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Ocean Wave Energy Conversion: A Review

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Journal of Marine Science and Engineering (JMSE)
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The globally increasing demand for energy has encouraged many countries to search for alternative renewable sources of energy. To this end, the use of energy from ocean waves is of great interest to coastal countries. Hence, an assessment of the available resources is required to determine the appropriate locations where the higher amount of wave energy can be generated. The current paper presents a review of the resource characterizations for wave energy deployment. The paper gives, at first, a brief introduction and background to wave energy. Afterward, a detailed description of formulations and metrics used for resource characterization is introduced. Then, a classification of WECs (wave energy converters) according to their working principle, as well as PTO (power take off) mechanisms used for these WECs are introduced. Moreover, different sources for the long-term characterization of wave climate conditions are reviewed, including in situ measurements, satellite altimeters, and data reanalysis on one hand, and numerical simulations based on spectral wave models on the other hand. Finally, the review concludes by illustrating the economic feasibility of wave farms based on the use of the levelized cost of the energy index.
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Citation: Bouhrim, H.; El Marjani, A.;
Nechad, R.; Hajjout, I. Ocean Wave
Energy Conversion: A Review. J. Mar.
Sci. Eng. 2024,12, 1922. https://
doi.org/10.3390/jmse12111922
Received: 5 September 2024
Revised: 14 October 2024
Accepted: 16 October 2024
Published: 28 October 2024
Copyright: © 2024 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
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4.0/).
Journal of
Marine Science
and Engineering
Review
Ocean Wave Energy Conversion: A Review
Hafsa Bouhrim 1, *, Abdellatif El Marjani 2, Rajae Nechad 2and Imane Hajjout 3
1LMCPS2ET Laboratory, Electromechanical Department, Higher National School of Mines-Rabat (ENSMR),
Hadj Ahmed Cherkaoui Avenue, Agdal, B.P.753, Rabat 10000, Morocco
2
EMISys Research Team, Turbomachinery Lab, Mohammadia School of Engineers, Mohammed V University in
Rabat, Agdal, B.P.765, Rabat 10000, Morocco; elmarjani@emi.ac.ma (A.E.M.); nechadr@gmail.com (R.N.)
3Energy and Agroequipment Department, Institute of Agronomy and Veterinary Hassan II, B.P.6202,
Rabat 10000, Morocco; hajjoutima@gmail.com
*Correspondence: bouhrim.hafsa@gmail.com
Abstract: The globally increasing demand for energy has encouraged many countries to search for
alternative renewable sources of energy. To this end, the use of energy from ocean waves is of great
interest to coastal countries. Hence, an assessment of the available resources is required to determine
the appropriate locations where the higher amount of wave energy can be generated. The current
paper presents a review of the resource characterizations for wave energy deployment. The paper
gives, at first, a brief introduction and background to wave energy. Afterward, a detailed description
of formulations and metrics used for resource characterization is introduced. Then, a classification of
WECs (wave energy converters) according to their working principle, as well as PTO (power take
off) mechanisms used for these WECs are introduced. Moreover, different sources for the long-term
characterization of wave climate conditions are reviewed, including in situ measurements, satellite
altimeters, and data reanalysis on one hand, and numerical simulations based on spectral wave
models on the other hand. Finally, the review concludes by illustrating the economic feasibility of
wave farms based on the use of the levelized cost of the energy index.
Keywords: wave energy; wave energy converters; wave energy indices; numerical wave models;
resource assessment; levelized cost of energy
1. Introduction
Ocean renewable energy resources are an emerging alternative to conventional fossil
fuel resources (e.g., petroleum oil, natural gas, and coal), contributing, at the same time,
to the energy independence of coastal regions. Among these resources, wave energy is
considered the most promising, given its (i) highest power density of about 2 to
3 kW·m2,
and, when compared to wind (0.4–0.6
kW·m2
) and solar (0.1–0.2
kW·m2
) energy den-
sities, the mean wave power density is 10 times higher than that of wind and 100 times
that of solar [
1
]. Moreover, wave energy is promising due to its (ii) predictability [
2
,
3
]
and
(iii) limited
environmental and visual impacts [
4
]. Additionally, apart from energy
production, coastal protection can be assured by using wave farms to restrict erosion pro-
cesses [
5
,
6
]. Figure 1presents the worldwide distribution of annual mean wave power
density, with the indication of important wave directions as arrows. As indicated, the high
energy zones are located between 40
and 60
in both the Northern Hemisphere (NH) and
Southern Hemisphere (SH), with annual mean wave power values in the SH greater than
in those in the NH, [7,8].
Wave energy depends on the geographical location and time [
9
,
10
]. The global wave
energy potential in deep waters was evaluated in the range of 1 to 10 TW, which is sig-
nificant for the universal power demand [
11
,
12
]. Although waves lose their energy when
advancing from deep to shallow water waves because of phenomena like wave breaking
and bottom friction [
11
,
13
], both offshore and nearshore areas were considered for wave
J. Mar. Sci. Eng. 2024,12, 1922. https://doi.org/10.3390/jmse12111922 https://www.mdpi.com/journal/jmse
J. Mar. Sci. Eng. 2024,12, 1922 2 of 25
farms. Different WECs (wave energy converters) were designed and employed for wave
energy extraction and transformation into electricity. These WECs were developed for
specific properties, such as the following: different wave climate conditions, different
locations, wave characteristics, and sea water depth.
J. Mar. Sci. Eng. 2024, 12, x FOR PEER REVIEW 2 of 27
for wave farms. Dierent WECs (wave energy converters) were designed and employed
for wave energy extraction and transformation into electricity. These WECs were
developed for specic properties, such as the following: dierent wave climate conditions,
dierent locations, wave characteristics, and sea water depth.
Figure 1. The worldwide distribution of the annual mean wave power in kW/m [8].
Therefore, an important step towards the seing up of a pilot plant for wave energy
exploitation using WECs is the wave energy resource characterization. Studies on the
assessment of available wave energy resources oer the possibility to identify the most
energy-rich areas and quantify their wave energy, which is usually given as a function of
the total annual mean wave power, and to describe this resource in terms of sea wave
parameters, such as signicant wave height, energy period, and mean wave direction [14].
An accurate estimate of available wave energy resources is needed in order to choose the
appropriate WEC for a location of interest and tune an existing WEC design [15,16].
Similar to the wind industry, the wave energy distribution on a seasonal scale should
cover a period of at least 10 years of historical records with at least three hours as a time
step, as this will avoid the inter-annual uctuations in sea waves [17,18]. Moreover, the
resource should be described using the scaer diagram showing the bivariate distribution
of the available wave energy as a function of wave height and energy period; this diagram
would give an insight into the pairs of signicant wave height and energy period that
eectively contribute to the total energy. Another aspect to take into consideration is the
resolution of the scaer diagram, as it must be the same or ner than the one of the used
wave energy conversion system to identify its power output. In recent years, systems
based on Articial Intelligence have been used for wave forecasting based on several
computing methods, including the following: Articial Neural Networks (ANNs) [19],
Bayesian Networks (BNs), Fuzzy Inference System (FIS), and Decision Trees (DTs) [20].
The current paper is organized as follows: Section 2 is devoted to the available
sources used for long-term characterization and analysis of wave climate conditions at
dierent scales and locations, including in situ measurements, satellite altimetry, and
reanalysis archives. In Section 3, a critical comparative description of the existing spectral
wave models is presented, complemented by a review of their applications for dierent
areas around the world. The wave energy theories and their variability indices are
introduced in Section 4, along with up-to-date State-of-the-Art sustainability metrics for
the long-term characterization of wave energy. Then, Section 5 investigates the existing
WECs, their classications, and a summary of PTO systems integrated in WECs. In Section
Figure 1. The worldwide distribution of the annual mean wave power in kW/m [8].
