Effects of nanocoatings on the temperature-dependent cell parameters and power generation of photovoltaic panels

Photovoltaic modules are tested at a temperature of 25 °C (at STC), where the module’s nameplate datasheet values are determined. Practically, the average annual surface temperatures in the tropical and temperate zones are considerably higher than the STC temperature (Ehsan et al. 2014). Depending on their installed location, heat generated by rising temperatures can reduce the panel’s output efficiency by 10–25% (Honsberg and Bowden 2019). The peak or maximum power temperature coefficient (%/°C or mV/°C) in the panel’s datasheet indicates how much power the panel will lose when the temperature rises by 1 °C above STC. For a panel constantly exposed to temperatures above 30 °C, the generation efficiency decreases between 1% and 2% due to temperature (Andreev et al. 1997).

The L1280S mono-crystalline silicon modules used in this work have a maximum power temperature coefficient of − 0.45%/°C. Surface meteorological data (NASA 2021) shows that the location has a climatological monthly average of 33.92 °C in maximum temperature and 27.73 °C in average temperature. This implies that the module’s power generation will decrease by − 4% and − 1.23% at maximum and average temperatures, respectively. Since these temperature values are monthly averages for a given month averaged for that month over the 30 years, the actual dip in power generation due to increased temperature is high due to the rapid environmental phenomena.

Effect on transmittance

Transmittance, denoted as \(T\), is the ratio of the light passing through a specimen to the light incident on it (Brydson 1999). Studying its transmittance can determine the optical properties of any given sample. According to the Beer–Lambert law, the final transmittance of the sample depends on the sum of optical depths of its individual attenuating species (Höpe 2014), where the optical depth or optical thickness (τ) is the natural logarithm of the ratio of incident to transmitted radiant power through a material. For \(N\) attenuating species in the material sample, transmittance \(T\) is given by

Hence, every layer on the surface of the panel glass, including specialized coatings, accumulated dust etc., will attenuate the transmission of light through it. Therefore, the optical effects of the coating on the PV panel’s glass cover and, ultimately, its power generation can be studied by transmission characterization.

Optical tests cannot be conducted directly on the PV glass without damaging it as it is hermetically sealed with the module to protect the underlying solar cells from damage (Deb and Bhargava 2022). Standard, optical quality microscope slides made of soda-lime glass (75 mm length × 25  mm height × 1.0 mm thickness) are used to simulate the PV glass surface. Variations in dimensions as per the glass manufacturer are ± 1 mm in size and ± 0.1 mm in thickness. As every layer on the glass surface will attenuate light transmission, all the slides are thoroughly cleaned using a lint-free cloth and Isopropyl Alcohol (IPA). The dimensions, especially thickness, of all slides have been reconfirmed using a calibrated Vernier scale to ensure uniformity in the test samples.

As transmittance can be analyzed for a sample in either solid, liquid, or gaseous forms, the coating solutions' optical properties are also studied in their original liquid state. The transmittance tests on the coating solutions “A”, “B”, and “C” have been conducted using a Shimadzu-make UV-2600 UV–Vis spectrophotometer. It is a single monochromator system without the two-detector integrating sphere (Shimadzu Corporation 2022a) and has a measuring range of 200–700 nm, configured on the UVProbe software. The device has two pre-installed cuvettes for holding the reference and sample liquids. The standard operating procedure for measuring the transmittance of dissolved materials inside the carrier is to use either the carrier solution itself as the reference liquid or other standard reference materials (SRM) (Mavrodineanu 1972). As the exact composition of the nanocoating solutions, especially the carrier liquid, is unknown, distilled water has been used as a reference for all the samples. The transmittance values of the coating solutions are shown in Fig. 2.

Fig. 2figure 2

Transmittance plot of the nanocoating solutions

It can be observed from the figure that sample “C” exhibits the best transmittance values in its original liquid form, whereas sample “A” has comparatively lower transmittance to light. This can be directly correlated with the appearance of these samples in their liquid form—sample “A” has a milky white appearance, sample “B” has a yellowish appearance and sample “C” has a clear, transparent appearance. However, the appearance of these solutions in their liquid form does not correlate to better transmission performance after application on the glass surface.

