5.1. Assessment of Solar Resources
In addition to the on-site solar monitoring system, solar radiation data from the Southern Africa University Radiometric Network (SAURAN) was considered. SAURAN is an inter-university initiative that involves installing and operating ground-based solar weather stations in different regions in Southern Africa. Solar radiation parameters monitored at the stations are GHI, DNI, and DHI [
45]. A SAURAN station in Alice, which was less than 5 km from the on-site solar monitoring system, was used in this study. SAURAN data were applied in the study to provide comparative verification of the on-site measured data. The on-site measured and SAURAN GHI, DNI and DHI data and resultant monthly irradiation of Alice over a year are presented in
Figure 9.
A total of 17,520 data entries were obtained from both stations over a year with 30 min logging intervals. From the on-site station, 0.86%, amounting to 150 data entries, were missing for all parameters. This amount does not include a system malfunction, as shown in
Figure 7, which impeded the SGD from tracking the sun, resulting in irregular DNI and DHI data obtained in January. The total amount of lost data increased to 1628, i.e., 9.3% of the entire data collected, while the SAURAN data suffered from only two missing data entries, i.e., less than 1%. A statistical description of the on-site measurement is presented in
Table 5.
The Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) statistics tools were used to compare and verify the on-site measurements. Both tools are expressed as
and
In the context of this study, on-site measurements were considered as predicted variables (
), while SAURAN measurements represent the actual values (
). The number of data entries,
N, was 17,520 (
N). As shown in
Table 4, a fairly low RMSE and MAE were obtained between the two measurements for all parameters, considering that GHI, DNI, and DHI were as high as 1317, 1047 and 633.5 W/m
2, respectively. However, the RMSE and MAE for DNI were approximately twice those of GHI and DHI. This resulted from the high level of accuracy and sensitivity of the DNI observations. The horizontal balancing and stability of the sun tracker have an immense impact on the DNI compared to the other parameters. Further, seasonal variation was more evident in GHI compared to DNI and DHI. This can be attributed to the method of observation given in
Section 1. As a result, the range was higher for GHI.
The average total GHI in the winter season was 103.71 kWh/m
2, while in the summer season it was 167.24 kWh/m
2, where June to August was considered the winter season and September to May the summer season [
46]. SolarGIS data was found to be closer to the values in
Table 5 than the deduced values from
Figure 9, with a difference of 0.14, 0.42 and 0.13 kWh/m
2 for GHI, DNI and DHI, respectively. Like the mean daily irradiation in
Table 5, SolarGIS daily irradiation was calculated from annual forecast irradiation without considering seasonal variation and periodic cloudy covers. Thus, the daily total GHI from
Figure 9 was computed for the winter and summer seasons and grouped into 0.99 kWh/m
2 width classes to distinguish between clear and cloudy sky days. GHI was selected as the determinant parameter, since it is related to DNI and DHI.
Figure 10 and
Figure 11 show the respective summer and winter average days GHI, DNI, and DHI in the various classes.
As shown in
Figure 10, the total daily GHI ranged from 0.37 to 9 kWh/m
2. Based on the daily irradiance distribution in each class, days with peak irradiance <500 W/m
2, i.e., approximately half of the solar constant (1367 W/m
2) value, were considered cloudy sky days. However, clear sky days were characterised by maximum irradiance ≥500 W/m
2. Therefore, classes with a total daily GHI between 0 and 2.99 kWh/m
2 indicated cloudy skies, while 3 to 9.99 kWh/m
2 indicated clear sky days. The GHI, DNI, and DHI distribution pattern in each class given in
Figure 10 supports the above assumptions and classification, as the GHI and DHI were approximately equal on cloudy sky days with a relatively lower DNI. A reverse scenario was observed on clear sky days: as the DHI decreased, GHI and DNI increased. These findings align with the solar radiation components theory [
6], as explained in
Section 1. Also, as presented in
Table 6, the values of the parameters justify the classification of both days.
In
Figure 10, the bars represent the number of days on which a particular class occurred in the year. For example, the total daily GHI class of 0–0.99 kWh/m
2 occurred twice, in September and October. This represents only 0.7% of the entire days of the summer season. The average GHI, DNI, DHI distribution on both days constitute the respective solar irradiance profiles given in the class. Similarly, the class with the highest total daily GHI of 9–9.99 kWh/m
2 occurred 14 days in the season, with 50% of the days occurring in January. Classes 4–4.99 and 6–6.99 kWh/m
2 were the most dominant, with each class representing 15% of the total summer days. Moreover, class 4–4.99 kWh/m
2 was mostly observed in April, making up half of the days in the month, while 6–6.99 kWh/m
2 was experienced on 12 days in September.