Therefore, an important step towards the setting up of a pilot plant for wave energy
exploitation using WECs is the wave energy resource characterization. Studies on the
assessment of available wave energy resources offer the possibility to identify the most
energy-rich areas and quantify their wave energy, which is usually given as a function
of the total annual mean wave power, and to describe this resource in terms of sea wave
parameters, such as significant wave height, energy period, and mean wave direction [
14
].
An accurate estimate of available wave energy resources is needed in order to choose the
appropriate WEC for a location of interest and tune an existing WEC design [
15
,
16
]. Similar
to the wind industry, the wave energy distribution on a seasonal scale should cover a
period of at least 10 years of historical records with at least three hours as a time step, as
this will avoid the inter-annual fluctuations in sea waves [
17
,
18
]. Moreover, the resource
should be described using the scatter diagram showing the bivariate distribution of the
available wave energy as a function of wave height and energy period; this diagram would
give an insight into the pairs of significant wave height and energy period that effectively
contribute to the total energy. Another aspect to take into consideration is the resolution of
the scatter diagram, as it must be the same or finer than the one of the used wave energy
conversion system to identify its power output. In recent years, systems based on Artificial
Intelligence have been used for wave forecasting based on several computing methods,
including the following: Artificial Neural Networks (ANNs) [
19
], Bayesian Networks (BNs),
Fuzzy Inference System (FIS), and Decision Trees (DTs) [20].
The current paper is organized as follows: Section 2is devoted to the available sources
used for long-term characterization and analysis of wave climate conditions at different
scales and locations, including in situ measurements, satellite altimetry, and reanalysis
archives. In Section 3, a critical comparative description of the existing spectral wave
models is presented, complemented by a review of their applications for different areas
around the world. The wave energy theories and their variability indices are introduced in
Section 4, along with up-to-date State-of-the-Art sustainability metrics for the long-term
characterization of wave energy. Then, Section 5investigates the existing WECs, their
classifications, and a summary of PTO systems integrated in WECs. In Section 6, the
economic aspect of wave energy farms is discussed, introducing the LCOE (levelized cost
of energy) index. Finally, the conclusions are listed in Section 7.
J. Mar. Sci. Eng. 2024,12, 1922 3 of 25
2. Available Wave Energy Resource Data
Several sources are available for long-term characterization and analysis of wave con-
ditions at different scales and locations, including in situ measurements, satellite altimetry,
and reanalysis archives. Each of these sources has its characteristics and is subject to some
limitations. Satellite altimeters have huge spatial coverage of the ocean under a wide range
of wave climate conditions [
21
], with low temporal resolution (e.g., daily), whereas in situ
measurements are specific to particular oceanic areas and various ranges, in spite of having
high temporal resolution.
The wave energy resource assessments were carried out using visual observations
from buoys despite being restricted to local conditions [
16
]. Thereafter, wave energy
assessments included buoy data combined with deep water spectral models to evaluate the
offshore wave resources, overcoming the restrictions of the first assessments, that is, the
limited period of measurement and the uncertainties linked to the extrapolation of local
data to other sites [
16
]. As an example, Lenee-Bluhm et al. [
22
] utilized archived spectral
registrations from ten buoys to evaluate and analyze the wave energy potential of the
northwest United States. Wu et al. [
23
] used available data from six buoys to evaluate the
seasonal variations in available wave power on the East China Sea. The characteristic of
this method is that it can provide valuable sea state information with satisfactory accuracy
when using precise and continuous buoy data. However, the quality and consistency of
these estimations have been questioned in many research studies, as in [24].
Buoy systems are not widely available and do not have a large coverage area, essen-
tially because of high costs and the difficulty related to harsh wave climate conditions [
10
].
For this reason, recent tools used satellite altimetry measurements for long-term global
surveillance of the sea state [
25
,
26
]. Usually, wind and bathymetry data are used as input
for such models. The typical output parameters are significant wave height,
Hs
, energy
period,
Te
, and mean wave direction. Assessments of wave energy resources were carried
out at global [
27
,
28
], regional [
29
,
30
], and local levels. The accuracy of satellite measure-
ments compared to in situ measurements from buoys around the globe were assessed in
numerous studies [
31
33
]. According to Le Traon et al. [
34
], satellite altimetry provides
precise observations on significant wave height with excellent coverage. However, the
estimation of wave height is significantly less accurate in coastal and inland areas, mainly
due to difficulties in estimating high-frequency atmospheric signals and mostly problems
related to land contamination in radar altimeter footprints [35].
Until now, a number of satellite altimeters have been successfully operated by various
international agencies (Table 1). They have offered a homogeneous, high-precision, and
long-time series of observations, particularly over the ocean.
Table 1. Non-exhaustive review of satellite altimeters used for wave energy assessments.
Satellite Mission Region Exact Repeat
Mission (Days) Covered Period Spatial
Resolution References
TOPEX/Poseidon South China sea 10 2004 - [36]
AVISO multi satellites
merged altimeter data Northwest Pacific 24 2009–2014 1×1[37]
China sea 24 2009–2013 1×1[38]
ENVISAT Indonesia 35 2002–2012 1×1[39]
JASON-2
Andaman Sea Coast of
Thailand 10 2014 - [40]
SARAL/Altika North of Scotland 35 2014 11 km ×5 km [41]
Multi-mission
altimeter Southeast Australia - 1985–2020 1×1[25,42]
Re-analysis data overcome the shortcomings of the above-mentioned methods regard-
ing their higher temporal resolution of 1 to 6 h and their global spatial coverage. There are
diverse wave data re-analyses with various spatio-temporal resolutions to be exploited for
J. Mar. Sci. Eng. 2024,12, 1922 4 of 25
wave energy assessment, such as CFSR (Climate Forecast System Reanalysis), HIPOCAS
(Hindcast of Dynamic Processes of the Ocean and Coastal Areas of Europe), ECMWF (Eu-
ropean Centre for Medium-Range Weather), NOAA (National Oceanic and Atmospheric
Administration), NOGAPS (Navy Operational Global Atmospheric Prediction System),
and NARR (North American Regional Reanalysis).
3. Spectral Wave Models
In recent years, third-generation wave models have been widely used for wave energy
resource characterization, including global [
7
,
15
,
43
] to regional scales. These models
include the following: WAM [
44
,
45
], WWIII model [
46
], SWAN [
47
], MIKE21-SW [
48
],
and TOMAWAC [
49
]. The selection of a spectral wave model can be based on the area of
interest, computational resource, type of study, etc. [50].
The fundamental similarity of these spectral wave models lies in the resolution of the
balance equation with sinks and sources; however, differences in source terms of numerical
implementation and parametrization of the physical processes were noticed. While WAM
is built around one set of terms, WW3 and SWAN provide a variety of source terms and
parametrization available for the user. WAM and WW3 were originally applied for wave
prediction at oceanic scale or large areas, whereas SWAN is mostly used in the case of
shallow water and coastal or small zones, apart few exceptions, e.g., [
51
]. For instance,
Rute Bento et al. [
52
] evaluated the wave power in Galway Bay using WW3 for both wave
generation and deep-water propagation and SWAN for shallow and intermediate sea wave
propagation. Rusu et al. [
53
] described the development of a wave prediction system along
the Iberian coast based on two wave models: WAM for the oceanic region and SWAN for
the nearshore area. Nevertheless, WW3 and WAM models have been updated, adding new
source terms and parametrizations to account for nearshore processes. As a result, all three
models are suitable for wave energy simulation in coastal regions [45].
