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Water Conservation Potential of Self-Funded Foam-Based Flexible Surface-Mounted Floatovoltaics

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A potential solution to the coupled water–energy–food challenges in land use is the concept of floating photovoltaics or floatovoltaics (FPV). In this study, a new approach to FPV is investigated using a flexible crystalline silicon-based photovoltaic (PV) module backed with foam, which is less expensive than conventional pontoon-based FPV. This novel form of FPV is tested experimentally for operating temperature and performance and is analyzed for water-savings using an evaporation calculation adapted from the Penman–Monteith model. The results show that the foam-backed FPV had a lower operating temperature than conventional pontoon-based FPV, and thus a 3.5% higher energy output per unit power. Therefore, foam-based FPV provides a potentially profitable means of reducing water evaporation in the world’s at-risk bodies of fresh water. The case study of Lake Mead found that if 10% of the lake was covered with foam-backed FPV, there would be enough water conserved and electricity generated to service Las Vegas and Reno combined. At 50% coverage, the foam-backed FPV would provide over 127 TWh of clean solar electricity and 633.22 million m3 of water savings, which would provide enough electricity to retire 11% of the polluting coal-fired plants in the U.S. and provide water for over five million Americans, annually.
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energies
Article
Water Conservation Potential of Self-Funded
Foam-Based Flexible Surface-Mounted Floatovoltaics
Koami Soulemane Hayibo 1, Pierce Mayville 2, Ravneet Kaur Kailey 2and
Joshua M. Pearce 1,2,3,*
1Department of Electrical & Computer Engineering, Michigan Technological University,
Houghton, MI 49931, USA; khayibo@mtu.edu
2Department of Material Science & Engineering, Michigan Technological University,
Houghton, MI 49931, USA; pjmayvil@mtu.edu (P.M.); rkailey@mtu.edu (R.K.K.)
3School of Electrical Engineering, Aalto University, FI-00076 Esburg, Finland
*Correspondence: pearce@mtu.edu
Received: 20 October 2020; Accepted: 25 November 2020; Published: 28 November 2020


Abstract:
A potential solution to the coupled water–energy–food challenges in land use is the concept
of floating photovoltaics or floatovoltaics (FPV). In this study, a new approach to FPV is investigated
using a flexible crystalline silicon-based photovoltaic (PV) module backed with foam, which is less
expensive than conventional pontoon-based FPV. This novel form of FPV is tested experimentally
for operating temperature and performance and is analyzed for water-savings using an evaporation
calculation adapted from the Penman–Monteith model. The results show that the foam-backed FPV
had a lower operating temperature than conventional pontoon-based FPV, and thus a 3.5% higher
energy output per unit power. Therefore, foam-based FPV provides a potentially profitable means
of reducing water evaporation in the world’s at-risk bodies of fresh water. The case study of Lake
Mead found that if 10% of the lake was covered with foam-backed FPV, there would be enough
water conserved and electricity generated to service Las Vegas and Reno combined. At 50% coverage,
the foam-backed FPV would provide over 127 TWh of clean solar electricity and 633.22 million m
3
of
water savings, which would provide enough electricity to retire 11% of the polluting coal-fired plants
in the U.S. and provide water for over five million Americans, annually.
Keywords:
water; floatovoltaic; photovoltaic; energy water nexus; dual use; water conservation; FPV;
floating photovoltaic; solar energy
1. Introduction
Water scarcity [
1
,
2
], the energy crisis [
3
], and food scarcity [
4
,
5
] are the largest currently coupled
challenges [
6
] facing the global community, where they most severely aect the arid and semiarid
regions of the world [
7
]. There is a wide scientific consensus that combustion of fossil fuels for
energy is increasing atmospheric carbon dioxide (CO
2
) concentrations and driving climate change [
8
].
This anthropogenic climate change is increasing globally averaged mean annual air temperatures
and driving changes in precipitation, which are expected to continue and increase [
9
,
10
]. The IPCC
(Intergovernmental Panel on Climate Change) warns that the climate change over the next century will
aect rainfall, river flows and sea levels all over the world [
11
], which will negatively impact agricultural
yield [
12
]; particularly in already-malnourished sub-Saharan Africa. de Wit and Stankiewicz [
13
]
predict rainfall in sub-Saharan Africa could drop by 10% causing surface drainage to drop 30–50% by
midcentury, which would cause major water shortages. It is widely agreed that to prevent the worst
of climate change, humanity needs to rapidly convert fossil fuel-based energy systems to renewable
energy systems [
14
]. Solar photovoltaic (PV) technology is the most widely accessible, sustainable,
Energies 2020,13, 6285; doi:10.3390/en13236285 www.mdpi.com/journal/energies
Energies 2020,13, 6285 2 of 24
and clean renewable source of energy that can be scaled to meet humanity’s energy needs [
15
,
16
].
To meet these needs, however, a substantial amount of land is still needed for PV to replace fossil fuels
and this creates competition for limited land resources between food and energy [
17
]. A utility-scale
PV plant land occupation varies between 20 km
2
/GWh and 40 km
2
/GWh depending on the type
of solar panels used [
18
]. Despite life cycle carbon emissions [
19
], PV is more land ecient than
all carbon capture and sequestration plans for coal [
20
], but with nearly a billion people already
living undernourished, further reductions in agricultural land are not acceptable during a world
food crisis [21].
A potential solution to these coupled water–energy–food challenges is the concept of floating
photovoltaics or floatovoltaics (FPV), which has been rapidly gaining a base in scientific literature [
22
28
].
FPV is growing fast and is expected to have an average growth rate of above 20% in the next five years
due to extremely low costs (with an FPV bid recently coming in for a system in Thailand at under USD
0.50/Wp) [
29
]. FPV are easier to install and simpler to decommission than conventional PV systems
and the racking costs are less, which lead to these overall cost savings [
29
]. As FPV are located near or
immersed in water, the operational temperature is reduced, which raises the solar energy conversion
eciency [
23
,
26
,
30
34
]. In regions where water scarcity is an issue and particularly when this issue is
likely to be aggravated by climate change, FPV can also be used to reduce water loss because it can
reduce water evaporation by more than 70% [
32
,
35
37
]. The Penman–Monteith daily evaporation
method indicates that FPV could even cut evaporation by as much as 90% [
38
]. Studies in China [
39
]
and India [
40
,
41
] have all indicated massive potential water savings for both small and large FPV
coverage areas. This is particularly important for preservation of water sources in arid and semi-arid
regions, especially with water shortages in the region [
42
]. FPV, therefore, also holds substantial
promise when coupling with existing hydro power to make dual use of the electrical infrastructure
while improving the water resource itself [
39
,
43
]. Similar advantages are to be expected for hybrid
systems with pumped storage [
44
]. Finally, there is also evidence that FPV deployment reduces the PV
degradation rate below 0.5% per year [
45
], which improves the levelized cost of solar electricity further.
FPV research has focused on several system design strategies [46]:
(1)
Tilted arrays of solid modules (normally on top of pontoon structures) [36,4749];
(2)
Submerged PV modules (with and without a pontoon) [24,30,33,34,50];
(3)
Micro-encapsulated phase change material (MEPCM)-based pontoon modules [5153];
(4)
Thin-film PV (no ridged pontoon supporting structure) [24,26,54].
The thin-film FPV design has the advantage of reducing racking costs even more so than pontoon
style FPV, as it clearly stops more evaporation and gains an advantage by the operational temperature
being lower. However, the temperature coecients are better for amorphous silicon (a-Si:H) thin
film materials than those of crystalline silicon (c-Si) so the benefits of the water cooling are muted for
a-Si:H-based FPV.
In this study, a new approach is used with a flexible crystalline silicon module on a similar foam
system to that described by Pierce et al. [
54
] for a-Si:H FPV. This approach enables a larger solar electric
output gain (or FPV boost) and as solar is largely already profitable, there is an opportunity for the
electricity production value of c-Si flexible foam-backed FPV to subsidize a means of water conservation
by cutting water evaporation losses. To build on past FPV work and investigate the potential of FPV
coupled to hydro power in the U.S., the water saving potential at Lake Mead using FPV is investigated
in this study. Lake Mead is an artificial reservoir created by the United States government to run the
Hoover Dam, which was built in 1935 [
55
,
56
]. This novel form of FPV is analyzed for water-saving
using an evaporation calculation adapted from the Penman–Monteith daily evaporation model [
57
] that
is approved by the Food and Agriculture Organization of the United Nations (FAO) [
58
]. An energy
production analysis is performed and an open source spreadsheet was developed to simulate the
evaporation and the energy yield of the flexible FPV [
59
], as well as to investigate the impact of using
passive water-cooled FPV, where the cooling potential was measured experimentally for a foam-based
Energies 2020,13, 6285 3 of 24
FPV. The potential is determined for a case study based on the coverage of FPV ranging from 10% to
50% [
60
] of Lake Mead. The results are compared to “conventional” tilted pontoon-style FPV and are
discussed in the context of the energy–water–food nexus.
