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Offshore floating photovoltaics system assessment in worldwide perspective

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Abstract

Floating solar photovoltaics (FPV), whether placed on freshwater bodies such as lakes or on the open seas, are an attractive solution for the deployment of photovoltaic (PV) panels that avoid competition for land with other uses, including other forms of renewable energy generation. While the vast majority of FPV deployments have been on freshwater bodies, in this paper, we chose to focus on offshore FPV, a mode of deployment that may be particularly attractive to nations where the landmass is constricted, such as is the case in small islands. There is a wide perception that seawater cooling is the main reason for the enhanced performance of offshore FPV panels. In this paper, a worldwide assessment is made to validate this perception. To this end, a technology‐specific heat transfer model is used to calculate PV system performance for a data set of 20 locations consisting of one system located on land and another one offshore. The analysis assumes that the floating offshore panels are placed on metal pontoons and that all panels are based on monocrystalline silicon technology. Our analysis shows that the energy yield difference, between land‐based and offshore systems, for the time period of 2008 and 2018, varies between 20% and −4% showing that offshore FPV yield advantages are site‐specific. In addition, the effect of other environmental factors, namely, irradiation level difference, ambient temperature, wind speed, precipitation, and sea surface temperature, is studied in this paper, which leads to the formulation of two different regression models. These can be used as a first step in predicting yield advantages for other locations.
RESEARCH ARTICLE
Offshore floating photovoltaics system assessment in
worldwide perspective
S. Zahra Golroodbari | Abdulhadi W.A. Ayyad | Wilfried van Sark
Copernicus Institute of Sustainable Institute,
Utrecht University, Utrecht, The Netherlands
Correspondence
S. Zahra Golroodbari, Copernicus Institute of
Sustainable Institute, Utrecht University,
Princetonlaan 8a, 3584CB Utrecht, The
Netherlands.
Email: s.z.mirbagherigolroodbari@uu.nl
Funding information
Rijksdienst voor Ondernemend Nederland
Abstract
Floating solar photovoltaics (FPV), whether placed on freshwater bodies such as lakes
or on the open seas, are an attractive solution for the deployment of photovoltaic
(PV) panels that avoid competition for land with other uses, including other forms of
renewable energy generation. While the vast majority of FPV deployments have
been on freshwater bodies, in this paper, we chose to focus on offshore FPV, a mode
of deployment that may be particularly attractive to nations where the landmass is
constricted, such as is the case in small islands. There is a wide perception that sea-
water cooling is the main reason for the enhanced performance of offshore FPV
panels. In this paper, a worldwide assessment is made to validate this perception. To
this end, a technology-specific heat transfer model is used to calculate PV system
performance for a data set of 20 locations consisting of one system located on land
and another one offshore. The analysis assumes that the floating offshore panels are
placed on metal pontoons and that all panels are based on monocrystalline silicon
technology. Our analysis shows that the energy yield difference, between land-based
and offshore systems, for the time period of 2008 and 2018, varies between 20%
and 4% showing that offshore FPV yield advantages are site-specific. In addition,
the effect of other environmental factors, namely, irradiation level difference, ambi-
ent temperature, wind speed, precipitation, and sea surface temperature, is studied in
this paper, which leads to the formulation of two different regression models. These
can be used as a first step in predicting yield advantages for other locations.
KEYWORDS
climate zones, floating PV, offshore, photovoltaics, yield assessment
1|INTRODUCTION
Solar photovoltaics (PV) presently account for roughly 28% of the
total of 3.07 TW of installed renewable energy technologies,
1
a fact
which reflects rapid levels of technological growth, as well as
increased economic confidence with investors increasingly choosing
to invest in PV installations. This is also highlighted by, among others,
the World Energy Outlook 2020 published by the International
Energy Agency, which dubbed solar PV as the new king of electricity
supplywithin their Net Zero Emissions by 2050 scenario
(NZE2050),
2
an outlook that envisages an annual installation of
500 GWp of solar PV capacity.
The annual energy yield of PV panels is determined by a number
of factors. Most obviously, these include the conversion efficiency of
Wilfried van Sark, ISES member
Received: 19 October 2022 Revised: 23 February 2023 Accepted: 31 May 2023
DOI: 10.1002/pip.3723
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium,
provided the original work is properly cited.
© 2023 The Authors. Progress in Photovoltaics: Research and Applications published by John Wiley & Sons Ltd.
Prog Photovolt Res Appl. 2023;31:10611077. wileyonlinelibrary.com/journal/pip 1061
the PV panel, which in turn is the result of the specific cell technology
used (e.g., monocrystalline/polycrystalline silicon [Si], thin films based
on cadmium indium gallium selenide [CIGS] or cadmium telluride
[CdTe], a number of climatological/meteorological factors [irradiance,
temperature], and installation details [orientation, tilt, mounting struc-
ture]). There is well-established literature covering the interplay
between some climatological/meteorological factors, such as solar
irradiance and temperature, and the performance of photovoltaic
panels (see, e.g., Pearsall
3
). Performance variation across the globe has
been correlated with KöppenGeiger (KG) climate zones
4
for Si, CdTe,
GaAs, and perovskites,
5
while recently a PV-specific KG climate classi-
fication has been suggested, which divides the globe into 12 zones
based on the performance of PV panels.
6
The KG climate classification
system divides the world into various regions into three separate
levels. Differences across the zones are based on temperature; the
amount and pattern of precipitation; and, indirectly, irradiation.
6
Other various local effects such as dust and humidity
7
pose an
additional challenge to understanding which locations across the
globe are likely to have the best-performing solar PV installations. This
is obviously also a question of economic importance, as the economic
feasibility of any solar PV installation will be due in part to climatologi-
cal considerations. A recent detailed exploration of this has been per-
formed for mainland China, a large and ecologically/climatologically
diverse landmass.
8
The authors of that paper in addition suggest that
it would be most advantageous for a given electricity grid that PV
installations connected to it were divided between land-based and
offshore floating PV.
As a further example of increased interest in FPV, in the
Netherlands, a recent roadmap for future PV deployment has shown
that half of the potential can be found offshore, on the North Sea
9,10
in addition to considerable inland FPV potential as well.
