Authors:

Jose V.Taboada (MSc Student at University of Stavanger)

Hirpa G.Lemu (Associate Professor at University of Stavanger)

Jose A.Perez (Professor at University of Vigo)

“Comparative analysis of two Offshore

Wave Energy Conversion devices:

Cape Verde vs. Flexible Drive Line

designs”.

OBJECTIVES Make a brief Comparative Analysis, from Design and Application point of

view, of the available WEC devices (Capa Verde vs. FDL).

Targeting the “Fetch Area” on the Power Sea-State(Mw/m) along the North Atlantic Seas( North Sea and Norwegian Continental Shelf): “High wave Energy Density on the Fetch, to achieve an Optimum Energy Conversion”.

Select appropriate and suitable WEC energy equipment: “To extract the

Maximum and optimal level of Energy between the Wave and the

Oscillation is at an Optimum”.

Efficiency Degree of Performance on WEC’s Device (Cape Verde & FDL):

“Design, Constraints and Assumptions of each Device have to meet and

match, in based on their own Functional Requirements as WEC’s models.

Consequently, fulfill the Requirements (Efficiency +Maximum Power

Absorption)”.

Economical Goal on WEC’s: “Optimize the ration between Absorbed and

Incident Power, but to Minimize the Price(Kw/€) on the absorbed and

converter useful wave power. WEC devices have to be Efficiency and

Reliable all at once”.

Outline1. INTRODUCTION

2. CHARACTERISTICS AND TYPE OF WAVES

2.1. Wave theories and range of validity.

2.2. Sea Water Propagation.

3. WORKING PRINCIPLE OF OFFSHORE WAVE ENERGY CONVERTERS(OWEC).

3.1. Cape Verde principle by EWE.

3.2. Flexible driveline(FDL) model.

4. WEC ANALYSIS AND DESIGN PHILOSOPHY OF A BUOY.

4.1. Wave Energy Data Resources

4.2. Classification of WEC’s

5. TOPOLOGY LAY-OUT OF LIFTING SYSTEM

5.1. Mooring Analysis

5.2. Buoyancy Estimations

5.3. Equipment assembly and Lifting process

6. HYDRODYNAMIC LOAD

7. MACHINERY DIMENSIONING AND DESIGN PHILOSOHIES

7.1. Mechanism Functionality.

7.2. Dimensioning Process of Machinery.

8. ECONOMICAL ESTIMATE ANALYSIS.

9. CONCLUSIONS.

1.INTRODUCTION

Global Classification of six major renewable energy resources in the

Oceans : Waves, Tides, Ocean Currents, Thermal, Salinity gradients,

Biomass.

“Wave Energy can be considered as an undiffused form of solar

energy”

The Water of the oceans is in constant movement, the gravitational pull of

the sun and moon oscillates the surface of the oceans twice a day while the

wind disturbs it into waves (Figure 1).

Winds are created by the differential warming of the earth and, like they

pass over open bodies of water, and they transfer some of their energy to a

form of waves.

World Global Situation

Fig 1. Concept of Wave Energy (wavetrain2.eu)

Global Distribution of Time-average Wave Power

WEC devices demands specific conditions to satisfy the requirements for an

efficiently capture of Energy from the waves. The better conditions are

distributed: 30°latitude & 60°North and South hemisphere

Also, the Islands hold a good fetch area to implement these devices.

Fig 2. Annual global gross theoretical wave power for all WorldWaves grid points worldwide

(http://www.oceanor.com/related/59149/paper_OMAW_2010_20473_final.pdf)

2.CHARACTERISTICS AND TYPE OF WAVES.

2.1. WAVE THEORIES AND RANGE OF VALIDITY:

Three main Wave parameters: the wave height (H), the wave period (T)and water depth (d). The wave theories and their applicability, can be classified as bellow:

• Linear Theory (Airy = Stokes 1st order): This is the simplest wave theory form. It is also referred to as small amplitude wave theory, Linear Wave Theory, Sinusoidal wave theory or Airy Theory.

• Stokes 2nd or Higher (3rd, 4th and 5th) order: This is a theory that is applicable for Intermediate and deep water locations i.e., for water depth to wavelength ratio of d/λ≫0.15.

