simulation of an ocean wave energy converter using...

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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 d v,prop damping coefficient Ns/m D damping force N 7th International Fluid Power Conference Aachen 2010 1

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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

7th International Fluid Power Conference Aachen 2010

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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.

7th International Fluid Power Conference Aachen 2010

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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 OCEAN WAVE ENERGY AND ITS CONVERSION MECHANISMS

2.1 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/:

)cos(2

tkxH (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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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.

Point absorber Attenuator Terminator

Exa

mpl

e

/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.

direction of travel example particle orbit

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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/.

xdF v,propdamping (2)

As will be explained in section 4 the damping acts analogue to a Coulomb friction model,

)xsign(DFdamping (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 factorselectric simplicity 40% number of electric components on boardmechanic simplicity 20% number of mechanic PTO components on boardmaintainability/accessability 15% distance to shore, location in waterrisk of damage 15% size of WEC, survivabilityeffects 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

7th International Fluid Power Conference Aachen 2010

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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 near-

shore 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.

xxxF ,,,

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:

/Sor93/

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amFFFFFF WECresistancefrictionspringdampingwaveWEC (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.

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

Wave parameter:

H = 3 m

T = 10 seconds

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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

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