The transmittance of glass with and without the coatings has been studied using a Jasco-make V-670 UV–Vis–NIR spectrophotometer. Any light that is not absorbed by a glass or reflected at its surface will be transmitted through the glass (Kopp Glass Inc 2022). The V-670 double-beam spectrophotometer utilizes a unique, single monochromator (with automatically exchanging dual gratings) design, covering a wavelength range from 190 to 2000 nm (JASCO Deutschland GmbH 2022). Transmittance values are captured using the Spectra Manager II software at a periodicity of 0.5 nm. Referencing/calibration of the equipment has been carried out using a plain slide without any coating. The slides have been coated with the solutions “A”, “B” and “C”. It is to be noted here that the manufacturer-recommended application procedure using a low volume, medium pressure (LVMP) spray gun could not be employed due to the small dimensions of the glass slides. The transmission characterization tests have been carried out in two phases—one with a single layer of coating on the slide surface and the second with multilayer coating (three layers). Multilayer tests have been conducted to study the optical effects of coating the glass surface with multiple layers and also to crosscheck the coating procedure laid out by the manufacturers. For example, the manufacturer of “A” has declared that multiple layers will not affect the first coat. In contrast, the manufacturer of “C” asked to avoid multiple layers as the subsequent layers will not stick to the original. Each coating layer has been allowed to cure before the application of the next layer. Figure 3a, b shows the transmittance plots for the nanocoating solutions with a single coat layer and multiple layers of coating juxtaposed with an uncoated slide. While the transmittance values were captured for the entire spectrum on the spectrophotometer, the figure shows values from 190 to 1000 nm, covering the ultraviolet, visible and near-infrared regions of the electromagnetic spectrum.

Fig. 3figure 3

Transmittance plots of coated surfaces with single and multiple layers

It can be observed from Fig. 3a that all the coated surfaces show improved transmittance when compared to the uncoated slide. All the test samples (including the uncoated) show transmittance of over 90% around the visible spectrum (around 380–750 nm). Sample “C” exhibits higher transmittance values followed by “B” and “A”, respectively. The values drop drastically to nearly 20% around the near ultraviolet region (around 250–320 nm), corresponding to the spectrum regions of UV-A and UV-B subdivisions as per ISO 21348:2007 (International Organization for Standardization (ISO) 2002). The sudden decreases in the transmission indicate absorption bands (Optics for Devices, SCHOTT North America Inc. 2005). Apart from the drop around this region, all coated glass surfaces exhibit transmittance across the entire radiation spectrum. However, it is observed that the uncoated, clear glass slide does not transmit wavelengths from 190 to around 350 nm and transmits all wavelengths above 350 nm. This behaviour in clear glass has also been recorded in the solar transmittance studies conducted by Shimadzu Corporation (2022b), a leading measurement instrument manufacturer, especially for molecular spectroscopy. Since solar transmittance, an index of the transmission characteristics of sunlight, includes visible to near-infrared light, its value will be slightly lower than that of the visible light transmittance (Shimadzu Corporation 2022b).

Applying multiple layers of coatings on the glass surface decreases the transmittance values marginally, as shown in Fig. 3b. While the single-coated surfaces of all coatings show transmittance values above 90% in the visible spectrum, it drops to 80–90% after multiple layers of coating. After the application of three layers of coating, it is observed that sample “A” shows higher transmittance values than “B” and “C”, respectively. This finding conforms with the application guidelines for the coatings provided by the respective manufacturers and reiterates the importance of correct application. Transmission characterization studies show that applying nanocoatings improves the glass's transmittance values.

