Analysis of Performance Yield Parameters for Selected Polycrystalline Solar Panel Brands in South Africa

Abstract

Electricity access is an essential factor for any nation’s fast-growing economic and technological development. Therefore, to meet the fast-growing world population, the adoption of a mix of energy sources, including renewable energy, is one of the ways to address the paucity supply of energy worldwide. In this paper, the performance yields of five solar photovoltaic (PV) modules, named PV1, PV2, PV3, PV4, and PV5, from different manufacturers were analyzed and compared to their respective cost benefits for profitable customer’s choice. The study on the panels was conducted at the geographical locations of 25.7535° S latitude and 28.2079° E longitude, with an average perimeter of 525.6 m in Pretoria, South Africa. The panels were installed without shading under the same condition of solar irradiation. The power output of each module was collected three times a day for six months. The analysis showed that the power outputs or performances of the respective modules are majorly affected by their surface temperatures as indicated by the values of multiple regression correlation of 92.9%, 96.9%, 99.1%, 97.2%, and 77.5% between the respective modules’ power outputs and temperature. The study also showed a techno-economic evaluation method that helps to economically alleviate the cost of solar PVs and balance the choice of the PV panels according to their short-term performances.

1. Introduction

Energy has been described as an essential factor for the economic and technological development of any part of the world. Among the different energy sources, electrical energy is one of the important types used daily to carry out various activities. The advancement of a country is measured in terms of per capita consumption of electrical energy [1]. However, because of epileptic electricity supply, emission issues, and environmental concerns, it has become necessary to diversify the supply of electrical energy to meet the various power requirements. One of the options for diversification is renewable electrical energy from solar photovoltaic (PV) systems. PV system in the simplest form is very clean and has been described as an electrical power generation system from solar energy, which varies significantly in size and application. It can be built to handle anything from very small loads of a few watts to big utility-scale power plants that can generate tens of megawatts or more.

PV panels are categorized into three, namely, crystalline silicon, amorphous silicon, and other PV panels with thin film technology. Photovoltaic panels made of crystalline silicon are the market’s most established, reliable, and effective. Crystalline panels may also be classified as mono-crystalline or poly-crystalline. The production process and the factors that affect their efficiencies have been described by many researchers [2,3,4]. Therefore, accurate product selection and energy performance projection depend on knowledge and understanding of the PV module’s performance under site-specific operating conditions. Finding a solar module brand with amazing features and high-quality products can be challenging. Degradation assessment is a crucial part of the technique for calculating module energy rating, which is an evaluation of performance based on energy output under actual operating circumstances rather than power output measured in the lab under standard test conditions. As a result, the energy rating is thought to be more indicative of the modules outside performance, and it will be used to classify module performance in numerous typical climatic zones in the future. The present implementation of an ad-hoc standard (IEC 61853), which is now partially published, attests to its growing importance within the PV research community. The causes and mechanisms of deterioration are widely understood spotted soiling that can result in cell cracks, hot spots, bubbles, delamination, discoloration, module breakages, corrosion of the metallic connections, and other problems [5,6].

High operating and maintenance costs from the coal-fired energy source over the years have contributed to the inability to meet the high electricity demand in South Africa (SA), which therefore facilitates high electricity tariffs in the country in recent years. The activities of these coal-fired power plants have also contributed significantly to the nation’s carbon emissions, causing the impairment to the natural endowed environment. Recently, it was reported that the production and utilization of coal in the United States (US) had reduced due to the projected potential worst impact on the environment as other sources of electricity are gaining more ground and becoming affordable [7,8]. These effects have all encouraged the rapid development and increasing of low-cost clean energies from solar and wind sources in SA. On the other hand, the rise in solar PV systems in SA alongside other developing countries in Africa and the rest of the world still causes misperceptions in assessing the quality of the PV modules based on the cost. In order words, quite a large number of users still find it difficult to assess the performances or yields of these PV modules based on their respective costs. Generating electricity from the solar PV system requires a lot of funds and PV modules are not the only components needed for the exercise. Many people’s priority is to waive funds on modules as much as possible to complement the cost of other equipment for the PV system installations. In South Africa, there are different brands of PV manufacturers with different prices, warranties, performances, and yields. Given this, it is necessary to enquire about the class of PV modules, irrespective of the manufacturer, that can proffer optimum yield and performance for electricity generation at affordable cost and satisfaction to customers. This will in turn save funds for other essential components in the solar system installation and reduce the cost of energy to customers.

