Renewable Energy 35 (2010) 443–455

Contents lists available at ScienceDirect

Renewable Energy
jou rn al home pa ge : ww w .e ls e v ie r. co m / l oc a te / r e n e n e

Case study feasibility analysis of the Pelamis wave energy convertor in Ireland,
Portugal and North America
G.J. Dalton*, R. Alcorn, T. Lewis
Hydraulics and Maritime Research Centre (HMRC), University College Cork, Youngline Industrial Estate, Pouladuff Road, Cork, Ireland

a r t i c l e i n f o
a b s t r a c t
Article history:
Received 16 February 2009 The performance and economic viability of the Pelamis wave energy converter (WEC) has been inves-
Accepted 1 July 2009 tigated over a 20 year project time period using 2007 wave energy data from various global locations:
Available online 5 August 2009 Ireland, Portugal, USA and Canada. Previous reports assessing the Pelamis quote a disparate range of
financial returns for the Pelamis, necessitating a comparative standardised assessment of wave energy
Keywords: economic indicators. An Excel model (NAVITAS) was created for this purpose which estimated the annual
Pelamis wave energy converter energy output of Pelamis for each location using wave height (H s) and period (Tz) data, and produced
Hs and Tz financial results dependant on various input parameters. The economic indicators used for the analysis
Annual energy output were cost of electricity (COE), net present value (NPV) and internal rate of return (IRR), modelled at
Cost of electricity a tariff rate of V0.20/kWh). Analysis of the wave energy data showed that the highest annual energy
Feed-in tariff
output (AEO) and capacity for the Pelamis was the Irish site, as expected. Portugal returned lower AOE
Learning/production curve
similar to the lesser North American sites. Monthly energy output was highest in the winter, and was
particularly evident in the Irish location. Moreover, the difference between the winter wave energy input
and the Pelamis energy output for Ireland was also significant as indicated by the capture width, sug-
gesting that Pelamis design was not efficiently capturing all the wave energy states present during that
period. Modelling of COE for the various case study locations showed large variation in returns,
depending on the number of WEC modelled and the initial cost input and learning curve. COE was
highest when modelling single WEC in comparison to multiples, as well as when using 2004 initial costs
in comparison to 2008 costs (at which time price of materials peaked). Ireland returned the lowest COE
of V0.05/kWh modelling over 100 WEC at 2004 cost of materials, and V0.15/kWh at 2008 prices.
Although favourable COE were recorded from some of the modelled scenarios, results indicated that NPV
and IRR were not encouraging when using a V0.20/kWh tariff. It is recommended that a tariff rate of
V0.30/kWh be considered for Ireland, and higher rates for other locations. In conclusion, Ireland had the
most abundant wave energy output from the Pelamis. COE returns for Ireland were competitive for large
number of WEC, even at peak costs, but it is recommended that careful analysis of NPV and IRR should be
carried out for full economic assessment. Finally, a standardised method of COE reporting is recom-
mended, using fixed WEC number or MW size, as well as standardised learning/production curves and
initial costs, to facilitate confidence in investment decisions based on COE.
© 2009 Elsevier Ltd. All rights reserved.

1. Introduction
same time period [2]. Moreover, there is rising demand by both
public [3] and state for increased use of renewables in energy
This article is an economic feasibility analysis study of the
supply. A combination of all renewable sources, including wave
Pelamis device, using wave energy data collected from 6 case
energy, will be required to meet those targets. Wave energy is still
study locations in Europe and North America. The study stems
in the nascent stage [4], requiring substantial subsidies and
from the increasing need for alternative energy sources as
support for research and development to bring the technology to
Europe faces a renewable energy target of 20% target by 2020
the commercial stage [5]. However, there is a lack of confidence by
[1], and some countries such as Ireland setting even higher targets
business and investors that renewable energy is economically
of 40% for the
feasible for commercial energy supply [6].
The cost of electricity (COE) is the benchmark criterion by
which most renewable energy (RE) projects are judged [7]. COE
* Corresponding author. Tel./fax: þ353 21 4250028.
refers to electricitycost where there is zero revenue or tariff from an
E-mail address: g.dalton@ucc.ie (G.J. Dalton).
electricity

0960-1481/$ – see front matter © 2009 Elsevier Ltd. All rights reserved.
doi:10.1016/j.renene.2009.07.003
 Average €/ ton, gross No. 1 heavy melt steel
Glossary 400
350
AOE Annual energy output
COE Cost of electricity 300
CRF Capital recovery 250

€/ton
factor GHG Greenhouse
200
gases
Hs, Tz Significant average wave height, mean period or 150
zero crossing 100
IC Initial cost
50
IRR Internal rate of
return NPV Net present 0
2001 2002 2003 2004 2005 2006 2007 2008 2009
value
O/M Operation and maintenance Fig. 1. Historical heavy melt steel price, American metal market, 2001-2007 (www.
RC Replacement cost scrapmetalpricesandauctions.com/iron-steel).
RE Renewable energy
REC/ROC Renewable energy credits/renewable obligation
certificates peak recorded rate over a five year period. As a result of using this
FIT/REFIT Feed-in tariff/renewable energy feed-in tariff rate, costs in Euro will make final COE results in this article appear
RES Renewable energy system lower that they would at a lower exchange rate. Various initial
Tf Technology costs (IC) will be modelled and their impact on COE assessed.
factor USA EC USA east
coast USA WC USA west 3. Size/number of the WEC farm and dependence on cable
coast size
utility company. However, COE can also be interpreted as the elec-
Large scale purchasing of WEC coupled with learning/produc-
tricity tariff rate returning a zero net present value (NPV). This
tion curves (defined later) has a moderating influence on IC.
arbi- trary method of defining COE is not ideal, and other
Additionally, a collection of WEC can be serviced by one cable,
benchmark financial criterion or indicators such as NPV and internal
which has the required kV rating and capacity to cater for the load.
rate of return (IRR) are preferred to compare project viability [8].
Thus savings will accrue if the optimal number of WEC is matched
Nevertheless, due to its prevalent use COE will be the major
to whatever cable size is chosen.
indicator of this report.
There have been many studies which have provided COE
4. Feed-in tariffs
figures for wave energy projects. However at present, it is difficult
to compare COE results from reports and studies due to the large
There is much debate at present concerning appropriate price
variation in quoted figures. It is essential that correct COE are
support schemes or power purchase arrangement (PPA) to stimu-
forecast so that investors can budget for long-term projects, as
late growth in the wave energy sector.
well as policy makers who are nominating feed-in tariff rates
Fixed tariff or feed-in tariff (FIT) rates are gaining consent as
intending to support and accelerate growth in wave energy
the most successful method to stimulate RE development [11,12].
industry. COE is directly related to the quantity of energy input to
The main proponents of the scheme are Germany and Spain [13],
the system, and thus is very dependant on location of the energy
and has resulted in a RE boom in those respective states, almost
source. This paper will present wave energy data collected from
exclusively in on-shore large wind and PV projects. The Irish and
various global loca- tions and assess the corresponding COE
Portuguese governments are the only two states that have prom-
resultant.
As with all analysis, there are many variables which can impact ised an FIT or renewable energy feed-in tariff (REFIT) for electricity
on the final COE result. This report will conduct sensitivity on the produced by wave energy. Ireland is promising V0.22/kWh,3
following variables and assess their impact on COE. and Portugal a range of tariffs ranging from V0.07–26/kWh [14]
(Table 1). Spain, France, Denmark and Germany have also
proposed wave energy FITs, but they are modest and not been
2. Impact of the cost of materials and initial cost (IC) implemented at the time of this paper.