2. Materials and Methods
2.1. Data Collection
2.1.1. Lake Evaporation Data
Most of the weather data used in this study were collected on Lake Mead through buoys installed
by the United States National Oceanic and Atmospheric Administration’s National Data Buoy Center
(NOAA-NDBC) [
61
]. The rest of the data were obtained from open-access weather data made available
by the McCarran International Airport’s weather station in Las Vegas [
62
], and from SOLCAST, a solar
data provider [63].
The main characteristics of the lake dier slightly from one study to another and depend on the
year the study was conducted. In this study, the lake characteristics’ values used for the evaporation
calculation are taken from the National Park Service (NPS) website [
64
]. According to the NPS, as of
2010, the lake has a maximum surface area of 159,866 acres (647 million m
2
), and a maximum capacity
of 29,686,054 acre-feet (36,617 million m
3
). The mean depth of the lake is estimated to be 55.5 m by the
National Park Service [
56
]. The elevation of the lake is 328.574 m above sea water level. The weather
buoy used to collect the data is located in the North Boulder Basin of the lake at a geographical position
of latitude 36.087 N and longitude 114.728 W. The temperature sensor for air temperature collection is
located at a height of 2 m above the lake surface while the anemometer is at 3 m above. Additionally,
the atmospheric pressure sensor is located at 330.574 m above sea water level or 2 m above the lake
surface, and the water temperature is measured at 0.5 m below the lake surface [65].
The buoy installed in Lake Mead’s North Boulder basin by the NOAA-NDBC has been capturing
dierent types of variables since 2016, which are stored in a historical database on the agency’s website.
Among the data required to conduct an evaporation calculation using the Penman–Monteith model,
the wind speed (w
s
), the atmospheric pressure (P), the maximum (T
w,max
), minimum (T
w,min
), and daily
mean (T
w
) water temperature; and the air temperature were obtained from the NOAA-NDBC historical
database. The rest of the data were not captured by the buoy; therefore, alternative methods have been
used to gather the required data. According to Moreo and Swancar, when data are not available for the
study location, nearby airport weather data can be used instead [
55
]. In this study, the nearest airport
close to Lake Mead is the Las Vegas Airport. The relative humidity (Rh) data have thus been obtained
from the Weather Underground website that has made data from the Las Vegas Airport available.
The remaining variable is the daily incoming solar irradiation or global horizontal irradiation (R
S
) that
has been obtained from SOLCAST’s historical database [
63
]. This variable is also used for the solar
energy production modeling.
The raw data from the NOAA-NDBC database were collected with an interval of 10 min starting
at 00 h 00 min each day while the data from the Las Vegas Airport were measured with an 1 h interval
starting at 00 h 56 min each day. Since daily data were required for the calculation, a mean daily value
has been calculated for each variable. First, the data obtained from the NOAA-NDBC were cleaned by
keeping only hourly data at the beginning of the hour (00 min) in order to match the data from Las
Vegas Airport. A MATLAB code [
66
] was developed to perform this operation. Then, the same code
was used to strip the missing data from the data table. A line of data was considered missing from
the data table if one or more of the variables were not recorded by either the NOAA-NDBC station
sensors or the Las Vegas Airport station sensors. After that, the data were reported in a spreadsheet
that was used to calculate the mean daily value of the wind speed (w
s
), the atmospheric pressure
(P), the water temperature (T
w
) and the air temperature (T
a
) by averaging the hourly data for each
day. Another method used in the literature to calculate daily mean weather data is to calculate
the average of the maximum and minimum value of the day [
67
]. However, studies have shown
Energies 2020,13, 6285 4 of 24
that if data are available, it is best to calculate the mean daily temperature by averaging the hourly
values [
68
,
69
]. The spreadsheet was also used to retrieve the maximum (T
w,max
), and minimum (T
w,min
)
daily temperatures as well as the maximum (Rh
max
), and minimum (Rh
min
) daily relative humidity.
The number of missing data points was 246 hourly data. Instead of having total hourly data of
8760 points, 8514 data points were used for this study after the data cleaning process. There was no
more than 3 missing data points for a single day except for 5 specific days that are the 4th, 60th, 97th,
318th, and 347th day of the year 2018. These 5 days were, respectively, missing 4, 4, 10, 5, and 16 data
points. The days with the highest number of missing data were the 97th and 347th day of the year.
Since there are only two such days among the 365 that populated the year 2018, it has been considered
that it will not have a significant impact on the results. Therefore, the available data were representative
in estimating the mean daily values of the variables for each day.
2.1.2. FPV Panel Data Collection
In a previous study, it was found that polyethylene (PE) foam was the most cost-eective way to
add buoyancy to flexible solar modules [
54
]. This study uses this after-market conversion method
to convert SunPower SPR-E-Flex PVs into FPVs [
70
]. The density of the green polyethylene 1.2 lb
1
2
(12.7 mm) was used to determine the area of foam needed to make the panel rise by approximately
10 mm above the water’s surface [
71
] using the calculations detailed in [
54
]. The foam was cut into
about 50 mm by 240 mm sections that were placed evenly on the backside of module. The sections
were then adhered using 3 M 5200 fast-set waterproof adhesive. Each foam piece had a line of adhesive
caulked onto its perimeter and through the center. Then, the foam piece was pressed on the surface of
the panel to adhere it, see Figure 1. The FPV with PV control was deployed in Chassell Bay, MI during
the summer of 2020 to determine operational temperature and performance. This resulted in the FPV
floating directly above the water surface, but still enabling wave action to clear the modules as shown
in Figure 2.
Energies 2020, 13, x FOR PEER REVIEW 4 of 25
hourly values [68,69]. The spreadsheet was also used to retrieve the maximum (Tw,max), and minimum
(Tw,min) daily temperatures as well as the maximum (Rhmax), and minimum (Rhmin) daily relative
humidity. The number of missing data points was 246 hourly data. Instead of having total hourly
data of 8760 points, 8514 data points were used for this study after the data cleaning process. There
was no more than 3 missing data points for a single day except for 5 specific days that are the 4th,
60th, 97th, 318th, and 347th day of the year 2018. These 5 days were, respectively, missing 4, 4, 10, 5,
and 16 data points. The days with the highest number of missing data were the 97th and 347th day
of the year. Since there are only two such days among the 365 that populated the year 2018, it has
been considered that it will not have a significant impact on the results. Therefore, the available data
were representative in estimating the mean daily values of the variables for each day.
2.1.2. FPV Panel Data Collection
In a previous study, it was found that polyethylene (PE) foam was the most cost-effective way
to add buoyancy to flexible solar modules [54]. This study uses this after-market conversion method
to convert SunPower SPR-E-Flex PVs into FPVs [70]. The density of the green polyethylene 1.2 lb ½”
(12.7 mm) was used to determine the area of foam needed to make the panel rise by approximately
10 mm above the water’s surface [71] using the calculations detailed in [54]. The foam was cut into
about 50 mm by 240 mm sections that were placed evenly on the backside of module. The sections
were then adhered using 3 M 5200 fast-set waterproof adhesive. Each foam piece had a line of
adhesive caulked onto its perimeter and through the center. Then, the foam piece was pressed on the
surface of the panel to adhere it, see Figure 1. The FPV with PV control was deployed in Chassell Bay,
MI during the summer of 2020 to determine operational temperature and performance. This resulted
in the FPV floating directly above the water surface, but still enabling wave action to clear the
modules as shown in Figure 2.
(a)
(b)
Figure 1. Cut away view showing adhesive underneath foam attached to c-Si-based flexible
photovoltaic (PV) module: (a) top view and (b) orthogonal view.
Figure 1.
Cut away view showing adhesive underneath foam attached to c-Si-based flexible photovoltaic
(PV) module: (a) top view and (b) orthogonal view.
The NanoDAQ monitoring board used in [
54
] was used in this study to measure module power
and temperature of both the control (flat land-based mounted dry PV set at zero degree tilt angle)
and wet FPV (floating on lake surface). The thermistors used for measuring temperature were held
in place on the panels using 3M VHB tape. The air and water temperature were also measured with
thermistors. The SunPower panels came with MC4 connectors installed on 12 AWG (2 mm
2
) wires.
MC4 connectors were added to the 14 AWG (1.6 mm
2
) wires coming from the NanoDAQ, including
the load wires. An additional hole was made in the NanoDAQ waterproof case and sealed using 3M
5200 to use the battery’s USB port to power it. An AC load with a timer was used to drain the battery
during mid-day to ensure there was a load to produce the power measurement. The schematic of the
wiring diagram for the experimental set up is shown in Figure 3.
Energies 2020,13, 6285 5 of 24
Energies 2020, 13, x FOR PEER REVIEW 5 of 25
Figure 2. Closeup of floating photovoltaic/floatovoltaic (FPV) corner after deployment, showing
water coverage from a modest wave (top left).
