Numerical modelling of wave energy resources and assessment of wave energy

extraction by large scale wave farms

Vengatesan Venugopal1, Reddy Nemalidinne1, Arne Vogler2

1. Institute for Energy Systems, School of Engineering, The University of Edinburgh, Faraday Building, King's Buildings, Colin Maclaurin Road, Edinburgh, UK, EH9 3DW, V.Venugopal@ed.ac.uk

2. Marine Energy Research Group, Lews Castle College, University of the Highlands and Islands, Stornoway, Isle of Lewis, Scotland, GB-HS2 0XR, arne.vogler@uhi.ac.uk

Corresponding author: Vengatesan Venugopal, +44(0)131 650 5652, e-mail: v.venugopal@ed.ac.uk

Keywords: Wave Energy Converter, Wave Energy Extraction, Wave Farms, Spectral Wave Modelling

Abstract

This study reports the practicalities of applying a numerical model to assess the wave energy

extraction at proposed development sites in Orkney Waters, Scotland. A state-of-the-art

phase averaged spectral wave model, MIKE 21 Spectral Wave, in association with the wave-

structure interaction software tool WAMIT, has been employed to study the impact of energy

extraction by large arrays of Wave Energy Converters (WECs) on the wave height alteration

in the neighbourhood of WEC arrays. Two generic types of WEC, one representing surface

attenuators (deployed in deep water) and other representing Oscillating Wave Surge

Converters (deployed in shallow waters) are used for numerical modelling. The power

extraction performance of the WECs are initially modelled using WAMIT and validated with

data from literature. As MIKE 21 SW has limited ability in modelling complete dynamics of

a moving structure, each WEC has been modelled as a generic structure but with appropriate

reflection, transmission and energy absorption properties derived from WAMIT, and this

methodology is found to have worked well. In total there are 198 attenuators and 120

Oscillating Wave Surge Converters are constructed within the numerical model at potential

energy locations in Orkney Waters, and the wave-WECs array interactions for the year 2010

have been simulated. The results suggest that the wave farm will have an impact on the wave

climate immediately in the lee of the array, although the magnitude of these effects decreases

monotonically with distance from the farm.

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1. Introduction and Overview

Scotland is geographically well placed on the globe where large energetic waves from the

North Atlantic Ocean provide a high level of sustainable wave power resources. The Scottish

Government has committed to the development of a successful marine renewable energy

industry in Scotland as the country has an estimated 25% of Europe's tidal potential and 10%

of its wave potential (http://www.gov.scot/Topics/Business-Industry/Energy/Facts).

However, harvesting this energetic resource increases the number of challenges associated

with it. One of such challenges is to understand how nearshore coastal processes may be

modified by energy extraction, as the installed capacity of wave farms increases to hundreds

of MW in capacity. The extraction of wave energy from a wave farm produces a wave energy

deficit or shadow down region which in turn may affect the downstream sediment transport

and may thus result in beach erosion/deposition. The quantification of the wave energy

reduction and identification of induced wave height gradients is desired for an accurate

assessment of the environmental impact of a Wave Energy Converter (WEC) array on the

nearby marine environment.

The ability to predict the wave shadow is of topical interest due to significant stakeholder

concerns about potential impacts from wave shadowing arising from wave energy device

installations. The primary aim of this work is to assess the consequences wave energy

extraction by large scale wave arrays in the areas of the Crown Estate Round 1 lease sites in

the Pentland Firth and Orkney Waters (PFOW). Based on guidance from commercial

stakeholders two state-of-the-art modelling suites were initially selected for the TeraWatt

project, namely MIKE by Danish Hydraulic Institute and Delft3D by Deltares to predict the

physical effects of wave energy extraction and compare the advantages and disadvantages of

each modelling suite. Both models have produced good results of comparative quality. The

results included in the present paper are based on MIKE suite only as due to unforeseen

circumstances data from Delft3D model is not available for demonstration.

