7th International Fluid Power Conference
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Simulation of an Ocean Wave Energy Converter Using
Hydraulic Transmission
Yukio Kamizuru
RWTH Aachen University, Germany, Institute for Fluid Power Drives and Controls (IFAS)
Matthias Liermann
RWTH Aachen University, Germany, Institute for Fluid Power Drives and Controls (IFAS)
now at the American University of Beirut, Lebanon
Hubertus Murrenhoff
RWTH Aachen University, Germany, Institute for Fluid Power Drives and Controls (IFAS)
ABSTRACT
This paper gives an overview of different wave energy converter concepts. Due to their variety a
benchmark is conducted to provide a foundation for a systematic comparison of different
converter types. The benchmarking shows the advantages of wave power plants, where multiple
converters feed a pipeline, which is used to generate electricity centralised onshore.
The second part of the paper explains the modelling of a wave energy converter with hydraulic
power transmission. For this the mathematical model of ocean waves is discussed. To enhance
environmental and stability aspects of the converter an open, seawater based, hydraulic circuit
is developed and simulated.
NOMENCLATURE
η
surface elevation
m
ω
angular frequency
rad/s
a
acceleration
m/s²
dv,prop
damping coefficient
Ns/m
D
damping force
N
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k
wave number
rad/m
F
force
N
H
wave height
m
mWEC
mass of WEC oscillator
kg
p
pressure
N/m²
t
time
s
1
INTRODUCTION
Ocean waves inflict forces of up to several meganewtons on marine structures with a
period of typically 8 to 12 seconds. The world wide wave power capacity is assumed to
be of the same order of magnitude as the world electricity consumption, about 2 TW, of
which according to /Cru08/ 10 to 15 percent could be exploited. To harness this great
potential hydrostatic transmission could be a key technology. Hydraulic devices can
efficiently handle slow movements at high forces. The three major challenges engineers
are facing when dealing with this kind of renewable energy are:
1.
Corrosion. The corrosive environment of the oceans is a threat to components
and forces the developers to make use of innovative materials, coatings or high priced
stainless steel.
2.
Peak load. Wave energy converters (WEC) are subjected to extremely powerful
ocean waves in special weather conditions. This makes offshore maintenance difficult.
3.
Resonance tuning. The power absorption needs to cope with a highly irregular
excitation and has to operate close to the incoming wave train’s resonance to maximise
power output and efficiency.
The resonance tuning is most important for the hydraulic engineer. He/she not only has
to provide a stable, robust and efficient system technology, but also has to develop a
control algorithm to optimise the damping force in order to extract as much energy as
possible not only from one wave, but from a whole wave train that consists of a
spectrum of wave intensities at different wave heights and periods. After all, the wave
energy has to be converted into a generator torque. The drive technology should make
sure that the revolution of the generator stays constant at all times.
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This paper gives an introduction to the ocean wave energy resource and its
mathematical characterisation. Followed by a short overview of selected WEC concepts
and a benchmark, which considers stability and maintainability, a simulation
environment for WEC is explained.
2
2.1
OCEAN WAVE ENERGY AND ITS CONVERSION MECHANISMS
The resource – an introduction to wave theories
No wave is like the other. The physics of ocean waves is so complex that even with the
state of the art calculation of physical processes, simple variables like the velocity of
water particles, the pressure field or surface elevation do not reflect the reality in a
satisfactory way /Gra95/. The difficulty of understanding the physics of a real wave
results from the fact that the wind-borne ocean waves are a superposition of waves with
a variety of frequencies travelling at different speeds and from different directions.
Moreover the effects of the seabed on the movement of water particles are hard to be
considered in mathematic equations. Some abstractions which have to be made, in
order to mathematically describe the waves, are discussed in the following section.
The most common and simplest way to describe a wave is the application of the Airy
wave theory, also called linear theory /Cha05/. It is mainly based on the assumption of
potential flow, an even, solid sea bed, and infinitely small waves. The linear theory
reduces a wave to a sinusoidal curve /Sor93/:

H
 cos(kx  t )
2
(1)
Where η is the surface elevation at the specified time t and horizontal coordinate x.
H defines the amplitude of the wave. For WECs, in contrast to ships or offshore
platforms, the velocity of water particles and the pressure field below the surface are of
particular interest. The particle trajectories determined by the linear theory describe
closed orbits. By applying higher order theories a more realistic assumption can be
made. These take into account that wave crests are steeper than troughs and particle
orbits are not closed. The resulting net mass transport is called Stokes-drift.