The NanoDAQ monitoring board used in [54] was used in this study to measure module power
and temperature of both the control (flat land-based mounted dry PV set at zero degree tilt angle)
and wet FPV (floating on lake surface). The thermistors used for measuring temperature were held
in place on the panels using 3M VHB tape. The air and water temperature were also measured with
thermistors. The SunPower panels came with MC4 connectors installed on 12 AWG (2 mm
2
) wires.
MC4 connectors were added to the 14 AWG (1.6 mm
2
) wires coming from the NanoDAQ, including
the load wires. An additional hole was made in the NanoDAQ waterproof case and sealed using 3M
5200 to use the battery’s USB port to power it. An AC load with a timer was used to drain the battery
during mid-day to ensure there was a load to produce the power measurement. The schematic of the
wiring diagram for the experimental set up is shown in Figure 3.
Figure 3. Wiring diagram for NanoDAQ monitoring board.
The FPV utilized mooring similar to that used in [54] except for the inclusion of a buoy. The wet
FPV was moored by using an anchor and a towing ring on land. A rope was looped through the
grommets in the solar PV and overhand loop knots were tied to secure the FPV in place. Energy
generation of dry PV and wet FPV, temperature of air, water, PV, and FPV were recorded in 15 min
increments.
2.2. Water Evaporation Modeling
The Penman–Monteith model used in this study is a datum intensive water evaporation model
because it requires the measurement of several weather data. Some of the data can be calculated, but
Figure 2.
Closeup of floating photovoltaic/floatovoltaic (FPV) corner after deployment, showing water
coverage from a modest wave (top left).
Figure 3. Wiring diagram for NanoDAQ monitoring board.
The FPV utilized mooring similar to that used in [
54
] except for the inclusion of a buoy. The wet FPV
was moored by using an anchor and a towing ring on land. A rope was looped through the grommets
in the solar PV and overhand loop knots were tied to secure the FPV in place. Energy generation of dry
PV and wet FPV, temperature of air, water, PV, and FPV were recorded in 15 min increments.
2.2. Water Evaporation Modeling
The Penman–Monteith model used in this study is a datum intensive water evaporation model
because it requires the measurement of several weather data. Some of the data can be calculated, but the
accuracy of the model is increased if they are measured. The Penman–Monteith model was originally
designed to calculate the evapotranspiration losses from leaves’ and canopies’ surfaces [
57
]. However,
the method has been adapted in several studies to estimate the evaporation of surface water [
72
75
].
One important thing to note regarding the use of the Penman–Monteith evapotranspiration model for
lake evaporation is the use of water temperature instead of air temperature in some of the parameters’
calculations: the outgoing longwave radiation, the partial vapor pressure at the water surface and slope
of the temperature saturation water vapor curve. The original Penman–Monteith model estimates the
evapotranspiration of crops; therefore, the model only uses the air temperature in its implementation.
The use of water temperature instead of air temperature has been validated in several lake evaporation
studies [72,74,75].
The Penman–Monteith [57] equation adapted to open water surfaces is [74,75]:
EL=1
λ××(RNHS)+86400 ×ρa×Cpa×(PwPa)
ra
+γmm·day1(1)
Energies 2020,13, 6285 6 of 24
where E
L
(mm/day) is the daily evaporation rate and Cp
a
(kJ/kg/
C) and
ρa
(kg/m
3
) are, respectively,
the heat capacity, and the density of air. The other parameters in the Penman–Monteith equation need
to be calculated and depend on several weather data. The weather data needed to calculate these
parameters are comprised of: the daily maximum (T
a,max
) (
C) and daily minimum (T
a,min
) (
C) air
temperature; the daily maximum (T
w,max
) (
C), daily minimum (T
w,min
) (
C), and daily mean water
temperature (T
w
) (
C); the daily maximum (Rh
max
) (%), and daily minimum relative humidity (Rh
min
)
(%); the daily mean dew temperature (T
d
) (
C), the daily mean atmospheric pressure (P) (kPa); the daily
mean wind speed (w
s
) (m/s) at a height of 2 m above the water surface; and the daily incoming solar
radiation (R
S
) (MJ/m
2
/day). The other parameters that are needed to calculate the components in the
evaporation model of Penman–Monteith include: the altitude of the lake’s location (h) (m); the surface
area (A) (m
2
), and the eective depth (d
w
) (m) of the lake reservoir; and the latitude of the location of
the water surface (φ)(rad).
When all the listed parameters are available, the computation of the lake water evaporation using
the Penman–Monteith model starts with the calculation of the mean saturation vapor pressure (P
w
)
(kPa), and the actual vapor pressure of the air (Pa) (kPa) [58,67,73]:
Pw=1
2×0.6108 × exp 17.27 ×Tw,max
Tw,max +237.3!+exp 17.27 ×Tw,min
Tw,min +237.3!! (kPa)(2)
Pa=1
2×0.6108 ×Rhmin
100 ×exp17.27×Tw,max
Tw,max+237.3 +Rhmax
100
×exp17.27×Tw,min
Tw,min+237.3  (kPa)(3)
After the calculation of the two vapor pressures, the slope of the saturation vapor pressure curve
() (kPa/C) is calculated [58,67,73]:
=4096 ×Pw
(Tw+237.3)2kPa·C1(4)
Then, the latent heat of vaporization (
λ
) (MJ/kg), which depends on the water temperature,
is calculated [58,73]:
λ=2.501 0.002361 ×TwkPa·C1(5)
From the latent heat of vaporization, the psychrometric constant (
γ
) (kPa/
C) can be deduced [
58
,
67
],
γ=Cpa×P
RMW ×λkPa·C1(6)
In Equation (6), R
MW
=0.622 and is equal to the molecular weight of water vapor over the
molecular weight of dry air.
After that, the wind function f
w
(MJ/m
2
/kPa/day) is needed to estimate the aerodynamic resistance
of the water surface. The formula used to calculate the wind function is proposed by
McJannet et al.
[
76
].
The formula was found to work well with the Penman–Monteith evaporation model. The wind function
calculation by McJannet’s formula depends on the wind speed as well as on the surface area of the lake.
fw=(2.36 +1.67 ×ws)×A0.05 MJ·m2·kPa1·day1(7)
Once the wind function is known, a combination of the Penman–Monteith model equations
presented in the works of Zotarelli et al. and Finch et al. gives the value of the aerodynamic resistance
(s/m) [67,75]:
ra=ρa×Cpa×86400
1000 ×γ×fws·m1(8)
Energies 2020,13, 6285 7 of 24
The two remaining terms are the net solar radiation (R
N
) (MJ/m
2
/day) and the change in water
heat storage flux (H
S
) (MJ/m
2
/day). The net solar radiation’s calculation depends on the net longwave
radiation (RNL) (MJ/m2/day) and the net shortwave radiation (RNS ) (MJ/m2/day) [58,67,73].
RN=RNS RNL MJ·m2·day1(9)
The net shortwave radiation is calculated using the albedo (a) and the measured incoming solar
radiation (RS) (MJ/m2/day) [58,67,7375]:
RNS =(1a)×RSMJ·m2·day1(10)
The net longwave radiation is calculated by taking the dierence between the outgoing longwave
radiation (R
OL
) (MJ/m
2
/day) and the incoming longwave radiation (R
IL
) (MJ/m
2
/day). The incoming
longwave radiation is given by the Equation (11) [77,78]
RIL =σCf+1Cf10.261 ×exp7.77 ×104T2
a(Ta+273.15)4MJ·m2·day1(11)
In Equation (11),
σ
[MJ/m
2
/T
4
/day] is the Stefan–Boltzmann’s constant, T
a
is the daily mean air
temperature and Cfis the cloud coverage fraction that has been estimated as follows [79]:
Cf=1.1 RRatio ;RRatio 0.9
Cf=2(1RRatio);RRatio >0.9 (12)
The parameter R
Ratio
is the ratio of the incoming solar radiation (R
S
) to the clear sky radiation R
CS
(MJ/m2/day). The clear sky radiation is calculated using Equation (13) [75,78,79]:
RCS =0.75 +2·105×h×REX MJ·m2·day1(13)
The extraterrestrial radiation R
EX
(MJ/m
2
/day) depends on the latitude of the lake, the sunset
hour angle, the solar declination angle, the solar constant, and the inverse relative distance from the
sun to earth. This calculation is a well-known procedure that has been detailed in the guide for crop
evapotranspiration calculations by the FAO [
58
]. The outgoing longwave radiation depends on the
water surface temperature and is calculated as:
ROL =ε×σ×(Tw+273.15)4MJ·m2·day1(14)
T
w
(
C) is the mean daily water temperature and
ε
is the emissivity of the water surface.
The emissivity of water surface varies between 0.95 and 0.99 for water temperatures below 55
C [
80
].