This paper aims to analyze the performance yield and cost benefits of solar photovoltaic (PV) modules to ensure an informed and profitable choice of solar PV modules. This research focuses on the method of analyzing PV modules and predicting their performance yield and benefits just from their costs within over few years of usage. The specific objectives are to estimate the solar PV yields from different selected PV manufacturers, analyze the performance of the PV modules, carry out cost comparisons, and predict if the cost justifies the quality of the selected solar PV modules. Preliminary studies were carried out in the study area and the PV panels were set up for data collection. The daily power outputs of the panels obtained were plotted against the number of days to study the trend of power output yield and were compared to the respective costs of the panels. Analyses of the weekly power outputs at different times of day (10 a.m., 2 p.m., and 5 p.m.), and the maximum and minimum power outputs were also considered. The result obtained was compared to the costs of the modules to justify their respective performances. The process was repeated for the rest of the months considered in the study. Response surface methodology and statistical regression analysis (SRA) was later applied to determine the analyze the measured parameters and optimize the strength of the relationship between response variable, PV power output, and factor variables via the application of analysis of variance (ANOVA). Thereafter, the main factor affecting the power output of the panels was predicted through the results obtained.

As a unique contribution to knowledge, the work revealed that the power outputs or performances of the respective modules are majorly affected by their surface temperatures rather than their individual costs. This has not been shown by any previous peer-reviewed literature. The work also presented a novel techno-economic evaluation method to economically alleviate the cost of solar PVs and balance the choice of PV panels according to their short-term performances.

The rest of the work is organized as follows: Materials and methods that include the study area, the PV module mounting method, and experimental and data collection analysis are presented in Section 2. Results are discussed in Section 3, while Section 4 contains the conclusion of the work.

2. Materials and Methods

2.1. Study Area

Preliminary studies are carried out in the study area of the data collection. The research and data collection were conducted on the roof of a building at 85 Steve Biko Road, Sunnyside, Pretoria, South Africa. The average annual rainfall of the study area is 464 mm, which is half of the world’s average [9]. The geographical location of the study site are 25.7535° S latitude and 28.2079° E longitude on the earth’s surface. The location of the study area as captured by Google Earth (3D) is shown in Figure 1a. The study environment has an average perimeter of 525.6 m and an enclosed vicinity area of 16,535.88 m² (178,012 ft²) as shown in Figure 1b (yellow line) [10,11]. South Africa receives appreciable solar irradiation for a good part of the year, which makes it a relatively rich region to harvest solar energy with good solar irradiance for energy utilization [12,13].

2.2. Materials

The major components and materials used for this research include solar modules, batteries, watt meters, a digital thermometer, a digital multimeter, cable, mounting hooks, cable logs, and wood.

Table 1. List of major components and materials.

S/N	Component	Specifications	Reason for Selection
1	Digital Multimeter	DT9205A Measurement Range: 0.1 R–200 MR Size: 186 × 86 × 33 in mm Display: 1999 Operating condition: 0–50 °C	To take readings of the resistance in the cables and other electrical conductors and also measure voltage and current.
2	Wattmeter	Rated Current: 150 A	To measure the power output produced by the solar modules.
3	Battery	Brand: Lead-acid Rechargeable battery Rated Capacity: 12 V 20 Ah	To provide a load to the circuit and storage of energy produced by the modules.
4	Cables	Standard: National Electrical Code (NEC) [14,15,16]	To create a circuit for the flow of electrical power.
5	Solar Modules	Type: Silicon-based Polycrystalline Solar PV Module Rated Power: 10 W Rated Voltage: 12 V	To harvest electrical energy (DC voltage, current, power) through a photovoltaic system.
6	Wood	Dimension: 50 × 50 mm Square Shape	To provide support for mounting the solar modules and other equipment.
7	Digital Thermometer	Accuracy: ±0.02 Calibrated Scale: Celsius and Fahrenheit	To measure the ambient temperature and temperature of each module.

shows the list of the materials used and the reasons for their selections.