Although much of the existing literature on wave energy is related to device development, a

small number of studies have been carried out to investigate the wave height reduction in the

lee of WEC arrays. Miller et al. [1] used the third generation phase averaged spectral wave

model, SWAN, to investigate the effects of the scale of energy extraction and incident wave

parameters on the far field wave energy deficit. Venugopal and Smith [2] used the MIKE 21

Boussinesq wave (BW), which is a phase resolving model, to assess the resulting wave field

around a single row of overtopping type WECs which partially reflect energy to achieve a

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wave energy deficit in the down wave region rather than by specifically extracting it. Palha et

al. [3] used the parabolic mild slope wave model REF/DIF to assess the wave shadow in the

lee of a series of large energy sinks that represent clusters of devices. Beels et al. [4] used the

time dependent mild slope wave model MILDWave to assess the wave shadow in the lee of a

2D array of Wave dragon overtopping type WEC devices. Noggard and Anderson [5]

investigated potential benefits to shore protection by simulating an array of Wave Dragon

overtopping type WECs in the relatively near-shore region using the MIKE 21 Boussinesq

wave model. Monk et al. [6] developed an approximate analytical solution to assess the

distributed wave field about a single row array of overtopping WEC devices, represented as a

series of partially absorbing and transmitting breakwater segments. In the named studies

WECs were implemented through different means, e.g. as small islands or obstructions with

defined coefficients for transmission and absorption, and where possible reflection. A

common problem to all previous, and also to the model discussed in this paper, is the lack of

validation data from field deployments. Another challenge is related to the performance

parameters of different WEC systems, as these are often not available to the scientific

community for reasons of confidentiality.

In this paper the MIKE 21 Spectral Wave model (SW) [7] is used to simulate large scale

WEC array based on the planned developments in Orkney waters. Energy extraction is

represented through arrays of surface attenuators in deep or intermediate water depth,

together with oscillating wave surge energy converters in the shallow waters and results are

compared against a baseline scenario without WEC deployments. Modelling a realistic wave

energy device with energy extraction in MIKE 21 SW module is not a direct process as this

tool does not have the ability to model moving bodies dynamics, however, the hydrodynamic

coefficients describing energy loss, wave scattering, wave diffraction and wave transmission

can be implemented if these coefficients are known for a particular energy device. In order to

generate the hydrodynamic coefficients the state of art wave-structure interaction software

tool WAMIT (http://www.wamit.com/), which is capable of analysing wave interactions with

fixed and floating offshore structures has been used, and the wave absorption, reflection and

transmission characteristics of the devices are obtained. These hydrodynamic parameters

were then input to MIKE 21 SW to model the wave device.

The initial part of this paper provides a detailed description of the model and this is followed

by an overview of results obtained for the year 2010 without the implementation of energy

extraction (baseline). Following on from that baseline scenario details are given on the

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approach used in this paper for the representation of WECs, and the simulated consequences

of the large scale energy extraction on the surrounding wave field are presented and

compared against the baseline.

2. Study area

Exposed to energetic seas from the Atlantic and strong tidal currents driven by a semidiurnal

ebb/flood cycle that combines the Atlantic with the North Sea, the waters surrounding the

Orkney Islands, together with the Pentland Firth at the north of Scotland are a core area for

wave and tidal energy extraction targeted by government and licensing authorities. In 2010

lease agreements for site developments were in place between project developers and The

Crown Estate for a total rated capacity of 1,600MW shared between six wave and five tidal

energy extraction projects (see Figure 1). A number of prototype device deployments have

been completed at the European Marine Energy Centre (EMEC), and as part of previous and

ongoing research and site development projects considerable baseline data has been gathered

in terms of bathymetry and wave observations in the area. The combination of real sites with

planned developments and access to relevant datasets required for setting up and running

resource models made the area around Orkney an obvious candidate for use as model domain

in this project.

3. Model Overview

MIKE 21 SW is a third generation spectral wind-wave model utilising unstructured meshes

[7] to simulate the growth, decay and transformation of wind-generated sea and ocean swells

in offshore and coastal areas. The wind waves are expressed by the wave action density

spectrum. The MIKE 21 spectral wave model includes two methods of wave simulation,

namely, (i) the directional decoupled parametric formulation and (ii) the fully spectral

formulation, both based on the wave action conservation equations in either Cartesian (for

small scale applications) or spherical (for large scale applications) co-ordinate systems [8],

[9]. The model accounts for the physical phenomenon of wave growth from wind, energy

transfer due to non-linear quadruplet or triad wave–wave interaction, and includes energy

dissipation terms for white-capping, bottom friction and depth-induced breaking. The wind

input is based on Janssen’s [10-11] quasi-linear theory. A cell-centered finite volume method

is applied in the discretization of the governing equations in geographical and spectral space

and a multi-sequence explicit method is applied for the wave propagation with the time

integration carried out using a fractional step approach. The model generates phase averaged

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wave parameters as output for either the total computational domain, or selected parts

thereof. Further details can be found in the MIKE 21 wave modelling user guide [7].