Effect on \(}}_\mathbf}\) and \(}}_\mathbf}\)

Huang et al. (2011) have conducted experimental investigations to observe the effect of operating temperatures (between 40 and 80 °C) on \(_}\) at different values of solar radiation (200–1000 W/m2). The investigations show that irrespective of the value of solar radiation, \(_}\) decreases uniformly with rise in cell operating temperature. In contrast, studies have found that \(_}\) of the panels is not affected by dust accumulation (Ndiaye et al. 2013). To cross verify its relationship with dust accumulation, \(_}\) of the four panels—an uncoated panel, and the panels coated with “A”, “B”, and “C” is monitored using Keysight Technologies’ 34972A data logger for 10 days (September 3–12, 2021). The values are captured every 10 s in the data logger. Since the entire data set for the duration comprises nearly 5000 values per channel, plotting all the values results in various fine-scale structures and rapid phenomena due to frequent environmental changes. The data set, hence, needs to be smoothed to create an approximating function that attempts to capture important patterns in the data. In smoothing, the data points are modified so that individual points are reduced, and points that are lower than the adjacent points are increased, leading to a smoother signal. Adjacent-Averaging (AA) smoothing algorithm is applied to the data sets in OriginLab Corporation’s Origin scientific graphing and data analysis program. AA essentially takes the average of a user-specified number of data points around each point in the data and replaces that point with the new average value (OriginLab Corporation 2022). Each smoothed point is the average of the data points within a moving window, which is user-defined based on the original plot’s total number of data points.

It is observed that the \(_}\) of all four panels remained consistent despite a gradual increase in dust accumulation as the number of days of exposure increased, as also noted by Ndiaye et al. (2013) and Paudyal et al. (2017). Figure 4 shows the comparison between \(_}\) of the uncoated panel and the panels coated with samples “A”, “B”, and “C” for 10 days. The data sets for all plots are smoothed using a 50-point AA algorithm. The average recorded \(_}\) of the uncoated panel for the duration is 16.23 V. The maximum recorded voltage is 19.41 V. The average and maximum \(_\) values for “A” are 15.44 V and 19.09 V, respectively. Similarly, the average and maximum recorded \(_}\) for “B” are 16.97 V and 19.46 V, respectively. 16.62 V and 19.46 V are the respective values for “C”. All the maximum recorded open-circuit voltages are observed on the same day for all panels. Panel coated with “C” has reached closest to the L1280S’ nameplate \(_}\) value of 20 V at STC. The average voltage difference between “A” and uncoated panel is observed to be − 0.80 V for the entire period. The difference between “B” and uncoated is 0.15 V and that between “C” and uncoated is 0.39 V. The average recorded atmospheric temperature during this period is 30.78 °C with a peak of 36.13 °C.

Fig. 4figure 4

\(_}\) of the three coated panels with the uncoated panel

Solar irradiance (W/m2) of the location also affects the open-circuit voltage of the panel. Figure 5 shows the recorded \(_}\) of all four panels (coated and uncoated) with irradiance during the day (September 12, 2021). All the data displayed in this work, citing time of day, is plotted from 6 am to 7 pm on all days. It is observed from the figure that the \(_}\) rises and drops rapidly during the early morning and late evening, respectively, with minor variations during the majority of the day in response to changes in irradiance. It is noted that the \(_}\) is mainly independent of irradiance for all the panels. It can be observed from both figures, Figs. 4 and 5, that coatings “B” and “C” have higher open-circuit voltages than the uncoated panel under the same environmental conditions. However, “A” has recorded slightly lower \(_\) values than the other panels.

Fig. 5figure 5

\(_}\) of all panels with irradiance (September 12, 2021)

Equation (1) shows that the short-circuit current (\(_}\)) is a function of solar irradiance. \(_}\) values of all panels are recorded along with the irradiance. Figure 6a–c shows the recorded short-circuit current for all the panels along with irradiance during the day. It is clearly seen from the figure that the coated panels, “\(A\)” and “\(B\)”, have recorded higher \(_}\) values than their corresponding uncoated panel during most of the day. However, “C” has recorded slightly lower \(_}\) values that its corresponding uncoated panel. It can also be confirmed from the figure that \(_}\) is directly proportional to solar irradiance, unlike \(_}\). The \(_}\) values follow the same pattern as irradiance during the day. The average recorded \(_}\) for the day from “A” is 1.59 A against its corresponding uncoated panel’s average of 1.55 A. Similarly, the average \(_}\) from “B” is 1.71 A against 1.67 A from its uncoated panel. The values for “C” and its uncoated pair are 2.03 A and 2.07 A, respectively, which corroborates panel “C” recording slightly lower \(_}\) values.