One of the major differences between the three models, SWAN, WW3, and WAM, is
the numerical scheme used for the resolution of the action density equation. SWAN uses
an implicit numerical propagation scheme, which enables much larger time steps for high
computational efficiency rather than the restriction by stability criteria associated with
explicit schemes in shallow waters. WW3 employed explicit numerical schemes; thus, the
model time steps were limited by the CFL (Courant–Friedrichs–Lewy) stability criteria.
Studies on model performance revealed that the two spectral models WW3 and SWAN
can accurately forecast wave energy resource statistics and that their accuracy is highly
improved by grid refinement [
54
,
55
]. Furthermore, these models can assess the spatial
variation of sea wave characteristics at fine resolutions over vast areas covering different
sea states, e.g., [
55
,
56
]. For instance, SWAN [
57
] supports an unstructured flexible mesh,
providing an effective and feasible modeling approach of areas having complex geometries
with many shoreline curves (i.e., major U.S. coastal regions).
According to [
58
], under extreme wave conditions, great differences are noticed among
hindcasts at mid-high latitudes greater than 40
north, reaching 2.5 m, and a large area is
concerned with differences above 2 m. A growing underestimation by WW3 compared to
WAM when moving to harsh conditions was observed.
Table 2gives non-exhaustive review of these different spectral wave model applica-
tions for wave energy assessment in different areas.
J. Mar. Sci. Eng. 2024,12, 1922 5 of 25
Table 2. Non-exhaustive review of spectral wave model applications for wave energy assessment in different areas.
Study Area Authors
Spectral Models
Covered Period Spatial—Temporal
Resolutions Main Results
SWAN
WW3 WAM MIKE21-SW TOMAWAC
Australia
Southeast Australia [42] X 40-year
(1981–2020) 0.25×0.25—1 h
Wave power in the western regions is between
30 and 65 kW/m, whilst less than 10 kW/m are
found in nearshore areas of New South Wales,
eastern Victoria, and northeastern Tasmania.
Australian shelf [59] X 10-year
(1997–2008) 0.1×0.1—6 h
The southern Australian shelf is concerned with
the greatest values of mean wave power
25–35 kW/m.
Moderate values of wave power (10–20 kW/m)
are found in New South Wales and southern
Queens land shelves.
For almost all the northern Australian shelf,
wave power is below 10 kW/m.
Southwestern coast
of Australia [60] X 38-year
(1980–2017) Annual mean wave power is of 47.2 kW/m.
Spain
Death coast [61] X 44-year
(1958–2001) Annual mean wave power of about 50 kW/m.
Galicia [62] X X 9-year
(1996–2005)
from 3
in the high seas
to 0.25(or 30 km) near
the coastline—15 min
The annual mean wave power varies from
~15 kW/m to 50 kW/m.
Canary Island [63] X X 33-year
(1979–2011)
0.05×0.1—6 h/
0.5×0.5Average annual energy availability of
25–30 kW/m.
Menorca [64] X 17-year
(1996–2013) 0.25×0.25—1 h
The mean wave power of the most energetic
area is reaching 8.9 kW/h. Lower mean wave
power values (by about 5%) are obtained by
comparing the results of this study with buoy
data records.
Lanzarote [65] X 44-year
(1958–2001) 0.25×0.25—3 h
The average wave power values exceeding
31 kW/h with more than 270 MW h/m of
annual energy.
Black sea
[66] X 20-year
(1997–2016) 0.312×0.312—3 h Mean wave power values in the range of 2.5 to
3 kW/m.
[67] X 31-year
(1979–2009)
The average wave power reaches higher values
(about 10 kW/m) in the western region of
Karaburun.
J. Mar. Sci. Eng. 2024,12, 1922 6 of 25
Table 2. Cont.
Study Area Authors
Spectral Models
Covered Period Spatial—Temporal
Resolutions Main Results
SWAN WW3 WAM
MIKE21-SW TOMAWAC
China
Gulf of Beibu [68] X 34-year 0.1×0.1—6 h The highest wave energy flux is in the order of
1.5 kW/m.
South China Sea [36] X 30-year
(1986–2015) 0.25×0.25—3 h Annual wave energy density up to 65 kW/m.
Thailand
Gulf of Thailand [69] X 10 years
(2004–2014) 0.0167×0.0167—5 min
Andaman Sea [40] X 1 year 0.5or ~55 km—3 h
The highest wave energy density (about
10.19 kW/m) is reached at the coastal area of
Phuket Province.
Korea
Korean Seas [70] X 12-year
(2007–2018) 0.0625×0.05—1 h
Annual mean wave power values in the range
of 0.6–13.3 kW/m in the Yellow Sea, 3–9 kW/m
in Korea Strait, 3–8 kW/m in East Sea, and
7–12 kW/m in the vicinity of Jeju Island.
Korean Peninsula [71] X 25-year
(1979–2003) 1/6or ~18 km
The annual mean wave power was found to be
11 kW/m in the southwestern side, 4 kW/m in
the southern side, and 6 kW/m in the eastern
side of peninsula.
Brazil
Alcatrazes
island [72] X 14-year
(2005–2018) 1×1.25
The annual mean wave power ranging between
2 and 17 kW/m.
south-southeastern
Brazilian Shelf [73] X 18-year
(1997–2014) 30 arc minutes—3 h
The average wave power on Laguna, Ilhabela,
and Farol Island is about 9.08 kW/m,
10.01 kW/m, and 15.93 kW/m, respectively.
Coast of Santa
Catarina [74] X 10-year
(2004–2014) 0.75×0.75The annual mean wave power at 20 m depth
varies from 8 kW/m in sheltered zones to about
14.5 kW/m.
Italy
Sicily [75] X 11-year
(1995–2005) 1×1—3 h
The highest value of wave energy density
1240 kW/m is found at the Capo Gallo site
while maximum energy values of 31.50
MWh/m correspond to Mazara del Vallo sites.
Sardinia [76] X 20-year
(1989–2009) 1.5×1.5—6 h The yearly offshore mean wave power varies
between 8.91 kW/m and 10.29 kW/m.
Malaysia East coast of
Peninsular Malaysia [77] X 31-year
(1979–2009) ~38 km—2 min
The annual average wave power for sites in the
northern (southern) section of the coast ranges
from 2.6 to 4.6 kW/m (0.5–1.5 kW/m).
J. Mar. Sci. Eng. 2024,12, 1922 7 of 25
Table 2. Cont.
Study Area Authors
Spectral Models
Covered Period Spatial—Temporal
Resolutions Main Results
SWAN
WW3 WAM MIKE21-SW TOMAWAC
United state
Hawaii [78] X 10-year 1.25×1.25—3 min The mean wave power ranges between 15 and
25 kW/m.
California coast [79] X
GoM (Gulf of
Mexico), East and
West Coasts
[80] X 36 years
(1979–2015) 0.167×0.167—3 h
The annual mean wave power values in most of
the GoM sites are greater than 35 kW/m.
Portugal Western Portuguese
Coast [81] X 15-year
(1995–2010) 0.5×0.5
Values of mean wave power in north and center
west Portuguese coast varies from 28.11 kW/m
to 30.90 kW/m, whereas the southwest coast
wave power ranges between 21.51 kW/m and
22.96 kW/m.