Steel is currently the main material constituent of a WEC, and 4.1. Wave energy device – Pelamis
thus has the largest influence on initial cost (IC). Steel has had
major price fluctuations over the past few years (Fig. 1). Recent The WEC chosen for analysis in this report was the Pelamis, as
factors influencing steel prices fluctuation were increasing it is the only WEC to date that has a published and reliable power
demand from China for raw materials, which led to a price performance matrix (Table 6). The Pelamis wave energy converter
escalation [9], followed by the credit crunch and global recession is developed and manufactured by Pelamis Wave Power (PWP)
in mid 2008, causing steel prices to eventually fall to 2007 prices (formerly known as Ocean Power Delivery Ltd), an Edinburgh-
[10]. The final cost of manufactured steel, typically grade 50 based company originating from the Wave Power Group at the
(S355), painted with corrosive protection, can cost anywhere from University of Edinburgh in 1998 [15,16]. The Pelamis is a semi-
V5000–7000/ton,1 and this price had not substantially fallen at submerged snake-like device consisting of articulated cylindrical
the time of writing this paper, although is forecast to do so in
2009. US currency conversion to Euro used in this report was
1.57 (July 2008),2 which was the

1
Personal communication Paul Collins, Malacky Walsh Engineers, Cork. 3
2
http://www.ndp.ie/viewdoc.asp?Docid¼2034&mn¼newx&nID¼&UserLang¼
http://finance.yahoo.com/q/bc?s¼EURUSD¼X&t¼5y&l¼on&z¼m&q¼l&c¼ EN&CatID¼15&StartDate¼1þJanuaryþ2008
Table 1
Countries which have feed-in tariff programs.

Country Application and restrictions Proposed tariff

Ireland Applies to all developments V0.22/kWh
Portugal Demonstration projects 0–20 MW V0.26/kWh
Pre-commercial 20–100 MW V0.16–0.21/kWh
Commercial 20–100 MW V0.10–0.16/kWh
Commercial 100–250 MW V0.08–0.11/kWh
Commercial 250 þ MW V0.075/kWh

sections linked by hinged joints (Fig. 2). The version used in this
assessment was 120 m long, 3.5 m in diameter, rated at 750 kW
and weighed 700 ton.
PWP has raised some £40 m to fund the development of
Pelamis technology from a variety of financial and industry
backers. Major shareholders include; Emerald Technology
Ventures, Norsk Hydro Technology Ventures, BlackRock
Investment Managers, 3i, Carbon Trust, Nettuno Power, Tudor
Global and Scottish Enterprise.
PWP have their first major demonstration project in Aguça-
doura, Portugal. The multiple Pelamis units making up the Aguça-
doura wave farm constitute both the world’s first, multi-unit, wave
Fig. 2. Pelamis prototype [15].
farm and also the first commercial order for wave energy
converters. The Aguçadoura project is owned and operated by
a joint venture company called Companhia da Energia Hawaii, where there was a lower predicted wave intensity, the
Oceaˆnica (CEO) which is currently 77% owned by a subsidiary of power output of the device was reduced from 750 kW to 500 kW.
Babcock and Brown Limited and 23% by Pelamis Wave Power However the efficiency was increased to 88% and the availability
Limited. Since the financial crisis accelerated in the last quarter of to 95%. Costs quoted by the EPRI report for the single WECS,
2008, Babcock and Brown Limited has had its shares mooring and cables were used in this present article. The initial
suspended and has been in a managed process of selling its cost of the WECS was $2,415,000 or V1,533,207, at 2004 prices.
assets. Pelamis are in the process of searching for a new partner. Full COE analysis was only conducted by EPRI on the large
The E.ON energy group are the second major developer using the commercial project. COE quoted was $0.11/kWh (approximately
Pelamis. E.ON plans to deploy the latest Pelamis design, the ‘P2’, in V0.08/kWh) for an electricity tariff rate of V0.07/kWh. A further
the European Marine Energy Centre (EMEC) in 2010. Future plans report by EPRI was conducted 2 years later (2006) by Bedard
for the EMEC and the Orcadian Wave Farm will consist of four [19], and reported a slightly lower COE, with a range of V0.05–
Pelamis generators supplied by PWP to ScottishPower 0.08/kWh.
Renewables supported by £4 m funding from the Scottish The most recent report on Pelamis was conducted in Canada
Executive providing. Original plans by E.ON to test the Pelamis at examining a proposed 25GWh (27 Pelamis) wave power plant
Wave Hub site have been shelved as of April 2009 until a future [20]. The capacity factor for the Pelamis at the locations sampled
date. were approximately 20% and cost of electricity ranged from
Other wave energy device contenders currently on the market
V0.23–0.38/ kWh, depending on the location. The article
include two Irish companies, Ocean Energy Buoy 4 and Wavebob.5
mentioned that the output was low in comparison to the EPRI
Both these designs have completed the quarter stage prototype
report which used the same device design. It commented that the
development stage and are planning the full scale pre-commer-
design was intended for North Atlantic waters, which have
cialised testing in the near future. Table 2 lists the other wave
different sea states to those of Canada. Another Canadian study
energy companies that are the late stages of prototype, pre-
looking at 15 Pelamis quoted a COE of between
commercial testing and commercial phases of development.
V0.10–0.15/kWh [21].
The major Irish report studying the Pelamis was produced by
ESBI [22] for SEI. The COE reported was V0.105/kWh. A second Irish
4.2. Previous COE wave energy studies using the Pelamis
report was undertaken by Bacon [23] in 2005. However the per
kWh reading quoted was not for cost of electricity but value of the
Table 3 lists the major wave energy reports where the Pelamis
electricity produced to the country, and this was V0.097/kWh
was assessed and COE was quoted.
based on a scenario of 50kW/m power and a tariff for 2010 of
The largest study was conducted by Previsic [18] in 2004 for
V0.08–.10/kWh, decreasing to V0.05/kWh by 2020.
EPRI in California, US. Two feasibility analyses were conducted;
Two British studies forecasted COE of V0.08/kWh and V0.10/
the first was a pilot test with one device near shore in 25 m of
kWh [24,25] (the latter examined 4000 Pelamis and assumed
water in the location off San Francisco, and the second was a
a V0.05/kWh renewable subsidy).
commercial test, with 213 devices in 50 m of water depth in a
Finally, the Pelamis Company itself has published data of the
location off Hawaii. An adjustment was made for the shallow water
Pelamis performance, and quotes a COE of V0.08–0.16/kWh [16].
site in San Francisco adding a power conversion efficiency factor
Overall, almost all of the studies reported a COE of between
of 80% and device availability 6 at 85%. For the second
V0.05 and 0.20/kWh with or without a subsidy or feed-in tariff.
commercial project in