Fig. 6figure 6

\(_}\) for coated and uncoated panels with irradiance

Effect of nanocoatings on surface temperature

To study the effect of superhydrophobic nanocoatings on panel surface temperatures, the coating samples “A”, “B”, and “C” are applied over the module surface and then exposed to the environment. A set of uncoated and coated panels are installed on the module mounting structure sequentially. Three different panels (but the same L1280S) are used as the uncoated panel against each coated panel. All panels are cleaned thoroughly using acetone solution before coating and again with water before installation on the structure. They are not further cleaned afterward to observe the effect of dust accumulation on solar panel surface temperatures after prolonged environmental exposures. The solar modules' top and bottom surface temperatures are monitored and recorded for 10 days for each set of panels (from June 27 to July 6, 2021 for “A”, from July 17 to 26, 2021 for “B”, and from August 19 to 28, 2021 for “C”). The tests are conducted in the order the coatings are applied to the panel surfaces by their respective manufacturers. The thermocouples are fixed on all panels' top and bottom surfaces (one each). Keysight Technologies’ 34972A LXI Data Acquisition/Switch Unit is configured to capture the temperature data along with voltage and current every 10 s. With a recording duration of over 13 h (6 am to 7 pm) from sunrise to sunset, nearly 5000 values per day are captured for each channel. The plots of top and bottom surface temperatures of all three coated panels against their respective uncoated panel after continuous exposure, smoothed using a 100-point AA algorithm, are shown in Fig. 7a–c. The uncoated panel's top and bottom surface temperatures are higher than that of all three coated panels. It can also be seen that the recorded temperature patterns vary every day depending on the meteorological conditions.

Fig. 7figure 7

Top and bottom surface temperatures of coated and uncoated panels after prolonged exposure

The average top surface temperature for “A” is 48.15 °C, against its corresponding uncoated panel average of 51.63 °C. The average top surface temperature for “B” is 43.49 °C against its corresponding uncoated panel average of 46.67 °C. Similarly, the average top surface temperature for “C” is 44.64 °C, against its corresponding uncoated panel average of 46.90 °C. The lowest recorded top surface temperatures for “A” and uncoated are 27.29 °C and 30.45 °C, respectively. The highest recorded top surface temperatures are 66.93 °C and 73.66 °C, respectively, for the same pair. The lowest recorded top surface temperatures are 28.17 °C and 31.64 °C for “B” and uncoated, respectively. For the same pair, the highest recorded top surface temperatures 65.12 °C and 67.16 °C, respectively. Similarly, the lowest recorded top surface temperatures are 26.17 °C and 31.71 °C for “C” and uncoated, respectively. The highest recorded top surface temperatures 67.55 °C and 70.22 °C, respectively, for the same pair.

The average bottom surface temperature for “A” is 49.56 °C\(,\) against its corresponding uncoated panel average of 49.95 °C. The average bottom surface temperature for “B” is 46.01 °C, against its corresponding uncoated panel average of 46.34 °C. Similarly, the average top surface temperature for “C” is 45.09 °C\(,\) against its corresponding uncoated panel average of 46.89 °C. The lowest recorded bottom surface temperatures for “\(A\)” and uncoated are 26.79 °C and 31.27 °C, respectively. The highest recorded bottom surface temperatures 66.80 °C and 69.31 °C, respectively, for the same pair. The lowest recorded bottom surface temperatures are 32.56 °C and 32.68 °C for “B” and uncoated, respectively. For the same pair, the highest recorded top surface temperatures 64.91 °C and 68.53 °C, respectively. Similarly, the lowest recorded bottom surface temperatures are 30.83 °C and 32.27 °C for “C” and uncoated, respectively. The highest recorded bottom surface temperatures 67.64 °C and 69.80 °C, respectively, for the same pair.