• Stream function Theory: Mainly applicable for Shallow waters. The characteristics of the wave, according to this theory, is described by UrsellNumber – a number that is derived from the Stokes wave expansion for long-wave limits of shallow waters having the wavelength much larger than the water depth.

Fig 3. Ranges of Validity for wave theories

(Shore Protection Manual, Volume I (1984))

2.2. SEA WATER PROPAGATION:

Waves propagate over slowly varying depths and currents. At areas where

the uniform-wave theories are applicable, depths (D) and current induced

changes of wavenumber (k), wave frequency (ω) and direction (θ) govern

propagation changes and wave current interactions. As result, the length (λ

= L) is changed.

Although, the Fluid motion varies, depending on the location (Shallow,

Transitional, and Deep waters), the “Particle Orbit” can be distinguished

with a variation on the trajectory as depicted in next figure bellow:

Fig 4. Change in orbital motion of water particles

(Passy’s World Mathematics, website)

The Dispersion of the currents and their transported Hydrodynamic Load

are function of: Kinematics of the waves + Potential Energy down to sea

bead. On the research work made, was assumed that the seabed remains

at a constant depth of 75m. See figure bellow.

Fig 5. Representation of a Regular Wave

[Shore Protection Manual, 1984]

3.WORKING PRINCIPLE OF “OWEC”

Ocean Wave Converter (OWEC)

The conceptual working principle of WEC’s, can be stated in very common terms as follows: the Force produced in a system by an Incident wave conditions relative motion between the Absorber/Floater (Buoy) and Resistance point, which acts directly on it, and drives a working fluid through an generator principal mover.

The integrity Power Take Off (PTO) system for each device will be different for each emplacement (Near shore and Offshore).

Functional Requirements demand that the device motion results in the power take off extraction, by the Kinematic movement and the Potential energy of the waves.

The devices can have different Shape for each emplacement locations due to the variation in global distribution of the amount of energy.

«Consequently, the Design and Location of the devices should fulfill thedemands for Maximum possible Efficency and Power absorption».

3.1. Cape Verde principle by EWE AS: (Project 1)

This research focuses on the Point Absorber, the main purpose of this

mathematical model is to find out the wave loading on a fixed or floating floater of

agreed design; in absorber hydrodynamics, is the response of a specific floater

design to certain Fetch Area conditions that is of interest.

The device must perform sufficiently well to absorb an acceptable amount of

power for moderate and small seas, that means shallow water and near shore.

Where a reliable level of Input Energy is crucial.

Fig 6. Cape Verde model by EWE AS.

Conversion Global System Outline:

Fig 7. Conversion System of Cape Verde

3.2. Flexible Drive Line by Euro Wave Energy (Project 2)

The initial patent showed above, consisted in three main parts; Buoyancy,

Main module, Tension legs, and Anchor Seabed.

Being the main part of the entire system, the main Module, which one is

formed by: Drive line (wire cable or chain) + Generator Subsea.

The input energy transmitted into the subsea generators, are driven from the

Lineal Movement up and down by the entered mechanism.

Fig 8. Flexible Drive Line (FDL) by EWE AS

Initial Conversion System Outline:

Fig 9. Initial Conversion System of FDL.

Advantages and Differences of the Two Devices:

Table 1.Advantages and Differences(Cape Verde Model vs. FDL)

4.WEC ANALYSIS AND DESIGN OF A BUOY.

4.1. WAVE ENERGY DATA RESOURCES:

The wave energy resource capacity study is based on Sea State

Parameters: Hs, Ts, Fp, θm , Pw and dw.

Give a useful indication to estimate the wave power.

Annual Scatter Diagram contains the long-term statistical representation

of sea states. Calculations conducted based on this annual Scatter Diagram

shows that the energy along the Norwegian shore line is best extracted in

sea-states with Hs (range from 0.5m to 16,5 m) and Ts (from 3,5sec 18,5

sec).