An average value of ε=0.97 has been used in this study. The net longwave radiation is therefore:
RNL =RIL ROL MJ·m2·day1(15)
The water heat storage flux (H
S
) (MJ/m
2
/day) expresses the change in the heat stored in the water
from one day to another. The heat storage flux calculation methods used in two different studies by
Abtew et al., and Finch et al. are suitable for shallow water bodies evaporation [
73
,
75
]. Since Lake Mead
is a deep lake, the equilibrium temperature approach proposed by de Bruin has been used instead.
In this approach, an equilibrium temperature is used to estimate a mean daily uniform temperature of
the water body for each day [
81
]. The heat storage flux’s formula using de Bruin’s method is [
78
,
81
83
]:
HS=ρwCpwdw×Tuw,jTuw,j1
tMJ·m2·day1(16)
Energies 2020,13, 6285 8 of 24
The constants’ values
ρw
(kg/m
3
), Cp
w
(MJ/kg/
C), d
w
(m) are, respectively, the density of water,
the heat capacity of water, and the depth of the lake. T
uw,j
and T
uw,j1
are, respectively, the mean
uniform water temperature for day (j), and day (j
1).
tis the time step for the temperature estimation.
The mean uniform water temperature (T
uw,j
) depends on the equilibrium temperature (T
e
) (
C) and the
time constant (τ) (day):
Tuw,j=Te+Tuw,j1Te×exp1
τ(C)(17)
Te=Twb +RN,wb
4×σ×(Twb +273.15)3+fw×(wb +γ)(C)(18)
τ=ρw×Cpw×dw
4×σ×(Twb +273.15)3+fw×(wb +γ)(day)(19)
R
N,wb
(MJ/m
2
/day), T
wb
(
C), and
wb
(kPa/K) are, respectively, the net radiation at the wet-bulb
temperature, the wet-bulb temperature, and the slope of the saturation vapor pressure curve at the
wet-bulb temperature. The wet-bulb temperature (T
wb
) is calculated using the following equation [
78
,
83
]:
Twb =
0.00066 ×100 ×Ta+(4098×Pa×Td)
(Td+237.3)2
0.00066 ×100 +(4098×Pa×Td)
(Td+237.3)2
(C)(20)
The saturation vapor pressure curve at the wet-bulb temperature wb (kPa/K) is calculated by:
wb =4096 ×0.6108 ×exp17.27×Twb
Twb+237.3
(Twb +237.3)2kPa·K1(21)
The net radiation (RN,wb) at the wet-bulb temperature is:
RN,wb =(1a)×RS+RIL ROL,wb MJ·m2·day1(22)
In Equation (22), R
OL,wb
(MJ/m
2
/day) is the outgoing longwave radiation at the wet-bulb
temperature and is calculated by:
ROL,wb =Cf×σ×(Ta+273.15)4+4×(Ta+273.15)3×(Twb Ta) MJ·m2·day1(23)
After the calculation of all parameters, the lake evaporation’s value (E
L
) can be calculated using
Equation (1).
2.3. Energy Production Modeling
The power output of a PV module (P
out
) (W) is calculated by applying dierent losses to the
incoming solar irradiance and is given by:
Pout =IS×AP×ηP(W)(24)
where I
S
(W/m
2
) is the incoming solar irradiance, A
P
(m
2
) is the eective area of the solar panel,
and
ηP
(%) is the eciency of the PV system. In this study, the eciency of the system includes the
electrical eciency of the module, which is dependent on the operating temperature, the shading losses,
the soiling and hotspot losses, and the mismatch losses. Additionally, the solar irradiation component
used is the global horizontal irradiation because the inclination of the panels is 0
. The power output
is calculated hourly and summed up to determine the energy production of the system over a year.
Energies 2020,13, 6285 9 of 24
2.3.1. FPV Operating Temperature
The energy produced by a photovoltaic system depends on the electrical eciency of the modules.
The electrical eciency of the modules
(ηe)
changes with the operating temperature of the cell and is
calculated using Equation (25) [45,84]:
ηe=ηre f ×h1β×Teo Tre f i (%)(25)
where
ηre f
(%),
βre f
(%/
C), T
eo
(
C), and T
ref
(
C) are, respectively, the reference eciency of the panel,
the temperature coecient of the panel, the eective operating temperature of the panel, and the
reference temperature.
The data collected from the FPV test bed are used to determine the eective operating temperature
(T
eo
) of the FPV. The model describing the temperature dependence on the ambient temperature and
the solar power in nominal operating cell temperature (NOCT) conditions is a linear model [8486]:
Tcell =Tme +k×IS(C)(26)
T
Cell
(
C) is the operating temperature of the solar cells, k(
C. m
2
/W) is the coecient of the
relationship, I
S
(W/m
2
) is the solar irradiance, and T
me
(
C) is the ambient temperature of the location
of the solar module. This model is well-adapted for oshore, roof or ground mounted, PV systems but
needs to be modified to accurately describe FPV systems. A study conducted by
Kamuyu et al.
[
45
] has
proposed a solar cell temperature calculation in FPV using the air temperature, the water temperature,
the solar irradiance, and the wind speed. Kamuyu et al.’s study focused on FPV mounted at a
tilt angle relative to the water’s surface where the air temperature and wind speed played a larger
role in determining the module temperature than the water temperature. In this study, because the
modules are on/under the water surface, wind speed is neglected, and the water temperature plays
the dominant role in module temperature. Thus, the Kamuyu approach for pontoon-based FPV was
adapted and used here with experimental data for solar flux, air temperature, water temperature,
and module temperature. The approach used was a multilinear variable regression. The regression has
three independent variables that are the solar irradiance (I
S
), the water temperature (T
w
), and the air
temperature (T
a
). The last variable of the regression, the FPV module’s eective operating temperature
(T
eo
), depends on the previous three. The goal of the regression is to find a linear relationship between
the module’s eective operating temperature (T
eo
), and the three independent variables in the form of:
Teo =α0+α1Tw+α2Ta+α3IS(C), (27)
where
α0
is a constant term;
α1
,
α2
, and
α3
are the regression coecients relative to the water
temperature, air temperature, and solar irradiance, respectively.
The solar module temperature dataset from the test bed has been stored in a MATLAB column
vector, and the independent variables have been stored within a MATLAB numeric matrix to which
an additional unit column has been added at the beginning to account for the coecient
α0
. Then,
the regression is performed using a dedicated MATLAB function called “regress” [
87
]. The “regress”
function performs a multivariable regression on experimental data and outputs the coecients of the
regression as well as other values such as the R-squared value of the regression and the residuals.
The experimentally obtained coecients are used in the case study of Lake Mead to estimate the
eective operating module temperatures that are, in turn, used in the energy yield simulation.
2.3.2. Other Loss Factors
This study focuses on the FPV system; therefore, the other factors considered are only related to
the panels. In the case of a complete system design, losses from other equipment such as the inverter or
transformer need to be considered. Other factors that could impact the eciency of the floating solar
Energies 2020,13, 6285 10 of 24
PV modules are the same as conventional land-based PV systems. These factors are solar irradiance
losses, shading losses, soiling, mismatch losses, and DC cabling losses [60,88,89].
The foam-based support as well as the PV are mounted flat on the water surface (e.g., tilt angle =
0 degrees); therefore, they are not exposed to the optimum amount of solar irradiation for any location
other than those on the equator. A study conducted by Jacobson et al. has provided an estimate of the
optimal tilt for fixed tilt solar PV systems for dierent locations throughout the world [
90
]. The loss
due to the tilt angle has been taken into account in this study and only the global horizontal irradiation
for the energy yield calculation is used.
The impact of shading losses on FPV is low because water surfaces are flat and there are no nearby
obstacles that could cause a direct shade to the modules. In the case of foam-based FPV, there is no
mutual shade between the modules either because the mounting systems are flat on the water surface.
Lake Mead is located in a mountainous region; therefore, far horizon shading may occur during certain
times of the day or the year but is expected to be minimal. A detailed shading losses analysis has not
been conducted during this study and an estimated value of zero percent has been used.
Soiling can be significant on FPV panels. Soiling in the case of FPV systems is mostly due to
bird dropping or algae growth [
54
]. According to a report on FPV systems by the World Bank Group,
nesting birds have been found to prefer the use of FPV modules as a nesting place [
60
]. In the report of
the World Bank Group, however, the floating systems used were inclined; thus, allowing the presence
of sheltered places where the birds were nesting. In the case of foam-based FPV, it has been assumed
that the eect of birds will be lower because the modules are mounted directly on the water surface
and the mounting system oers no sheltered space for nesting. A detailed study of the impact of birds
nesting on foam-based FPV panels would be interesting for future studies. In addition, by ensuring the
FPV are above the water surface, the growth of algae on the front surface of the FPV can be minimized.
Mismatch losses and DC cable losses can be higher in FPV systems due to the relative movement
of the modules on the water surface, but an optimum design can minimize these losses [60].
2.3.3. Parameters Used for Energy Yield Simulation
The energy production model simulates a floating solar PV system on the surface of Lake Mead.
The area covered by the solar PV installation is described in Section 2.4. The values used for the energy
production simulation as well as the sources of the values are given in Table 1.