The performance of solar PV modules or arrays depends heavily on the principles of solar radiation and the effects of temperature. This requires calculating the temperature and solar energy incident on a PV array at any given time, as well as calculating the total solar energy collected based on how well the PV modules are functioning. Three times a day, at 10:00 a.m., 2:00 p.m., and 5:00 p.m., respectively, the data for this study were gathered. This is carried out to maximize the impact of temperature on each module. A 10 W solar module, a wattmeter, and a battery are all included in each setup, and they are all wired together to create a circuit. Both the current and voltage generated by the module when it is exposed to sunlight pass through the wattmeter and are kept in the battery for storage. A digital thermometer was used to measure the ambient temperature and the temperature of each module, and the data was collected at three distinct intervals: at 10 a.m., 2:00 p.m., and 5:00 p.m. Thus, data is retrieved from each system configuration. Performance is assessed by comparing the power (in watts) generated by the five modules, and the effect of temperature on performance is also examined. The site’s ambient temperature as well as the temperature of each module system are read using a digital thermometer, and each temperature measurement is shown on the thermometer’s screen. The digital thermometer type utilized in this study has a very narrow margin of error—roughly plus or minus 0.02 degrees. Compared to the traditional mercury type, it is more accurate. It can display readings in both Celsius and Fahrenheit and makes use of infrared technology, as shown in Figure 2. each reading temperature was recorded at various times of the day.

2.3. Methods

2.3.1. PV Modules Mounting Method

PV modules are mounted on a wooden frame support on top of a 4-storey building’s free space as shown in Figure 3. The wood has a rectangular cross-section with dimensions of 50 mm × 50 mm. These woods were fastened together in a tripodal shape with the nails to form a structure that can support the mounting of the PV modules. The PV modules were tilted at an angle of 35° to receive maximum solar irradiance. Ground-mounted PV systems are simple to install and maintain, but land availability and cost are important concerns in metropolitan locations. The rooftop PV system, on the other hand, does not require any land and prevents direct solar radiation from reaching the roof’s external surface. The optimized rooftop PV has a capacity utilization factor (CUF) of 26.7 percent, whereas the ground-mounted PV has a CUF of 23.8 percent. The rooftop PV system is more economically viable than the ground-mounted PV system for various reasons, which include, but are not limited to, minimum shading, no land requirement, reduced installation cost, and aesthetics [18].

2.3.2. Experimental and Data Collection Analysis

Solar radiation principles and measurement are critical to the performance of solar PV modules or arrays. This includes calculating the amount of solar power incident on a PV array at any given time and estimating the total solar energy received based on the PV modules’ performance. Solar radiation is the basic source of energy that powers a PV system; thus, the modules must be accurately positioned and quantified to make reasonable performance estimates in the design. The data for this study were collected three times a day, at 10:00 a.m., 2:00 p.m., and 5:00 p.m., respectively. This is done so as to ensure that each module obtains peak energy, especially between 9 a.m. and 3 p.m. at a given temperature. Each setup contains a 10 W solar module, a wattmeter, and a battery connected with a cable to form a circuit. When the module gets exposed to sunlight, both the current and voltage produced by the module go through the wattmeter and are stored inside the battery for storage. The wattmeter, at the same time, helps in making use of the variables it receives from the PV modules (voltage and current) in estimating the amount of power equivalence being deposited in the battery through its logic control unit. Therefore, the value of the power by each module was read from the screen of the wattmeter at a given ambient and surface temperature. Comparisons of the power (in watts) produced by the five modules are made to determine their performance, and the impact of cost on performance is investigated. Response surface model and ANOVA were applied to analyze and optimize the measured parameters for the best decision [19]. Each of these systems forms a circuit, and the experimental set-up was produced with Microsoft Visio Professional Software, Version 2016. The picture of the set-up on site is shown in Figure 3, while the experimental setup is shown in Figure 4.

3. Results and Discussion

3.1. Analysis of the Average Power Generated in Watts

The power outputs from the PV modules for the periods of June 2021 to August 2021 and from January 2022 to March 2022 are presented. In this study, the average power produced in watts from each PV module, as obtained from the raw data, of power output under solar irradiation in the morning (10:00 a.m.), afternoon (2:00 p.m.), and evening (5:00 p.m.). The average daily value of each PV module was presented.

3.1.1. Average Daily Power Generated from June 2021 to August 2021

The power outputs from the PV modules for June 2021 are presented in Figure 5. In this study, the average power produced in watts from each PV module was obtained from the raw data of power output under solar irradiation in the morning (10:00 a.m.), afternoon (2:00 p.m.), and evening (5:00 p.m.).