4
4.3. Case study locations
http://www.oceanenergy.ie/
5
http://www.wavebob.com/
6
Availability is defined probability of the whole system functioning at any Four countries were chosen for this study. Ireland has one of
specific time, taking into account maintenance and breakdowns. the highest wave energy climates in the world on a kW/meter
basis, as
Table 2
Wave energy companies that are presently at the prototype or pre-commercial phase of development. (Phase of development 1 ¼ initial design, 3 ¼ prototype testing, 4 ¼ pre-
commercial testing, 5 ¼ commercial arrays). (Data obtained from [17]).

Country Company Device Type Prototype rating Phase Scale Test rating
Ireland Ocean Energy OE Buoy Floating OWC 2 MW 3 01:04 15 kW
Ireland Wavebob Wavebob Inertia 2 MW 3 01:04 15 kW
UK Pelamis Wave Power Pelamis Inertia 750 kW 4–5 01:01 750 kW
UK Aquamarine Power Oyster Inertia 500 kW 3–4 01:01 500 kW
AWS Ocean Energy Wave Swing Inertia 2 MW 3 01:01.8 250 kW
Canada Finavera AquaBuOY Inertia 250 kW 3 01:02 25 kW
Norway Fred Olsen FOBOX3 Inertia 2.5 MW 3 1.3 50 kW
Australia Oceanlinx Oceanlinx Floating OWC 2 MW 3 01:03 45 kW
USA OPT PowerBuoy Inertia 150 kW 3 01:01.5 40 kW
Denmark Wave Dragon Wave Dragon Floating Overtopping 7 MW 3 01:05.2 20 kW
Denmark WavePlane WavePlane Floating Overtopping 500 kW 3–4 1:1–2 250 kW
Denmark Wavestar Wavestar Inertia 5 MW 3 01:10 5.5 kW

well as a promised FIT of V0.22/kWh.7 Portugal is making the

most progress in wave energy deployment, having both the Pilot moderate condition with 1.5% of the data blank, which was readily
Zone test area, as well as Pelamis currently doing tests in the correctable. The Portuguese data was also private and available for
country. Furthermore, Portugal has promised an FIT of a fee. The data was recorded in 10 min durations. The data was
V0.26/kWh for the first 20 MW of wave energy installed [14]. presented in unprocessed form, where unrecorded data was not
Finally, the North American continent was chosen, due to its presented, i.e. unrecorded data was not presented as a blank. Pro-
interest in wave energy technologies, as well as comparison of cessing of this data required a Matlab [28] program to average the
wave climates between east and west coasts (Table 4). data in hourly increments.9 Blanks that were larger than 1 h and
up to 5 h in duration were interpolated. The month of February
had 10 days of missing data. The gaps were filled by using data
5. Assessment methods
from 5 days prior and 5 days after the gap.
The platform for NAVITAS was Microsoft Excel spreadsheet
5.1.2. Power matrix and energy matrix
[26], and the results from NAVITAS were validated using a similar
The total annual energy output (AEO) for the year was
model called RETScreen [27]. NAVITAS proceeds through the
calculated in NAVITAS by multiplying each cell point of the scatter
analysis in two stages:
plot of hours with the corresponding cell of a WEC power matrix.
For this report, the power matrix of the Pelamis was used [15]. A
1. Energy and power calculations.
capacity factor10 (or sometimes called the load factor or utility
2. Economic analysis.
factor [18]) is incor- porated in the power matrix. The Pelamis
power matrix is presented in Table 6. Power peaks at 750 kW for a
number of sea states.
5.1. Energy calculation
Wave energy input (WEI) is calculated using the following
equation:
5.1.1. Scatter plot of hours
Unprocessed wave energy data consists of a wave energy
WEI ¼ 0:55 Hs2Tz (1)
spectrum. Significant average wave height (Hs) and period (Tz)
parameters are extracted from the data, using the Bretschneider WEI is a product of the energy input and the ‘apparent’ width of
spectrum function which has been found to be the best suited a WEC. Although the width of the Pelamis is 3.5 m, the apparent
function for deep sea long-fetch locations. The data is processed width used was 8.75 m, due to lateral motion of the WEC and wave
and averaged in either 10, 30 or 60 min units. NAVITAS requires attenuation along the WEC.
the data in 60 min increments. A ‘scatter plot’ or ‘diagram’ (also
known as a joint probability distribution) of hours was created for
each month, which is a table showing the frequency in hours of 5.2. Economic inputs
occur- rence of each sea state. Not all combinations of height and
period occur (or are even possible) in a real sea state, thus most of 5.2.1. Initial cost
the scatter plot cells were empty. A total year’s scatter diagram The project lifespan of 20 years was used. Initial costs (IC) for the
was produced summing the cell points for each month, totalling WEC only reflected the purchase of the Pelamis device from the
8760 h for the entire year (or 8784 in a leap year). manufacturer, and any sundry costs such as planning and
Data for the locations was obtained from various wave energy installing of the device. The remainder of other costs (except cable
centres and websites, listed in Table 5. Data from USA and costs) was calculated as a percentage of the IC. This method
Canadian websites was publically available from their websites. allowed for simplified cost and sensitivity analysis. The IC of the
The Canadian data was in excellent condition with no modification Pelamis WEC chosen for this report was V1,533,00011 obtained
needed. The NOA data had some blanks recorded (0.05%), but from the 2004 EPRI report in California [18]. The figure included
were minor and easily corrected. The Irish data was obtained from costs for both the steel sections and all the internal components.
HMRC, which collected the data from the M buoys, owned by the The weight of the Pelamis was 700 ton, giving V2200/ton. Table
Marine Insti- tute.8 The data was available for a fee. The quality of 7 lists the cost of the other components which were based as a
the data was in percentage of the IC.