Table 1. Energy modeling simulation parameters.
Parameters Value Source
Solar PV temperature model (Equation (27)) This study
Reference eciency of the module
23% [70]
Module inclination 0This study
Shading losses 0% This study
Soiling 3% [60]
Mismatch losses 6% [89]
DC cable losses 3% [89]
2.4. Water Savings Capability and Eciency of the System
The water savings capability of the FPV system investigated in this study has been estimated to
be 90% of the volume of water corresponding to the surface covered by the FPV. This assumption
is supported by previous studies that found that covering water surfaces with pontoon-based FPV
could reduce the evaporation losses by more than 90% [
38
,
91
]. Thus, the resulting values are extremely
conservative as here the FPV covers the entire water surface and is not a tilted FPV mount as in [
38
,
91
].
When planning an FPV installation on a water surface, the percentage coverage of the water by the solar
systems depends on the type of activities that are being performed on the body of water. According to
the World Bank Group, the FPV system should not cover more than 50% of the water surface if used
Energies 2020,13, 6285 11 of 24
for fishing and not more than 60% if the water body is not used for fishing [
60
]. Therefore, a sensitivity
analysis will be run on the coverage percentage to investigate the energy production and water saving
capability of the foam-based FPV system in this study from 10% to 50% in 10% increments because
Lake Mead is used for fishing. Then, the water saving capability is estimated by multiplying the water
evaporation rate and the surface coverage. The result is adjusted by 90%. The cost of water saved
annually is estimated using the average water cost in Nevada where Lake Mead serves as a clean
water source. The cost of water according to Las Vegas Valley Water District ranges from USD 0.35/m
3
to 1.37/m
3
for a family size residential home, according to the size of the installed water meter [
92
].
On the other hand, the wholesale electricity rate of the power produced at the Hoover Dam, located in
Nevada, is USD 0.02/kWh [93,94]. These values are used to estimate the lowest and highest potential
energy revenues of the foam-based FPV system.
3. Results
3.1. Water Evaporation
The results from the water evaporation model simulation at Lake Mead show an evaporation rate
estimate of 1957 mm in 2018. This result is in agreement with the results of the study conducted by
Moreo and Swancar [
55
] on Lake Mead during the period of March 2010 through February 2012 using
the eddy covariance evaporation method. The study estimated the lake evaporation from March 2010 to
February 2011, and from March 2011 to February 2012. According to the two authors, the evaporation
rate for the first study period had a minimum value of 1958 mm and a maximum value of 2190 mm;
while the minimum value was 1787 mm and the maximum value was 1975 mm for the second study
period. The result obtained in this present study is located within the result interval of Moreo and
Swancar’s study. Another early study by Westenburg et al. provided the evaporation data for Lake
Mead from 1997 to 1999 [95]. The average evaporation rate for that period was 2281 mm.
Figure 4a shows the monthly results of the evaporation rates’ simulation using 2018 data.
The evaporation rate is low in the winter and increases in summer. The evaporation rate at the peak of
the summer, in June, is approximately five times more important than the lowest evaporation rate of
the winter, in December. Figure 4b shows the daily evaporation estimates throughout the year.
Energies 2020, 13, x FOR PEER REVIEW 11 of 25
Therefore, a sensitivity analysis will be run on the coverage percentage to investigate the energy
production and water saving capability of the foam-based FPV system in this study from 10% to 50%
in 10% increments because Lake Mead is used for fishing. Then, the water saving capability is
estimated by multiplying the water evaporation rate and the surface coverage. The result is adjusted
by 90%. The cost of water saved annually is estimated using the average water cost in Nevada where
Lake Mead serves as a clean water source. The cost of water according to Las Vegas Valley Water
District ranges from USD 0.35/m3 to 1.37/m3 for a family size residential home, according to the size
of the installed water meter [92]. On the other hand, the wholesale electricity rate of the power
produced at the Hoover Dam, located in Nevada, is USD 0.02/kWh [93,94]. These values are used to
estimate the lowest and highest potential energy revenues of the foam-based FPV system.
3. Results
3.1. Water Evaporation
The results from the water evaporation model simulation at Lake Mead show an evaporation
rate estimate of 1957 mm in 2018. This result is in agreement with the results of the study conducted
by Moreo and Swancar [55] on Lake Mead during the period of March 2010 through February 2012
using the eddy covariance evaporation method. The study estimated the lake evaporation from
March 2010 to February 2011, and from March 2011 to February 2012. According to the two authors,
the evaporation rate for the first study period had a minimum value of 1958 mm and a maximum
value of 2190 mm; while the minimum value was 1787 mm and the maximum value was 1975 mm
for the second study period. The result obtained in this present study is located within the result
interval of Moreo and Swancar’s study. Another early study by Westenburg et al. provided the
evaporation data for Lake Mead from 1997 to 1999 [95]. The average evaporation rate for that period
was 2281 mm.
Figure 4a shows the monthly results of the evaporation rates’ simulation using 2018 data. The
evaporation rate is low in the winter and increases in summer. The evaporation rate at the peak of
the summer, in June, is approximately five times more important than the lowest evaporation rate of
the winter, in December. Figure 4b shows the daily evaporation estimates throughout the year.
(a) (b)
Figure 4. Water evaporation simulation results for Lake Mead: (a) simulated evaporation values (mm)
for each month of the year 2018; (b) simulated evaporation values (mm) for each day of the year 2018.
3.2. Energy Production
3.2.1. FPV Operating Temperature Model
The multilinear regression on the collected data yielded the coefficients 𝛼, 𝛼, 𝛼, and 𝛼,
which describe the relationship between the FPV effective operating temperature (Teo) and the
independent variables: the water temperature (Tw), the air temperature (Ta), and the solar irradiance
51.5
74.9
111.0
190.3
235.5
294.6
266.9 282.0
210.3
127.0
71.0
42.6
0.0
50.0
100.0
150.0
200.0
250.0
300.0
350.0
Monthly evaporation (mm)
Month of the year
-2.0
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
1
14
27
40
53
66
79
92
105
118
131
144
157
170
183
196
209
222
235
248
261
274
287
300
313
326
339
352
365
Evaporation (mm)
Day of the year
Figure 4.
Water evaporation simulation results for Lake Mead: (
a
) simulated evaporation values (mm)
for each month of the year 2018; (
b
) simulated evaporation values (mm) for each day of the year 2018.
3.2. Energy Production
3.2.1. FPV Operating Temperature Model
The multilinear regression on the collected data yielded the coecients
α0
,
α1
,
α2
, and
α3
,
which describe the relationship between the FPV eective operating temperature (T
eo
) and the
Energies 2020,13, 6285 12 of 24
independent variables: the water temperature (Tw), the air temperature (Ta), and the solar irradiance
(I
S
). The regression coecients have been obtained with an R-squared value of 0.8276. Figure 5
shows the statistical results of the regression. The R-squared value combined with the random
distribution of the residuals’ plot on Figure 5b show that there is a linear relationship between T
eo
and
the independent variables.
Energies 2020, 13, x FOR PEER REVIEW 12 of 25
(IS). The regression coefficients have been obtained with an R-squared value of 0.8276. Figure 5 shows
the statistical results of the regression. The R-squared value combined with the random distribution
of the residuals plot on Figure 5b show that there is a linear relationship between Teo and the
independent variables.
(a)
(b)
Figure 5. Multilinear regression results of the FPV panels effective operating temperature (Teo): (a)
simulated FPV temperature plotted against the measured temperature for 15 June 2020; (b) residuals
distribution plotted against the simulated FPV temperature for 15 June 2020.
Equation (28) is proposed as a model that represents the effective operation temperature of FPV
mounted on a foam-based support.
𝑇𝑒𝑜 =13.25540.0875×𝑇𝑤+1.2645×𝑇𝑎+0.0128×𝐼𝑆 (°C)
(28)
Figure 6 shows the simulated operating temperature using the proposed model, the operating
temperature of a titled aluminum pontoon-based mount FPV model based on the original Kamuyu
et al.’s model (for pontoon-based tilted FPV), and the measured operating temperature for June 15
2020. The simulated temperature is at times higher or lower than the measured temperature, but the
overall trend of the two temperature profiles matches. The model proposed in this study is compared
to the unadapted tilted FPV model and the current model (which is an adaptation of Kamuyu et al.’s
model for foam-backed flat-surface FPV) and provides a better description of a foam-based FPV
panel’s operating temperature. The proposed model in this study has a similar profile to Kamuyu’s
model, and the proposed model provides a better description of the foam-based solar module’s
behavior.
Figure 6. Measured FPV operating temperature compared to simulated FPV operating temperature
for 15 June 2020.
Figure 5.
Multilinear regression results of the FPV panels’ eective operating temperature (T
eo
):
(
a
) simulated FPV temperature plotted against the measured temperature for 15 June 2020; (
b
) residuals’
distribution plotted against the simulated FPV temperature for 15 June 2020.