While most deployments of FPV to date have been on freshwater
bodies,
11
we focus in this paper on offshore FPV (OFPV). For our pur-
poses, we include sites that are rough 56-km offshore from the
selected port site. OFPV will be particularly attractive for small island
nations, for example, Malta,
12
the Maldives,
13
and Singapore.
14
Like-
wise, OFPV is a particularly good option for nations with compara-
tively large coastal areas, such as the Netherlands.
15
In such
situations, there may be no choice but to consider OFPV in order to
achieve the two aims of reducing carbon emissions while maintaining
energy security.
In other situations, land-based PV systems might compete with
other essential demands on land use, such as agriculture, nature
reserves, and recreation. Our choice of distance to offshore sites does
not directly take into account factors such as wave height or the tem-
perature differences between sites, but it is a choice aimed at ensur-
ing a number of factors. First, based on several constraints, for
example, the energy losses in electricity transmission lines as well as
the possibility of building infrastructure and underwater cabling to
connect an offshore PV site to an onshore connection near the port
site, 56 km is estimated as the maximum possible distance. Second,
offshore sites that are much less than 50 km away from the port
would be too close to the port to give a reliable indication of
differences, based on the spatial resolution of our basic dataset.
16
Finally, once a distance of 50 km is decided for the offshore site, it
seemed intuitively correct to ensure that the inland sites we studied
were equidistant from the port, thus ensuring consistency across our
set of sites.
It is straightforward to see that deploying OFPV will offer advan-
tages in certain contexts. While there has been immense progress
made in this field in recent years,
17
economic obstacles may hamper
the further deployment of OFPV.
18,19
To put this into a quantitative
context, a recent review paper
20
suggests that the total cumulative
capacity of FPV amounts to a marginal 2.6 GW and is concentrated in
three countries (cf. the widely reported 270 GW of solar PV, which
was installed worldwide in 2022). Consequently, it is important to
understand exactly which sites globally can expect to have the most
pronounced advantage for the use of OFPV, and these would then
become the sites at which further exploration becomes feasible at
first.
More recently, detailed performance data on FPV comes from the
Singapore Tengah Reservoir,
14
in which the performance of eight dif-
ferent commercially available FPV technologies are tested. Rigorous
testing from this site has allowed for a comparison of the performance
of different panel technologies on FPV structures, and in particular
how different PV technologies perform when used in FPV installa-
tions. Some of the main findings from this test bed include that ambi-
ent temperatures over water are typically 23C lower than on land,
and wind speeds over the water body are also generally higher.
14
As
humidity above water is also relatively higher, the heat flux on the
floating system location is decreased.
Some literature exists on the performance benefits of OFPV com-
pared with conventional, land-based PV systems. An early overview
of FPV designs provided estimates of 10% larger energy yields com-
pared with similar installations on land,
19
which is explained by the
cooling effect of the underlying water body leading to lower PV mod-
ule temperatures. There is also another thermal modeling based on
fish farm floater technology which concluded relatively different
results than the earlier studies. This research conducted by a group of
researchers in Norway
21
demonstrates that in order for any apprecia-
ble improvements to PV yield, one would need to take the site-
specific water temperature into account. In this study, two adjacent
PV strings were compared: One in direct contact with water and the
other installed above water and there is an air gap between the back
sheet and the water surface. The comparison results showed that a
string directly in contact with the water body on average exhibits a
5%7% higher energy yield than the string that was cooled by air, the
results are based on experiments between the months of May
and July.
Since any benefits or drawbacks from deployment on the water
are dependent on both the site and the technology to be used, there
is no single reference that can indicate a quantitative improvement in
PV yield. In Olivera-Pinto and Stokkermans,
22
for instance, two pon-
toon floaters technologies are chosen. The first technology is made
out of HDPE where the panels are in contact with air and the polymer
material from their back sheet. The second one is based on a meshed
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network galvanized steel frame where the panels are mainly in contact
with air and the galvanized steel frames in a small ratio of the back
sheet area. The results based on simulations in PVSyst
23
have demon-
strated the energy yield advantage of 0.31%0.46% for HDPE struc-
ture and 1.8%2.59% for galvanized steel frame structure. This shows
the energy yield advantage is mainly technology and site-specific.
As another example, an OFPV system on the west coast of
Norway shows energy yield advantages of 6%10% larger yield for a
system in contact with water.
24
A theoretical study for an OFPV sys-
tem with horizontally placed modules on the North Sea about 50 km
off the coast showed an annual yield enhancement of 13% com-
pared with a land-based system, which is due to increased offshore
irradiance as well as cooling of the modules.
15
Here, it was found that
the PR advantage is 4%. While weather and wind patterns have
been considered, the effect of waves is found to be of limited impor-
tance. This contrasts with the case for tilted panels, where it would be
expected that powerful waves could have led to dynamic variations in
POA. Another theoretical study shows that energy loss to moving
modules due to waves can range from 3% for medium wave intensity
up to 9% for extreme wave intensity.
25
Based on the mathematical
modeling of OFPV system on the North Sea, on an annual basis, we
would expect that waves and their impact on the pontoons on which
offshore FPV are sited would lead to variations of about 1%2% in
yield.
15
The studies reported above show that offshore deployment of
FPV has resulted in improved PV yields and that benefits are corre-
lated with geography and meteorological conditions. While technol-
ogy and the mounting type are also important, our approach aims to
develop a model that neutralizes these impacts and isolates geography
as a determinant factor of PV performance and the differences
between offshore and onshore PV installations. Therefore, the aim of
this research is to study the effect of geographical characteristics of
the locations as well as the meteorological variables to find a mean-
ingful correlation for the performance of OFPV systems. To this end,
we consider 20 different locations across the globe from different
continents and climate zones to simulate expected offshore perfor-
mance advantages using irradiation, temperature, and relative humid-
ity data, based on the NASA POWER database.
16
The effect of salinity and bio-fouling on panel degradation and
system efficiency are studied in Setiawan et al
26
and Suzuki et al.
27
However, due to the fact that not all of the water bodies in this study
follow the same trend with respect to bio-fouling based on different
water characteristics, we did not consider this important effect to pre-
vent the complexity in this study. Moreover, for such large-scale FPV
systems, the waves could be relatively damped for the panels if the
modules are protected from water splashing based on waves. That is
the reason we also neglect the salinity effect. The humid environment,
as well as the above-mentioned parameters, could affect the speed of
aging on the FPV system as discussed in detail in Zaharia et al.