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example
particle orbit
direction of travel
Figure 1: Visualisation of particle trajectories under a wave train /Kam09/
Figure 1 shows particle trajectories calculated with the so called second order Stokes
theory. One can see that the particle displacement decreases with water depth. The
same applies to the variation of pressure below the surface. The particle movement
corresponds to the kinetic energy of the wave, the pressure at a certain depth
corresponds to the potential energy. These findings explain why it is necessary to place
WECs close to the water surface, where the highest amount of energy can be captured.
2.2
Wave energy converters and their categories
Conversion principles can be roughly divided into three different categories: point
absorbers (PA), attenuators and terminators /Cru08/. Figure 2 illustrates the three
categories by an example each.
Attenuator
Terminator
Example
Point absorber
/Gra95/
Figure 2: Classification and examples of WEC
The three classes of WECs describe the relationship of the structure to the incident
wave front. A point absorber is usually axis symmetric to the heave axis and small
compared to the wave lengths. The picture in Figure 2 shows a submerged PA, which
extracts power from waves by using the pressure differences of crests and troughs. A
gas filled chamber is used as a spring to provide the restoring force needed for the
upward movement under troughs.
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Attenuators are characterised by their great length and the alignment with the direction
of travel of the incoming waves. The attenuator shown in Table 1 consists of a row of
pontoons, connected to each other by hinges and cylinders, which provide the damping.
This floating concept is called the Cockerell Raft and utilises the relative movement of
the pontoons to extract energy from the waves /Gra95/.
The terminator illustrated in Figure 2 comprises a flap connected through hinges to a
base, which is mounted on the sea bed. The terminator uses, like the Cockerell Raft,
cylinders as the damping mechanism. The flap can be designed as a lifting body, which
provides the restoring force, making a spring needless. The velocity of the water
particles exerts a force on the flap and causes its movement
The main thing most WEC have in common is the principle of absorption. Waves induce
an oscillating motion to a spring mass damper system. Hence a cylinder or linear
generator can be applied to facilitate the power take-off (PTO).
2.3
Manifolding wave energy converters
In this section two different approaches are presented, which mainly differ in the point
where the mechanical energy is ideally converted into electricity. If wave energy is
converted into electricity in each WEC the authors refer to a decentralised system. The
opposite is the transportation of fluid power energy to a remote location, for example
with a pipeline, and to convert it into electricity inside a station. This method will be
referred to as a centralised system. Both approaches have their justification, but for
many cases the advantages of the centralised are on hand: Many converters can be
used to feed a pipeline, which transmits the absorbed wave power through a fluid
onshore. There, one or more turbines are used to generate electricity. This strategy,
also called manifolding, can reduce the mechanical and electrical complexity of the WEC
and hence contributes to the systems stability and maintainability since vulnerable
components are placed safely onshore. Figure 3 illustrates the differences of centralised
and decentralised systems and clarifies their complexity as well.
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Figure 3: Sketches of decentralised and centralised electricity generation
However by manifolding WECs a crucial disadvantage comes into effect: There is no
opportunity to control converters individually to maximise the power output for example
by applying velocity proportional damping (see equation 2) or more sophisticated control
algorithms /Sal02/.
Fdamping  dv,prop  x
(2)
As will be explained in section 4 the damping acts analogue to a Coulomb friction model,
Fdamping  D  sign(x)
(3)
where D is equal to the system’s pressure multiplied with the effective piston area.
Therefore, to absorb power from a wave, the wave force needs to exceed the chosen
damping force, which is applied by the system’s pressure. Hence, in contrast to velocity
proportional damping, part of the wave’s energy cannot be absorbed. On the other hand
the transformation of hydraulic into electric energy can be made more efficient in case of
the centralized electricity generation. In decentralized WECs a hydrostatic transmission
is used to tune the absorber according to the incoming wave front to stay close to
resonance and achieve an optimised power output. This forces the hydraulic motor to
operate often in inefficient regions, such as low pivoting angles and low system
pressures. By manifolding these problems can be reduced. Since the position of every
absorber will be statistically distributed, peaks of flow rates are minimised. The flow of
fluid to the onshore power station will have only small pressure ripples at a quasi
constant volume flow.
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3
BENCHMARKING WEC CONCEPTS
This chapter compares different WEC concepts and introduces a benchmark, which
considers the technological complexity of possible WEC configurations. The benchmark
considers the three above mentioned representative concepts.