Table 2

20 year return period Scatter diagram of Power sea-state(Mw/m) along the North Atlantic

Effective range of potential waves as a function of wave height. See figure

bellow:

The area under the curves from 3,5m to 6,5m can be application targets for

WEC’s devices in the area.

Fig 10. Effective Wave Power vs. Heights wave

Energy Spectrum Distribution:

Known as the Joint Probability Density Function for waves, where the long-

term distribution of the waves is applied, in order to establish a probability

distribution (Probability density function), which is used to represent the long-

term variability of sea states.

The design storm concept that combinations the significant wave height (Hs)

and spectral peak period (Tp) located along a contour line in the Hs and Tp

plane is applied.

• Pierson-Moskwotz (P-M Spectrum) : SPM (ω)

• Jonswap Spectrum : SJ (ω)

The suggested and most used wave spectrum is the well-know JONSWAP in

the design of an Offshore Structure in a fetch limited area.

The wave energy-density results allows us to identify a wave energy

interpreted along the peak values of Tp (from 15 sec to 19 sec) and Hs(from

13m to 17m) extended along the North Sea and NCS.

Fig 11. Hs and Tp with annual Pe=10exp-2 for sea-states of 3h duration.

Computing the data for the pick values given by the figure above and Scatter diagram, the JONSWAP spectrum obtained are represented as:

JONSWAP spectrum computed to described wind-induced extreme sea states, observing a drastic variation of wave frequency from a peak value of 3,37622 (ω = 0,37308 rad/sec and Hs = 13 m) to 3,9689 exp-6(Hs = 14 m).

Hence, suitable spectrum of wave energy density, suits bellow 13m(Hs) with lower wave frequencies (ω = 0,39 rad/sec), due to being the ones on North Sea to the South that give the right implementation of the WEC’s.

Fig 12. Energy Spectrum distribution obtained by JONSWAP spectrum model.

4.2. CLASSIFICATION OF WEC’s:

Fig 13. General Classification of WEC devices by Hagerman, G.1995 A[Brooke, J(2003)]

Hagerman, G.1995 a[6], he pointed out an illustrative classification according

to the Wave Propagation:

• Point Absorber :Quite small to the wave length and it can capture energy

from a wave front greater than the dimension of the absorber.

• Terminator : The horizontal axis is parallel to the incident wave crest. The

reflected transport waves determine the real efficiency of the device to use.

• Attenuator : Also called “linear absorber” (usually are placed in a line) the

principle axes are situated parallel to the direction of the incoming wave due to

orientation close to parallel to the direction of wave propagation.

4.3. SIZING AND SLECTION OF WEC’s:

The core issues considered during the sizing and selection of WECs are:

1. Collecting data from North Sea (Scatter Diagram)

2. Calculating the main wave Parameters and Assumptions.

3. Design and dimensioning of each WEC device.

4. Selecting the appropriate Generator AC.

How to Select appropriate Buoy??

Buoy Models: APB 2000 Aqua vs. Aqualine bøyer.

“Buoys shall fulfill the functionality that each WEC devices demands,

and at the same time to Take Off the most Optimal Level of Energy from

the waves”.

The outcome obtained by calculations, was the Optimal Value of the Potential

Energy Captured from the waves varied from 7.5 sec to 10.5 sec being the

significant one for OWEC on data targeted.

The APB 2000 Aqua reaching higher degree in H/D and λ…/D, so Wave

High optimal movement, therefore, better Efficiency Energy to be captured.

Fig 14. Wave Breaking Limit (APB 2000 Aqua vs. Aqualine Bøyer)

5.TOPOLOGY LAY-OUT OF LIFTING SYSTEM

5.1. MOORING ANALYSIS:

Mooring system on each WEC devices is designed according to the Sea State

Condition on the site. Specific mooring system properties and configurations to the

power captured have studied, according to the effect of mooring on motions and

power will significantly depend on its configuration.

# Cape Verde buoy: holds a slack mooring due to its shallow water installation.

# FDL model: demands heavy mooring system due to the installation hostile

environment in transitional water.

The mooring design layout roots from the Buoyancy Estimations itself that each

single WEC devices have. Design Premises are implemented to Minimize the

effect of the mooring on the wave following performance of the selected buoy, thus,

increasing the output energy absorption.