3.1 Model set-up

An unstructured computational mesh (see Figure 2) was constructed for the North Atlantic

region (10oE – 75oW and 10oN-70oN) using bathymetry data compiled from General

Bathymetric Chart for Oceans (GEBCO) [12] and Marine Scotland Science [13]. GEBCO

bathymetry data with a spatial resolution of 30 arc seconds was used for most parts of the

model domain and only the area around Orkney, Pentland Firth, Shetland and northwest of

the Isle of Lewis was covered by bathymetry datasets obtained from Marine Scotland

Science. The unstructured mesh of the computational domain visible in Figure 1 was

triangulated using the natural neighbour interpolation method [7]. Finer mesh resolutions

were produced for Pentland Firth and Orkney Waters with a mesh area of 0.0005 square

degrees (approx. 1700m2 ), for the Hebrides and northwest Scotland of 0.001 square degrees

and 0.75 square degrees (approx. 2.5 km2) for the North Atlantic Ocean. Further details on

the model domain and setup are available in Venugopal and Nemalidinne [14].

3.2 Model forcing and physical processes

The model was forced with wind data obtained from the operational model of the European

Centre for Medium-Range Weather Forecasts (ECMWF) [15] at 6 hourly intervals with a

spatial resolution of 0.125o x 0.125o. To ensure fetch unlimited wave growth, decay and

transformation of wind sea and swells, the model was run in ‘fully spectral’ mode with

‘Instationary formulation’. The number of frequencies used for the model was 25 with fmin=

0.04 Hz and a logarithmic frequency distribution with a frequency factor of 1.1. The

directional discretisation had 24 directional bins, each with 15o resolution. A low order fast

algorithm has been chosen as the solution technique with the ‘maximum number of levels in

the transport calculation’ set as 32. A quadruplet-wave interaction has been applied. No

current, ice coverage and diffraction were included into the model. Dissipation due to

whitecapping based on the theory of Hasselmann [16] and Komen et al., [8], bottom friction

according to Nikuradse roughness [17] and depth-induced wave breaking based on the

specified gamma model [18], [19], [20] were considered in the simulations and the energy

transfer was activated. For a detailed description of the above source terms and basis for

selection of the appropriate values the reader is referred to the MIKE 21 SW user guide [7]

and [14].

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3.3 Validation of the wave model

Measured wave data from scientific buoys deployed around Scotland was used to calibrate

and validate the model. The successful calibration of the model is described in detail in [14]

and for this paper a further validation was carried out for the year 2010 for Scottish waters,

based on available measured wave data for Blackstone (56.062°N 007.056°W, depth = 97 m),

Orkney-E (58.970°N 003.390°W, depth = 53 m), and Firth of Forth (56.188°N 002.503°W,

depth = 65 m) and the results are presented in Figure 3. The results have shown good

comparison with measurements for most of the time period for all three sites and this was

particularly true for the significant wave height. As the hindcasting data covers a full

calendar year including both summer and winter months, it is evident that the model is able to

resolve wave conditions for different sea states throughout all seasons. Although the wind

input used here has a temporal resolution of 6 hrs, the impact of varying the resolution to 1 hr

and 3 hrs has also been examined in another publication by the authors (see [21]), however, it

was noticed that the temporal variation of wind speed has less impact on the resulting wave

parameters when large scale modelling is considered.

The performance indices (or quality parameters) for the significant wave height for the model

period of 2010 were calculated for the three buoy locations Blackstone, Orkney-E, and Firth

of Forth and are shown in Table 1. A good agreement between model and buoy data is

observed for all three locations and this is particularly remarkable for the Firth of Forth

location, where the significant wave height for the majority of the time period in the year

2010 is less than 2 m and yet the model was still able to predict this accurately.

Table 1 – Performance parameters for Significant wave height, Hm0, for the year 2010

Site Mean Bias RMSE SI R

Blackstone 2.03

m

0.23

m

0.45

m0.22 0.94

Orkney-E1.67 m 0.03 m

0.31

m0.19 0.95

Firth of Forth 1.15 m -0.10 m 0.25 m 0.22 0.96

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Alternative ways to inspect model results or to compare against measured data are to

represent the data as wave rose and scatter plots as shown in Figures 4 and 5. For the Orkney-

E site, both the data for significant wave height and peak wave period from the model and

buoy measurements are found to be in close proximity to or on the equality line illustrating

that the significant wave height was highly accurately resolved, and this is also indicated by

low values of Bias, RMSE, Scatter Index (SI) and high Correlation Coefficient (R) values as

shown in Table 1.