India
Indian coast [82] X 19-year
(2000–2018) 0.1×0.1—6 h
The spatio-temporal variability analysis of
wave energy flux reveals that southern coast of
India has the mean wave energy flux ranging
from 6 to 10 kW/m with a minimum monthly
(<2.0), seasonal (<1.0), and annual
(<0.2) variability.
Indian shelf seas [83] X 34-year
(1979–2012) 0.75×0.75—6 h
The yearly average wave power available on
the western shelf seas and along the eastern
shelf seas of India is about 19.5 GW and
8.7 GW, respectively.
Scotland Scottish coastlines [84] X 11-year
(2004–2014) 0.125×0.125—6 h Annual mean wave energy of 75–80 kW/m
France
Western Brittany [85] X 27-year
(1994–2020) 200 m—30 min Wave energy flux exceeding 40 kW/m
Franch Atlantic
coast [86] X X 33-year
(1979–1989) 0.0083×0.0083
Annual mean wave power of 25–30 kW/m in
the offshore western coast of France. In the
nested zone, the mean wave energy values
range from 8 to 10 kW/m around 40 km from
the coastline, up to 15–20 kW/m in the
southwestern region of the map.
Western French
coast [16] X X 3-year
(1998–2000) 0.083×0.083—6 h
The annual wave power of 20 to 25 kW/m.
A good agreement was obtained comparing the
model and measured data from three buoys.
J. Mar. Sci. Eng. 2024,12, 1922 8 of 25
Table 2. Cont.
Study Area Authors
Spectral Models
Covered Period Spatial—Temporal
Resolutions Main Results
SWAN
WW3 WAM MIKE21-SW TOMAWAC
Iberian
Peninsula [87] X X 32-year
(1979–2010) 0.37×0.37—3 h
Morocco Atlantic coast of
Morocco
[88] X 30-year
(1991–2020) 0.25×0.25—6 h Mean wave energy density is about 20 kW/m.
[89] X 44-year
(1958–2001)
Average wave power varies between 28 and
30 kW/m.
Iran
Persian Gulf [90] X 30-year
(1988–2017) 0.125×0.125—6 h
The maximum mean wave power is
approximately 0.33 kW/m at the southern Gulf,
whereas the lowest value of about 0.08 kW/m is
estimated in the Eastern Gulf within the Strait
of Hormuz.
Southern coasts of
Iran, Persian Gulf [91] X 25-year
(1984–2008) 0.2(~20 km)—3 h
Annual average wave power below 2.73 kW/m.
Ireland Aegean Sea [92] X 15-year
(1999–2013) 0.125—6 h Annual average wave power greater than
8 kW/m.
Sweden Baltic sea, Skagerrak
and Kattegat area [93] X 16-year
(1998–2013)
0.01×0.02
(~1.1 km)
The near-shore (<5 km from the coast) mean
wave power is between 0 and 6.3 kW/m within
the Swedish exclusive economic zone. At about
30 km from the coast, variations up to
7.5 kW/m are noticed.
Indonesia Indonesia [94] X 6.5-year
(2011–2017) 0.05×0.05 (~5.5 km)
The mean wave power is exceeding 30 kW/m
in locations south of Jawa, Bali, and West
Nusa Tenggara.
Chile Central-South Coast
of Chile [95] X 22-year
(1989–2013)
Annual mean wave power 25–30 kW/m.
Modeled data represent 10% compared to
observed data.
J. Mar. Sci. Eng. 2024,12, 1922 9 of 25
4. Wave Energy Resource Assessment
4.1. Wave Power Calculation
The wave power per unit of the wave crest length, P, measured in
kW
per meter, can
be evaluated using the following expression:
P=ρgZ2π
0Z
0cg(σ)E(σ,θ)dσdθ(1)
where
ρ
is the seawater density,
g=
9.81
m·s2
. is the gravity acceleration,
E(σ,θ)
is
the directional wave energy spectrum distributed over frequencies,
σ
, and direction of
propagation of the spectral component, θ, and cgis the group velocity.
In deep waters, the available wave power resource can be measured using two charac-
teristic parameters: the significant wave height
Hs(m)
and the energy period
Te(s)
. Both
are independent of the wave propagation direction. The significant wave height is approxi-
mately equal to the average height of the highest 1
/
3 of waves, and the energy period is
defined as the period of a single sinusoidal wave that would have the same energy as the
sea state [
96
,
97
]. Using deep water assumption, the wave power is estimated using the
following expression [87,98]:
P=ρg2
64π·H2
s·Te(2)
Even though the energy period,
Te
, could be modeled as illustrated in [
99
], in most
cases, it is rarely specified, and it is estimated based on the peak period,
Tp
, and a calibration
factor,
α
. This calibration factor is defined as
Te=α·Tp
and may have different values
depending on the shape of the wave spectrum. Thus,
α
increases towards unity with
decreasing spectral width [
100
] and
α=
0.86 for a fully developed sea in the case of
the Pierson–Moskowitz spectrum, as mentioned in [
74
,
101
]. Conversely, for a JONSWAP
spectrum with a peak enhancement coefficient of
γ=
3.3,
α
reaches 0.90 [
102
,
103
]. This
value was previously used in various studies [65,74,104106].
Figure 1presents the worldwide distribution of annual mean wave power density,
with the indication of important wave directions as arrows. As indicated, the high energy
zones are located between 40
and 60
in both the Northern Hemisphere (NH) and Southern
Hemisphere (SH), with annual mean wave power values in the SH greater than in those in
the NH [7,8].
4.2. Wave Energy Variability: Metrics and Indices
In addition to the amount of wave energy available in a specific site, another factor to
take into consideration when selecting an area for the future exploitation of wave energy
resources is its variability at different time scales (monthly, seasonal, and annual); it would
be suitable to develop a wave energy project in an area with moderate and steady energy
flux instead of an area with unsteady wave climate conditions since they are more reliable,
report a higher efficiency, and maximize the performances of the harvesting devices. Several
wave energy variability indices were introduced by [
63
,
107
] to characterize the variability
of the resource at various time scales. Among these indicators, those suggested by [
101
]
are employed: the coefficient of variation
(cov)
, the seasonal variability index
(Sv)
, and the
monthly variability index (Mv).
The coefficient of variation
(cov)
is obtained from the standard deviation,
σ
, of the
power time series P(t)and the average value P(t):
cov =σ[P(t)]
P(t)(3)
Figure 2illustrates the variation of the annual mean wave power as a function of the
coefficient of variation,
cov
, for some specific countries around the world. As indicated,
countries in the Northern Hemisphere (NH) are concerned with a greater variability com-
J. Mar. Sci. Eng. 2024,12, 1922 10 of 25
pared to countries in the Southern Hemisphere (SH) with about 1.5 in the North Atlantic,
while in the SH, the cov values are, in general, lower than 1.
J. Mar. Sci. Eng. 2024, 12, x FOR PEER REVIEW 11 of 27
compared to countries in the Southern Hemisphere (SH) with about 1.5 in the North
Atlantic, while in the SH, the cov values are, in general, lower than 1.
Figure 2. The mean wave power level versus the coecient of variation 𝑐𝑜𝑣 for typical sites (data
used in this gure are adapted from [2,108]).
The seasonal variability index 󰇛𝑆󰇜 is dened as follows:
𝑆=𝑃.−𝑃.
𝑃 (4)
where 𝑃. is the average wave power density corresponding to the highest-energy
season, 𝑃. is the average wave power density corresponding to the lowest-energy
season, and 𝑃 is the annual mean wave power (evaluated over the whole dataset). The
greater the value of 𝑆 , the larger the seasonal variability, with values lower than 1
indicating moderate seasonal variability.