Fig 15. Flow diagram Assembly of Cape Verde

Fig 16. Flow diagram Assembly of FDL

5.2. BOUYANCY ESTIMATIONS:

The Buoyancy or Restoring Force by each single Buoy (APB 2000 Aqua)

models has been researched separately for each single WEC. Due to the

functional requirements, what can be achieved from each one can be totally

different.

The whole restoring force (Fs) and the total mass (Mt), must be suitable to

have a right Buoyancy level (B).

For safety reasons, the chosen buoyancy was estimated at least 35% bigger

that the total mass of the whole equipment.

The Analysis is carried out for several Regular and Irregular wave

conditions using Orcaflex 9.5. Simulation has been performed with the

purpose to study the effects of Power Take Off (PTO) system.

The simulations applied, were done with input by one direction of motion

waves that means 180⁰ over plan XZ, for wind and waves data. The

outcome from “Theoretical approach + Simulations” resulted on the next

table bellow;

Table 3. Parameters and Dimensions

5.3. EQUIPEMENT ASSEMBLY AND LIFTING PROCESS:

Each WEC devices holds a different topology of the design considerations and

premises, due to the difference in functional requirements on each one.

# Cape Verde: holds an easy and simple mooring system, wire cable

connected directly from the Buoy to onshore equipment.

# FDL: the upper parts of the mooring have wire cable attached from the

Buoys lay-out to the main module, following lower part with chains to the each

single anchor.

The Assembly Philosophy, backgrounds from the installation of WEC’s farms,

where for FDL in transitional waters would require a dense arrangement of

converters to provide Efficiency and Economical exploitation of the

location with: Minimum of Electrical hook-up connection lengths and

Environmental Impact.

6.HYDRODYNAMIC LOAD

“Theoretical Approach + OrcaFlex 9.5”, shows differences starting from

3rd Stokes-order (Analytical) and the approach made through 5rd Stokes-

order(through OrcaFlex 9.5).

Hence, the outcome of the results obtained are slightly different with better

degree of accuracy results.

Cape Verde model has hydrodynamic load only on the Shape of the

floater (at S.W.L) and the Snatch Block, both being the resistance

points, due to the fact that the wire cable vanish under hydrodynamic

load.

FDL the Hydrodynamic Load is distributed values along the main

module (40m to 55 m depths), being the outcome response by

hydrodynamic load is considerable higher. This affects the mooring

attachment lines and WEC behaves efficient.

The whole Lifting and Assembly is divided into four parts:

1. Lifting and assembly of body2.

2. Hydrodynamic load on body 1(Main Body).

3. Buoyancy of main body.

4. Sea-bed Anchoring System.

These four points are those that provide the outcome result of the entered

hydrodynamic load. The Lifting System itself has to meet tow basic

Requirements:

1.Total Mass undersea.

2.Bouyancy, Restoring Force and Draft distance.

Parts’ Total Mass, Buoyancy on Main Body:

Sea-bed Anchoring System.

Take into account:

Hydrodynamic Load (previously calculated)

Safety Coeff. (Ts >3·Tb)

Dived in three main categories:

1. Two Principles legs (“Chain 28x150”)

2. Two Secondary legs (“Wire Cable 6x36”)

3. Anchors (“Sepla & Anchor Line”)

Seabed Anchor System

Anchor System roots from the Lower Mooring system (Chains + Wire cables) which

ones, has been dimensioning according to the Axial Tension Force along each

single mooring line, induced by the Hydrodynamic Load from currents and internal

Buoyancy into the main body. Anchors types: Sepla, Pader and Anchor Line.

Differences and Advantages :

SEPLA (Suction Embedded Plate Anchor):

- Vertical Orientation.

- Two bodies welding (Solid and Hallow)

- Two types;

·Small sizes (temporal installation)

·Biggest sizes (permanent installation)

- Big Flap area.

PADER:

-Two bodies (mooring connection and plate) connect by Padeyes.

-Triangular Stiff lifting bridle.

-Small Flap area.