28
Nonetheless, in this study, we assume that aging has a similar impact
on all FPV systems in all locations which is the reason it does not have
an effect on the performance difference between LBPV and FPV for
each location.
The rest of the paper is organized as follows: Section 2discusses
the implemented methodology, and Section 3presents and discusses
the obtained results. Finally, in the last section, conclusions are
presented.
2|VARIABLES AND DATA ACQUISITION
Solar irradiation and ambient temperature are two key parameters in
the solar PV system performance calculations. In this research, we will
broaden our model by considering other variables as well, namely
Atmospheric variables, climate zone, and ocean stream currents.
Atmospheric variables
Mekhilef et al
7
describe the multivariate interaction between solar
irradiance, dust levels, and relative humidity to impact the perfor-
mance of PV cells. Note that the influence of humidity can not be
addressed without considering ambient temperature and wind
speed. In Golroodbari and van Sark,
15
a so-called apparent temper-
ature is estimated for solar cell temperature calculations and also
the floating PV system performance analysis. In this research, first,
we calculated the heat index, which is also known as apparent tem-
perature. In the developed model the wind speed effect is consid-
ered in the cell temperature estimation. Both variables and their
effect will be discussed in detail in this section.
Climate zones and site locations
The KöppenGeiger climate zone typology
4
is by far the most
widely used system to classify climate systems globally. This sys-
tem divides the world map into different climate zones considering
precipitation and temperature. It is noteworthy to mention that lat-
itude and solar irradiance levels do not define climate. An illustra-
tion of that, the cities of Utrecht, the Netherlands, and Edmonton,
Canada, have about the same latitude. While the former has cli-
mate classification within the KöppenGeiger system of Cfb
(an oceanic climate with warm summers), while the latter has a
Dfbclassification (hemiboreal), and its climate is more similar to
Stockholm, Sweden, which is far (1450 km) to the north-east of
Utrecht.
Ocean stream current
An ocean current is a continuous, directed movement of seawater
generated by a number of forces acting upon the water, including
wind, the Coriolis effect, breaking waves, temperature, and salinity
differences. Ocean currents can be classified into two main ones:
(i) Surface circulation depending on wind speed, and (ii) deep water
currents or thermohaline circulation, depending on both tempera-
ture and salinity.
29
They cannot be separated by oceanographic
measurements.
2.1 |Data acquisition
In this paper, we utilize a dataset based on 20 port sites across the
world, which covers a wide geographical range. Each of the port cities
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was geocoded using an open street map API, giving a longitude and
latitude pair as well as a complete bounding box for each site (see
Table 1and Figure 1). Each coastal/port site is expanded into a site
twin by adding one corresponding offshore site and one correspond-
ing inland site. The offshore sites are generally chosen to be equidis-
tant (56 km) from the coastal/port site. Within the twins, the
bounding box for the coastal site was used to define the KG classifica-
tion for them, using the hddtools package.
30
One limitation of this
approach, in general, is that there is as of yet no readily available sur-
vey that classifies the open seas according to the KG system.
31
The geocoded coordinates (Table 1) were used as the starting
point from which the locations of the inland and offshore sites were
determined. The following approach was taken:
1. For sites connecting to the open water toward the North, the off-
shore site was found by adding 0.5to the latitude. The reverse
was done for sites with open water to the South: the offshore site
was found by subtracting 0.5from the latitude. Likewise, for each
triplet, the inland site was found by going in the opposite direction.
The choice of 0.5was deliberate with the intention to match the
TABLE 1 The offshore and inland
locations for a given port site are
equidistant (about 56 km apart) from
each of these sites. Country names relate
to the three-character ISO country code,
for example PNGis Papua New
Guinea. Ocean class (current) is defined
as Warm Stream; WS,Cold Stream:
CS,not applicable: NA.KG
classification definitions can be found in
Beck et al.
4
Country Latitude Longitude Ocean KG
No. Name code (degrees) (degrees) current class
1 Bandar Penawar MYS 1.56N 104.23E WS Af
2 Ciudad del Carmen MEX 18.65N 91.81 W WS Aw
3 DaNang Port VNM 16.08N 108.22E NA Am
4 El Emir URY 34.96S 54.94 W CS Cfb
5 Hengsha Island CHN 31.32N 121.85E NA Cfa
6 Katsuura JPN 35.16N 140.32E CS Cfa
7 Kwala Tanjung IDN 3.35N 99.45E WS Af
8 Limassol Port CYP 34.65N 33.016E NA Csa
9 Port Antonio JAM 18.18N 76.45 W WS Am
10 Port Coquitlam CAN 48.55N 124.43 W WS Cfb
11 Port Moresby PNG 9.47S 147.16E WS Aw
12 Port of Rotterdam NLD 51.98N 4.13E WS Cfb
13 Port Shepstone ZAF 30.73S 30.45E WS Cfa
14 Port Vell ESP 41.38N 2.18E NA Csa
15 Puerto Belgrano ARG 38.89S 62.10 W CS Cfa
16 Puerto Colombia COL 10.99N 74.96 W WS Aw
17 Puerto La Cruz VEN 10.21N 64.63 W WS BSh
18 Ras Laffan QAT 25.92N 51.58E NA BWh
19 South Golden Beach AUS 28.50S 153.55E CS Cfa
20 Tanzania Port TZA 6.82S 39.29E WS Aw
FIGURE 1 The locations of the
twenty sites for this study.
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level of accuracy in the downloaded data from NASA POWER
32
(see below).
2. For sites facing east or west, the longitude was modified by the
equivalent of 56 km. Note that the amount of longitude variation
varies with latitude: 1longitude represents about 111 km at the
Equator, but the same amount of longitudinal distance shrinks for
increasing latitude when measured in kilometers to the North and
South. For the data set used here, the largest (absolute) value of
latitude is 51.98(corresponding to the Dutch site), for which
56 km along the longitudinal direction is equivalent to about
0.82longitude.
The above selection rules ensure that there is no more than
56 km between a coastal site and the OFPV site, chosen as an upper
limit for the distances to ensure the feasibility of the siting.
2.2 |Meteorological data
Historical data based on satellite imagery of meteorological data for a
given set of longitude and latitude coordinates are available via the
NASA POWER service.