7 9
http://www.ndp.ie/viewdoc.asp?Docid¼2034&mn¼newx&nID¼&UserLang¼ Matlab file for data processing was created by Florent Thiebaut, HMRC, Cork.
10
EN&CatID¼15&StartDate¼1þJanuaryþ2008 Capacity factor is the ratio of the mean generation to the peak generation of
8
http://www.marine.ie/Home/ a WEC.
11
WEC $1,565,000 þ steel sections $850,000. US currency conversion to Euro was
1.57 (at July 2008).
Table 3
Wave energy device studies reporting COE using the Pelamis power matrix.

Study Reference Location Year Number of Pelamis COE V/kWh Subsidy

EPRI (Previsic) [18] California 2005 213 0.08 0.06
ESBI [22] Ireland 2005 209 0.105 –
St Germain [21] Canada 2005 15 0.10–0.15 –
EPRI (Bedard) [19] California 2006 44 0.05–0.12 –
Carbon Trusta [25] UK 2006 13,000 0.08–0.30 –
13
Allan et al. [24] Scotland 2008 4000 0.10 –
Dunnet and Wallace [20] Canada 2008 15–27 0.18–0.30 –
Pelamis [16] UK 2008 1 0.08–0.16 –
a
Pelamis not used in Carbon Trust.

The table also contains comparison costs to another report,

WEC, mooring and cable. Since the lifespan of Pelamis WEC used in
showing similarity in costs.
this report was 20 yrs (as quoted by Allan [24]), and the project
The only component that was not based on Previsic [18] IC was
lifetime of the analysis is 20 years, there was no replacement costs
cable cost, which were sourced from an ESBI [29] report. Cable
scheduled. Other lifetimes quoted are 15 yrs by Previsic [18].
cost for 0.5–1.9 MW capacity equalled the IC of one WEC ( Table 8).
No overhaul of the WEC device and infrastructure was included
This is in contrast to the cable costs of Previsic [18] and Allan,
either, as it was deemed that analysis of both overhaul and
Bryden et al. [24], who quoted 50% and 5% of IC respectively (Table
replacement impacts on COE would be extensive and the subject
7). Such variation in cable cost estimation will have profound
matter for a further paper.
impact on economics, and will need to be carefully assessed in
O/M costs are treated as a capital costs. Percentage O/M expenses
analysis.
were take in the range of 1–3% coinciding with studies of St Germain
As the cost of steel approximately tripled from 2004 to 2008, IC
[21] and Dunnett [20]. Previsic [18] and Allan [24] estimated O/M to
for the Pelamis in 2008 was similarly based on a tripling of costs
be around 40% for a project. Further investigation of high O/M
(Table 9). The IC for cabling has also increase in that period but
impact on COE will be the subject matter of a further paper.
not to the same extent. Thus a doubling of cable IC was used in
2008.
5.2.4. Salvage value
The salvage value is a positive credit tothe costs once the project
5.2.2. WEC number
has completed. The value assumes a linear depreciation meaning
A sliding scale was used to estimate the cost of WEC compo-
that the salvage value of a component is directly proportional to its
nents with increasing number. The sliding scale is based on the
remaining life. Salvage value is calculated by the following formula
learning curve [31], and does not factor mass production into the
[32]:
equation. This is because WEC production is deemed never to
reach the scale of automotive production. The formula for the
learning
curve is as follows: RC*RL (3)
S ¼ Lt
ðlnðtf Þ=lnð2ÞÞ
P ¼ A (2) Where S is the salvage value, RC is the replacement cost of the
component, RL is the years remaining and Lt is the components
Where P is the percentage scaling, A is the number of WEC
lifetime. The replacement cost is calculated for each replacement
components and ‘tf’ is the technology factor. The technology factor
time using the discount factor, and thus inflation is factored out of
of most industrial products is mostly between 0.85 and 0.95. For
the equation.
this project, 0.9 was chosen.
If the life of the item is less than the project lifespan, then the
It is assumed that there will be ideal grid pattern spacing for
remaining life (RL) of the component at the end of the project
multiple WECS and that there is no limitation on laying out
lifetime is given by:
converter cordons and cabling in the sea so that the technical
resource can be evaluated. It is assumed that an electromechanical RL ¼ Py — CY (4)
conversion efficiency of 85% is already incorporated into the energy
matrix of the Pelamis. Where Py is the project years and CY is the total years up to last
replacement of the component, and calculated as follows:
5.2.3. Overhaul, replacement and operation and maintenance
(O/M) Table 5
Table 10 lists the percentages of IC used to calculate the costs List of case study locations and sources for data.
for overhaul, replacement and operation/maintenance for either
the
LocationSource of data Data Quality of
availability data
Table 4
Ireland HMRC, Cork, Ireland. Fee payablea Moderate
Case study buoys and location details.