The monthly variability 󰇛𝑀󰇜 is dened as follows:
𝑀=𝑃.−𝑃.
𝑃 (5)
where 𝑃. is the average wave power density for the highest-energy month and
𝑃. is the average wave power density for the lowest-energy month. Obviously, the
values of 𝑀 are exceeding those of 𝑆.
Although 𝑀 and 𝑆 , dene the short-term variation on monthly and seasonal
scales, they do not take into consideration the long-term eect of climate change. In fact,
a number of research papers showed that the assessment of wave energy and its temporal
and spatial variation is not really sucient for selecting the optimum sites for wave energy
harvesting [109,110]. Within this regard, it was found that wave energy extraction in lower
energetic areas that provide more stable conditions may be more ecient [111]. More
recently, Kamranzad et al. [112] introduced an OHI (Optimum Hotspot Identier) for
determining the appropriate areas for wave energy harvesting applied to the Persian Gulf.
This identier enabled nding optimal locations based on three parameters: the mean
wave power, 𝑃, the frequency, f, of occurrence for waves with power greater than a
Figure 2. The mean wave power level versus the coefficient of variation
cov
for typical sites (data
used in this figure are adapted from [2,108]).
The seasonal variability index (Sv)is defined as follows:
Sv=PS.max PS.min
Pye ar (4)
where
PS.max
is the average wave power density corresponding to the highest-energy season,
PS.min is the average wave power density corresponding to the lowest-energy season, and
Pye ar
is the annual mean wave power (evaluated over the whole dataset). The greater the
value of
Sv
, the larger the seasonal variability, with values lower than 1 indicating moderate
seasonal variability.
The monthly variability (Mv)is defined as follows:
Mv=PM.max PM.min
Pye ar (5)
where
PM.max
is the average wave power density for the highest-energy month and
PM.min
is the average wave power density for the lowest-energy month. Obviously, the values of
Mvare exceeding those of Sv.
Although
Mv
and
Sv
, define the short-term variation on monthly and seasonal scales,
they do not take into consideration the long-term effect of climate change. In fact, a number
of research papers showed that the assessment of wave energy and its temporal and
spatial variation is not really sufficient for selecting the optimum sites for wave energy
harvesting [
109
,
110
]. Within this regard, it was found that wave energy extraction in
lower energetic areas that provide more stable conditions may be more efficient [
111
].
More recently, Kamranzad et al. [
112
] introduced an OHI (Optimum Hotspot Identifier)
for determining the appropriate areas for wave energy harvesting applied to the Persian
Gulf. This identifier enabled finding optimal locations based on three parameters: the
J. Mar. Sci. Eng. 2024,12, 1922 11 of 25
mean wave power,
Pme an
, the frequency,
f
, of occurrence for waves with power greater
than a threshold specified by the authors (P> 2 kW/m for the Persian Gulf), and the
previously cited monthly variability index
Mv
. The most suitable area was prescribed
by the highest mean wave power and frequency but the lowest
Mv
. Thereafter, the OHI
was used by García-Medina et al. [
113
] to identify the hotspots on the southern coast of
Alaska. It was found that the Southeast Alaskan and the Aleutian Archipelagos have
the most nearshore hotspots with OHI > 5 kW/m. Moreover, Martinez and Iglesias [
114
]
developed and applied a new index, named WEI (Wave Exploitability Index), to compare
mean and extreme wave heights. Alonso et al. [
115
] defined the ETER (exploitation to
extreme ratio) to quantify the effect of harsh wave climate conditions on the design and
optimization of a WEC for local applications. In order to reduce the uncertainties and
biases, Lavidas [
98
] suggested the SIWED (Selection Index for Wave Energy Deployments).
Additionally, Kamranzad and Takara [
116
] proposed a
SI p
(Sustainability Index), in order to
include the internal long-term change in wave energy in a specific region. Kamranzad and
Mori [
117
] suggested a novel CSI (Climate Stability Index) that determines both short-term
variations and long-term changes and helps define the stability in an area.
In addition to factors related to local sea state, such as the effect of climate change,
exploitable storage of wave energy, accessibility, and availability, etc., the characteristics
of WECs need to be considered in the prediction of power supply. For this consideration,
Kamranzad and Hadadpour [
118
] proposed an MCA (Multi-Criteria Approach) that com-
bines the above-mentioned factors to account for both WECs’ performance and the sea state
of the resource. The approach was applied in three hotspots of the seas surrounding Iran.
Based on a comparison of the MCA index in the hotspots with eight types of WECs, the
most suitable combination location/WEC was selected. The same approach was recently
applied by Kamranzad et al. [119] to the southern coasts of China.
To summarize, the main indices used to take into account the long-term variations in
wave climate conditions are given in Table 3.
Table 3. A non-exhaustive review of the resource-based indices for wave energy assessment.
Indices, Reference Formula Interpretation
OH I, [112]OH I =Pmean ·f
Mv
Where Mvdenotes the monthly variability, Pmean
the mean wave power, and fthe frequency.
Suitable areas are characterized by a greatest mean
wave power and frequency but the lowest Mv.
WEI, [114]
WEI =HR MS
Hmax
Where HRMS is the mean value of the
root-mean-square wave height, and Hmax is the
maximum individual wave height over the
considered period.
Higher values of WEI, indicates that the area is
suitable for wave energy exploitation.
SIWED, [98]
SIWED =eCoV Hm0·Cf
HEVA
Hmax
Where CoV Hm0the Coefficient of Variation, Cfthe
capacity factor, HEVA the value of return waves
based on extreme value analysis, and Hmax the
maxima value of wave height from the dataset.
Higher value of SIWED means that both the area of
study and the selected WEC have a better “match”
and can provide reliable energy production.
ETER, [115]
ETER =He
Hd
Where Heis the significant wave height
representative of sea conditions with a maximum
annual wave energy, and
Hd
is the significant wave
height representative of the most severe extreme
events that the project should be able to withstand.
ETER corresponds to the structural efficiency of a
WEC device. It is equal to the unity when
exploitation and extreme conditions are the same.
The lower this ratio is, the higher the gap between
the operational and extreme conditions employed
for a WEC design.
J. Mar. Sci. Eng. 2024,12, 1922 12 of 25
Table 3. Cont.
Indices, Reference Formula Interpretation
SI p, [116]
SI p=
Pannual.mean
max(Pannual.me an )×cosRat e o f chan ge
max(|R ate o f cha nge|)
Mv
Where
Pannual.mean
is the annual mean wave power.
The dimensionless forms of
Pannual.mean
and rate of
change have been used by dividing them by their
maximum value in the domain.
Higher values of SIpresult in higher wave energy
potential, smallest rate of change in the long-term,
and smallest monthly variability.
WEDI, [90]
WEDI =Pwave
Jwave
Where Pwa ve is the yearly mean wave power, and
Jwave to the highest storm wave power.
WEDI enables us to evaluate the potential hazards
that could arise in terms of extreme conditions at
WECs and offshore structures.
CSI, [117]
CSI =XH
|(MvFMvH)×MvH×(XFXH)|
Hand Fdenote historical and future periods,
respectively, and X the yearly average value of
each parameter.
Locations with higher values of CSI are those with
higher stability in both short and long-term.
ST, [120]
ST =PMmin
Pyear
Where PMmin is the mean wave power density in
the minimum energy month kW/m and Pyear is
the annual mean wave power density over the
covered period.
Higher values of ST indicate lower variations in
the wave energy density.
MCA, [118]
MCA = Ee
2000 ×accessibil ity×av ailability×E0
10,000 ×5
HS100
MvE0!