3.1
Establishing criteria to evaluate wave energy converter concepts
In recent years, survivability problems of ocean wave energy devices prevailed. Since
maintenance data of long term operation of wave farms is yet unavailable, the
benchmark is focussed on the stability and robustness of the systems. Table 1 gives an
overview of the criteria, their approximate weighting and influence factors.
criteria
weight influence factors
electric simplicity
40% number of electric components on board
mechanic simplicity
20% number of mechanic PTO components on board
maintainability/accessability
15% distance to shore, location in water
risk of damage
15% size of WEC, survivability
effects of damage
10% used fluid, urgency of recovery, effect on farm
sum 100%
Table 1: Benchmark criteria and their factors of influence
Economic criteria cannot be included in this benchmark, because reliable data
concerning costs of operation and maintenance, costs of electricity, and installation is
scarcely available. A few studies exist (see /Dun09/), but the lack of experience in
commercial plant operations would lead to a higher level of uncertainty of this
benchmark. Furthermore, the authors want to clarify that this benchmark is not
evaluating the efficiency of WEC, since information about their performance is rare. Also
the control strategies of the various concepts are a well protected property of WEC
manufacturers.
3.2
Results of the benchmark
Regarding the simplicity of the electric setup a concept with centralised electricity
generation has the greatest advantage. Vulnerable electric components are located
onshore and easy to reach for maintenance. Since a pipeline is needed, the centralised
electricity generation is more likely to be utilised for near-shore WECs, which is a
limitation for these systems. An additional feature is the usage of an open seawater
based circuit. Expensive return lines and working fluids are unnecessary, leading to
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higher cost efficiency. The problems to be encountered are the development of a
suitable technology for sea water hydraulics, such as filter technology, sealing systems,
corrosion and bio resistive components. Optional a reverse osmosis desalination plant
could be driven as well.
The next step is an analysis of the converter type. In the following a submerged point
absorber, a Cockerell Raft type WEC and a sea bed mounted terminator are evaluated.
A glance at the mechanic complexity of the three WECs shows advantages on the side
of the terminator and the submerged PA, since both are comprised of a single power
take-off per WEC. The attenuator needs at least one PTO per pontoon. The usage of a
gas spring, which can be implemented in a submerged PA, for the restoring force is not
optimal. The need for durable sealing systems and the possible occurrence of heating
problems decrease the survivability of such a WEC. Here simple lifting bodies should
prove better.
Also the size of a WEC matters. The larger the surface which opposes an incoming
wave, the higher the forces on the absorber. All three introduced absorbers can be sized
as needed, but then their location in the water is an important factor. Floating WECs
need to be moored to the ground and thereby a potential for average arises. Sea bed
mounted devices are insensible to this problem, but are exposed to changes of the
ocean floor, such as sediment transportation. However, recovery of damaged devices is
easier if the installation depth is small and sea bed mounted WEC cannot founder. An
important aspect is also the opportunity of securing a WEC in case of a storm, whose
potential energy exceeds the WEC’s capacity /Sal03/. By just applying safety factors the
expenditures to gain survivability grow too large and even then a possible loss of a WEC
cannot be avoided. An example for this can be found in the wind energy sector, where
pitch control is successfully employed to stall the rotor.
As a conclusion, a sea bed mounted terminator with centralised electricity generation
should be the choice, if a robust and easily maintainable WEC is targeted to achieve
long term results. The disadvantage that comes with this setup is the limitation to nearshore locations. As soon as more knowledge about this technology is available, offshore
locations with other devices can be investigated. The question, whether point absorbers,
like submerged PA, buoys or attenuators deliver the best performance, cannot be
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forecasted. A tailor made concept, which combines different types of WECs according to
the characteristics of the desired location, could lead to an optimal layout of a wave
energy plant.
4
SIMULATION OF WAVE ENERGY CONVERTERS
Each of the earlier introduced WEC concepts utilises a different absorption mechanism.
Namely the pressure difference under wave trains (submerged PA), hydrodynamics on
the water surface (Cockerell Raft), and the velocity of water particles (terminators). For
an initial setup of a WEC simulation, the absorption mechanism has to be modelled in
such a way that the mathematical description can be used within simulation software.
For this reason the concept of a submerged PA was chosen, because of the
uncomplicated determination of the force from the pressure on top of the device. Since
the simulation is structured modularly, the absorption principle can be exchanged
quickly, once a model for the specified WEC is developed. Figure 4 shows the structure
of the WEC simulation.