The winter season profiles presented in
Figure 11 reveal very similar attributes to the summer season profiles but a shorter total daily GHI range of 0.39 to 5 kWh/m
2. Similarly, days with total daily GHI between 0–2.99 kWh/m
2 were considered cloudy sky days, as their peak irradiance was below 500 W/m
2, while total daily GHI in clear sky days ranged from 3 to 5.99 kWh/m
2. In the winter season, class 3–3.99 kWh/m
2 was by far the most common, representing 57% of the entire number of days in the season. This was followed by class 2–2.99 kWh/m
2, which only occurred on 14 days in the season, i.e., approximately 15%. The maximum daily total GHI class of 5–5.99 kWh/m
2 occurred on five days in August only, while class 0–0.99 kWh/m
2 was observed a day in each of the three winter months. A summary of the winter season solar radiation on cloudy and clear sky days is given in
Table 7.
Comparing
Table 6 and
Table 7 as well as
Figure 10 and
Figure 11, DNI was higher than GHI, specifically, on clear sky days. This can be attributed to the pyranometer orientation and pyrheliometer operation (see
Section 4.2) concerning the daily seasonal movement of the sun in the sky. At midday in the southern hemisphere, the sun is low on the horizon in the winter season and high in the sky during summer. Since the pyrheliometer is constantly pointed towards the sun disc, the seasonal daily transverse of the sun in the sky has a minimum impact on the observed DNI. This was not the case for the GHI, which was monitored by a horizontally stationed pyranometer on a plane. The pyranometer receives less irradiance in the winter due to increased air mass (AM) as the sun angle reduces [
47]. Additionally, the mean DNI in the winter season was found to be higher than that of summer. According to Ziuku et al. [
48], similar findings indicated that the seasonal DNI difference could be attributed to the cold, dry winter clear sky conditions and the cloudy, rainy summer season, which are typically experienced in Southern Africa.
Figure 10 and
Figure 11, as well as
Table 6 and
Table 7, do not provide details of the frequencies of occurrence for DNI and DHI. Thus,
Figure 12 presents monthly bar charts of the daily total GHI, DNI, and DHI regarding their frequency of occurrence.
In
Figure 12, the January chart presents the total daily GHI only due to system malfunction, as indicated earlier. Thus, between February and December, the maximum daily DNI observed was 12 kWh/m
2, occurring on one day only in December. This was followed by 11 kWh/m
2 DNI, observed on ten days between February and December, while all days with 11 kWh/m
2 total daily DNI occurred in the summer season, with November having the most. The maximum daily total DNI observed during the winter was 8 kWh/m
2, occurring on 11 days in August. In both seasons, total daily DNI was as low as 0 kWh/m
2, with March (summer) having the most occurrences, i.e., 12 days.
The findings in
Figure 12 are comparable with those of a similar study conducted in the Northern Cape of South Africa, which is among one of the locations in the world with the highest amount of solar resources [
49,
50]. According to GeoModel (currently SolarGIS) [
49], Upington’s total daily GHI and DNI in the Northern Cape of South Africa also ranged from 0–9 kWh/m
2 and 0–12 kWh/m
2, respectively. However, approximately 7–7.99 kWh/m
2 total daily GHI was the most common in the summer season, as well as a total daily DNI of 8–8.99 kWh/m
2. In the winter season, daily 6–6.99 kWh/m
2 and 7–7.99 kWh/m
2 were observed to be the most common. The relatively large number of clear sky days in the Northern cape compared to other regions in the country made the province the solar park of the nation.
As indicated earlier, more than 50% of the country’s operating solar power plants (Solar PV and CSP) are located in the northern cape. According to Hermann et al. [
51], CSP plants can operate at an efficiency of 12% under an average annual DNI of 1800 kWh/m
2 and up to 16% under 4000 kWh/m
2/year, depending on the design. Raboaca et al. [
52] indicated that the average annual efficiency of a CSP plant could be up to 15% using a parabolic trough, 8–11% using a linear fresnel reflector, 17–35% using a solar trough and 25–30% using the parabolic dish. Based on the solar resources indicator in
Table 5,
Table 6 and
Table 7, deployment of CSP plants in Alice with optimum design could deliver up to 12% efficiency. Furthermore, a comparison of the solar resources in Alice with those in countries where solar power generation is practised on a large (utility) or small scale was conducted, as presented in
Table 8.