Equation (28) is proposed as a model that represents the eective operation temperature of FPV
mounted on a foam-based support.
Teo =13.2554 0.0875 ×Tw+1.2645 ×Ta+0.0128 ×IS(C)(28)
Figure 6shows the simulated operating temperature using the proposed model, the operating
temperature of a titled aluminum pontoon-based mount FPV model based on the original
Kamuyu et al.’s
model (for pontoon-based tilted FPV), and the measured operating temperature for
15 June 2020
.
The simulated temperature is at times higher or lower than the measured temperature, but the overall
trend of the two temperature profiles matches. The model proposed in this study is compared to the
unadapted tilted FPV model and the current model (which is an adaptation of Kamuyu et al.’s model
for foam-backed flat-surface FPV) and provides a better description of a foam-based FPV panel’s
operating temperature. The proposed model in this study has a similar profile to Kamuyu’s model,
and the proposed model provides a better description of the foam-based solar module’s behavior.
Energies 2020, 13, x FOR PEER REVIEW 12 of 25
(IS). The regression coefficients have been obtained with an R-squared value of 0.8276. Figure 5 shows
the statistical results of the regression. The R-squared value combined with the random distribution
of the residuals plot on Figure 5b show that there is a linear relationship between Teo and the
independent variables.
(a)
(b)
Figure 5. Multilinear regression results of the FPV panels effective operating temperature (Teo): (a)
simulated FPV temperature plotted against the measured temperature for 15 June 2020; (b) residuals
distribution plotted against the simulated FPV temperature for 15 June 2020.
Equation (28) is proposed as a model that represents the effective operation temperature of FPV
mounted on a foam-based support.
𝑇𝑒𝑜 =13.25540.0875×𝑇𝑤+1.2645×𝑇𝑎+0.0128×𝐼𝑆 (°C)
(28)
Figure 6 shows the simulated operating temperature using the proposed model, the operating
temperature of a titled aluminum pontoon-based mount FPV model based on the original Kamuyu
et al.’s model (for pontoon-based tilted FPV), and the measured operating temperature for June 15
2020. The simulated temperature is at times higher or lower than the measured temperature, but the
overall trend of the two temperature profiles matches. The model proposed in this study is compared
to the unadapted tilted FPV model and the current model (which is an adaptation of Kamuyu et al.’s
model for foam-backed flat-surface FPV) and provides a better description of a foam-based FPV
panel’s operating temperature. The proposed model in this study has a similar profile to Kamuyu’s
model, and the proposed model provides a better description of the foam-based solar module’s
behavior.
Figure 6. Measured FPV operating temperature compared to simulated FPV operating temperature
for 15 June 2020.
Figure 6.
Measured FPV operating temperature compared to simulated FPV operating temperature for
15 June 2020.
Energies 2020,13, 6285 13 of 24
The temperature profile of a foam-based FPV panel installed on Lake Mead has been simulated
using the proposed FPV operating temperature model and compared to a pontoon-based FPV as
described by Kamuyu’s model in Figure 7.
Energies 2020, 13, x FOR PEER REVIEW 13 of 25
The temperature profile of a foam-based FPV panel installed on Lake Mead has been simulated
using the proposed FPV operating temperature model and compared to a pontoon-based FPV as
described by Kamuyu’s model in Figure 7.
Figure 7. Operation temperature of an FPV installed on the surface of Lake Mead. (+) Operating
temperature using the proposed model in this study for foam-based FPV. (o) Operating temperature
using a ponton-based tilted FPV described by Kamuyu’s model.
The maximum temperature obtained with the model proposed in this study is 48.7 °C and the
minimum temperature is −8.5 °C. On the other hand, the maximum temperature and the minimum
temperature obtained if the FPV system was tilted are, respectively, 58.2 °C and −3.4 °C. Overall, the
temperature model used here based on experimental data during the summer months predicts a
lower temperature when the panels are in direct contact with the water surface.
3.2.2. Energy Yield and Water Savings of an FPV System Installed on Lake Mead
The temperature profile is used to estimate the electrical efficiency of the solar panel, which is
in turn used to simulate the energy yield of an FPV system installed on Lake Mead with historical
weather data. The energy yield has been simulated by assuming a coverage of the lake surface
between 10 and 50% in 10% increments. The results are shown in detail for the 10% coverage case
and the total energy production is shown for the other cases.
Figure 8 shows the comparison between the monthly energy production obtained using the
proposed model and the energy production of a tilted FPV for 10% coverage of the lake’s surface. As
can be seen in Figure 8 and expected from Figure 7, the proposed model predicts a slightly higher
energy production, about 3.5%, which is correlated with the lower operating temperature of the
modules. The maximum energy per month production is 3.2 TWh and occurs in the month of June,
while the minimum energy per month production is 1.1 TWh and occurs in December.
Figure 7.
Operation temperature of an FPV installed on the surface of Lake Mead. (
+
) Operating
temperature using the proposed model in this study for foam-based FPV. (
o
) Operating temperature
using a ponton-based tilted FPV described by Kamuyu’s model.
The maximum temperature obtained with the model proposed in this study is 48.7
C and the
minimum temperature is
8.5
C. On the other hand, the maximum temperature and the minimum
temperature obtained if the FPV system was tilted are, respectively, 58.2
C and
3.4
C. Overall,
the temperature model used here based on experimental data during the summer months predicts a
lower temperature when the panels are in direct contact with the water surface.
3.2.2. Energy Yield and Water Savings of an FPV System Installed on Lake Mead
The temperature profile is used to estimate the electrical eciency of the solar panel, which is
in turn used to simulate the energy yield of an FPV system installed on Lake Mead with historical
weather data. The energy yield has been simulated by assuming a coverage of the lake surface between
10 and 50% in 10% increments. The results are shown in detail for the 10% coverage case and the total
energy production is shown for the other cases.
Figure 8shows the comparison between the monthly energy production obtained using the
proposed model and the energy production of a tilted FPV for 10% coverage of the lake’s surface.
As can be seen in Figure 8and expected from Figure 7, the proposed model predicts a slightly higher
energy production, about 3.5%, which is correlated with the lower operating temperature of the
modules. The maximum energy per month production is 3.2 TWh and occurs in the month of June,
while the minimum energy per month production is 1.1 TWh and occurs in December.
Figure 9shows the result for the daily energy simulation when 10% of Lake Mead’s surface is
covered with a foam-based solar FPV system. The maximum daily energy production is 570 MWh on
6 January while the minimum daily production is 21 MWh on 18 June.
Energies 2020,13, 6285 14 of 24
Energies 2020, 13, x FOR PEER REVIEW 14 of 25
Figure 8. Monthly energy yield of a simulated foam-based FPV system installed on 10% of Lake
Mead’s surface using historical data from 2018. Comparison between the proposed model (c-Si
flexible foam-backed FPV) and a tilted FPV based on Kamuyu’s model (c-Si aluminum mount FPV).
Figure 9 shows the result for the daily energy simulation when 10% of Lake Mead’s surface is
covered with a foam-based solar FPV system. The maximum daily energy production is 570 MWh on
6 January while the minimum daily production is 21 MWh on 18 June.
Figure 9. Daily energy production results using the temperature model proposed in this study for
10% coverage of Lake Mead’s surface.
Figure 10 shows the simulated annual energy production, and the water saving capabilities of a
foam-based solar FPV system installed on the surface of Lake Mead as a function of coverage area
from 10–50%. For a coverage of 10%, the annual production using collected temperature data is 25.59
TWh, corresponding to a saved water volume of 126.64 million m3. When the percentage coverage is
increased, the energy production is increased linearly. For a coverage of 50% of the lake’s surface, it
is possible to harvest 127.93 TWh of electrical energy and save 633.22 million of m3 of water using
foam-based FPV panels.
1.2
1.5
2.1
2.7
3.0
3.2
2.8
2.6
2.3
1.8
1.3
1.1
1.1
1.4
2.0
2.6
2.9
3.1
2.7
2.5
2.2
1.7
1.3
1.1
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Energy (TWh)
Month of the year
Proposed Model
Kamuyu's Model
0.0
100.0
200.0
300.0
400.0
500.0
600.0
1
15
29
43
57
71
85
99
113
127
141
155
169
183
197
211
225
239
253
267
281
295
309
323
337
351
365
Energy (MWh)
Da y o f th e ye ar
Figure 8.
Monthly energy yield of a simulated foam-based FPV system installed on 10% of Lake
Mead’s surface using historical data from 2018. Comparison between the proposed model (c-Si flexible
foam-backed FPV) and a tilted FPV based on Kamuyu’s model (c-Si aluminum mount FPV).
Energies 2020, 13, x FOR PEER REVIEW 14 of 25
Figure 8. Monthly energy yield of a simulated foam-based FPV system installed on 10% of Lake
Mead’s surface using historical data from 2018. Comparison between the proposed model (c-Si
flexible foam-backed FPV) and a tilted FPV based on Kamuyu’s model (c-Si aluminum mount FPV).