With
Ee
the exploitable storage of wave energy per
unit area, and Hs100, the design wave height for
100-year return period.
The MCA accounts for the performance of systems
in addition to the sea state and sustainability of the
resources to identify the most suitable location for
a wave energy project. It is useful for combined
comparison of WECs and locations.
5. Wave Energy Conversion Technologies
Wave energy conversion systems convert the kinetic and/or potential energy from
incident sea waves into useful mechanical or electrical energy that can be integrated into
the storage or grid. The wave energy conversion chain for a WEC device is illustrated in
Figure 3.
J. Mar. Sci. Eng. 2024, 12, x FOR PEER REVIEW 13 of 27
The lower this ratio is, the higher the gap
b
etween the operational and extreme
conditions employed for a WEC design.
𝑆𝐼, [116] 𝑆𝐼=𝑃.
𝑚𝑎𝑥󰇛𝑃.󰇜×𝑐𝑜𝑠 𝑅𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒
𝑚𝑎𝑥󰇛|𝑅𝑎𝑡𝑒 𝑜𝑓 𝑐ℎ𝑎𝑛𝑔𝑒|󰇜
𝑀
Where 𝑃. is the annual mean wave power. The
dimensionless forms of 𝑃. and rate of change have
b
een used by dividing them by their maximum value in the
domain.
Higher values of 𝑆𝐼 result in higher wave
energy potential, smallest rate of change in
the long-term, and smallest monthly
variability.
𝑊𝐸𝐷𝐼,
[90] 𝑊𝐸𝐷𝐼=𝑃
𝐽
Where 𝑃
is the yearly mean wave power, and 𝐽 to the
highest storm wave power.
WEDI enables us to evaluate the potential
hazards that could arise in terms of extreme
conditions at WECs and offshore structures.
𝐶𝑆𝐼, [117]
𝐶𝑆𝐼= 𝑋
𝑀−𝑀×𝑀×󰇛𝑋−𝑋󰇜
H and F denote historical and future periods, respectively, and
X the yearly average value of each parameter.
Locations with higher values of CSI are
those with higher stability in both short and
long-term.
𝑆𝑇, [120] 𝑆𝑇=𝑃
𝑃
Where 𝑃 is the mean wave power density in the minimum
energy month kW/m and 𝑃 is the annual mean wave power
density over the covered period.
Higher values of ST indicate lower
variations in the wave energy density.
𝑀𝐶𝐴,
[118] 𝑀𝐶𝐴= 𝐸
2000×𝑎𝑐𝑐𝑒𝑠𝑠𝑖𝑏𝑖𝑙𝑖𝑡𝑦×𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦× 𝐸
10000×5
𝐻
𝑀
With 𝐸 the exploitable storage of wave energy per unit area,
and 𝐻, the design wave height for 100-year return period.
The MCA accounts for the performance of
systems in addition to the sea state and
sustainability of the resources to identify
the most suitable location for a wave energy
project. It is useful for combined
comparison of WECs and locations.
5. Wave Energy Conversion Technologies
Wave energy conversion systems convert the kinetic and/or potential energy from
incident sea waves into useful mechanical or electrical energy that can be integrated into
the storage or grid. The wave energy conversion chain for a WEC device is illustrated in
Figure 3.
Figure 3. Illustration of wave energy conversion chain.
There have been a large number of wave energy conversion systems, resulting from
the various ways of wave energy capture as well as the characteristics of the deployment
location. Recent studies reported about one hundred systems at dierent stages of
Figure 3. Illustration of wave energy conversion chain.
There have been a large number of wave energy conversion systems, resulting from
the various ways of wave energy capture as well as the characteristics of the deployment
location. Recent studies reported about one hundred systems at different stages of develop-
ment [
121
,
122
]. Table 4lists the installed capacity (kW) of wave energy conversion systems
around the world since 2016, including the installed capacity for the following: planned
projects, projects under development, and operational projects [123].
J. Mar. Sci. Eng. 2024,12, 1922 13 of 25
Table 4. Installed capacity of wave energy converters around the world since 2016 [124].
Country Planned Projects (kW) Installed (kW) Operational (kW) Total (kW)
Canada 0 0 11 11
New Zealand 0 20 0 20
Denmark 39 12 1 52
Italy 0 150 0 150
Mexico 200 0 0 200
Spain 0 230 296 526
Korea 0 0 665 665
China 0 400 300 700
Portugal 350 0 400 750
United States 1335 500 30 1865
Sweden 0 0 3200 3200
Ireland 5000 0 0 5000
In general, WECs can be classified according to their working principle, installation
locations, operation mode, and design geometries [
3
,
122
,
125
128
]. According to their work-
ing principle, WECs can be classified into three distinct categories, namely, oscillating water
columns (OWCs), overtopping devices, and oscillating bodies (also referred to as wave-
activated bodies), as illustrated in Figure 4. These conversion systems can either be fixed or
floating structures depending on the area in which they are placed (onshore or offshore).
J. Mar. Sci. Eng. 2024, 12, x FOR PEER REVIEW 15 of 27
Figure 4. Wave energy converters classied according to their working principle.
For all the wave energy conversion technologies, the power take-o (PTO)
mechanism is the most important component, as it directly connects to the amount of the
captured wave energy density into electricity. Many research works are actively working
to develop and improve the PTO system, using various concepts [142–146]. The most
common PTO mechanisms that can be used to convert the energy absorbed from sea
waves by WECs into usable electricity are based on hydraulic systems, air turbines, direct
electrical drive and direct mechanical drive (DMD) [122,147]. Figure 5 presents a
schematic illustration of the commonly used PTO systems.
Figure 4. Wave energy converters classified according to their working principle.
Oscillating water columns: consist of submerged air chambers related to the atmo-
sphere via a circular outlet inside which an air turbine is installed. The flow rate of
air through the air turbine is created by the incoming waves that compress and de-
J. Mar. Sci. Eng. 2024,12, 1922 14 of 25
pressurize air in the chamber based on the periodic motion of the water’s free surface.
Electricity can be generated by connecting the air turbine to a generator. These systems
are mostly integrated into breakwaters [
129
,
130
], such as Mutriku [
131
] operating for
almost 10 years. However, there are concepts appropriate for deeper waters [127].
Overtopping devices: are designed to capture the incident sea waves in a tank located
above sea level, then they deliver the water back to the sea using a low-head turbine
linked to a generator. These technologies can be placed onshore or offshore. Examples
of such devices include TAPCHAN [
132
], SSG [
133
], and Floating Structure Wave
Dragon [134].
Oscillating body devices: are made from several components able to oscillate and
move around a reference point. As the system is planted in the water, the sea waves
start to excite the device. The energy is captured using the relative motion of the bodies.
Examples of such devices include IPS buoy [
135
], Wavebob [
136
], Aquabuoy [
137
],
Pelamis [138], SEAREV [139], Oyster [140], and oscillating buoy WEC [141].
The devices exemplified in Figure 4are not intended to give an exhaustive list of
existing WECs. They were chosen among prototypes or projects that were the object of
extensive development efforts.
For all the wave energy conversion technologies, the power take-off (PTO) mechanism
is the most important component, as it directly connects to the amount of the captured
wave energy density into electricity. Many research works are actively working to develop
and improve the PTO system, using various concepts [
142
146
]. The most common PTO
mechanisms that can be used to convert the energy absorbed from sea waves by WECs into
usable electricity are based on hydraulic systems, air turbines, direct electrical drive and
direct mechanical drive (DMD) [
122
,
147
]. Figure 5presents a schematic illustration of the
commonly used PTO systems.