It is observed that the top and bottom surface temperatures (average, minimum and maximum) of the coated panels are lower than that of their corresponding uncoated panels, irrespective of the coating solution used and climatic conditions. This pattern is the same on all observed days. The AA algorithm makes it easier to plot the pattern from a large quantum of data. However, it is hard to discern the accurate representation of individual data blocks once they are smoothed. Figure 8a–c shows the plots of top and bottom surface temperatures of coated panels against their corresponding uncoated panels recorded on a day. Atmospheric temperatures recorded on the same dates for each set are also plotted. It can be seen from the figure that the top surface temperature of the uncoated panel is higher than its bottom surface temperature for most of the day. However, the top surface starts cooling off faster than the bottom later in the evening, which results in the bottom temperature being higher than the top on some occasions. These wide variations in top surface temperatures are also not uniform between the panels. They can be attributed to the top surface’s direct environmental exposure, which results in a quicker response to atmospheric changes. The trend is similar for the top and bottom temperatures for the coated panels, irrespective of the coating. However, it can be clearly observed that the uncoated panel's top and bottom temperatures are higher than the coated panels' top and bottom temperatures in absolute values for most of the day, especially during peak generation. This shows that the coating results in a better temperature performance of the solar panels in real-life conditions.

Fig. 8figure 8

Top and bottom panel surface temperatures for coated and uncoated panels with atmospheric temperature

As shown in Fig. 8, the panel surface temperatures have a nonlinear relationship with atmospheric temperature. While the atmospheric temperature gradually rises as the day progresses, the panel surface temperatures initially increase but start to decrease late afternoon. In the evening, all temperatures start decreasing proportionally. Since the surface temperatures directly result from conductive heat transfer, their response to environmental changes is more pronounced than that of the atmospheric temperature resulting from radiative heat transfer. Though the climatic conditions between the three different periods differ, the temperature patterns exhibited by all the panels are similar. It can be clearly seen from these figures that the surface temperatures also follow the same pattern as solar power generation in temperate climate zones, i.e., they are the lowest during the morning and late evening and reach their peak values around mid-day, which also coincides with theoretical maximum power generation.

Thermal imagery, or a thermogram, creates an image of an object using infrared radiation emitted from the object. Thermography can capture variations in temperature as the amount of radiation emitted by an object increases with temperature. Figure 9a, b shows the thermogram of the panel surfaces under two different conditions on the same day during peak generation hours captured using a Fluke Ti25 Thermal Imager. The panel on the left is coated, and that on the right is uncoated. Figure 9a shows the thermogram of the panels under a clear sky, and Fig. 9b shows the same under the cloud cover. It can be observed from the figures that, within a matter of 3 min, the surface temperatures drop drastically once the clouds move over the panel. This shows that the top surface undergoes instantaneous and wide variations in surface temperatures due to its direct environmental exposure. While it is difficult to discern between the panels in Fig. 9a, it can be observed from Fig. 9b that the coated panel cools off faster than the uncoated panel resulting in slightly lower surface temperatures in those conditions.

Fig. 9figure 9

Thermal images of the solar panels under clear and cloudy conditions

In general, the rate at which heat energy (of flux) is conducted between two bodies is a function of the temperature difference between them and the properties of the interface through which the heat is transferred (Sharaf et al. 2022). Hence, the heat transmitted from the top to the bottom surface is directly proportional to their temperature difference (Yanniotis 2008). Accurately modelling the heat transfer at the module's front and the back surface is challenging (Dupré et al. 2017). The transmission of heat energy from the top to the bottom surface of the panel will raise the temperatures of the solar cells that lie in the pathway. The average temperature difference between top and bottom surfaces (\(\Delta T\)) is observed to be − 1.41 °C in the panel coated with “A” against 1.68 °C in its uncoated pair. The difference is − 2.52 °C in panel coated with “B” against 0.33 °C in the respective uncoated panel. Similarly, the values for “C” and its pair are − 0.45 °C and 0.01 °C, respectively. Considering the varying conditions for each set of tests, the averages of \(\Delta T\) between all coated and uncoated surfaces can be regarded as their representative results. Since all the recorded temperatures in the location are above the STC, these temperature differences (\(\Delta T\)) can be taken as the temperature increase in the power temperature coefficient of the panels, which stands as − 0.45%/°C from the manufacturer’s datasheet. Accordingly, the uncoated panel will show a 0.303% drop in power generation, whereas the coated panels will show a 0.657% increase in generation.