Country Location Buoy Depth (m) Latitude/Longitude USA National Oceanic and Atmospheric Association (NOA),
PublicallyModerate
Fisheries and
available
Oceans Canada,
Ireland Belmullet M4 150 55 deg N, 10 deg W
Portugal Leixoes Leixoes 83 41 deg N, 08 deg W
USA - West California 46012 213 37 deg N, 122 deg W Canada PublicallyExcellent available
Coast (WC)
USA - East Cape Canaveral 41010 872 26 deg N, 78 deg W
Coast (EC)
Canada -West Graham Island C46183 no info 50 deg N, 136 deg W Portugal Instituto Hidrografico, Lisbon, Portugal Fee payableb Poor
Coast (WC)
Canada - East Nova Scotia C44137 no info 42 deg N, 62 deg W
Coast (EC) a
Email hmrc@ucc.ie.
b
Email ana.saramago@hidrografico.pt).
Table 6
Power matrix scatter plot for the Pelamis WECS [15].

Period (Tz)

1 2 3 4 5 6 7 8 9 10 11 12 13
Height (Hs) 0.5 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 0 0 0 0 29 37 38 35 29 23 0 0
1.5 0 0 0 0 32 65 83 86 78 65 53 42 33
2 0 0 0 0 57 115 148 152 138 116 93 74 59
2.5 0 0 0 0 89 180 231 238 216 181 146 116 92
3 0 0 0 0 129 260 332 332 292 240 210 167 132
3.5 0 0 0 0 0 354 438 424 377 326 260 215 180
4 0 0 0 0 0 462 540 530 475 384 339 267 213
4.5 0 0 0 0 0 544 642 628 562 473 382 338 266
5 0 0 0 0 0 0 726 707 670 557 472 369 328
5.5 0 0 0 0 0 0 750 750 737 658 530 446 355
6 0 0 0 0 0 0 750 750 750 711 619 512 415
6.5 0 0 0 0 0 0 750 750 750 750 658 579 481
7 0 0 0 0 0 0 0 750 750 750 750 613 525
7.5 0 0 0 0 0 0 0 750 750 750 750 686 593
8 0 0 0 0 0 0 0 0 750 750 750 750 625
8.5 0 0 0 0 0 0 0 0 0 750 750 750 750
9 0 0 0 0 0 0 0 0 0 0 750 750 750
9.5 0 0 0 0 0 0 0 0 0 0 0 750 750
10 0 0 0 0 0 0 0 0 0 0 0 0 750
10.5 0 0 0 0 0 0 0 0 0 0 0 0 0
11 0 0 0 0 0 0 0 0 0 0 0 0 0
11.5 0 0 0 0 0 0 0 0 0 0 0 0 0
12 0 0 0 0 0 0 0 0 0 0 0 0 0

● The electricity tariff rate from the utility company. In this

CY ¼ Lt*trunc Py report, the following rates were assessed: V0.00, V0.05,
Lt (5)
V0.10, V0.20, V0.30, V0.40.
If lifetime of the item is greater than the project lifespan:
5.2.6. Discount factor
RL ¼ Lt — Py (6) The discount factor (DF) translates expected financial benefits or
costs in any given future year into present value terms. The total
Any decommissioning costs are subtracted from the final
nominal profit is adjusted for cash depreciation by multiplying the
salvage value.
total nominal profit by a discount factor. DF is calculated using the
Salvage value can be a substantial especially if the replacement
discount rate12 (DR) in the following equation:
of an item is due close to the termination of a project.
1 (7)
5.2.5. Grid sales revenue DF ¼ ð1 þ DRÞn
Feed-in tariff refers to the regulatory, minimum guaranteed Where n is the number or years.
price per kWh that an electricity utility has to pay to a private,
The discount rate is used to convert between one-time costs
independent producer of renewable power fed into the grid [33]. It
and annualized costs and is calculated using the following
is defined in this report as the full price per kWh received by an
equation:
independent producer of renewable energy including the premium BR þ f
above or additional to the market price, but excluding tax rebates DR ¼ (8)
1—f
or other production subsidies paid by the government. Grid sales
are
a credit, and are added to other negative cost values for the each Where BR is the borrowing rate given for a loan and f is the inflation
year. The sales are the product of the following two variables: rate. By defining the discount rate in this way, inflation is factored
out of the economic analysis. All costs therefore become real costs,
● The total energy produced each year (referred to as the annual meaning that they are in defined in terms of constant Euros. The
energy output (AEO)). assumption is that the rate of inflation is the same for all costs. A
general inflation rate of 5% [32] was used for the project and
a borrowing rate of 10%,13 giving a project discount rate of 4.76%.
Table 7
Costs of WEC infrastructure, calculated as a percentage of the WEC IC. The majority The discount rate can vary up to 12%.
of Previsic [18] costings were used in the report, except cabling.

WEC parameter % of IC of WEC

5.3. Economic indicators
Previsic [18] Allen, Bryden et al. [24]
Mooring 10% 10 þ 20%
Cabling 50% (not used in this report) 5%
5.3.1. Net present value (NPV)
Replacement costs 90% The net present value is defined as the present value of invest-
Spare parts 2% ments future net cash flows minus the initial investment [34]. It is
Sitting and permits 2%
GHG investigations 0.05%
Management fees 10% 5%
12
Decommissioning fees 10% The discount rate is an interest rate commensurate with perceived risk used to
Grid connection 5% of AEO 1% convert future payments or receipts to present value.
13
Borrowing rate used was at peak 2008 rate.
Table 8
Table 9
WEC power output, corresponding cable kV and relevant cost V/km [30].
IC for 2004 and 2008 for WEC and cabling.
Range MW kV Cost per km Number of kms Cost
Year IC for 1 Pelamis WEC IC for Cable for 1 WEC
0.5–1.9 MW 10 V433,333 4 V1,733,333
2–5 MW 10 V433,333 4 V1,733,333 2004 V1,533,000 V1,733,333
5–19 MW 30 V1,300,000 4 V5,200,000 Mid 2008 V4,599,000 V3,466,666
Over 20 MW 110 V3,900,000 4 V15,600,000

derived by summing the discounted cash flows over the project 5.3.4. Total net cash (TNC)
lifetime, defined in the following equation: Total net cash (TNC) is calculated as follows:
X
NPV ¼ TNC*DF (9) TNC ¼ NP þ interest — fixed annual repayment (13)