J. Mar. Sci. Eng. 2024, 12, x FOR PEER REVIEW 16 of 27
Figure 5. Power take-o systems for wave energy conversion technologies, adapted from [148].
Air turbines are commonly used as PTO systems in OWC devices [149–153], whereas
hydraulic PTO systems or turbines are predominantly used for overtopping devices or
oscillating bodies [139,154]. Direct-drive mechanical and electrical types of PTO
mechanisms are used in the case of WECs that contain moving elements with relatively
large dimensions and mass [155,156]. PTO mechanisms have to be adapted to be
integrated into WECs, as the energy ow delivered by wave energy is random and highly
variable. As a result, air turbines can only reach eciencies of about 50 to 60%, while
hydraulic turbines eciencies can reach about 70 to 90%. Examples of PTO systems
integrated in wave energy conversion technologies are presented in Figure 6 and Table 5.
The advantages and challenges of each kind of PTO system can be found in [122].
Figure 5. Power take-off systems for wave energy conversion technologies, adapted from [148].
Air turbines are commonly used as PTO systems in OWC devices [
149
153
], whereas
hydraulic PTO systems or turbines are predominantly used for overtopping devices or os-
cillating bodies [
139
,
154
]. Direct-drive mechanical and electrical types of PTO mechanisms
are used in the case of WECs that contain moving elements with relatively large dimensions
and mass [
155
,
156
]. PTO mechanisms have to be adapted to be integrated into WECs, as
the energy flow delivered by wave energy is random and highly variable. As a result, air
turbines can only reach efficiencies of about 50 to 60%, while hydraulic turbines efficiencies
J. Mar. Sci. Eng. 2024,12, 1922 15 of 25
can reach about 70 to 90%. Examples of PTO systems integrated in wave energy conversion
technologies are presented in Figure 6and Table 5. The advantages and challenges of each
kind of PTO system can be found in [122].
J. Mar. Sci. Eng. 2024, 12, x FOR PEER REVIEW 16 of 27
Figure 5. Power take-o systems for wave energy conversion technologies, adapted from [148].
Air turbines are commonly used as PTO systems in OWC devices [149–153], whereas
hydraulic PTO systems or turbines are predominantly used for overtopping devices or
oscillating bodies [139,154]. Direct-drive mechanical and electrical types of PTO
mechanisms are used in the case of WECs that contain moving elements with relatively
large dimensions and mass [155,156]. PTO mechanisms have to be adapted to be
integrated into WECs, as the energy ow delivered by wave energy is random and highly
variable. As a result, air turbines can only reach eciencies of about 50 to 60%, while
hydraulic turbines eciencies can reach about 70 to 90%. Examples of PTO systems
integrated in wave energy conversion technologies are presented in Figure 6 and Table 5.
The advantages and challenges of each kind of PTO system can be found in [122].
Figure 6. Examples of PTO mechanisms: (a) hydro turbine; (b) air turbine; (c) direct electrical drive
PTO system; and (d) hydraulic.
Table 5. Examples of some wave energy converters with their power take-off (PTO) systems.
WEC Type WEC Name PTO References
Oscillating Water Column Pico Wells turbine [149]
LIMPET Wells turbine [157]
Mutriku Wells turbine [150]
Sakata Wells turbine [158]
Mighty Whale Wells turbine [159]
Oscillating bodies
Heaving system
Wave bob Hydraulic system [136,160]
AquaBuOY Impulse turbine [97,161]
IPS buoy Hydraulic oil system & linear generator [135]
Pitching system
Pelamis Hydraulic system [138]
Oyster Hydraulic system [140]
SEAREV Hydraulic system [139]
A prior characterization of wave energy resources is needed before any wave energy
conversion technology implementation. Within this regard, extensive research on wave
energy development indicates that WECs need to operate at an area with a minimum
value of annual mean wave power estimated at 20 kW/m to be viable [15,127,154,162]. In
addition to this condition, there are still many criteria to take into account in WECs’ design
stage, including survivability and reliability. In fact, in marine areas, WECs are subject to
extreme wave conditions that surpass its operational thresholds and hence cause numerous
failures like fatigue, corrosion, and extreme loads [163165].
J. Mar. Sci. Eng. 2024,12, 1922 16 of 25
6. Wave Energy Production
In the last few decades, numerous studies were carried out to quantify the energy that
can be generated if WECs are installed in marine areas [
166
172
]. Similarly, in the wind
industry, where the potential of wind turbines takes into account the specific power curve
in combination with wind measurements, the energy production of WECs in a particular
area emerges from the combination of the power matrix of the wave converter (given by
each WEC constructer either based on experiments or designed using numerical models)
with the characteristic matrices of the wave climate at the same area. Legaz and Guedes
Soares [
173
] used the power matrices of nine different WECs in order to evaluate their
performances in the Bay of Cádiz. In reality, the compatibility between the sea states in the
studied region and the power matrix of the WECs is of great importance in selecting the
appropriate device. The power matrix consists of a bivariate distribution of sea conditions
defined by
Hs
and
Te
values (energy bins). The corresponding WEC yearly energy output,
PE, given in kWh, is calculated using the following equation [17,172]:
PE=1
100
nT
i=1
nH
j=1
pij Pij (6)
where
pij
denotes the energy percentage corresponding to the bin defined by the
j
-th and
column and the
i
-th row of the power matrix, while
Pi j
is the expected electric power output
provided in the power matrix of the WEC for the same bin.
Given that the energy provided by WECs can considerably vary depending on the total
power installed or size, it would be suitable to compare the normalized power performance
using the capacity factor indicator,
Cf
. It compares the energy generated by a WEC during
a specific period with the energy that can be generated if it has worked at maximum rated
power. This parameter is expressed as the following:
Cf=100 PE
Np(7)
where
PE
is the average electric power generated by each WEC in a particular area, while
Npdenotes the maximum rated power of each device [17,174].
Within this regard, Rusu and Onea [
5
] assessed the performance of ten different WEC
devices operating in different European coastal areas and found that the Pontoon Power
converter has the highest value of the capacity factor of about 14.5% during the entire time
and 21.1% during the winter time. Sierra et al. [
64
] evaluated the performances of three
different WECs (Pelamis, AquaBuOY, and Wave Dragon) along the coast of Menorca, Spain.
For the three devices, the capacity factors of 9%, 10%, and 11% are obtained, respectively.
Lavidas and Venugopal [
175
] compared the performance of six wave converters for the
Greek coastal regions. They found that the zones with the maximum capacity factors are
located in both Crete Island and the southern Aegean Sea. Moreover, the Wavestar is
noted as the best device, being able to operate at nominal power for low wave heights and
periods. In western Britty, Guillou and Chapalain [
169
] investigated the effect of temporal
variability on the electricity production of three devices (Pelamis, AquaBuOY, and Wave
Dragon). In winter, the WECs’ performances indicated high variabilities with maximum
monthly mean values of a capacity factor of about 65% for Wave Dragon. For the Croatian
part of the Adriatic Sea, Pelamis wave energy converters are considered more suitable as
they are concerned with higher capacity factor values [
176
]. Bozzi et al. [
177
] assessed
the performance of several offshore WECs at a 10 km resolution along the Mediterranean
coastline. It was shown that most of the Mediterranean coastline areas can be successfully
exploited by downscaling (using the Froude Similarity Criterion) the existing wave energy
conversion devices. More precisely, the capacity of six of the studied WECs is higher than
0.2 along 40% of the shoreline and exceeds 0.3 at 8% of the studied areas for three other
WECs (AquaBuOY, Pelamis, and Wave bob). Marti´c et al. [
178
] analyzed and compared
the performance of both full-scale and downscaled WECs in terms of operating hours
J. Mar. Sci. Eng. 2024,12, 1922 17 of 25
and capacity factor. They found that for the Adriatic Sea, the downscaled WECs are
more suitable.