ANCHOR LINE:

- Two bodies welding (Shank and Fluke)

- Triangular Plate

- Mayor penetration on soil seabed.

Anchors :

·Sepla Anchor;

Principal Legs,

Chain 28x150

Treach = 49ton

·Anchor Line;

Secondary Legs,

Wire cable 6x36

Treach = 16ton

Functionally of each Anchor model, for the Main Body of FDL;

·Sepla Anchor; used for the two principal legs(chains) with ones have the maximum

vertical restoring force. As well as, must stabilized and attune the more rigid vertical

position along.

·Anchor Line; installed for each wire cable leg, the restoring force is considerably

smaller rather the principal legs. These legs will satisfice to reduce a Moment along

pitch direction(x) and the Displacement originated by Currents.

Properties and Parameters of Anchor model:

The first verification criterion that we must know, if our plate anchor can

resist the whole Resistant of Interlock, is showed below;

Zplate ≤ 4,5·Wplate

Depth penetration of Plate Plate width

The amount of Pulled Maximum Tension(Tmax) from each mooring line, so is the Maximum Admissible value that the Anchor can resist. The estimations and calculations made, conclude that this anchor models are at least 170% safe with respect to the transmitted tension from wire cable. Hence, the outcome obtained by analysis between mooring lines and anchors, results on the next relation:

Zplate & Wplate &Lplate Aarea TMax

Equilibrium Calculations of whole Anchor and Snatch block:

Stress front Life Cycle: (FEM Analysis)

Concluding, on Yield Tensile of material (strength steel) and Von-Misses

approximation criteria, that we can evaluate that this model could support

plenty Stress, for long Life Cycles.

7.MACHINERY DIMENSIONING AND PHILOSOPHIES7.1. MECHANISM FUNCTIONALITY

Each WEC’s device demands appropriate Transmission System according to

the Functionality that each WEC device described, the main requirements

and limitations on each are:

- Heavy Loads in Movement (Forward and Backward).

- Efficiency Transmission between the components.

- Reliable Life Cycle Cost (LCC).

This section is devoted primarily to dimension and design, one transmission

on WEC. Carry out in the next order;

1. Cape Verde device: Linear movement is transmitted by a Belts

transmission moored by cables on shore.

2. Flexible Drive Line: Linear movement through a Gear Rack

subsea transmission system.

Cape Verde: Linear Movement is transmitted by a Belts transmission

moored by cables on shore. Where the Linear movement is induced by the

oscillation of waves, hence, given input of Energy transmitted along the

Belt, and then, output into the Machinery.

FDL: Linear movement up and down, through a Gear Rack transmission in

underwater. The Gear Rack is attached along Main Module (1) with a total

length of 15metres, where the Body (2) moves up and down given input

energy to each Gear Rack, as result of output energy to the Subsea

Generators.

The entirely dimensioning of components, will implemented according to real

components from Manufacturer’s catalogues and theoretical estimations.

7.2. DIMENSIONING PROCESS OF MACHINERY

CAPE VERDE

- Lineal Force in movement

forward and backward along

Timing belt(7m)

- Constant linear velocity along

the whole timing belt.

- Input Power, is transmitted

directly to each shaft.

- Tangential Force average

(4568Kg) transmitted along the

Timing Belt.

FDL

- The system must described according with the Linear Movement over each helicoidally Drive Gear Tracks (eight).

- Four chains are joined to spreader bar.

- The Linear Movement (Up & Down), depends directly of the force (moving mass) by the Buoyancy on float at S.W.L.

- Linear speed movement between Modules (Body 1 & 2), along the Stroke Length lines (of 13m long).

Representation of forces transmitted Outside the Machinery;

Dimensioning process of Machinery for Cape Verde:

Analysis 1: Linear force transmitted from Outside to Inside machinery for Normal

Conditions of Sea behavior, tend to be constant for interval range (max & min).