The crests and troughs represent the maximum and minimum power outputs at any point of the plot. The data inspections for the month of June show the crests and troughs of the PV modules, which are directly superimposed above one another. The maximum and minimum outputs of the modules occurred at different days in the months considered. The data inspections from the chart revealed the maximum peak outputs of 7.17 W (28 June), 5.75 W (28 June), 4.42 W (8 June), 7.69 W (15 June), 5.19 W (17 June) and minimum peak outputs of 2.61 W (13 June), 2.61 W (19 June), 2.42 W (23 June), 4.08 W (13 June), and 2.03 W (3 June) for the PV1, PV2, PV3, PV4, and PV5, respectively.

The power outputs plot for July 2021 is presented in Figure 6. The data inspections for the month of July also show the maximum and minimum outputs on different days of the month. A check of the graph data shows that the maximum peak power of 5.17 W (28 July), 4.69 W (4 July), 3.25 W (4 July), 5.69 W (15 July), 3.33 W (4 July) and minimum peak power of 1.77 W (13 July), 1.40 W (19 July), 0.92 W (24 July), 2.78 W (14 July) and 0.50 W (24 July) for PV1, PV2, PV3, PV4 and PV5.

The inspection characteristics for the month of August 2021 (Figure 7) showed the maximum outputs of 7.04 W (28 August), 6.56 W (4 August), 5.12 W (4 August), 7.56 W (15 August), 5.20 W (4 August) and minimum peak power of 3.64 W (13 August), 3.27 W (19 August), 2.79 W (24 August), 4.65 W (14 August) and 2.37 W (24 August) for PV1, PV2, PV3, PV4 and PV5.

3.1.2. Average Daily Power Generated from January 2022 to March 2022

The power outputs from the PV modules for January 2022 are presented in Figure 8 for the average power produced in watts from each PV module under the same solar irradiation of the morning, afternoon, and evening. The data inspections for the month of January show the crests and troughs of the PV modules whose maximum and minimum power outputs took place at various days of the month. Checking the chart data, the maximum peak powers are 8.60 W (1 January), 6.90 W (28 January), 5.30 W (8 January), 9.23 W (15 January), 6.23 W (17 January) and identified the minimum peaks of 3.13 W (13 January), 3.13 W (19 January), 2.90 W (23 January), 4.90 W (13 January) and 2.43 W (3 January) for PV1, PV2, PV3, PV4 and PV5, respectively.

The inspections for the month of February, as shown in Figure 9, showed the maximum peak powers of 7.60 W (19 February), 5.90 W (19 February), 4.30 W (27 February), 8.22 W (6 February), 5.23 W (8 February) and the minimum peaks of 2.13 W (4 February), 2.13 W (10 February), 1.90 W (14 February), 3.90 W (4 February) and 1.43 W (22 February) for PV1, PV2, PV3, PV4 and PV5, respectively.

The analysis of the data for the month of March shows the crests and troughs of the PV modules which represent the maximum power outputs of 6.67 W, 5.40 W, 4.10 W, 7.70 W, 2.97 W; all occurring on March 4 and the minimum peaks of 2.43 W (9 March), 2.23 W (9 March), 1.13 W (9 March), 3.70 W (1 March) and 1.17 W (9 March) for PV1, PV2, PV3, PV4 and PV5, respectively. The module’s performances in the month of March are shown in Figure 10.

The costs of the modules as shown in Figure 11 are R170, R260, R141, R295, and R150 for PV1, PV2, PV3, PV4, and PV5, respectively. The order of cost magnitude of the modules is PV4, PV2, PV1, PV5, and PV3. PV4 is the costliest module among the modules for this study and it shows the highest power outputs at maximum and minimum power output conditions. However, other modules do not follow the trend, as PV2 is costlier than PV1, PV3, and PV5 by approximately 53%, 83.4%, and 73.3%, respectively.

Figure 12 and Figure 13 show the average maximum and minimum power outputs of the PV panels, respectively. Considering the analysis over all the months of data inspection, PV1 has an average value between 25–30% more power output performances than PV2 during the maximum peak conditions and shows no significant difference during the minimum power output conditions. PV2 on average has around 28–30% and 8–11% more power output than PV3 and PV5, respectively, during maximum peak conditions, and 27–29% and 7–9% during minimum conditions.