Table 6gives the essential characteristics of certain wave energy conversion technolo-
gies in terms of the rated power, the recommended depth for installation, and the power
matrix resolution. Another methodology for computing the power output for wave farms
is presented in references [179181].
Table 6. Non-exhaustive overview of WEC systems and their corresponding rated power and power
matrix resolution, see [17,170,174,177].
WEC System Rated Power (kW) Recommended Depth Power Matrix Resolution
Hs,Teor Tp
Reference
OWC 85 <20 1.0 m ×1.1 s [172]
Wave dragon 5900 >30 0.5 m ×0.5 s [182]
Wave Roller 1000 10–25 1.0 m ×1.0 s [172]
Oyster 291 10–25 0.5 m ×1.0 s [118]
OE (Ocean Energy buoy) 2880 >100 0.5 m ×1.0 s [160]
Wave star C6 600 10–30 0.5 m ×1.0 s [160]
AWS (Archimede Wave Swing) 2470 100 0.5 m ×0.5 s [182]
Wave bob 1000 >50 0.5 m ×0.5 s [160]
Pelamis 750 >50 0.5 m ×0.5 s [182]
Oceantec 500 50–100 [183]
CETO 260 20–50 0.5 m ×0.5 s [160]
Aquabuoy 250 >50 0.5 m ×1.0 s [161]
Another important parameter to consider is associated with the energy capture and
is often expressed as
Cw
(capture width). This parameter is defined as the ratio between
PE
and
Pw
and is known as the width of the wave front from which all the absorbed
power by the WEC can be extracted. The capacity factor is determined using the following
equation [171]:
Cw=PE
Pw(8)
Although these power performance metrics are important in selecting the suitable
WEC device for a particular region, the economic feasibility [
184
,
185
] is the most important
aspect for WEC developers when determining whether an energy technology can reach com-
mercialization [
186
]. In this context, the economic cost of a wave energy generation device
incurred over its entire life cycle is evaluated using the LCOE index in Euro/MW h, which
is widely reported in the literature [187189]. According to Vanegas-Cantarero et al. [190],
the LCOE can be calculated as follows:
LCOE =
Ca pEx +n
t=1OpExt
(1+r)t
n
t=1AEPt
(1+r)t
(9)
where ndenotes the device’s life expectancy in years, tis the year from the beginning of the
project, and ris the discount rate (%), which accounts for the value of money as a function
of time.
Ca pEx describes the total initial costs (here, units of $).
Ca pEx
describes costs (here, units of $) of the WEC project’s fixed assets, and
OpEx
includes ongoing costs (units of $) for running the project throughout its lifetime, and
AEPt
refers to the electricity generated by the project in year t.
AEP =PC ×Cf×AF ×8766 hour/year (10)
where
PC
is project capacity,
Cf
is the capacity factor, AF is the availability factor, and
8766 is the number of hours in a year, including leap years. The project capacity is defined
J. Mar. Sci. Eng. 2024,12, 1922 18 of 25
as the number of devices multiplied by the devices’ rated powers (units of power, e.g.,
kW or MW). The availability factor is the “Availability of a wave energy converters to
be in a state to perform a necessary function under given climate conditions at a given
instant of time over a given duration, assuming that the necessary external resources are
provided” [191,192].
It is useful to consider
AEP
as the product of (1) the power matrix of the WEC,
(2) the joint
occurrence frequency of
Hs
and
Te
for a WEC deployment area, (3) the ability
or inability of a WEC to operate in the wave conditions of the chosen area, (4) the percentage
of time the device is operational, and (5) the total number of devices within the WEC array.
7. Conclusions
In the current paper, a detailed review was carried out on wave energy resource
assessment tools and methods. The theoretical formulations used for wave energy density
calculation as well as the indices for the short-term variability of wave resource were
described. This section was complemented by a review of different metrics adopted to take
into consideration both the long-term variability of the wave resource and the characteristics
of WECs to account for in the prediction of power supply. Moreover, this paper highlights
the available data for long-term characterization and analysis of wave climate including in
situ measurements, satellite altimetry, and reanalysis archives. In fact, each of these sources
has its characteristics and is subject to some limitations. Satellite altimeters have huge
spatial coverage of the ocean under a wide range of wave climate conditions, with low
temporal resolution (e.g., daily), whereas in situ measurements are specific to particular
oceanic areas and various ranges in spite of having high temporal resolution. Re-analysis
data overcome these limitations as they are of high temporal resolution of 1 to 6 h and
global spatial coverage.
The existing numerical wave models and their area of application were presented.
Also, the wave energy potential of each area was indicated to give developers an idea
about the interesting locations for WEC deployment (Table 2). The results obtained from
numerical wave models are usually calibrated with available data from satellite altimeters
and buoys.
For wave energy exploitation, different WECs are presented. They may be classified
according to their working principle into three distinct categories: (i) OWC (oscillating
water column); (ii) overtopping devices; and (iii) oscillating bodies. For these WECs’
implementation, a prior characterization of wave energy resources is needed. Extensive
research on wave energy development indicates that WECs need to operate at an area
with a minimum value of annual mean wave power estimated at 20 kW/m to be viable.
Moreover, given that the energy generated by WECs can considerably vary depending
on the total power installed or size, it is important to compare the energy generated by a
WEC during a specific period with the energy that can be generated if it has worked at
maximum rated power. Finally, a brief discussion of the economic feasibility of wave farms
was provided based on the use of LCOE index. One of the challenges to address for future
deployment and the commercialization of WECs is the survivability issue of these devices
when experiencing extreme wave conditions.
Author Contributions: Conceptualization, H.B.; methodology, H.B. and A.E.M.; formal analysis, H.B.;
resources, H.B.; writing—original draft preparation, H.B., A.E.M., I.H. and R.N.; writing—review and
editing, H.B. and A.E.M.; visualization, H.B. and A.E.M.; supervision, H.B. and A.E.M. All authors
have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Conflicts of Interest: The authors declare no conflicts of interest.
J. Mar. Sci. Eng. 2024,12, 1922 19 of 25
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... Wave power (WP) has essential strategic value in remote seas where laying power grids is costly. By utilizing the vast and largely untapped energy from ocean waves, WP can reduce reliance on traditional fossil fuels and provide a reliable and continuous power supply [1][2][3][4][5]. It can offer green energy for observation equipment, oil drilling platforms, ranches, and other offshore facilities. ...
... It is necessary to carry out systematic resource assessments before planning WP deployment projects and designing the wave energy converters [2][3][4][5]. Take the South China Sea (SCS), the largest marginal sea in the western Pacific, as an example; due to its unique geographical characteristics and rich marine resources, many studies have been performed to assess the richness and stability of WP resources, based on in situ observations, satellite data, and numerical models [6][7][8][9][10][11][12][13][14][15][16]. ...
... Based on previous studies on WP assessments in different sea regions, e.g., [4,12,18], the following equation was used to calculate the WP density (Pw): ...
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... The energy available from the waves is determined by the wave height ( ) and the wave period ( ), along with other environmental parameters. The total power in the waves ( ) can be estimated using (1) [22]. ...
... The energy available from the waves is determined by the wave height (H) and the wave period (T), along with other environmental parameters. The total power in the waves (P wave ) can be estimated using (1) [22]. ...
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