F , x , x , x
/Sor93/
Figure 4: Overview of WEC simulation with Matlab/Simulink and DSHplus
As input parameters, the constants of a monochromatic wave (constant height and
period) are chosen. Thereof, the kinematics and the pressure field under the wave train
can be calculated with a given wave theory. Consequently the forces on the WEC are
simulated, whether the absorber utilises pressure differences, hydrodynamic processes
on the surface or the particle velocities. Once the forces, which act on the converter, are
known, a model of the hydraulic system can be implemented in the simulation
environment DSHplus /Flu09/.
A wave energy converter can be modelled analogous to an oscillator. The governing
equation is as follows:
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FWEC  Fwave  Fdamping  Fspring  F friction  Fresistance  mWEC  a
(4)
The considered forces include

wave forces (Fwave) calculated with the specified theory in connection to the given
absorption mechanism,

damping forces (Fdamping), applied by the hydraulic system to extract the power
from the waves,

spring forces (Fspring) to exert the restoring,

friction of the system (Ffriction) and

resistive forces (Fresistance), like drag caused by water.
Figure 5 shows the model based on the simulation tools Simulink and DSHplus.
Figure 5: Simulation structure in Simulink/DSHplus
First the defined forces from waves, friction, spring and resistance are determined.
These are then fed into a DSHplus model comprising the hydrostatic transmission.
Because of the open circuit, each WEC consists mainly of a cylinder with four check
valves (see figure 2). Together all WECs are connected to a single motor and a
generator. The WECs are now subjected to the forces of a single specified
monochromatic wave. The relative position of the WEC in the ocean is modelled with a
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time delay of the forces upon the single absorbers. With the simulation it is now possible
to model different wave energy converters and design the hydraulic components
according to an incoming regular wave. Figure 6 depicts both the surface elevation
caused by a wave and the displacement of eight absorbers. The varying behaviour of
single absorbers results mainly from the transient effect at the beginning of the
simulation.
Wave parameter:
H=3m
T = 10 seconds
Figure 6: Surface elevation and displacement of eight absorbers
The next steps include the implementation of non-monochromatic wave fields to analyse
the displacement of absorbers under more realistic conditions and an optimisation of the
hydraulic system.
CONCLUSION
In this paper different concepts of how to extract energy from ocean waves were
introduced. The wave energy resource was described and a model for a mathematical
abstraction of waves was given. A short overview of existing concepts with decentralised
electricity generation was followed by the introduction of a method called manifolding to
connect single absorbers feeding a central power generation station. Focussing primarily
on the stability and survivability, a comparison between wave energy converters was
used in order to create a benchmark. The result shows advantages on the side of sea
bed mounted converters that employ lifting bodies, such as air filled chambers, and
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central electricity generation to achieve first experiences in long term operation of WEC.
Based on these results a simulation model was set up at IFAS in order to analyse
different absorption mechanisms and to employ a centralised system. Further research
will include the variation of sea conditions and a deeper analysis of the implemented
components inside a wave farm.
ACKNOWLEDGEMENT
The authors would like to thank Matthias Schramm and Rasmus Börchers for the
assistance within this project.
REFERENCES
/Cha05/
Chakrabarti, S., Handbook of offshore engineering, Elsevier, Amsterdam,
Netherlands, 2005
/Cru08/
Cruz, J., Ocean Wave Energy, Springer, Berlin, Germany, 2008
/Dun09/
Dunnett, D., Electricity generation from wave power in Canada,
Renewable Energy, Elsevier, p. 179-195, 2009
/Flu09/
<http://www.fluidon.de>, Homepage Fluidon GmbH, Aachen, Germany,
visited December 2009
/Gra95/
Graw, K., Wellenenergie – eine hydromechanische Analyse,
BUGH Wuppertal, Wuppertal, Germany, 1995
/Kam09/
Kamizuru, Y., Recherche und Simulation von konventionellen Methoden
zur Nutzung der Meeresenergie und Erstellung von alternativen Konzepten
mit offenem Meerwasserhydraulikkreislauf, RWTH-Aachen, Aachen,
Germany, 2009
/Sal02/
Salter, S. H., Power conversion mechanisms for wave energy, Journal of
Engineering for the Maritime Environment, Professional Engineering
Publishing, p. 1-27, 2002
/Sal03/
Salter, S.H., Proposals for a component and sub-assembly test platform to
collect statistical reliability data for wave energy,
The Fourth European Wave Energy Conference, Cork, Ireland, 2003
/Sor93/
Sorensen, R., Basic wave mechanics: for coastal and ocean engineers,
John Wiley & sons, Inc., New York, USA, 1993