Figure 9 shows the result for the daily energy simulation when 10% of Lake Mead’s surface is
covered with a foam-based solar FPV system. The maximum daily energy production is 570 MWh on
6 January while the minimum daily production is 21 MWh on 18 June.
Figure 9. Daily energy production results using the temperature model proposed in this study for
10% coverage of Lake Mead’s surface.
Figure 10 shows the simulated annual energy production, and the water saving capabilities of a
foam-based solar FPV system installed on the surface of Lake Mead as a function of coverage area
from 10–50%. For a coverage of 10%, the annual production using collected temperature data is 25.59
TWh, corresponding to a saved water volume of 126.64 million m3. When the percentage coverage is
increased, the energy production is increased linearly. For a coverage of 50% of the lake’s surface, it
is possible to harvest 127.93 TWh of electrical energy and save 633.22 million of m3 of water using
foam-based FPV panels.
1.2
1.5
2.1
2.7
3.0
3.2
2.8
2.6
2.3
1.8
1.3
1.1
1.1
1.4
2.0
2.6
2.9
3.1
2.7
2.5
2.2
1.7
1.3
1.1
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
Energy (TWh)
Month of the year
Proposed Model
Kamuyu's Model
0.0
100.0
200.0
300.0
400.0
500.0
600.0
1
15
29
43
57
71
85
99
113
127
141
155
169
183
197
211
225
239
253
267
281
295
309
323
337
351
365
Energy (MWh)
Da y o f th e ye ar
Figure 9.
Daily energy production results using the temperature model proposed in this study for 10%
coverage of Lake Mead’s surface.
Figure 10 shows the simulated annual energy production, and the water saving capabilities
of a foam-based solar FPV system installed on the surface of Lake Mead as a function of coverage
area from 10–50%. For a coverage of 10%, the annual production using collected temperature data
is 25.59 TWh, corresponding to a saved water volume of 126.64 million m
3
. When the percentage
coverage is increased, the energy production is increased linearly. For a coverage of 50% of the lake’s
surface, it is possible to harvest 127.93 TWh of electrical energy and save 633.22 million of m
3
of water
using foam-based FPV panels.
Energies 2020,13, 6285 15 of 24
Energies 2020, 13, x FOR PEER REVIEW 15 of 25
Figure 10. Simulated annual energy production (TWh) and water saving capability (millions of m3)
of a foam-based solar FPV system installed on Lake Mead’s surface using historical temperature data
and the proposed model depending on the percentage coverage of the lake’s surface.
Table 2 shows the annual water and energy savings estimates related to the water savings and
energy production from the FPV. With houses with the least water consumption, the cost of the water
saved is estimated to be USD 44 million when 10% of the lake surface is covered, and USD 220 million
when 50% of the lake surface is covered. On the other hand, when the consumers’ water consumption
is on the high side, these costs increase, amounting to USD 172 million when 10% of the lake is
covered and USD 861 million when 50% is covered. Furthermore, the results for the energy
production show that USD 0.5 billion of energy can be generated when 10% of the lake surface is
covered. The value of the energy generated when 50% of the lake surface is covered is estimated as
USD 2.6 billion.
Table 2. Estimation of the yearly cost of water saved and energy produced using water and energy
cost range from Nevada for an FPV system covering 10–50% of Lake Mead’s surface.
Lake
Surface
Percent
Coverage
Water
Savings at
$0.35/m3
(Millions of $)
Water
Savings at
$1.37/m3
(Millions of $)
Energy
Revenues at
2¢/kWh
(Billions of $)
10% 43.99 172.19 0.51
20% 87.98 344.37 1.02
30% 131.97 516.56 1.54
40% 175.96 688.75 2.05
50% 219.95 860.94 2.56
The relative values of the water and energy provided by the foam-based FPV indicate that the
electricity production from the FPV could be used to subsidize water conservation in arid and semi-
arid areas. Thus, FPV could be a self-funded water conservation approach.
4. Discussion
The water evaporation calculation performed in this study predicts a significant water saving
potential for foam-based FPV systems on Lake Mead. The evaporation calculation using historical
data has shown an annual evaporation estimate of 1957.6 mm for the lake. The result of the calculation
25.59 51.17 76.76 102.35 127.93
126.64
253.29
379.93
506.58
633.22
10% 20% 30% 40% 50%
Percent coverage of the lake
Annual Energy Production (TWh) Annual Water Savings (million of m3)
Figure 10.
Simulated annual energy production (TWh) and water saving capability (millions of m
3
) of
a foam-based solar FPV system installed on Lake Mead’s surface using historical temperature data and
the proposed model depending on the percentage coverage of the lake’s surface.
Table 2shows the annual water and energy savings estimates related to the water savings and
energy production from the FPV. With houses with the least water consumption, the cost of the water
saved is estimated to be USD 44 million when 10% of the lake surface is covered, and USD 220 million
when 50% of the lake surface is covered. On the other hand, when the consumers’ water consumption
is on the high side, these costs increase, amounting to USD 172 million when 10% of the lake is covered
and USD 861 million when 50% is covered. Furthermore, the results for the energy production show
that USD 0.5 billion of energy can be generated when 10% of the lake surface is covered. The value of
the energy generated when 50% of the lake surface is covered is estimated as USD 2.6 billion.
Table 2.
Estimation of the yearly cost of water saved and energy produced using water and energy cost
range from Nevada for an FPV system covering 10–50% of Lake Mead’s surface.
Lake Surface
Percent Coverage
Water Savings at
$0.35/m3(Millions of $)
Water Savings at
$1.37/m3(Millions of $)
Energy Revenues at
2¢/kWh (Billions of $)
10% 43.99 172.19 0.51
20% 87.98 344.37 1.02
30% 131.97 516.56 1.54
40% 175.96 688.75 2.05
50% 219.95 860.94 2.56
The relative values of the water and energy provided by the foam-based FPV indicate that the
electricity production from the FPV could be used to subsidize water conservation in arid and semi-arid
areas. Thus, FPV could be a self-funded water conservation approach.
4. Discussion
The water evaporation calculation performed in this study predicts a significant water saving
potential for foam-based FPV systems on Lake Mead. The evaporation calculation using historical
data has shown an annual evaporation estimate of 1957.6 mm for the lake. The result of the calculation
performed in this study is in agreement with previous evaporation studies on Lake Mead [
55
,
95
].
Energies 2020,13, 6285 16 of 24
The simulation results show annual water savings ranging from 126.64 to 633.22 million m
3
depending
on the percentage of the lake surface covered by the FPV system. According to the United States
Environmental Protection Agency (US EPA), each American uses, on average, 88 gallons of water
per day, resulting in an annual water consumption of 32,120 gallons or 121.59 m
3
per capita [
96
].
The amount of water saved using foam-based FPV on Lake Mead will therefore be enough to supply
water to more than five million Americans in the case that 50% of the lake surface is covered. This would
make a significant impact on the cities near Lake Mead. The value is more than the four million
population of the second largest city in the country, Los Angeles [
97
] or the entire population of Nevada
of 3.1 million [
98
]. When 10% of the lake is covered by FPV panels, the amount of water saved is
enough to supply water to the populations of both Henderson (320,189) and Las Vegas (651,319) or
Las Vegas and Reno (255,601) in Nevada [
99
]. According to an analysis performed by Barsugli et al.,
Lake Mead has a 50% percent chance of going dry between 2035 and 2047 if nothing is done to stop
the current draw down and evaporation rate of the lake [
100
]. Other studies on the management of
the lake have resulted in the same conclusion [
101
,
102
]. These studies have shown the need for new
ways to mitigate lake evaporation not only on Lake Mead, but on other lakes in the world, especially
those located in arid environments. Floating solar photovoltaic technology provides a solution to limit
evaporation of water surfaces and provide electrical energy for the surrounding populations.
The energy production analysis has yielded an annual energy production ranging from 25.9 TWh
to 127.93 TWh for a coverage of the lake of 10%, and 50%, respectively. The energy production profile is
in accordance with a previous FPV study conducted by Kamuyu et al. [
45
], showing an improvement of
10% from a ground-mount system. This is confirmed by the study of Pierce et al., who determined that
the energy production improvement of an FPV systems is 5–10% compared to a ground-mount system
for mono and polycrystalline silicon [
54
]. This is due to the cooling eect of the water on the FPV
modules. According to the United States Energy Information Agency (US EIA), the average American
household electricity consumption is 10,649 kWh per year. This means that the energy production of
an FPV system covering 10% of Lake Mead has the capacity to power more than two million American
homes [
103
]. This is more than the electricity needed to power the homes in Las Vegas, Henderson and
Reno combined. On the other hand, the total electricity consumption in the U.S. according to 2018
statistics is 4178 TWh. This implies that the electricity production from a solar FPV system covering
50% of Lake Mead can supply 3% of the total electricity consumed in the U.S. and can replace more than
11% of the coal-fired power plants operating in the country; thus, contributing in a significant way to
the reduction in the national carbon dioxide emissions [
104
] and the concomitant air pollution-related
mortality [
105
108
]. This study is in agreement with past work showing enormous potential for FPV
on water bodies in the U.S. [109].