32
We used an hourly temporal resolution for
10 years of data, extending from January 2008 to January 2018. We
extracted hourly averages for irradiance H(in kWh/m2), clearness
index kT, temperature (ambient Taand sea surface Ts), wind speed vw,
and relative humidity RH. The ambient temperatures collected for the
offshore sites were the sea surface temperatures, while for the inland
and coastal sites, these were the air temperatures at 2 m height. Addi-
tionally, we downloaded solar azimuths and solar hour (cosines) values
in order to facilitate the transposition from direct normal irradiation
(DNI) to plane-of-array.
Further discussions about the uncertainty of the meteorological
data are provided in Section 4.
2.3 |Heat index
The heat index (HI)(
C) of a given combination of dry-bulb ambient
temperature and relative humidity (RH) is defined as the dry-bulb tem-
perature, which would feel the same if the water vapor pressure were
1.6 kPa.
33
The method of calculating heat index varies across environ-
mental studies, and many different methods for calculating this metric
are studied in research by Anderson et al.
34
In this work, we used Equation (1) subject to the correction factor
shown in Equation (2); the coefficients are tabulated at Table 2.
34,35
HI ¼a0þa1Tþa2RH þa3TRH þa4T2þa5ðRHÞ2
þa6T2RH þa7TðRHÞ2þa8T2ðRHÞ2ð1Þ
fHIjT<79
oFTð2Þ
where Tis the ambient temperature in F, RH is relative humidity in
[%] and HI is denoting the heat index. In other words, we set the heat
index to be the same as the temperature when the temperature value
is below 79 (C) Fahrenheit.
2.4 |Heat transfer
A one-dimensional heat transfer analysis model is developed in this
research to calculate the solar cell temperature considering the sea
surface temperature, and heat transfer in the system consisting of PV
module, pontoon, and ocean water. The pontoon is assumed to be
made out of steel, thus because of the good heat conductivity of steel
we assumed that the temperature of the pontoon is equal to the
water surface temperature at the beginning of the analysis.
As the solar panels during the day will have higher temperature
compared with the pontoon and sea surface temperature, we consider
the heat flux flow to go from the solar module toward the water. The
equilibrium equation of the one-dimensional heat transfer analysis is
defined as follows:
QPV ¼QPO ð3Þ
where Qi,iPV,PO is the heat flow rate (W/m2Þ, and PV and PO
denote the PV module and the pontoon, respectively. The heat flow
rates in Equation (3) are as follows:
Qi¼UiAiΔTið4Þ
where Uiis thermal transmittance, Aiis module/pontoon area, and
ΔTiis the temperature difference.
The Uvalue for the solar module is estimated using the same
model as discussed in Sánchez-Palencia et al.
36
In this model, the U
value for the module is a function of solar irradiation. After lineariza-
tion of this model, we could estimate the Uvalue for the solar mod-
ules in this model considering
U¼G
1500 þ2ð5Þ
TABLE 2 Coefficients for the HI calculations.
34,35
a0a1a2a3a4a5a6a7a8
42.4 2.05 10.14 0.22 6.84 1035.48 1021.23 1038.5310 41.99106
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in which Gis solar irradiance.
2.5 |Cell temperature
The efficiency of photovoltaic cells depends on the cell tempera-
ture, which is usually described by temperature coefficients for
the current, the voltage, and the power. In Tina et al,
37
thermal
analysis has been done considering the cooling effect of evapora-
tion and the coefficient values introduced by Faiman
38
have been
optimized based on their panel's characteristics. A similar method
used in this work, which is shown in Equation (6), is a simple
empirical model implemented by Koehl et al
39
to estimate the cell
temperature TCell
TCell ¼Tamb þG
U0þðU1vwÞð6Þ
where Tamb is ambient temperature, U0and U1are correlation coeffi-
cients (Table 3), and vwis local wind speed near the modules.
2.6 |Energy yield
To calculate the energy yield Yfor any PV system, we use
Y¼ηðTPV ,GÞHð1LoÞð7Þ
with ηthe efficiency of the PV panels used, which depends on PV
temperature (TPV [C]) and irradiance (G[W/m2]), H(kWh/m2) the
solar irradiation, and Lorepresenting losses due to system losses other
than caused by temperature, and which we assume to be 10%
throughout, based on typical performance ratio values found in the lit-
erature.
40
Temperature losses are accounted for in the definition of
the efficiency of the PV panels, as follows
41
:
η¼ηSTC 1βTPV 25
ðÞ
þγlog10ðGÞ
ðÞ
ð8Þ
where ηSTC is the nameplate or standard test conditions (STC
42
) effi-
ciency of the PV panel, βand γare material-specific properties, TPV is
the operating cell or panel temperature (in C), and Gis the solar irra-
diance (in W/m2). We use ηSTC ¼0:1935
15
(or a 1.6 m2sized 310 Wp
module), β¼0:0045C1, and γ¼0:12, both for crystalline silicon,
43
and Lo¼0:1, based on Reich et al.
40
We further define the absolute and relative offshore yield advan-
tage as
Yadvantage ¼Yoff shore Yinland ð9Þ
Yadvantage,rel ¼Yoffshor e Yinland
Yinland
100 ð10Þ
which provides the advantage (or disadvantage) when comparing an
offshore site with an inland site with >50-km distance in between.
Figure 2shows the algorithm flowchart of the whole methodol-
ogy discussed in this section to calculate the energy yield for this
study. The energy yield calculated from this algorithm will be used to
compare different locations in their offshore PV advantage in terms of
performance.
2.7 |Regression analysis
For finding the correlation between the independent variables and
the offshore PV advantage in Equation (10), two different methodolo-
gies are used: (i) Multiple linear regression (MLR) and (ii) multivariate
polynomial regression (MPR). Both methods will be discussed in the
following.
2.7.1 | MLR
MLR is a statistical technique that can be used to analyze the relation-
ship between a single dependent variable and several independent
variables. The objective of multiple regression analysis is to use the
independent variables whose values are known to predict the value of
the single dependent value. The general form of the regression equa-
tion with multiple predictors is
44
^
y¼b0þX
n
i¼1
bixi,i½1,nð11Þ
where b0is the intercept, and biis coefficient number i,nis the num-
ber of independent variables, and xiis variable number i. The ordinary
least squares (OLS) regression can be used as a method to derive the
regression coefficients. This method is based on minimizing the sum
of the squares of the deviations of the observed and predicted values
of ^
y.