4. Predictions without Energy Extraction 

The efficiency of Wave Energy Converters (WEC) depends on the characteristics of the site

specific resource, and key parameters are the wave height and period of the different sea

states. Power Matrices are a standard way of expressing WEC performance against particular

sea states and the selection of the most appropriate site and technology for wave farm

operation in a specific region should be based on a thorough analysis of the energy

production of different combinations of different types of WECs at a range of sites. To be

able to undertake such an assessment an accurate and detailed resource characterisation at

each location of interest has to be conducted.

The approach taken here is to run the MIKE 21 Spectral Wave model for the year 2010, with

and without WECs, and to subtract the results from each other to produce maps of the

differences in wave parameters following the inclusion of WECs.

The evolution of mean significant wave height (Hm0) for the pre-device model, for the study

area around Orkney is shown in Figure 6 for the period January to December 2010, which is

extracted from the validated model described in section (3) above. Note that this is one of the

strategic deployment zone identified by the Crown Estate in Figure 1. As expected the wave

height decreases as the wave progresses from a westerly direction across the domain into

reduced water depths. The annual average wave height varies from about 1.6 m to about 2.5

m at the sites where nearshore arrays are proposed (refer to Figure 1).

5. Implementation of Energy Extraction

5.1 Wave Energy Converters and its Array Layouts

Marine Scotland Science developed possible array layout scenarios from Environmental

Statements submitted by developers. WECs were considered as arrays at the following three

sites identified within the TeraWatt project to enhance the understanding of the impact of

removing wave energy on physical processes within the region (see Figure 7).

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Two generic types of WEC are used, a surface based line attenuator and an Oscillating Wave

Surge Converter (OWSC). The first device is based on the Pelamis Wave Energy Converter,

which has been in operation for over a decade with considerable sea trial experience, and is

an attenuator designed to operate in deep water. This converter type consists of semi-

submerged cylindrical sections, moored perpendicular to the wave front. The segments move

relative to one another as waves pass along the length of the machine and the wave induced

motion causes hydraulic cylinders to pump high pressure oil through electric generators.

Based on the power matrix of an early prototype the Pelamis machine attains its maximum

power of 750 kW for a range of values of the wave height and period, generally with Hm0 >5

m and periods around 6-12 s. The second device, an OWSC, used in this study is based on the

Oyster 800 by Aquamarine Power, an Oscillating Wave Surge Converter that is fixed to the

seabed with a hinged flap protruding the surface, where it is pushed backwards and forwards

in an oscillating motion through the wave action. For the first generation Oyster prototypes

power is produced onshore by pumping water through a closed loop towards a Pelton wheel.

The maximum power of this device is rated as 800 kW. The WEC arrays proposed by the

developers are:

i) Marwick Head: An array of 66 Pelamis type devices with a 350 x 400 m (cross stream x

down stream) staggered spacing across 4 rows was considered.

ii) West Orkney: Arrays of 132 Pelamis devices with a 400 x 400 m distance between the WECs in two staggered rows, and 10 times the device length between the arrays (1800 m) were considered.

iii) Brough Head: Single row of 120 Oyster devices (26 m wide and 45 m spacing) was

distributed as 4 arrays along the 12.5 m depth contour.

For the detailed methodology used for the array layouts see O’Hara Murray et. al., (this

issue).

5.2 Implementation of Energy Removal in MIKE 21 Spectral Wave

This study explores a new method of removing energy from the model domain as the MIKE

21 SW model has no built-in algorithm for simulating WECs. By including individual WECs

or WEC arrays as additional source terms representing the energy extracted and redistributed

by the WECs in spectral wave models as used in this study, it is possible to assess the

hydrodynamic behaviour and power performance of WEC array. Such an approach in the

representation of WECs in the most commonly used coastal modelling packages has

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significant practical implications on the development of software tools for the planning of

wave farms.

Since the horizontal dimensions of WECs are usually smaller than the mesh resolution used

in the computational grid, the generic wave energy device in the MIKE 21 SW are modelled

using a sub-grid scaling technique. The location of a WEC is given by a number of geo-

referenced points which together make up a polyline. The location and geometry of these

polyline structures are included when the mesh is created.