The PV modules generate electricity throughout the day, but the power generation is maximum only when the sun shines directly on them, which depends on the angle of rays that hit the modules. The analysis showed that peak power occurs at 2 p.m. when the sun rays are at right angles or perpendicular to the modules, and when the rays deviate from the perpendicular, solar energy gets reflected. The highest solar generation during daytime is usually from 11 a.m. to 4 p.m. [20,21]. It can also be inferred from the charts that all the PV modules attained their highest power outputs both in maximum and minimum conditions in January and lowest in the month of July. Watt-Peak (WP) analysis from this study allows for a power comparison between the outputs that PV modules from different manufacturers. The higher WP for the same surface area, the more efficient the module is. The WP is also used to calculate the size of a PV facility according to the desired amount of energy obtained, considering sunlight conditions. A different output is produced by solar modules depending on the PV system’s region and its sunlight conditions [22]. The factors that influence the power outputs of the modules go beyond the cost of the module; rather, the tilt, orientation, latitude, climate, and temperature can have major impacts on a solar system’s performance [23,24].

To inquire if any further level of relationship can be established from the different method, response surface methodology (RSM) and contour plots (CP) from the Design Expert Software (Version 11) were used to optimize the PV panel parameters. According to the literature, RSM is a powerful tool that has an edge and many merits when matched with other statistical and analyzing tools. It stands out when handling a small number of experiments and optimizes the process parameters in an effective way; it can also be used to check or generate the relationship among useful variables in 3D form [25,26,27,28]. Figure 14, Figure 15 and Figure 16 show the Watt-Peak analyses at the maximum and minimum conditions against the average cost (AC) and average power (AP) dissipated by the PV panels over the months of study using both RSM and CP. In the first case, both AC, which identifies the uniqueness of the brands considered, and maximum Watt-Peak (Max WP) were regressed with AP generated. The ANOVA analysis showed that the model between the PV cost, Max WP, and AP was not significant having indicated the p-Value of 0.0556 (since p > 0.05) and p-Value of 0.2935 and 0.0753 for AC and Max WP, respectively. Figure 14a,b shows the surface and contour plots, respectively.

Figure 14a represents the surface plots of AC and Max WP against AP of the PV panels and Figure 14b is the contour plots of AC and Max WP against AP of the PV panels. Analysis from Figure 14a,b shows that even though the AP of most of the panels increases with both Max WP and AC, the trend was different for PV1 (R170), which is less costly than PV2 (R260) but has approximately 24.64% and 14.06% more Max WP and AP, respectively, than PV2 under same condition.

Figure 15a shows the surface plots of AC and Min WP against AP of the PV panels and Figure 15b shows the contour plots of AC and Min WP against AP of the PV panels. They are the second part of the analysis, where the AC and minimum watt peak (Min WP) were regressed with AP. In this case, the p-Values of the model, Min WP, and AC were 0.0256, 0.0339, and 0.9278, respectively. This shows again that the AC of the panel is not significant in the model optimization, having high p-Value of 0.927, which is grossly above the statistical benchmark of 0.05. Information from the Figures revealed that PV3 has 84% and 6.75% Min WP and AP than PV5 whose costs are R141 and R150, respectively. This shows that PV3 could perform better during low sunshine conditions despite its lesser cost than PV5. A similar trend was observed from PV1, which has approximately 26.43% and 14.06% Min WP and AP than PV2 whose costs are R170 and R 260, respectively.

3.2. Effects of Temperature on the Power Output

To determine how the temperatures, or either of the temperatures, affect the power output of each module, the statistical regression analysis (SRA) was performed on the average atmospheric temperature, the temperatures of the modules, and the power produced by each module under the same conditions each day. The results are shown in

Table 2. Statistical regression summary of the data collected.

S/N	Regression Summary Parameters	PV1	PV2	PV3	PV4	PV5
1	Multiple R	0.920	0.969	0.991	0.972	0.775
2	R Squared (R2)	0.846	0.939	0.981	0.946	0.600
3	Adjusted R Squared	0.802	0.921	0.976	0.930	0.486
4	Observations	10	10	10	10	10

,

Table 3. ANOVA for the sum of squares (SS).

	df	PV1	PV2	PV3	PV4	PV5
Regression	2	4.570	13.322	29.167	11.885	2.465
Residual	7	0.831	0.869	0.556	0.683	1.641
Total	9	5.402	14.191	29.723	12.568	4.106

and

Table 4. ANOVA for the mean of squares (MS), F-statistic values, and p values.