Satellite-based (GSA and SolarGIS) data were used in the comparison of solar resources presented in
Table 8. The difference between the on-site (
Table 5) and satellite-based GHI, DNI and DHI were respectively 50, 143 and 49 kWh/m
2. Satellite-based data were adopted to ensure an unbiased comparison. The difference between the average annual solar irradiation in other regions and that of Alice was used to establish the comparison. Hence, a negative value indicates that the annual solar irradiation of Alice is higher than that of the specified region, and vice versa. Among the 19 locations considered in the comparison, only seven experienced higher GHI and DNI than Alice, i.e., Fuentes de Andalucia in Spain, Calama, the Atacama Desert in Chile, Arizona (both locations) in the US, Langkzi, Zhongba and Gongha in China and Ouarzazate in Morocco. The average annual GHI for regions such as Meuro in Germany, Kimberly in Canada and Gangwon in South Korea were less than that of Alice by 679, 422, and 311 kWh/m
2, respectively. A minimum of 85 kWp solar PV plant is operational in all three regions, with Germany having the maximum installed solar PV plant of 166 MW. Also, the average annual DNI in Delingha, China, with a 50 MW tower CSP plant, is less than 24 kWh/m
2.
5.2. Performance Analysis of a Solar PV System in Alice
The performance of the solar PV system relative to the weather conditions in Alice is covered in this section. During this research, the house was occupied by a member of the university staff and his daughter. Between 08h00 and 15h00 from Monday to Friday (weekdays), the occupants were observed to be out for their daily activities. On Saturday and Sunday (weekends), the house was unoccupied.
Two months of data, including a typical summer (March) and winter months (August), were considered in analysing the solar PV system performance. The on-site measured global horizontal irradiance (GHI), solar PV power generation, and the house load demand in the two months covered, are presented in
Figure 13.
In
Figure 13, the period when the batteries were used to power the house load (discharge) is indicated with −ve Amps, while +ve Amps implies that the batteries were charging. Also, the short regular peaks represent low-demand periods (LDP). During these periods, only the refrigerator and a few lights were operational. On the other hand, the irregular upward peaks resulted from the use of a pressing iron, electric stove, microwave oven, electric kettle or other high energy consuming appliance. These periods are classified as high-demand periods (HDP) in the analysis and discussion of the results hereafter.
Table 9 contains a summary of the solar PV generation amounts in the summer and winter months, as well as the battery charge/discharge rate and house demand during both periods mentioned above.
Furthermore, the summer and winter daily solar irradiation, the house cumulative energy consumption and solar PV energy were deduced and are presented in
Figure 14a,b. In
Figure 14, the full-blue bars represent HDP, while LDP is represented with white grid bars. In
Figure 4a, HDP showed a daily average of 8.15 kWh energy consumption, amounting to a total of 114.05 kWh. In the same period, the generated solar PV energy was 245.88 kWh, which is equivalent to a daily average of 17.56 kWh. The generated solar PV energy was found to be 50% more than the house’s total energy consumption. The house energy consumption decreased by 38.93 kWh. Finally, solar PV energy generation decreased by 8.47 kWh in LDP.
As indicated in Equation (7), CUF is expressed in the number of hours per year, 8760, i.e., 365 days multiplied by 24 h. Since daily CUF was considered in the study due to data availability, 24 h was used to multiply the installed peak power as given in Equation (7). The average summer month CUF was 7%. A maximum CUF of 13% was observed on 1st of March, which was a HDP, while 15th of March, a LDP, was found to have the lowest CUF, i.e., 4%. However, the 8th and 26th of March were not considered in the above CUF because the solar PV system was not operating fully on those days.
A 7% average CUF was also obtained in the winter months. In the same period, 14% CUF on the 20th of August was the highest value obtained; this day was categorised as HDP, while for LDP, 25th of August had the lowest CUP, i.e., 3%. The total global horizontal irradiation in the winter months was 130.93 kWh/m
2, equivalent to a daily average of 4.22 kWh/m
2. The resultant generated solar PV energy was 246.29 kWh, equivalent to 13.9 kWh/day. However, only 159.80 kWh energy was consumed during HDP and 50% less during LDP in the winter month. Equations (1) to (6) were employed to further evaluate the performance of the solar PV system, and the findings are presented in
Figure 15 and
Figure 16.