The values of the wave energy transmission factors are still not completely understood (due

to a lack of installed systems for validation) or openly disclosed by the WEC developers.

Moreover, these values depend not only on the farm geometry, but on a wider range of

factors, and they often appear to have a dynamic behaviour relationship with the impacting

wave conditions. Given that this work is concerned with surface attenuator and Oscillating

Wave Surge Converter type technology as represented by Pelamis and Oyster devices

respectively, the values of the reflection, transmission and energy loss coefficients were

obtained from a proper wave-structure interaction prediction tool, WAMIT, to represent

various scenarios.

Although the MIKE21 SW model does not have the ability to model the entire dynamics of a

floating wave energy device, it can model wave propagation accurately over varying complex

bathymetry in coastal to ocean scale regions, thus it makes a highly suitable tool to study

wave forecasting or hindcasting. On the other hand the wave structure interaction tool

WAMIT, as demonstrated through various studies is powerful and accurate in modelling any

type of fixed and floating offshore structures, but its downside is that it cannot be applied to

varying bathymetry or wave forecasting or hindcasting and therefore its use in modelling

realistic oceanic scale array to assess environmental impact is less proved. Hence the method

to use WAMIT to determine the energy absorption, reflection and transmission characteristics

of WECs and then transfer these into MIKE 21 for large scale array modelling and at the

same time for studying WECs interaction with marine environment on a wider scale is

chosen. The facility available with MIKE 21 allows one to model the WEC as a line or point

structure, and the former was chosen for this study to model the WECs. MIKE 21 also allows

the structure to be modelled as a submerged, emergent, or sub-aerial structure.

The following methodology was adopted in modelling the devices. The energy transmission

through any WEC structure can be represented by the energy balance equation,

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(1)

where, CT is the transmission coefficient, CR is the reflection coefficient and CL is the energy

loss coefficient. The reflection and transmission coefficients are calculated in normalised

form as ratios of reflected wave height to incident wave height, and, transmitted wave height

to incident wave height respectively.

The information on energy loss or energy absorbed by a device could be obtained from power

matrix produced by developers. The power matrices for Pelamis and Oyster devices are

extracted using the data from [22-23] and a metric known as Power Capture Ratio (PCR) is

produced. The PCR which is a measure of wave power absorbed by a device can be

calculated for different range of significant wave heights (Hm0) and energy periods (Te) as,

(2)

where, Pm is the power produced by a device based on its power matrix for a chosen pair of

wave height and energy period and P is theoretical energy flux calculated for the same pair of

wave parameters, using Eqns (3-4),

(3)

(4)

where, is the group velocity corresponding to the energy period (Te), is the sea

water density taken as 1025 kg/m3, g is the gravitational constant, k and L are the wave

number and wave length respectively, computed with ‘Te’ for the depth ‘d’ using the linear

wave ‘dispersion relationship’. Now the energy conservation equation (1) may be rewritten

as [see ref. 24, page 170],

(5)

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While CT , CR and CL (or PCR) are wave period dependent which means they change with sea

states, determining the energy coefficients for every wave frequency, while it is possible to

do, is laborious, and considering the time and resources available, the wave periods that

correspond to the maximum power output from both the attenuator (Pelamis) and terminator

(Oyster type device) have been selected and corresponding energy coefficients have been

chosen to model the WECs in MIKE 21 SW model. This approach may be justified as the

main interest is to evaluate the impacts on the environment when the devices operate at its

best.

However, before using these coefficients in MIKE 21, the WAMIT results are to be validated

which was done by comparing the results produced from WAMIT with published literature.

Two different WAMIT models have been constructed, one representing the Pelamis device

(of length 120 m and diameter 3.5 m) and another for Oyster type devices which are hereafter

denoted as OWSC (Oscillating Wave Surge Converter). Two types of OWSCs were tested;

OWSC 1 has a width of 18m, immersion depth of 9.4m and thickness of 4m and operating in

a constant water depth of 10.9m, and OWSC 2 has a width of 26 m, immersion depth of 9m

and thickness of 4m and is operating at a water depth of 12.5m. The results are shown in

Figures 8 and 9 for Pelamis and OWSCs respectively. For Pelamis type device, the PTO was

modelled by three hinges but with different PTO (Power Take-Off) damping (hinge 1 = 1.9

x106 Nms, hinge 2 = 1.2 x106 Nms and hinge 3 = 1.9 x106 Nms) as was done in experiments

by Retzler [25], and a good agreement between WAMIT and experiments for power capture

width can be seen in Figure 8. Similarly for Oscillating Wave Surge Converters, The values

of wave excitation force, added inertia, radiation damping and q-factor, all presented against

the wave periods (see Figure 9) for OWSC 2 showed an excellent match with Renzi et al.