It can be clearly seen that the difference between the top and bottom average surface temperatures are all negative for the coated panels and positive for the uncoated panels. This indicates that the average bottom surface temperatures of the coated panels are higher than their top surface temperatures. As the conduction of heat flux is a function of temperature difference, it is conclusive that the coated surfaces are conductive in nature. The coated surface has conducted most of the heat across the panel depth instead of absorbing it. Since the top surface is colder than the bottom surface, further conduction of heat will not happen, resulting in lower solar cell operating temperatures. The thermal images also corroborate this in Fig. 9, where the coated surface is observed to cool off faster than the uncoated panel. In contrast, the average top surface temperatures of the uncoated panels are higher than their bottom surface temperatures. This means that its surface absorbs more heat from the environment, resulting in higher solar cell operating temperatures. It can be concluded that the nanocoatings, irrespective of their composition, result in better cell operating temperatures for the solar panels.

Effect on voltage, current, and power generation

Solar irradiance, along with the temperature of the location, also affects the power generation (Ehsan et al. 2021). Irradiance and atmospheric temperatures are also monitored on all days, along with the load voltage, load current and power generation of the uncoated and coated panels, “A”, “B”, and “C”. The plots of power generated from the coated and uncoated panels with atmospheric temperature and irradiance against time, captured on a particular day, are shown in Fig. 10a–c. Power generated from the coated and uncoated panel, and the atmospheric temperature is plotted along the primary Y-axis. Irradiance is plotted along the secondary Y-axis.

Fig. 10figure 10

Power generated from coated and uncoated panels with atmospheric temperature and irradiance

Since no 2 days are similar due to varying environmental conditions, the power generation trend differs significantly between the tests. The power generation is affected substantially by the clearness index (CI). CI is defined as the ratio of global solar irradiance measured at ground level and its counterpart estimated at the top of the atmosphere (Ehsan et al. 2014). It can be seen from Fig. 10 that the Y1 and Y2 scales in all three plots are different. The day during comparison of “A” vs uncoated (July 5, 2021) has a smooth trend indicating a clearer day but with lower power generation values. The day during the comparison of “B” vs uncoated (July 25, 2021) has recorded higher power generation values but with many variations in the values, indicating widely varying clearness index. The power generation trend falls midway between both these days for the day during the comparison of “C” vs uncoated (August 26, 2021). It is also evident from Fig. 10 that power generation follows the same pattern as that of solar irradiance during the day. Figure 10 also shows the direct proportionality of power generation with irradiance, wherein the days with higher irradiance have recorded higher instantaneous power generation. However, power has a nonlinear relationship with atmospheric temperature. It increases with atmospheric temperature to a certain extent and then decreases despite rising temperatures during the latter part of the day.

Figure 11a–c shows the plots of power generated from all three coated panels with their respective uncoated panels for a prolonged duration of time. Solar irradiance for the same period is also shown in the figure. All values are averaged using a 50-point AA algorithm. It can be clearly seen that solar irradiance has a direct effect on power generation. The figure shows that the coated panels have a higher instantaneous power generation over their uncoated panels, irrespective of the variations in irradiance and other climatic conditions. However, their trend mimics the variations in irradiance during the day. It is also observed from the figure that the difference in instantaneous power generated between the coated panels and their corresponding uncoated panels' increases as the duration of exposure to the environment. The average difference between the averages of the instantaneous power generated by “A” during the day and that of the uncoated panel is observed to be 0.32 W during the first half of observation and 0.44 W during the second half. Similarly, the average difference between “B” and the uncoated panel is 0.00 W during the first half and 0.52 W during the second half. The corresponding values for “C” and uncoated panel are 0.76 W and 1.36 W, respectively.