TABLE 3 Koehl correlation coefficients for different technologies.
39
Monocrystalline Polycrystalline Microcrystalline Amorphous Cadmium
PV technology silicon (m-Si) silicon (p-Si) silicon (a-Si) silicon (c-Si) telluride (CdTe)
U030.02 25.73 23.37
U16.28 10.67 5.44
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2.7.2 | MPR
The MPR model provides an effective way to describe complex non-
linear inputoutput relationships since it is tractable for optimization,
sensitivity analysis and prediction of confidence intervals.
45
MPR for a
second-order polynomial is defined in Equation (12).
^
y¼b0þX
n
i¼1
bi,1xiþX
n
j¼1
X
n
i¼1
bi,jxixj,i,j½1,nð12Þ
where parameters are defined as in Equation (11), noting that an addi-
tional variable jis used. In this research, the collected data are used
to find a correlation between variables and the absolute and rela-
tive yield advantage. Thus, in addition to the methodology for
deriving the coefficients, it is essential to define the correct inde-
pendent variables. We will discuss these variables later in the fol-
lowing section.
3|RESULTS AND DISCUSSIONS
In this section, the solar cell operating temperature for both offshore
and land-based systems will be discussed, considering different vari-
ables, that is, wind speed, relative humidity, ambient temperature, and
FIGURE 2 The flowchart for the described methodology to calculate the energy yield.
FIGURE 3 (A) Ambient temperature and (B) heat index, for all locations at both land-based and offshore system sites.
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sea surface temperature. Moreover, the energy yield for all 20 loca-
tions will be compared between offshore and land-based systems.
Figure 3shows the average ambient temperature and a heat
index of all locations between this research time interval. Listing is
done alphabetically, as in Table 1. Due to the fact that for computing
the heat index we only consider the effect of relative humidity, it is
clearly shown that the heat index is not necessarily lower for the off-
shore system. However, we should take into consideration that ambi-
ent temperature and heat index are not the only parameters relevant
to the performance of offshore systems.
3.1 |Operating temperature for modules
Figure 4A shows the average operating cell temperature for all loca-
tions for both offshore and land-based PV systems. The analysis of
temperature differences between offshore and inland sites for the
different locations showed that in almost all of the cases, the mod-
ule temperatures at offshore sites were lower compared with the
land-based sites which is the result of the water cooling effect for
this specific FPV structure with steel pontoons. The average cell
temperature difference is defined in Equation (13). The maximum
value for this variable is 0.32C which belongs to Port Coquitlam
located in British Columbia, Canada, and the minimum value is
14C belonging to Puerto Colombia located in Atlántico Depart-
ment, Colombia.
ΔTCell ¼TOff shore TLandbased ð13Þ
The positive value for the Port Coquitlam site is a result of the
effect of the Alaska Current. This is a southwestern shallow warm-
water current alongside the west coast of the North American conti-
nent beginning at about 4850N, which is quite close to the location
of the site. It has been mentioned by Walsh et al
46
that due to the
high latitude marine heat wave in 2016, the Gulf of Alaska (GOA) and
the Bering Sea have been anomalously warm for several years with
the heat peaking in 2016.
These years are within the time range of our data set. These tem-
perature variations will have an effect on the sea surface temperature
and, as a result, will affect the equilibrium operating cell temperature
as well.
However, the condition is different for the Puerto Colombia site.
The large difference between the land-based and offshore tempera-
ture is also discussed in Ortiz-Royero et al.
47
: Strong outbreak of cold
air from the north called northersnot only brings the sea surface
and ambient temperature on the offshore side down but also may
cause gales and very strong waves toward the coastal areas.
48
Figure 5shows different temperatures, namely, apparent temper-
ature (HI), sea surface temperature, cell temperature only with wind
cooling effect (initial temperature), and final equilibrium operating cell
temperature. Although the average sea surface temperature in most
of the locations is higher than the HI, shown in Figure 5A, the water
cooling effect is clearly shown in Figure 5B, and for all of the loca-
tions, the average of the final cell temperature is lower than its initial
value.
3.2 |Yield advantage
In order to calculate the energy yield advantage, we use the equiva-
lent of 1 MWp of panels. For this, an area of about 5200 m2would be
needed all placed horizontally on various connected pontoons assum-
ing that we use the 310-Wp module as mentioned above. We present
our results in specific annual yields of kWh/kWp. Table 4provides the
calculated energy yields for the sites within each location as well as
the absolute and relative yield advantage.
The energy yields depend on irradiance and conversion efficiency,
which mainly depends on the cell operating temperature which itself
is a function of ambient temperature and sea surface temperature for
FPV systems, and also wind speed.
FIGURE 4 Average (A) cell temperature and (B) irradiation levels, for all locations for both offshore and inland sides.
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To have a better understanding of the energy yield tabulated in
Table 4, let us first discuss the irradiation level difference for the loca-
tions and between the sites. Figure 4B shows the average irradiation
during the period of this study for all locations and sites. In 70% of
the locations, the average value for irradiation at the offshore site is
higher than at the land-based site. The maximum and minimum irradi-
ation level difference between the land-based and offshore systems
are found for the DaNang Port and Port Shepstone sites, which is
13.94% and 5.42%, respectively.
Although 30% of the locations show a relatively lower average
irradiation level on the offshore sites, the temperate difference com-
pensation leads to an increase in energy yield of some of the sites:
Only 20% of the locations show a negative energy yield difference.
For instance, at the Port Vell site, although the irradiation level
FIGURE 5 (A) Heat Index and sea surface temperature; (B) initial and final cell temperature of the offshore side for all locations between the
years 2008 and 2018.
TABLE 4 Average annual yields in
kWh/kWp across all locations for
offshore and land-based PV systems.