[26], though not graphically reproduced here. Thus the WAMIT model has been verified,

further simulations were carried out for the wave conditions corresponding to the maximum

power production for each device and the values of transmission and reflection coefficients

have been obtained. The values of the wave transmission/reflection coefficients for Pelamis

type devices selected were CT = 0.99 and CR = 0.01, and for OWSC, CT = 0.75 and CR = 0.25.

To verify the validity of the above coefficients and method, wave climate modification for an

array of devices from both WAMIT and MIKE 21 have been compared in Figure 10, for

significant wave height Hm0 = 3m and peak wave period Tp = 7.5s. In total, three Pelamis

type devices (Figure 10, subplots at the top) and five OWSCs (Figure 10, bottom subplots)

were simulated using JOWNSWAP wave spectrum with a peak enhancement factor of 3.3

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and a directional standard deviation = 5°. Despite some differences in wave height

distribution, the general wave propagation pattern in MIKE 21 agreed well with WAMIT. It

is also clear that MIKE 21 shows a large reduction in wave height immediately downstream

of the device and no alteration to the upstream wave field; this is expected as the wave

diffraction which was included in WAMIT was not considered in MIKE 21. Nevertheless, as

the far field wave conditions being less affected in MIKE 21, and no other single software

tool that can model both WEC and wave environments, it was decided to accept this solutions

for further modelling. A maximum difference of up to 30% in wave heights between WAMIT

and MIKE 21 results are seen, particularly very close to downstream of the WECs, however,

this difference is found to be minimum further downstream.

6. Results and Discussions

The WEC array models were simulated for the same time period as the baseline model (as in

Figure 6), to be able to evaluate the wave farm impact by comparing model outputs with and

without WECs. Following the implementation of the WEC arrays (both attenuator and

terminators) in the model for 2010 it is observed that the mean significant wave height is

decreased downwave of the arrays and this is visible in Figure 11. Further, the absolute mean

difference in the significant wave height as a result of inclusion of the WEC arrays is shown

in Figure 12. A clear reduction of wave height is observed downwave following the inclusion

of WEC arrays with the largest differences being visible in the region immediately behind the

wave array. At the point of maximum impact, i.e., downstream of array close to coast, a large

decrease in wave height based on the annual mean wave conditions is noticed and this

constitutes a reduction of maximum of up to 1 m or just above (i.e difference in mean wave

height computed with WEC minus no WEC) of the incident wave height. The wave height is

decreased because of the energy extraction by the WEC array, which is indicated by a

negative value in the downstream of the arrays (Figure 12). Furthermore, the results show

that as the downstream distance increases the individual effects of each device reduces and an

evenly distributed reduction in wave height is observed. The impact of the wave farms

decreases with increasing distance, and this is due to restoring processes e.g. diffracted wave

energy penetrating into the lee of the wave farm from both sides.

A comparison of the baseline data time series against the WEC array scenario is shown in

Figure 13 for a location indicated by the red coloured point to the west of the Bay of Skaill in

a water depth of 8m. Significant wave height, peak wave period and mean wave direction of

the both cases are presented for the year 2010, and, it is clear that a significant reduction in

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wave height is obvious. The fact that, the wave heights are reduced and the wave directions

and wave periods are less affected, which demonstrates that changes to sediments and beach

erosion at this site might be less significant, however this needs further research.

In order to provide a quantitative comparison between the baseline scenario and the model

outputs with WEC arrays included, scatter plots for the hindcast significant wave height,

peak wave period and mean wave direction are shown in Figure 14, for the same location in

the Bay of Skaill. It is evident from the scatter plot that the significant wave height predicted

with included WEC arrays is smaller than for the baseline scenario without WECs. The

correlation between baseline and with WECs case is highest for wave period and lowest for

wave height indicating that the impact of WEC deployments on wave period is less than on

wave height.

To provide a detailed analysis of energy extraction, the percentage change in significant wave

height for each node is calculated and shown in Figure 15. The location of each device is

indicated by a large reduction in wave height leeward of the device as indicated in the

theoretical test in Figure 10. The maximum percentage height difference results from a

situation where a very small original wave height undergoes a substantial change due to wave

farm even though the absolute difference is minimal.

