). The paper describes each
of the wave forecasting problem domains, details appropriate model structures and how those models
are parameterized, and also offers a number of case studies to illustrate each modeling methodology
Wave Energy Control Systems: Robustness Issues
While traditional feedback control systems enjoy relatively good sensitivity properties, energy maximising wave energy converter (WEC) control systems have particular characteristics which challenge the application of traditional feedback and robust control methods. In particular, the relationship between plant and controller is largely defined by the need to maximise power transfer, and the controller contains a feedforward component which is difficult to robustify. Typically, WEC control systems are based on linear model descriptions, but this belies the true nonlinearity of WEC hydrodynamics (particularly under controlled conditions) and the associated power take-off (PTO) system. This paper examines two popular WEC control structures and examines the sensitivity of these structures to parameter variations, both in terms of closed-loop transfer functions and power absorbed. Some recommendations are also given on which WEC parameters need to be modelled with high accuracy
Finite-order hydrodynamic approximation by moment-matching (FOAMM) toolbox for wave energy applications
—Cummins’ equation is commonly used to describe
the motion of Wave Energy Converters (WECs), where the
radiation force is characterised by a convolution operation. The
computational effort associated with the solution of the convolution term, often represents a drawback for e.g. optimisation
or exhaustive-search studies. To overcome this disadvantage, and
given that the convolution operator intrinsically defines a dynamical system, the convolution term is commonly approximated
using suitable finite-order parametric models. To this end, the
Centre for Ocean Energy Research has recently presented a
moment-matching based identification method for the radiation
force subsystem and the complete force-to-motion WEC dynamics
(i.e. wave excitation force to device velocity). Motivated by
the theory and the obtained results, already reported by the
authors, the FOAMM MATLAB application has been developed,
which systematically implements the moment-matching based
identification strategy from raw frequency-domain data, provided
by hydrodynamic solvers, in a user-friendly fashion. The aim
of this paper is to describe the theoretical background behind
the identification strategy, and the structure, organisation and
characteristics of the developed application. Additionally, the
relevant modes of operation, along with the different options of
the toolbox are explained, and, at the end, a step-by-step example
of how to use the FOAMM application is provided, along with
recommendations from the author
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
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
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