Where TNC is the total net cash for that year and DF is the NP is the net profit and is defined as:
discount factor, which is defined as:
NP ¼ GS þ S — IC — RC — Oh — O=M — interest — tax (14)
1 Where GS is the grid sales, S is the salvage value, RC is the
DF ¼
ð1 þ rÞ n replacement cost, Oh is the overhaul cost and O/M is the operating
Where ‘r’ is the discount rate and ‘n’ is the number of years. The and maintenance cost.
discount rate is the reward an investor demands for accepting
a delayed payment. 5.3.5. Equity/debt, tax calculation and depreciation
In general, only positive NPV are considered viable commercial The project assumed 100% equity financing, with no debt.
projects. NPV is a simple mathematical concept that doesn’t Assessment of the implications of a project funded with a certain
include any arbitrary variables. percentage of borrowings requiring tax and depreciation analysis
The total annualized cost (TAC) is the sum of the annualized would be outside the scope of this paper.
costs of each system component. It is calculated by multiplying the
NPV and the capital recovery factor (CRF). CRF is a ratio used to
6. Data analysis and results
calculate the present value of an annuity (a series of equal annual
cash flows). The equation for the capital recovery factor is:
6.1. Number of hours per sea state
1ð1 þ rÞ n
Results displayed in Table 11 show that the wave energy period
CRF ¼ (10)
1ð1 þ r Þ— 1 (Tz) recording the highest frequency of hours was 5–7 s in all
locations. The wave height (Hs) of approximately 1–2.5 m was
5.3.2. Cost of electricity (COE)
most common for all locations, except Ireland, where the highest
The (levelised) cost of electricity (COE) is defined as the
inci- dence of wave height occurred between 1–3.5 m. Wave
average cost per kWh of useful electrical energy produced by the
heights in Portugal recorded in 2007 were measurably smaller
system, and is calculated by dividing the total annualized cost
than the other locations.
(TAC) of producing electricity by the annual electric output (AEO).
The equation for the COE is as follows:
6.2. Annual energy output

TAC
COE AEO The AEO of the Pelamis at the Irish location had the highest
¼ (11)
energy return of the global locations selected for comparison in
5.3.3. Internal rate of return (IRR) 2007, where the total AEO produced by the Pelamis WEC device
was 2.5 GWh (Fig. 3). The Irish energy output figures were
Internal rate of return indicates the business return according approximately 40% higher than the Californian and Nova Scotia
to alternative return that may be gained on the same investment.
site outputs, double the Portuguese output and approximately
The internal rate of return is the discount rate that will create a
three times of the remaining sites. The output at the USA WC site
zero net present value. The IRR is based on the NPV formula
was similar to the output quoted in Previsic’s [18] Californian
(Equation (9)), and is solved iteratively for when NPV ¼ 0. report.
The capacity of the Pelamis decreased for each location in
proportion to the drop in AOE, with the capacity at the Irish site
X cðnÞ
NPV 0 ð Þ ¼IC— þ ð1 þ IRRÞn (12) reaching 38% and dropping to a low of 10% in USA EC. The
capacity results indicate that the Pelamis operated closer to its
optimal
Where ‘c’ is the cost for year ‘n’ and NPV(0) is the NPV value equal rating in the Irish location, and that perhaps smaller rated devices
to zero. would be more suitable for locations such as Canada WC and USA
In this report, an IRR threshold of 10% was required for a project EC. The capture width on the other hand did not have much vari-
to be considered financially viable.14,15 ation, implying that the Pelamis was performing equally in all
locations.

Table 10
14 Operating costs for WEC, mooring and cable.
Personal communication Tony Dalton, chief financial accountant for LET
Systems, Cork. Variable Calculation method
15
IRR requirement for investors is a different scenario (not applicable here). Here,
Overhaul/refurbishment Replacement Nil Nil
investors judge IRR on their initial investment made and the exit price of the O/M 1% or 2% or 3% of IC
company. The investment is more high risk and thus IRR would be expected to be
higher, at around 30%.
Table 11
Surface plot of hours for some of the case study locations.

Period (Tz)

1 2 3 4 5 6 7 8 9 10 11 12 13
Heights (Hs) Ireland
0.5 17 39 13 0 0 0 4 0 0 0
1 148 312 93 32 13 0 1 0 0 0
1.5 75 560 372 187 64 11 2 0 0 0
2 6 427 623 321 172 47 8 0 0 0
2.5 99 508 363 182 67 10 0 0 0
3 10 248 394 193 83 18 2 0 0
3.5 86 436 244 74 15 7 1 1
4 14 213 246 97 23 7 8 0
4.5 83 218 124 22 4 3 2
5 17 175 118 26 3 5 3
5.5 88 122 36 2 1 0
6 30 86 37 3 3 0
6.5 45 32 4 4 1
7 24 48 15 4 0
7.5 9 30 10 2 0
8 2 20 16 4 0
8.5 10 9 7 0
9 5 18 1 2
9.5 2 8 2 0
10 1 4 0 1
10.5 1 0 0

Heights (Hs) USA WC

0.5 0 17 15 4 1 0 0 0 0 0
1 12 271 198 224 222 54 19 1 0 0
1.5 223 516 516 457 227 70 21 4 3
2 70 550 561 390 279 93 84 8 2
2.5 5 319 445 287 260 97 51 10 1
3 77 360 216 157 110 55 5 0
3.5 7 173 154 107 42 34 6 0
4 86 86 69 23 25 14 0
4.5 7 57 28 16 2 4 0
5 32 21 4 3 1 0
5.5 25 18 0 7 0 0
6 3 14 0 4 1 0
6.5 5 0 2 1 0
7 3 2 0 1 0
7.5 1 1 0 0
8 1 2 0 0
8.5 1 0 0
9
9.5
10
10.5

Heights (Hs) Canada EC

0.5 7 27 35 66 49 6 18 75 10 0 0
1 96 176 498 591 308 113 85 88 73 12 0
1.5 40 140 666 422 284 83 19 54 46 14 6
2 2 57 429 399 258 83 16 7 0 3 0
2.5 17 249 435 256 55 23 2 3 1 0
3 3 89 240 179 68 15 0 0 0 0
3.5 26 119 355 80 20 3 0 0 0
4 5 67 146 79 13 3 0 0 0
4.5 2 42 111 80 30 6 1 0 0
5 15 71 65 15 3 0 0 0
5.5 5 43 67 23 4 0 0 0
6 1 15 50 27 7 1 0 0
6.5 4 25 19 6 0 3 0
7 2 15 10 6 2 1 0
7.5 9 16 4 0 0 0
8 1 11 6 0 0 0
8.5 1 3 1 2 0 0
9 4 0 0 0
9.5 2 0 0 0
10 1 0 0 0
10.5
 Table 11 (continued)