The results of this study show that there are several benefits to implementing a foam-based
FPV solar plant. Foam-based FPV avoids the issues related to land use in ground-mounted solar
PV [
110
] and since the floating device is made of low-cost material, the racking cost is lower than
other raft racking FPV technologies [
54
]. In addition, FPV systems in general have the potential
to form agrivoltaic type systems [
111
] by merging with aquaculture to form aquavoltaics [
112
,
113
].
The flexible foam-backed FPV approach used here even makes mobile FPV possible. The FPV approach
demonstrated here is less expensive than conventional pontoon-based FPV and has a slightly higher
energy output per W because of the modules’ close proximity to the water. FPV racking in general is
less costly than conventional ground mounted PV. Thus, as PV is already often the least costly method
for new electricity production, it provides a potentially profitable means of reducing water evaporation
in the world’s dwindling bodies of fresh water. Overall, the results of this study appear extremely
promising. Solar FPV is a fairly new technology that is growing at a tremendous rate, but for it to
reach its full potential, future work is needed to explore policies that sustain the development of this
technology while also minimizing negative externalities. To accomplish this, a full life cycle analysis
(LCA) study is needed on this technology.
Energies 2020,13, 6285 17 of 24
Future work is also needed to experimentally verify the results of this study in dierent locations
throughout the world. In addition, future work is needed to investigate fouling (and means to prevent it)
in dierent bodies of water. More data should also be collected to further refine the temperature model
and improve the energy production accuracy of the results shown here. Foam-based technology used as
a floating device needs to be investigated more in order to have a commercially viable mass-produced
FPV foam racking. The work shown here and completed previously was accomplished using
after-market alterations of flexible PV modules. It should be pointed out that economic calculations
used here assumed a 25 year lifetime for the PV modules. Although they are rated for extreme
environments, guaranteed to resist corrosion and waterproof, the flexible SunPower modules only
carry a 5 year warranty rather than the industry standard 25–30 year warranty. Future work to test the
long-term performance of such systems is needed to ensure the reliability and safety of a foam-backed
FPV as described in this article. In addition, future technical work is needed to investigate the potential
for making flexible modules rated for high voltages that would be more appropriate for utility scale
systems such as described in this study. The cost of the FPV racking would be further reduced
by integrating bulk purchased foam into the PV manufacturing process. In addition, closed loop,
circular economy [
114
116
] and industrial symbiosis [
117
] could be applied to the FPV manufacturing
process. This would be expected to further reduce the cost of the FPV as well but may also necessitate
policy intervention to ensure end of life recycling [
118
]. The polyethylene foam used here could be
fabricated from recycled plastic waste [
119
121
], thereby further improving the environmental balance
sheet for foam-backed FPV. Future studies can potentially look into the long-term stability of foam
in water by analyzing the eect of dierent qualities of water on this material. Another aspect of
foam-based rack where future work is needed is the mooring technology used to secure the FPV.
Finally, the environmental impacts of the floating solar systems on marine life have not been fully
established [60] and will be an interesting subject for future studies.
5. Conclusions
This study introduced a new approach to FPV using a flexible crystalline silicon module backed
with foam, which is less expensive than conventional pontoon-based FPV racking and land-based
PV racking. The results show that the foam-backed FPV had a lower operating temperature than
conventional pontoon-based fixed tilt out-of-water FPV and thus a higher energy output per unit
power because of the modules’ close proximity to the water. Thus, because PV costs are now normally
the least costly method of new electricity production, the hypothetical large-scale foam-based FPV
provides a potentially profitable means of reducing water evaporation in the world’s at-risk bodies of
fresh water.
The case study of Lake Mead found that if 10% of the lake was covered with foam-backed
FPV, there would be more than enough solar electricity generated to power the homes in Las Vegas,
Henderson and Reno combined and enough water savings for Las Vegas and Reno. At 50% lake
coverage, the foam-backed FPV would provide over 127 TWh of clean solar electricity and 633.2 million
m3of water savings, which would provide enough electricity to retire 11% of the polluting coal-fired
plants in the U.S. and water for over five million Americans, annually.
Author Contributions:
Conceptualization, J.M.P.; methodology, K.S.H., P.M. and R.K.K.; software, K.S.H.;
validation, K.S.H. and R.K.K.; formal analysis, K.S.H., P.M., R.K.K. and J.M.P.; investigation, K.S.H. and R.K.K.;
resources, J.M.P.; data curation, K.S.H. and P.M.; writing—original draft preparation, K.S.H., P.M., R.K.K. and
J.M.P.; writing—review and editing, K.S.H., P.M., R.K.K. and J.M.P.; visualization, K.S.H. and P.M.; supervision,
J.M.P.; project administration, J.M.P.; funding acquisition, J.M.P. All authors have read and agreed to the published
version of the manuscript.
Funding: This research was supported by the Witte endowment.
Acknowledgments:
The authors would like to acknowledge technical support from Shane Oberloier, helpful
conversations with Nelson Sommerfeldt, as well as the support of SOLCAST who provided historical solar data
for the simulations performed in the study.
Conflicts of Interest: The authors declare no conflict of interest.
Energies 2020,13, 6285 18 of 24
Glossary
Symbol Name Unit
Paactual saturation vapor pressure (kPa)
raaerodynamic resistance (s/m)
ρaair density (kg/m3)
aalbedo -
haltitude (m)
Taaverage daily air temperature (C)
Taaverage daily air temperature (C)
Paverage daily atmospheric pressure (kPa)
Tdaverage daily dew temperature (C)
Twaverage daily water temperature (C)
wsaverage daily wind speed (m/s)
RCS clear sky radiation (MJ/m2/day)
Cfcloud coverage fraction -
dweective depth of the lake (m)
Teo eective operating temperature (C)
ηre f eciency at reference temperature (%)
ηeelectrical eciency (%)
εemissivity of water -
Teequilibrium temperature (C)
REX extraterrestrial radiation (MJ/m2/day)
ISglobal horizontal irradiation (W/m2)
RSglobal horizontal irradiation (MJ/m2/day)
Cpaheat capacity of air (kJ/kg/C)
Cpwheat capacity of water (MJ/kg/C)
HSheat storage flux (MJ/m2/day)
RIL incoming longwave radiation (MJ/m2/day)
ELlake evaporation (mm)
λlatent heat of vaporization of water (MJ/kg)
φlatitude (rad)
Ta,max maximum daily air temperature (C)
Rhmax maximum daily relative humidity (%)
Tw,max maximum daily water temperature (C)
Pwmean saturation vapor pressure (kPa)
Tuw mean uniform temperature of water (C)
Ta,min minimum daily air temperature (C)
Rhmin minimum daily relative humidity (%)
Tw,min minimum daily water temperature (C)
RNL net longwave radiation (MJ/m2/day)
RN,wb net radiation at wet-bulb temperature (MJ/m2/day)
RNS net shortwave radiation (MJ/m2/day)
RNnet solar radiation (MJ/m2/day)
ROL outgoing longwave radiation (MJ/m2/day)
ROL,wb outgoing longwave radiation at wet-bulb temperature (MJ/m2/day)
Pout output power (W)
APphotovoltaic surface (m2)
ηPphotovoltaic system eciency (%)
γpsychrometric constant (kPa/C)
Tre f reference temperature (C)
wb saturation vapor pressure curve at wet-bulb temperature (kPa/K)
slope of saturation vapor pressure curve (kPa/C)
σStephan–Boltzmann constant (MJ/m2/K4/day)
Energies 2020,13, 6285 19 of 24
Asurface of the lake (m2)
βtemperature coecient of the PV panel (%/C)
τtime constant (day)
ttime step (h/day)
ρwwater density (kg/m3)
Twb wet-bulb temperature (C)
fwwind function (MJ/m2/kPa/day)
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... This study focused specifically on land-based PV, however, the same study could be repeated for the burgeoning field of floating PV (or floatovoltaics) [30,46,60] with aquavoltaics, which is another approach to maximize surface area utility by combining PV with aquaculture [51,85]. There is already evidence that this form of PV has the potential to be environmentally superior to the land-based PV [47], which may impact public perception. ...
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... In order to utilize solar photovoltaic (PV) technology to offset enough fossil fuel production to halt climate destabilization, large surface areas are needed [1]- [6]. Cities, where the majority of humanity calls home [7], lack adequate surface area for PV to meet electrical needs even without including electrification of heating and transportation to eliminate the need for all fossil fuel combustion. ...
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... In order to utilize solar photovoltaic (PV) technology to offset enough fossil fuel production to halt climate destabilization, large surface areas are needed [1][2][3][4][5][6]. Cities, where the majority of humanity calls home [7], lack adequate surface area for PV to meet electrical needs even without including electrification of heating and transportation to eliminate the need for all fossil fuel combustion. ...
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