Yield Offshore Relative
Offshore Inland advantage offshore advantage
No. Site (kWh/kWp) (kWh/kWp) (kWh/kWp) (%)
1 Bandar Penawar 1658.65 1514.35 144.30 9.53
2 Ciudad del Carmen 1899.62 1677.71 221.90 13.22
3 DaNang Port 1589.96 1328.50 261.45 19.68
4 El Emir 1639.97 1549.98 89.99 5.80
5 Hengsha Island 1259.64 1263.69 4.05 0.32
6 Katsuura 1304.28 1321.14 16.86 1.27
7 Kwala Tanjung 1472.17 1484.61 12.44 0.83
8 New Limassol Port 1818.66 1654.61 164.05 9.91
9 Port Antonio 1750.85 1699.01 51.84 3.05
10 Port Coquitlam 1255.03 1115.08 139.95 12.91
11 Port Moresby 1711.61 1469.96 241.64 16.43
12 Port of Rotterdam 1117.90 1037.93 79.97 7.70
13 Port Shepstone 1584.99 1646.81 61.81 3.84
14 Port Vell 1550.65 1521.49 29.15 1.91
15 Puerto Belgrano 1681.68 1632.73 48.94 2.99
16 Puerto Colombia 1932.02 1700.09 231.91 13.64
17 Puerto La Cruz 1943.69 1727.55 216.13 12.51
18 Ras Laffan 1811.22 1677.09 134.13 7.99
19 South Golden Beach 1752.98 1668.95 84.03 5.03
20 Tanzania Port 1889.43 1653.09 236.33 14.29
Note: The colored values in the table belong to the locations with negative advantage of the offshore
system.
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difference is 1.71%, the energy yield difference is 1.91%, which is
indicating that the offshore PV system performs relatively better for
this location in comparison with the land-based PV system.
Considering the data in Table 4, we would like to compare the
two best and two worst case results for the energy yield advantage,
namely, DaNang port and Port Moresby as two higher values and
Port Shepstone and Katsuura as two lower cases. Figure 6shows
the scatter plots of energy yield versus irradiation for each location.
For the two best locations, not only the irradiation level is much
higher for the offshore side but also the slope of the scatter plot of
energy yield versus irradiation is bigger. For the other two locations,
the scatter plots for land-based and offshore sides are almost similar,
which means that in terms of energy yield, the offshore system does
not have a better performance compared with the land-based
system.
Figure 7shows the final cell temperature versus the fluid
temperature, which is considered as water for offshore and air for the
land-based system. As shown for the two best locations the dry-bulb
temperature for the land-based system is relatively higher compared
with the other two locations. This means that the land-based system
in the two worst-case scenarios performs better compared with the
land-based systems of best case scenarios, in terms of the effect of air
temperature on final cell temperature. However, the water cooling
effect is much more tangible for the environments where the mini-
mum temperature is higher.
It helps to focus on one specific location to illustrate some of the
main conclusions in this paper.
We consider the case of Qatar, with latitude and longitude
values as follows: coastal site 25.915N, 51.580E, offshore site
26.420N, 51.580E. Both Qatar sites have high levels of irradi-
ance,buttheoffshoresitereceives consistently higher irradiance
than the other site (see Figure 8A). Partial explanations for this
include a higher level of diffuse radiation on the open seas due to,
for example, cloud conditions or a relatively low level of localized
pollution.
Yet, as with many of the other sites, the offshore site for Qatar
shows higher apparent temperatures than the inland site. However,
the water cooling effect and the higher irradiation level cause the off-
shore floating system performing significantly higher, and as tabulated
in Table 4the energy yield advantage is 7.99%.
Finally, let us consider the two locations with maximum and mini-
mum temperature differences, which were named before, that is,
Puerto Colombia and Port Coquitlam. Figure 9shows some informa-
tion about these two locations. Although the final cell temperature of
the offshore site for Port Coquitlam is almost always a positive value,
it barely exceeds 20C. However, this value for the land-based side of
this location belongs to a very wide range from very low to very high
temperatures. In contrast, the final cell temperature for the offshore
site of Puerto Colombia is limited and is always above 20C. This
value for the land-based site in this location is also always above 20C
FIGURE 6 Scatter plots of energy yield versus irradiation level in hourly time resolution for (A) DaNang Port, (B) Port Moresby, (C) Port
Shepstone, (D) Katsuura.
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and PV cells could get very hot. This affects the cell efficiency, which
is clearly shown in Figures 9C,D. A wide range of the final cell temper-
ature due to the ambient condition is shown in the cell efficiency for
Port Coquitlam, and it shows that the cell efficiency for the offshore
system is not always better than the land-based for this location.
Energy yield for Port Coquitlam is 12.9% higher, as also shown in
Table 4, the average irradiation level is higher at the offshore site for
this location also and the effect of temperature difference is counted.
However, the energy yield difference for Puerto Colombia is 13.64%,
which is mainly the effect of temperature difference.
3.3 |Regression analysis
Having studied the performance difference between land-based and
offshore systems, we will discuss how we can find a reliable
FIGURE 7 Scatter plots of final cell temperature versus ambient temperature in hourly time resolution for (A) DaNang Port, (B) Port Moresby,
(C) Port Shepstone, (D) Katsuura.
FIGURE 8 (A) Average Irradiation levels per annum and (B) annual energy yield, for Ras Laffan located at Qatar for both land-based and
offshore system sites.
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correlation between the offshore yield advantage defined in
Equation (10) and the environmental variables. To this end, first, we
need to define the independent variables and thereafter develop the
two regression methods, that is, (i) MLR and (ii) MPR. We will ana-
lyze the accuracy of the model by calculating the metrics R2and root
mean squared error (RMSE).
In the below list, we summarize the five main environmental/
meteorological variables that we will examine in our regression model:
ΔG(%)
Equation (14) represents the difference in irradiation level between
offshore (GS) and land-based (GL) sites.
ΔG¼GSGL
GL
100 ð14Þ
Pr (mm/h)
The precipitation is expressed in average rainfall thickness per hour
(mm/h). This metric is one of the important metrics in the Köppen
Geiger climate zone typology.
TS(C)
Average sea surface temperature during the study period repre-
senting either the system to be on the warm or cold stream. Due
to the fact that the cold and warm streams on the sea surface may
vary by the passage of time, this variable is more reliable than a
FIGURE 9 Scatter plots of (A,B) final cell temperature versus fluid temperatures, namely, water and air, (C,D) cell efficiency versus irradiation,
(E,F) energy yield versus irradiation in hourly time resolution for Port Coquitlam and Puetro Colombia.
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boolean variable which represents to have either a cold or warm
stream on the location.
ΔvW(%)
Equation (15) represents the difference in wind speed between
offshore (vW,S) and land-based vW,Lsites.