Period (Tz)
1 2 3 4 5 6 7 8 9 10 11 12 13
Heights (Hs) Portugal
0.5 5 135 297 252 110 25 0 0 0 0 0
1 174 594 506 329 177 107 47 0 0 0
1.5 24 603 624 414 269 203 88 32 1 0
2 142 433 341 212 219 101 47 1 0
2.5 8 203 236 160 183 94 45 21 0
3 52 165 135 98 101 40 13 1
3.5 7 35 83 83 75 62 13 1
4 10 40 41 26 30 5 0
4.5 10 17 25 8 3 0
5 2 16 29 3 4 4
5.5 3 16 9 1 8
6 1 1 2 1 1
6.5 6 1
7 3 2
7.5
8
8.5
9
9.5
10
10.5

The monthly energy output produced by the Pelamis device Electricity demand or load in Ireland varied by only 12%
varied considerably throughout the year for each location, as is between summer and winter months (2005 data shown in the
evident by the trendline graph in Fig. 4. Supply in winter was graph) [35]. The correlation between the AEO and the Irish load
approximately 3–7 times that of the summer supply. It is inter- was only 0.76. This variation in supply especially for the summer
esting to observe the minimum monthly output in the Irish site
was in June/July, while in the remainder of the locations was in 0.45
August/ September.
The monthly AEO profile of the Irish site matches the WEI 0.4
closely except on the winter months (Fig. 5). The capture width
was maximum in the summer months, with an apparent width of
7–8, dropping to 5 in the winter months. The capture width results 0.35
Monthly energy output (GWH)

suggest that the Pelamis device is operating more optimally during

the summer months and is not using all the available energy 0.3 R2 = 0.84
during the winter months. This could be due to either to R2 = 0.81
inefficiency of design, or extreme weather conditions necessitating
0.25
device shut- down (i.e. Pelamis power matrix has a zero power
output over a certain height and period).
0.2 R2 = 0.71
R2 = 0.72
3.00 R2 = 0.67
40%
0.15
Annual energy output (GWh)
2.50 Capacity % 35%
0.1
30%
2.00 R2 = 0.47
Annual energy output

( ) Capture Width 0.05

25%
Capacity (%)

1.50
20% 0
Jan Mar May Jul Sep Nov
1.00 15%
(GWh)

Poly. (Ireland ) Poly.

10%
0.50 (USA WC)
(6)(7) (7)(6)(6) (7)
5% Poly. (Canada- EC)
Poly. (Portugal)

0.00 0% Poly. (Canada- WC)

Poly. (USA- EC)

Fig. 4. Monthly energy output trendlines in GWh for the case study locations. 3rd
Fig. 3. Annual energy output (AEO) (in GWh) for 6 case studies and their respective order polynomials were used to calculate the trendlines, except for USA EC where 4th
capacity and capture width (represented as a number in the energy output bar). order polynomial was used.
 Irish LoadEnergy inputEnergy output Mid-2008 costs
2
IrelandPortugal USA WCCanada WC
1.8 Canada ECUSA EC
( ) Capture Width
0.8 3000 1.6
1.4

COE (€/kWh)
0.7 1.2
2500
Monthly energy output (GWh)

1
0.6
0.8

Monthly Irish load (GWh)

2000 0.6
0.5
0.4

0.4 1500 0.2

(5) (5) 0
(5) 1 5 10 20 30 40 50 100 200 500 1000 2000
0.3
1000 Number of WEC
(7)
0.2 (6) (8)
Fig. 7. Impact on COE for 1–2000 WEC based on mid 2008 prices (zero tariff rate
(7)
(6) used) for various WEC numbers.
0.1 (7) 500
(8)
(7) (8)
0
0
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
mid 2008 prices
Fig. 5. Graph of monthly energy input and monthly energy output produced by the 120
Pelamis (2007–2008) and monthly load for Ireland in 2005. 100 1 WEC20 WEC
80 5 WEC50 WEC
months will have worrying implication for base load supply if WEC 10 WEC100 WEC
60
power was to be used on a large scale. A healthy energy mix will
COE (€c/kWh), NPV (€M)

40
require a more even energy output profile, and will perhaps need 20
to be supplement by other renewables such as solar which have an 0
inverse annual profile. It also has worrying implications for busi- -20 COE NP V COE NPV
ness which already has the perception that renewable energy does -40 ff
€0.10/kWh tari €0.20/kWh tariff
not have the capacity to supply power required or be reliable [6]. -60
-80
-100
6.3. COE, NPC and IRR -120
-140
The COE of Pelamis projects in the various global case study -160
locations is presented in Fig. 6, based on 2004 initial capital cost (IC) -180
of the Pelamis [18] and a zero tariff rate (projected 2008 costs are -200
assessed later). Results showed that COE for 1 WEC varied from
Fig. 8. Analysis of COE and NPV for various tariff rates and WEC number, 2008 prices.
a low of V0.16/kWh in the Irish site, up to V0.62/kWh on the USA
Case study location investigated was Ireland. (Note: COE is in Euro cent, while NPV is in
EC. COE dropped in all cases by approximately 50% when 5 WEC millions of Euro).
were assessed, with a low of V0.09/kWh for the Irish site. COE
savings arose mainly due to the same cable size used for both 1
and

2004 costs
2 Mid-2008 costs
IrelandPortugal 15
1.8 Canada WC USA EC
USA WC IrelandPortugal
1.6 Canada EC 10 USA WCCanada WC Canada ECUSA EC

1.4
5
COE (€/kWh)

1.2
1 0
1510 20 30 40 50 100 200 500 1000 2000
IRR (%)

0.8 -5
0.6
-10
0.4
0.2 -15

0 -20
1 5 10 20 30 40 50 100 200 500 1000 2000
Number of WEC -25
Number of WEC
Fig. 6. COE results for 1–2000 WEC, based on 2004 IC costs from EPRI [18] and a zero
tariff rate. Fig. 9. IRR for various tariff rates at peak 2008 prices and V0.20/kWh tariff rate.
Table 12
Table list COE results from three papers, which used multiple WEC numbers and/or tariff rates. The same WEC number, tariff rates and IC (based on year) were used as input in
the NAVITAS model, with wave energy data from a similar location, and results compared.