To better visualise the impact, the variation in the significant wave height along a line

transect (B1-B2) through the mid-section of an array and extending up to the 8 m depth

contour line was computed from mean conditions and is shown in Figure 16. This plot also

has two other transects (A1-A2 and C1-C2). The model results indicate a reduction of

significant wave height across the arrays for all locations. The transect line B1-B2 ending at a

point in Bay of Skaill shows a wave height reduction of up to 60% from offshore to nearshore

due to the cumulative effects of all wave farms. Large reductions have also been noticed for

transects A1-A2 and C1-C2, and the maximum impact is observed for transect A1-A2

directly downwave of the WEC array. These changes of significant wave height represent the

net change of wave conditions due to energy absorption by WECs, interaction between

devices within an array and between adjacent arrays, scattering by the array and local

bathymetry effect. The magnitude of reduction clearly varies with both the number of devices

installed in each row and their alignment. It is to be kept in mind that the results presented

above are purely numerical simulation based and no validation with real scale deployments

has been done, hence usage of this data to be treated with caution.

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7. Conclusions

Arrays of two different wave energy converters (WECs) proposed by the device developers

in the Orkney Islands have been modelled using the industry standard software tool MIKE 21

spectral wave model, to assess the consequences of energy extraction by large scale wave

farms on the regional sea state distribution around the farms. The proportions of wave energy

absorption, reflection and transmission by the WECs within the MIKE tool have been

modelled by their respective energy coefficients obtained from the state of art wave-structure

interaction software WAMIT after a validation exercise.

This study demonstrated that the WEC arrays altered the wave climate within an array and

also the neighbouring array. Cumulative wave height reduction downstream of the WEC

array and farther down the coastline appears to be significant, and, its magnitude depends on

the array layout and number of co-located arrays. The average yearly reduction in wave

height immediately to the lee side of the array was observed to be very high, and its

magnitude varies from arrays to arrays. With increasing distance from the arrays towards the

shoreline, a recovery in wave heights or energy restore is evident, and energy progresses into

the downwave shadow region of the arrays from the sides.

In this study the effect of devices is modelled using frequency independent transmission

coefficients, rather than using a more detailed approach, due to unavailability of precise

device specific data. Further work is required in investigating frequency dependent

behaviour and dynamic response characteristics of coefficients for absorption, transmission

and reflection.

Acknowledgements

Work presented in this paper is part of the TeraWatt project and the authors wish to

acknowledge support from the UK Engineering and Physical Sciences Research Council

(EPSRC) under grant reference number EP/J010170/1. The authors are also grateful to Cefas

(UK) for wave buoys data, European Centre for Medium-Range Weather Forecasts

(ECMWF) for providing wind data, European Marine Energy Centre (EMEC) for providing

wave buoy data for Orkney, The Crown Estate, UKHO and Marine Scotland Sciences for

providing bathymetry data.

References

[1] D. L. Millar, H. C. M. Smith, and D. E. Reeve, “Modelling analysis of the sensitivity of

shoreline change to a wave farm,” Ocean Eng., vol. 34, no. 5–6, pp. 884–901, 2007.

14

[2] V. Venugopal and G. H. Smith, “Wave climate investigation for an array of wave power

devices,” 7th Eur. Wave Tidal Energy Conf., pp. 1–10, 2007.

[3] Palha, L. Mendes, C. J. Fortes, A. Brito-Melo, and A. Sarmento, “The impact of wave

energy farms in the shoreline wave climate: Portuguese pilot zone case study using

Pelamis energy wave devices,” Renew. Energy, vol. 35, no. 1, pp. 62–77, 2010.

[4] Beels, P. Troch, G. De Backer, M. Vantorre, and J. De Rouck, “Numerical

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[6] K. Monk, Q. Zou, and D. Conley, “An approximate solution for the wave energy

shadow in the lee of an array of overtopping type wave energy converters,” Coast.

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Institute, Denmark; 2012.

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MSInteractive/datatype/Bathymetry/data . accessed on 28/05/14.

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using a large scale North Atlantic Model”, Renew. Energy, vol. 76, pp. 503-525, 2015.

[15] ECMWF. http://www.ecmwf.int/; accessed on 28/05/14.

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[16] Hasselmann K. On the spectral dissipation of ocean waves due to whitecapping,

Bound. Layer Meteor. 1974; 6: 107-127.