	PV1	PV2	PV3	PV4	PV5
Regression	2.285	6.661	14.584	5.94249	1.23269
Residual	0.119	0.124	0.079	0.09754	0.23444
PV Module	F-statistic Value	Significance for F (p Value)	Test if p $\le$ 0.05
PV1	19.240	0.001430473	Significant
PV2	53.680	5.67382 × 105	Significant
PV3	183.666	8.94218 × 107	Significant
PV4	60.924	3.73738 × 105	Significant
PV5	5.258	0.040349409	Significant

.

Table 2 shows the Statistical Regression Summary of the influence or effects of the atmospheric and module surface temperatures on the power produced by the PV Modules. The single summary multiple regression (Multiple R) numbers obtained in the table shows the values for each PV module. Multiple R is a number that shows how well the independent variables are related to the dependent variable; in other words, it is a single summary number that shows the correlation and strength of the relationship between two or more variables. The more it is close to +1 or −1, the stronger the relationship between the variables [29]. The Multiple R of the values 0.920, 0.969, 0.991, 0.972, and 0.775 were obtained for PV1, PV2, PV3, PV4, and PV5, respectively, which shows that the considered temperature has a greater relationship with the power produced by the PV module. The Table also shows the summary data for the coefficient of determination (R²) of each PV module. R² is the summary number that indicates how well the level of variation in one variable is directly related to the variation in another variable [29,30,31,32]. In this work, the R² of values 0.846, 0.939, 0.981, 0.946, and 0.600 are obtained for PV1, PV2, PV3, PV4, and PV5, respectively, which shows that the approximate values of 85%, 94%, 98%, 95% and 60% of the variation in PV power output (Watts) of the respective module brands are explained by the atmospheric temperature and respective module surface temperatures [30,31].

Table 3 and Table 4 show the results of the analysis of variance (ANOVA). ANOVA is a tool that provides more insight into the breakdown of the variation of the dependent variable (power output) to the explained and unexplained portions. Table 3 shows ANOVA for the sum of squares (SS). The sum of squares (SS) regression is the variation explained by the regression line while the sum of squares (SS) residual is the variation of the dependent variable not explained by the regression line [31]. Table 4 shows the values of the ANOVA for the mean of squares (MS), F-statistic, and p-Values. The F-statistic value is the ratio of the mean square regression to the mean square residual at the degrees of freedom (df) of regression and residuals, respectively [29,30,31,32,33]. The p-Value associated with each PV’s F-statistics value in Table 4 is the probability calculated F-statistics value is greater than the critical value. If this p-Value < 0.05 at a 95% confidence interval, the prediction is significant, and at least one of the independent variables is not equal to zero; this shows that there is a relationship between the dependent variable (power output) and at least one of the independent variables (atmospheric and module surface temperatures [28]. However, if the p-Value is greater than 0.05, then it shows that there is no relationship between the variables and none of the independent variables influences the dependent variable [30,31]. The p-Values obtained for f-statistics in this study are $1.43\times {10}^{-3}$, $5.67\times {10}^{-5}$, $8.94\times {10}^{-7}$, $3.74\times {10}^{-5}$, and $4.03\times {10}^{-2}$ PV1, PV2, PV3, PV4, and PV5 modules, respectively. This shows that atmospheric and module surface temperatures or at least one of the temperatures are significant to the power output performance of the PV module [33,34].

Table 5. Fitness of the regression coefficients for the temperatures considered for each PV module.

			Coefficients	Standard Error	t-Stat	p-Value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
1	PV1	Intercept	18.566	2.727	6.808	0.00025	12.118	25.014	12.118	25.014
		Atm Tempt	−0.067	0.071	−0.939	0.37904	−0.235	0.101	−0.235	0.101
		PV1 Tempt	−0.364	0.059	−6.132	0.00048	−0.505	−0.224	−0.505	−0.224
2	PV2	Intercept	14.688	2.334	6.292	0.00041	9.168	20.207	9.168	20.207
		Atm Tempt	−0.010	0.073	−0.136	0.89597	−0.182	0.162	−0.182	0.162
		PV2 Tempt	−0.249	0.024	−10.361	1.7 × 105	−0.306	−0.192	−0.306	−0.192
3	PV3	Intercept	19.130	1.854	10.316	1.7 × 105	14.745	23.514	14.745	23.514
		Atm Tempt	−0.003	0.058	−0.054	0.95835	−0.141	0.134	−0.141	0.134
		PV3 Tempt	−0.349	0.018	−19.166	2.6 × 107	−0.392	−0.306	−0.392	−0.306
4	PV4	Intercept	17.093	2.079	8.220	7.7 × 105	12.176	22.011	12.176	22.011
		Atm Tempt	−0.045	0.064	−0.693	0.51058	−0.197	0.108	−0.197	0.108
		PV4 Tempt	−0.241	0.022	−11.017	1.1 × 105	−0.293	−0.189	−0.293	−0.189
5	PV5	Intercept	15.253	4.513	3.380	0.01177	4.580	25.925	4.580	25.925
		Atm Tempt	0.009	0.103	0.090	0.93109	−0.233	0.252	−0.233	0.252
		PV5 Tempt	−0.457	0.144	−3.176	0.01559	−0.797	−0.117	−0.797	−0.117