ΔvW¼vW,SvW,L
vW,L
100 ð15Þ
Considering the above-mentioned independent variables, we are
able to define the MLR and MPR as shown in Equation (16) and
Equation (17), respectively.
d
ΔEY¼α0þα1ΔGþα2Pr þα3TSþα4ΔvWð16Þ
d
ΔEY¼β0þβ1ΔGþβ2Pr þβ3TSþβ4ΔvWþβ5ΔG2þβ6Pr2
þβ7T2
Sþβ8Δv2
Wþβ9ΔGPr þβ10ΔGTSþβ11ΔGΔvWþβ12PrTS
þβ13PrΔvWþβ14 TSΔvW
ð17Þ
The intercept and coefficients of MLR and MPR methods are
shown in Tables 5and 6, respectively. In addition to the coefficients,
the R-squared shown as R2and root mean square error (RMSE) values
for both methods are also calculated and listed in the tables.
Although the MPR method is much more complex, it leads to a
higher R2compared with the MLR method. This means that the data
MPR method fitted the data better compared with the MLR method.
However, it should also be taken into consideration that the MPR
method is very sensitive to outliers, thus the presence of outliers
could affect the performance of the model. For RMSE, this is the
other way around, representing that the standard deviation of the
residuals is smaller for the MPR method. Residuals indicate how far
the estimated points are from the real data, and RMSE shows how
these residuals diverge.
One way to demonstrate the validity of the main results is that
different multivariable regression methods return relatively big
R-squared values. R-squared is a measure of how closely the data in a
regression line fit the data in the sample. The closer the R-squared
value is to 1, the better the fit. Both methods lead to good fits, as is
also evident from Figure 10.
One example that shows latitude cannot by itself play a key
role in this prediction is a simple comparison between Ciudad del
Carmen (18.65N, 91.80W) and Port Antonio (18.17N, 76.44W).
Thesetwoportsarelocatedwithmoreorlesssimilardistancesto
the Equator, but the average energy yield advantage for Ciudad del
Carmen is 13.22% while it is 3.05% for Port Antonio. This differ-
ence can be explained by investigating which variable plays the
most important role in this comparison. To this end, we first con-
sider the average sea surface temperature and the average wind
speed for both locations.
Although the presented regression model has a high level of accu-
racy, this should not be taken as the model for a person to decide
whether or not offshore FPV is definitely a feasible option for a given
location. Instead, the model could be one tool of many to help focus
attention on the correct geographic and climatological factors that
determine the viability of offshore FPV.
3.3.1 | Sensitivity of models
One way to study the sensitivity of a function is to use partial deriva-
tives with respect to the independent variables. Thus, model sensitiv-
ity called MSen
can be defined as in Equation (18).
MSenjθ¼d
ΔEY
θð18Þ
where θis the independent variable in the aforementioned models.
Considering Equation (18), sensitivity of the MLR model,
Equation (18) can be expressed in terms of its coefficients for each
variable, as MLR is a linear model. From the data in Table 5, it is clear
that MLR has the highest sensitivity to precipitation, representing
KöppenGeiger climate classification and the second variable which
makes the highest sensitivity is the difference of irradiation level
between offshore and land-based systems.
TABLE 5 Coefficients and metrics for MLR model.
α0α1α2α3α4R2RMSE
2.4494 1.1271 5.4096 0.0496 0.3629 0.9792 0.8972
TABLE 6 Coefficients and metrics
for MPR model. β0β1β2β3β4β5
4.7643 0.9415 41.386 0.2562 0.4946 1.8310e3
β6β7β8β9β10 β11
18.9158 1.3257e2 2.4814e10.7400 2.1005e24.9547e2
β12 β13 β14 R2RMSE
1.7674 3.3123 3.6208e3 0.9927 0.5295
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To have a fair comparison for the sensitivity, the sensitivity func-
tion for the MPR model with respect to precipitation and irradiation
level difference is derived and shown in Equations (19) and (20).
MSenjPr¼d
ΔEY
Pr
¼β2þ2β6Prþβ9ΔGþβ12TSþβ13 ΔvWð19Þ
MSenjΔG¼d
ΔEY
ΔG¼β1þ2β5ΔGþβ9ΔPrþβ10TSþβ11 ΔvWð20Þ
Considering the values for the coefficients in Table 6, we can con-
clude that this model similar to MLR is more sensitive to variation in
precipitation than would otherwise be expected. It is important to
interpret this result correctly: Specifically, it means that differences in
precipitation between offshore and onshore siteswhich we take to
be a proxy for the KG climate classificationcan suffice to explain a
large part of the difference in performance between land-based and
offshore PV systems. Equally important, this is also a predictive model,
which avoids the direct use of the KG climate classification system
but which instead can use another geography- and climate-related
metrics to determine where deploying PV panels offshore would
(or would not) be favorable.
4|DISCUSSION
4.1 |Locations and dataset
For each location, the offshore FPV pontoons are located 56 km
away from the associated coastal site. This decision was to overcom-
pensate for a potential lack of accuracy in the data: Since the data
provided by NASA POWER have an accuracy that does not go beyond
0.5latitude or longitude, the decision was made to ensure that all
sites are at least 0.5apart which translates to roughly 56 km.
For the sake of practicality, the number of locations is limited to
20, producing data for a total of 40 sites. Although these cover a rea-
sonable extent of the globe, it remains possible that expanding the
data set to include a greater number of locations could lead to as-yet
unclear trends/relationships becoming apparent.
4.2 |Validity of data
Ultimately, the validity of the results presented here is based on the
validity of NASA's Modern-Era Retrospective analysis for Research
and Applications Version 2, or MERRA-2. MERRA-2 dates back to
1980 and is based on microwave radiation images. Each image is
based on data collected over three hours and fitted onto a map with a
0.5-degree resolution, roughly equivalent to 50 km in the latitudinal
directions (hence, the choice of 50 km when deciding the distance
between offshore, coastal, and inland sites). The intensity of micro-
wave radiation levels allows for the interpolation of solar insolations
and temperatures; wind speeds are likewise calculated. A full descrip-
tion of the MERRA-2 project is available in review form in a paper by
Geralo and co-authors.
49
Notably, the NASA POWER dataset is freely
available for use and covers the entire globe, so a spatial resolution of
5˜0 km is a fairly reasonable compromise.