Report Country Report findings NAVITAS simulation

WEC Tariff quoted in COE quoted in Data Buoy Year used COE calculated using
number report report (V/kWh) used for NAVITAS for IC NAVITAS (V/kWh)
Previsic [18] California 213 WEC V0.06/kWh V0.08/kWh California 46612 2004 V0.07/kWh
Allan [24] Scotland 4000 WEC V0.05/kWh V0.10/kWh Ireland M4 2008 V0.13/kWh
Dunnet et al. [20] Canada 27 WEC None V0.30/kWh Canada EC C44137 2008 V0.34/kWh

5 WEC as well as scaling of capital costs for multiple WEC. COE same WEC number and tariffs for each location, using wave energy
tailed off for larger WEC numbers, with values for 100 WEC data from data buoys in similar locations and the same year for IC.
ranging in Ireland at V0.05/kWh to V0.20/kWh in the USA EC. It is COE results from the NAVITAS matched COE from the reports
impor- tant to remember that there was no tariff paid for COE closely, providing validation of the NAVITAS model (Table 12).
results just presented. COE value is often mistakenly thought of as
the value when profit occurs. A COE of zero is the tariff where the
project only pays for itself. NPV and IRR are preferred when 7. Summary and conclusion
discussing profit- ability, and will be discussed latter.
The performance and economic viability of the Pelamis WEC
has been investigated using 2007 wave energy data from various
6.4. Sensitivity analysis
global locations. For this purpose, an Excel based model, NAVITAS,
was created which estimated the annual energy output of the
Results so far have been based on 2004 costs for Pelamis,
Pelamis for each location, and produced financial results
sourced from Previsic [18]. Results presented in Fig. 7 show the
dependent on various input parameters.
impact of a threefold increase in steel prices as well as a two fold
The annual wave energy output (AEO) and capacity the Pelamis
increase in cable costs on, which are approximately equal to prices
was highest from the Irish location followed by USA WC, Canada
at their peak in mid 2008, before global recession began. Impact
EC, Portugal, Canada WC and finally USA WC. The AEO results
on COE was greatest for small number of WEC, with COE for 1
corre- spond well with widely published wave energy data given in
WEC in Ireland at V0.40, ranging to V1.60/kWh for USA EC. The
kW/m [22,36–38]. AEO and capture widths varied substantially
range of COE values also increased measurably for WEC arrays
between winter and summer seasons, particularly in the Irish
over 100 in number, with the range of COE for Ireland and USA EC
location. The results imply that although the Pelamis is operating
for 100 devices at V0.15 and 0.58/kWh respectively.
at a better rating during the winter months, much of the available
As already mentioned, COE is not an indication of profit, and is
energy is being wasted. This could be either due to inefficiency in
calculated using a zero tariff rate. Most WEC projects will be sup-
design or that the site location was too stormy necessitating
ported by an FIT, with rates varying from country to country. Results
shutdown of the Pelamis during those periods (i.e. many sea states
presented in Fig. 8 which assessed the Irish returns, demonstrate
recorded during the winter months had corresponding zero in the
that although attractive COE of V0.10/kWh and below resulted for
Pelamis power matrix). The large annual variation in output also
over 5 WEC with a tariff of V0.10/kWh, a negative NPV was
did not correlate well with the Irish annual load, implying that
returned, which becomes more negative as WEC number other renewables or storage will be necessary to cater for the
increases. A tariff rate of V0.20 is required to return a positive summer months.
NPC, which almost exponentially increases over 50 WEC.
Economic returns using the energy data showed the same
In conclusion, COE gives an idea of the competitiveness of
trends as the energy output; i.e. Ireland returns the most positive
a project in comparison to other project, but gives no indication of
economic results while USA EC the worst. Results were very
NPV return, which is of prime importance for investors. Negative
sensitive to initial costs (IC) chosen (either 2004 or 2008 in this
COE is required for positive NPV values when using FIT. Large
article) and the number of WEC. Single Pelamis WEC for the
numbers of WEC are required to move NPV into the positive at
various site locations had COE ranging from V0.16/kWh for the
a tariff of 0.20/kWh.
Irish site to V0.62/kWh USA EC at 2004 prices. COE increased
IRR is often used as the preferred indicator for financial
substantially when using peak 2008 prices, ranging from V0.40 to
comparison between projects. For long-term projects such as wave
V1.60/kWh. High sensitivity of economic performance to IC of
energy projects, only returns above the market borrowing rate of
materials in this report is similar to those experienced in other
10% are considered viable. It is observed from Fig. 9 that none of the
renewables such as wind and PV [39]. COE would have been
case study locations returned an IRR above 10%, indicating that
higher if lower exchange rates between US dollar and Euro were
none of the sites are economically viable, despite some sites
used in the modelling.
returning attractive COE and NPV. The poor IRR reflect the fact In reality, all commercial ventures contain multiple numbers of
that relatively low returns resulted from the high initial costs WEC, and in all the case study sites for WEC number over 100
incurred. units, COE under V0.20/kWh were returned for IC based on 2004
prices. High WEC numbers improved COE for two reasons. The
6.5. Comparison to other reports most obvious factor is that high WEC numbers benefit from
economies of large scale production with cost reductions esti-
This section reviews three reports which quoted COE for Pela- mated using learning or production curves. To a lesser extent, but
mis, and examines their WEC number and any tariff rates used and equally important, are savings accrued from cabling, where one
the year in which the study was made. It is observed that low COE cable size can be used for certain multiples of WEC or MW outputs.
were reported for large numbers of WEC in the Californian and Thus in this study, the one 110 kV sized cable could be used for
Scottish studies [18,24], while the Canadian study, which did not over 26 units Pelamis. When using peak 2008 prices for large
use a tariff, was much higher [20]. Modelling was carried out on number of WEC, the only site location that had COE under V0.20
the was the Irish site.
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