A rated peak power of 3.8 kWp was used to deduce the final yield, which amounted to an average of 1.70 kWh/kWp/day in the summer months. The obtained final yield only covered days on which the solar PV system was fully operational. The house energy consumption pattern contributed to the low final yield; this is supported by the findings of Seme et al. [
16]. The inverter AC energy output, which is equivalent to the house energy consumption, was substituted into Equation (4) to compute the solar PV system PR
AC and was found to vary from 19 to 85% in the summer months.
As shown in
Figure 14 and
Figure 16, the lowest total global horizontal irradiation and maximum PR
AC were observed on 25 March (excluding the 10 and 26 March). Theoretically, the PR tended to increase with a decrease in the global horizontal irradiation due to its inverse relationship with the module temperature [
69], as demonstrated in
Figure 15 and
Figure 16. This is more evident in the PR
DC plot, as a dip in the ambient air and module temperatures was observed on days such as the 8th, 10th, 14th, 20th, 21st, and 31st of March. On these days, the average PR
DC was 95%, while the average ambient air and module temperatures were 18.3 °C and 22.2 °C, respectively. The relatively high PR
DC, as well as the inverse relationship between the PR and temperature obtained in this study, agree with the findings of Romero-Fiances et al. [
20]. The authors [
20] highlighted that PR
DC overestimates solar PV system performance due to a lack of inverter loss, spectral effects and under-rated STC peak power. Regarding efficiencies, the average PV module efficiency was 12%, i.e., 4% lesser than the rated value. An average of 44% efficiency was obtained for the inverter; this low efficiency was also attributed to the occupants’ energy usage pattern. As alluded to earlier, minimum loads were utilised in the house during typical solar PV system generation peak periods, i.e., between 9h00 and 15h00, since the occupants were out for their daily activities. As a result, the inverter dissipated a large amount of the generated PV DC energy while the MPPT operated in float mode. This also affected the PR values of the system.
Similarly, an average final yield of 1.70 kWh/kWp/day was observed in the winter months, with a maximum of 3.36 kWh/kWp on 28 August. However, the PRAC for the winter months was found to be marginally higher, ranging from 15% to 87%. This finding agrees with Marion et al. [
18], who indicated that the winter season tends to have a higher PR than the summer season due to lower solar radiation and cooler ambient air temperature, reducing the module operating temperature. The measured module temperature was found to support the argument of Marion et al. [
18], as the average temperature in the winter month drops by 8.9 °C. In the PR
DC evaluation, slightly contradictory findings were observed. Although the maximum PR
DC of 120%, which could be overestimated, as highlighted earlier, was observed in the winter months, the summer month average PR
DC was 5% higher. This finding can be attributed to the influence of solar radiation on the PR
DC, which was 20 kWh/m
2 higher in the summer months. Furthermore, an average PV module efficiency of 12% was also obtained in the winter months, while the inverter efficiency was found to be between 21% and 77% during that time.
In addition to the explanation of Marion et al. [
18] regarding seasonal PR variation, PR was also influenced by the daily total AC consumption in the study house, which was equivalent to the total AC energy generation (
EAC) of the solar PV system, as determined using Equations (1)–(7). From Equation (4), the final yield was shown to influence PR
AC, i.e., an increase in the final yield would result in a higher PR
AC under similar weather conditions. Recall that final yield deals with solar PV system performance relative to the load, while reference yield deals with available solar radiation (GHI). Based on the basic operation of a solar PV module, in the presence of the sun and absence of load, the module’s internal load resistance increases, resulting in near-zero current flow. The connection of a load, on the other hand, reduces the internal load resistance, leading to the flow of current and power generation. Therefore, the house’s inconsistent and relatively low energy consumption compared to a grid-tied solar PV system led to different daily and low PR
AC. The operation of the solar PV system in open-circuit voltage (Voc) mode also influenced the module efficiency, as the internal resistance increased the operating temperature. In general, the performance of the solar PV system indicated that the technology is a viable source of energy, i.e., comparable to the performance of solar PV systems in other regions, given the local solar radiation and air temperature [
69].