Throughout this paper, we sought to limit and understand the
sources of the inaccuracy of the data sources in question. NASA
POWER data purports also to give optimal radiationfor tilted
panels, yet, at the time of writing, the reliability of the model which
produces optimal insolation could not be guaranteed for arbitrary
locations.
50
Our choice of GHI radiation was thus aimed at reducing
at least one important source of uncertainty. It also implies a limitation
on our paper, in that we can consider only horizontally tilted panels.
This excludes the studying of panels that are tilted to capture optimal
levels of solar insolation; allowing for optimization of tilt panels would
change the workings of this paper.
FIGURE 10 Comparison between prediction values versus actual values implementing (A) the MLR and (B) the MPR method.
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A small number of papers mostly focused on agricultural produc-
tion have attempted to define the limits of the accuracy of NASA
POWER's data, mostly by seeking to cross-validate the information
from ground-based satellites. For example, Sayago and co-authors val-
idated NASA POWER's solar radiation estimates against ground
weather measurements across central Spain.
51
The authors report
that, even in the worst cases, the value of R2, the coefficient of deter-
mination, was no less than 0.85. Likewise, the same study reports an
RMS error of 1:78 MJ
dm2on a daily basis, or roughly equivalent to about
180 kWh per year. This suggests that high-insolation sites would be
less affected than those which receive relatively less solar insolation.
Bai and co-authors
52
verify NASA satellite data in China and found
the solar radiation data derived from NASA POWER to be generally
reliable for use when modeling maize crop yields, while the same
authors reported that the NASA POWER data tended to underesti-
mate the air temperatures. Our own adjustment of the temperature
(see Section 2.2) accounts at least partly for this loss. Clearly, NASA
POWER comes with its set of shortcomings and is likely to impact dif-
ferent sites unequally. Nonetheless, it remains the only truly world-
wide
53
dataset, which provides all of the meteorological data which
we could have needed. As a preliminary effort before further research
is conducted, we judge NASA POWER to be sufficient for our needs.
4.3 |Economics
This paper deals with determining the most favorable locations for the
deployment of offshore FPV in terms of energy yield. It is also clearly
possible to state, based on the results, that there are some locations
on the globe for which offshore FPV is simply not the most viable
option. This conclusion may come from an analysis of many different
metrics. Generally, the investment and installation costs of OFPV will
be higher than land-based systems, while the cost of land will be
absent for floating systems. On the other hand, the open water
(ocean/sea) condition could be an important metric to estimate the
OFPV system CAPEX based on the necessity of specific design for the
structure, mounting, mooring, and anchoring systems. However, we
excluded this aspect from our analysis and it is left for future work.
Although more focused on meteorological and climate/geography
considerations, there is a clear economic motivation for this work as
well. An economically viable OFPV system will have a yield advantage
that will offset higher investment and installation costs. A recent
example of a hybrid offshore wind and PV system corroborates this.
54
Of particular economic interest to this project is the differences
in the lifetimes of the different solar panels. For example, a report by
Zaharia and co-authors has been able to quantify the decomposition
of solar panels as a consequence of corrosion caused by salinity in
(e.g.) seawater.
55
Over the course of several years, it is likely that the
contact between offshore solar panels and seawater would lead the
offshore solar panels to degrade more rapidly than land-based PV
panels; this, in addition to the infrastructure investment required to
deploy PV panels offshore will influence any possible decision to
deploy PV panels offshore. This again, however, is outside of the
scope of our paper as we are specifically interested in determining the
extent to which geography and meteorology will shape the decision
to build offshore solar PV at a specific location.
5|CONCLUSIONS
In this paper, a detailed model has been developed that allows deter-
mining the potential yield advantage that offshore floating PV systems
may have across the globe. For this model, we considered steel pon-
toons for all the OFPV systems and assumed that panels on land are
air-cooled. We implemented our model for 20 different locations across
the globe, at different climate zones. While existing literature shows
considerable yield advantages, we have found that the advantage may
also be negative: in specific locations, offshore floating PV has a lower
annual yield than a land-based system. Based on our model the average
energy yield difference considering the time period of 2008 and 2018
varies from almost 20% to 4% for different locations.
To study the effect of different variables on this energy yield
advantage, we have developed two regression models that can be
used to predict offshore yield differences compared with land-based
systems. The major finding of this study on the energy advantage
between offshore and land-based PV systems is that the energy
advantage is clearly site-specific. Further, we developed a meaningful
regression model which quantifies a very definite correlation between
a number of geographical and meteorological values and the energy
(dis)advantage of deploying PV panels offshore.
We conclude that there is no iron-clad guarantee, or any type of
general rule of thumb,that deploying PV panels on bodies of water
results in an improved yield of electrical energy. Yet in cases where
competition for land or the need to avoid shading from the built envi-
ronment necessitates moving offshore, then the approach developed
in this paper can be used to make site selections. In other words, there
will be some use cases where building offshore FPV might appear
promising, and in such situations, having access to a geography-based
regression model such as this model will help decision-makers better
understand their options.
ACKNOWLEDGMENTS
The authors would like to gratefully thank Dr. Pita Verweij for the
valuable insights she gave in the pathway of this research. This work
is partly financially supported by the Netherlands Enterprise Agency
(RVO) within the framework of the Dutch Topsector Energy (projects
Comparative assessment of PV at Sea versus PV on Land, CSEALAND,
and North Sea Two, NS2).
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are openly available in
NASA POWER at https://power.larc.nasa.gov/data-access-viewer/.
ORCID
S. Zahra Golroodbari https://orcid.org/0000-0002-5843-0463
Wilfried van Sark https://orcid.org/0000-0002-4738-1088
GOLROODBARI ET AL.1075
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How to cite this article: Golroodbari SZ, Ayyad AWA, van
Sark W. Offshore floating photovoltaics system assessment in
worldwide perspective. Prog Photovolt Res Appl. 2023;31(11):
10611077. doi:10.1002/pip.3723
GOLROODBARI ET AL.1077
1099159x, 2023, 11, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/pip.3723 by Utrecht University Library, Wiley Online Library on [18/10/2023]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License
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... In our earlier work [7], we laid the groundwork for world-scale modeling of the performance of solar PV panels that were placed on offshore pontoons in sites across the globe. In the present research, we will follow the same methodology, but we plan to develop our model and also include additional locations, and make adjustments to the comparative dataset. ...
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