*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.

**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 α0, α1, α2, and α3, 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 (*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.

**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.

$$T\_{\varepsilon 0} = -13.2554 - 0.0875 \times T\_w + 1.2645 \times T\_d + 0.0128 \times I\_S \tag{28} \tag{28}$$

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 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.

**Figure 6.** Measured FPV operating temperature compared to simulated FPV operating temperature for 15 June 2020.

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 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 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.** 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 m<sup>3</sup> of water using foam-based FPV panels.

**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.

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]. The simulation results show annual water savings ranging from 126.64 to 633.22 million m<sup>3</sup> 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 m3 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 effect 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.

Future work is also needed to experimentally verify the results of this study in different locations throughout the world. In addition, future work is needed to investigate fouling (and means to prevent it) in different 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 effect of different 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.