Analysis 2: Linear force transmitted from Outside to Inside machinery for Extreme

conditions of Sea behavior

Dimensioning Process;

1.Lineal Force in movement (forward to backward) FT=4567,75Kg

2.Linear Velocity constant. (7m timing belt)

Criteria Establish for whole dimensioning process;

- Maximum Input Power(Kw)

- Maximum Efficiency (%)

Power Transmitted; (from Outside to Inside) Trans.Power Trans.Forces

1. Drivers chain wheels

2. Wheels (a&b)

3. Shaft Drivers

4. Torque Limiters Concentration of Stress

5. Gear Boxes

6. Generators AC.

·

Dimensioning process of Machinery for FDL:

Second model of WEC requires other procedures in Design & Dimensioning due

to the Dimensions are considerable big, as well the functional requirement of

the subsea equipment.

Main requirements/details :

- Heavy mass (14049,32Kg) moving up & down High stress originated.

- Bouyancy Body 2(2000kg) calculated on section 5.2.

- Max. Stroke length of 13m.

Calculations Velocities and Times:

- Lineal Speed during Fall and Time (around *0.934m/s in *14.846 sec).

- Lineal Speed during Up and Time (around *0.3767m/s in *37.159 sec).

*For normal Sea-State Conditions.

The entirely dimensioning must be carry out from Outside to Inside. The

order of elements, are integrate;

1. Gear Rack.

(3179 rpm and 1210 rpm)

2. Shaft Drivers.

3. Torque Limiters.

4. Generators Subsea.

Transmission system calculated from commercial catalogues. Principal

limitations of Gear Rack selected;

-Linear Force, maximum mass in movement supported (Fmax=25KN!)

-Max. Output Torque.

-Nominal diameter of drivers gears racks(d)

-Output revolutions (475rpm)

Results of Dimensioning model “Flexible Drive Line”

With a total number of 16 generators subsea from Sicei s.r.l., the total amount

of energy obtained in Offshore will be around 0,422MWatts.

8.ECONOMICAL ESTIMATE ANALYSIS

Wave Power Resource

Directionality Factor

Capture Efficiency….

Power Chain Efficiency

Availability

O&M Cost

Capital Costs

Site Selection (Location)

Power Levels in

the Sea.

How much

(Kw/m)?

Available Wave

Power

Captured Wave

Power

Maximum Annual

Output

Actual Annual

Output

Cost of Electricity

(Euro/Kwh) ??

Device

Selection

Annual Cost

Mean Wave Power (Kw/m) Water Depth’s

CONCLUSIONS Investigated the Potential to Optimize the Maximum wave power that

can be extracted: Power Sea-State (Mw/m) + Joint Probability Density Function for Waves (Energy Spectrum by SJ-JONSWAP)

Parameters (H, T, λ, D, K, ω, Ɵ) of the oscillation system was chosen and researched, according to the Location (Shallow & Transitional Waters) in order to convert an Optimum amount of Energy.

Choose appropriate Power Transmission System according to the Functionality that each WEC device described.

CAPA VERDE MODEL: (Potout≈ 470Kw)

- Shallow Waters Installation: High average of high waves(Hs=3,5m to 6,5) is considerable upper due to the need to meet the requirements of the carried out Mechanical Design.

- Buoy with small Mass that Natural Frequency is always higher that the Wave Frequency. Instead provide the system with a device by which the Buoy can hold in a fixed Displacement position during certain time intervals of the Oscillation Cycle.

FLEXIBLE DRIVELINE(FDL): (Potout≈ 0,422Mw)

- Transitional waters Installation: Higher extraction of Energy from the waves.

- Lineal Movement up-down: Optimal input Energy into the subsea gear boxes along the 15m stroke length.

Optimum Motion is more important the smaller the physical size of the WEC.

Wave Energy is available in a relatively narrow spectral Frequency band, so the Point Absorber is very Effective Energy Converter.

“Quasi Dynamic and Static developed method”: was to reduce the Uncertainties given by the Damping and Stiffness effect, and have combined Heave Natural Period of around 7,5 sec to 10,5 sec(Optimal Range Energy Capture!).

Economical Considerations: shall come from the outcome of the Assumptions made along the Design Stage and the Design Philosophies on the Machinery, as well as the Goals set up to meet the Technological developments limitations on WEC’s devices.

(Time for Questions)

josevazta@hotmail.com / jv.taboada@stud.uis.no