Fig. 11figure 11

Power generated from coated and uncoated panels with irradiance after prolonged exposure

Figure 12a–c shows the recorded panel load voltage and current values plotted with the power generation on the same days for all three coated panels against their respective uncoated panel. Power generation and voltage values are plotted along the primary Y-axis, and the current is plotted along the secondary Y-axis. The power, voltage, current, temperature and irradiance scales in all the plots are varied according to the recorded absolute values for each day. The legend for all parameters is kept uniform throughout this work for better representation. It is clear that both the load voltage and current values recorded from the coated panel are higher than those from the uncoated panel during much of the day.

Fig. 12figure 12

Load voltage and current of coated and uncoated panels with power generation

Effectively, the power generation from the coated panel is also observed to be higher than that of the uncoated panel. During the monitoring period, “A” shows a 2.91% improvement in instantaneous power generation over the uncoated panel. Similarly, “B” and “C” have shown nearly 2.43% and 12.99% improvement in the instantaneous power generation, respectively, over their uncoated panel pairs. Considering the varying conditions for each set of tests, the averages of \(\Delta P\) between all coated and uncoated surfaces can be regarded as their representative results. Hence, the nanocoatings show approximately 6.11% improvement in power generation under all environmental conditions, irrespective of their composition. It can also be surmised from Figs. 5, 10, and 12 that the load voltage, the load current (and effectively, power generation), and the short-circuit current (\(_}\)) all follow the same trend as solar irradiance during the day, unlike the open-circuit voltage (\(_}\)), which shows minimal variations to changes in irradiance.

Economic analysis

BHEL, Tiruchirappalli has five grid-interactive solar installations, totalling 12.62 MWp, in various generation capacities (20 kWp—1 no.; 50  kWp—2 nos.; 5 MWp—1 no.; 7.5 MWp—1 no.). The two large-scale, grid-interactive power plants (5 MWp and 7.5 MWp) are used for captive power generation. The 5 MWp plant generated 5,450,796 kWh in 2019 fiscal and 4,481,469 kWh in 2020. The 7.5 MWp plant generated 8,837,700 kWh in 2019 and 5,516,496 kWh in 2020. Both plants generated a cumulative 24,286,461 kWh in 2019 and 2020 combined, which accounts for nearly 31.1% of the factory’s consumption of 78,115,461 kWh in 2 years. Despite a 42% reduction in energy consumption in 2020 over 2019 due to the lockdown imposed by the Government of India in response to the COVID-19 pandemic and the change in the business portfolio, the share of renewable energy in the campus’ annual consumption increased to 34.8% in 2020 (of 28,723,365 kWh) from 28.9% in 2019 (of 49,392,096 kWh). The campus incurred significant energy bill expenditures of INR (Indian Rupees) 292,054,237 in 2019 and INR 177,108,629 in 2020, totalling a massive expenditure of INR 469,162,866 (in actuals). The normalized operating cost of electricity per kWh is the average of the monthly normalized unit cost obtained by dividing the energy bill by the actual metered consumption from power utility and diesel generator (DG), which comes out to be INR 8.89 in 2019 and INR 11.17 in 2020. The factory’s energy bill would have been even higher if not for the two large-scale solar plants. Consuming the 24,286,461 units generated by both plants in 2019 and 2020 from the utility grid would have added nearly INR 220,534,359 (INR 120,453,973 in 2019 and INR 100,080,386 in 2020) to the energy overheads for the organization, which is approximately 47% of the bill in its entirety for those 2 years. These rates are calculated from the monthly solar generation values priced at the monthly normalized operating cost of electricity per unit.

With this generation values constant under the same conditions, the anticipated reduction in power generation due to the power temperature coefficient is − 43,294 kWh in 2019 and − 30,294 kWh in 2020. If all the 19,968 panels of 250 Wp power in the 5 MWp plant and the 25,420 panels of 300 Wp power in the 7.5 MWp plant had been coated with superhydrophobic nanocoating since 2019, the estimated increase in power generation due to the power temperature coefficient is 93,875 kWh in 2019 and 65,687 kWh in 2020. Reduction in the panel operating temperatures due to the application of the superhydrophobic nanocoating leads to the generation of

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