[17] Weber SL. Bottom friction for wind sea and swell in extreme depth-limited situations,

J. Phys. Oceanogr. 1991; 21: 149-172.

[18] Nelson RC. Design wave heights on very mild slopes: An experimental study, Civil.

Eng. Trans., Inst. Eng. 1987; 29: 157-161.

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43-59.

[20] Ruessink BG, Walstra DJR, Southgate H.N. Calibration and verification of a

parametric wave model on barred beaches. Coastal Eng. 2003; 48: 139-149.

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September 2015.

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converters. Renewable Energy, 2012. 41: p. 44-63.

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[24] McCormick, M.E., Ocean Engineering Mechanics: With Applications. 2010,

Cambridge; New York: Cambridge University Press.

[25] Retzler, C. Measurements of the slow drift dynamics of a model Pelamis wave energy

converter. Renewable Energy, 31(2), 257-269, 2006.

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of oscillating wave surge converters, Renewable Energy, 63, 55-68, 2014.

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Figure 1. Location of Pentland Firth showing wave and tidal energy leasing sites (http://www.thecrownestate.co.uk/energy-and-infrastructure/wave-and-tidal/the-resources-

and-technologies/3).

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Figure 2. Computational domain for North Atlantic wave model.

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Figure 3. Comparison of significant wave height, between measurements and MIKE21 model:

(a) Blackstone - top, (b) Orkney-E – middle (c) Firth of Forth – bottom.

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Figure 4. Wave rose diagram of the MIKE21 model data at Orkney location:

The left hand plot is for Hm0 (m) and the right hand plot is for Tp(s).

Figure 5. Comparison between measurements and MIKE21 model at Orkney location:

Shown is Hm0 (m) on the right, and Tp (s) to the left.

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Figure 6. Mean significant wave height for the period January to December, 2010 without energy extraction.

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Figure 7. Map of the Orkney showing the layout of 300 WEC devices.

22

Marwick Head

West Orkney

Brough Head

Figure 8. Validation of WAMIT results for Pelamis wave energy converter with experimental results from [24]. Three hinges with different PTO damping (hinge 1 = 1.9 x106 Nms, hinge 2 = 1.2 x106 Nms and hinge 3 = 1.9 x106 Nms) have been used.

23

Figure 9. Validation of hydrodynamic coefficients for OWSC 1 (width = 18 m, immersion depth = 9.4 m, thickness = 4m, operating water depth = 10.9 m) and OWSC 2 (width = 26 m, immersion depth = 9 m, thickness = 4m, operating water depth = 12.5 m). (a) Wave excitation forces, (b) Added inertia, (c) radiation damping and (c) q-factor.

24

4 6 8 10 12 140.0

0.5

1.0

1.5

2.0

2.5

F ext f

or O

WSC

2 (x

107 N

.m)

T (s)

OWSC 1 OWSC2 n = 0 n = 1

n = 2

(a)

0

1

2

3

4

5

F ext f

or O

WSC

1 (x

106 N

.m)

4 6 8 10 12 140.0

2.5

5.0

7.5

10.0

12.5

B a (x

107 k

g.m

2 /s)

T (s)

OWSC 1 OWSC 2 n = 0 n = 1

n = 2

(c)

4 6 8 10 12 140.0

2.5

5.0

7.5

10.0

12.5

I a (x

107 k

g.m

2 )

T (s)

OWSC 1 OWSC 2 n = 0 n = 1

n = 2

(b)

4 6 8 10 12 14-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

q

T (s)

OWSC 2 n = 1 n = 2

(d)

WAMIT MIKE21 SW

(a) Surface Attenuato

r

(b) OWSC

Figure 10. Comparison of WEC performance between WAMIT and MIKE21 SW models for (a) surface attenuator and (b) OWSC. Wave conditions:

Hm0 = 3m, Tp = 7.5s and θ = 0deg.

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Figure 11. Mean significant wave height for the period January to December, 2010 with energy extraction.

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Figure 12. Absolute difference of mean significant wave height with and without energy extraction for the period January to December, 2010.

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Figure 13. Comparison of time series of wave height, wave period and wave direction at Bay of Skaill between Baseline and WEC scenarios.

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Figure 14. Scatter plot of significant wave height, peak period and mean wave direction at Bay of Skaill, comparing model predictions with and without WECs.

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Figure 15. Percentage change in significant wave height.

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Figure 16. Wave height reduction across three transect lines post array deployments.

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