shows the analysis of the regression coefficients of the two temperatures considered for each PV module. This analysis provides more of a third level of test or information on which of the two independent variables is significant in our analysis. The value of the p-Value associated with each coefficient indicates the probability that its calculated t-statistics is greater than its critical value. In other words, the coefficient is significant if p-Value < 0.05 at a 95% confidence level [29,30,31,32,33,34,35]. The p-Value of each coefficient in PV module analysis is presented in Table 5. A close inspection of the table shows that the surface temperature of each PV module is significant on the respective PV module power output; this is because in each case, the p-Value < 0.05. In addition, the atmospheric temperature is not significant to the power output. This shows that the temperature (from the solar system) that builds upon the surface of the module has a greater effect on the power output performance than the temperature of the surroundings. One of the key factors affecting the amount of power that a PV system produces is temperature. The more the surface gets heated up above the optimal temperature the less power is produced. Solar cells are made from semiconductor materials such as crystalline silicon. These semiconductors are sensitive to temperature change. A decrease in the open-circuit voltage of solar cells results in less power being generated, i.e., the more the surface of the PV module is heated above the ideal temperature, the less power is generated [36]. Figure 16, therefore, presents the results of the statistical regression analysis (SRA) between the average module’s temperature and the power produced by each module under the same condition per day.

4. Conclusions

This research carried out the analysis of the performance yield of same-capacity five solar photovoltaic (PV) modules of different costs. Evaluations of the PV modules were carried out under the same conditions from June 2021 to August 2021 and January 2022 to March 2022, respectively, and the results obtained were evaluated and analyzed. The results showed that, for the six months, the average power output produced by PV1, PV2, PV3, PV4, and PV5, respectively, are 4.96, 4.30, 3.22, 5.97, and 2.98 W for the given period of months. The analysis showed that, even though PV4 was most the expensive panel and showed highest power outputs at maximum and minimum power output conditions, the RSM and ANOVA showed that within a few years in service, the costs of the PV panels did not have much effect on the performances in terms of outputs at various tested conditions. It was discovered as other modules do not show a similar trend. PV2 was found to be costlier than PV1, PV3, and PV5 by approximately 53%, 83.4%, and 73.3%, respectively, but PV1 has an average of around 34% of power output performance more than PV2 during the maximum Watt-Peak conditions (Max WP) and 27% during the minimum power output conditions. PV2 on average has around 28–30% and 8–11% more power output than PV3 and PV5, respectively, during maximum peak conditions and 27–29% and 7–9% during minimum conditions. The ANOVA analysis to study the effect of temperature showed Multiple R values of 0.920, 0.969, 0.991, 0.972, and 0.775, R2 values of 85%, 94%, 98%, 95% and 60%, and the p-Values obtained are $1.43\times {10}^{-3}$, $5.67\times {10}^{-5}$, $8.94\times {10}^{-7}$, $3.74\times {10}^{-5}$, and $4.03\times {10}^{-2}$ PV 1, PV 2, PV 3, PV 4, and PV 5 modules, respectively. Therefore, from the study conducted, the surface temperatures of the modules have a more direct influence on the power output performance of the modules than the costs of the modules. Environmental factors are another aspect that can be implicated in the fluctuating power production, as dirt and dust build up on a PV module’s surface, they might obstruct some irradiances and lower power production [37]. The numerical value of each cost is a discrete variable and fixed throughout the investigation/time. It could be assigned by the respective manufacturers due to various reasons which all vary from one region to another, while the temperature is a continuous parameter measured throughout the experiment and can take on any value in the range of the manufacturer’s specifications. Therefore, the cost of complicated manufacturing processes, taxes, strict economic activities, exchange rates, and technologies that vary from one country or region to another could be the reason why some modules are slightly costlier than others [38,39,40].