1. Introduction
An accurate estimation of electric power production (EPP) from a photovoltaic (PV) system, taking into account in-situ conditions, is an essential first step toward the design of a PV project. Various researchers have developed models and software that can be utilized to estimate EPP from a PV system [
1,
2,
3,
4,
5,
6,
7,
8,
9]. These models and software are classified into two groups according to the type of input data used (i.e., monthly irradiance or hourly irradiance). PV*SOL [
10], Polysun [
11], INSEL [
12], and RETScreen [
13] software employ monthly irradiance values as input data to simulate EPP, whereas the System Advisor Model (SAM) [
14], PVWatts [
15], and PVsyst [
16] software employ hourly irradiance data. Using hourly data is generally preferred for estimating the PV-based EPP, even when both monthly and hourly irradiance data are available in the region of interest. This is because the EPP results estimated from hourly data are generally more accurate and reliable than are those estimated from the monthly data [
17]. In addition, using hourly irradiance data enables the estimation of hourly EPPs from the PV system and the consideration of the system load, a factor that could change by the hour in the economic evaluation process of a PV project [
18].
The EnergyPlus website [
19], operated by the United States (US) National Renewable Energy Laboratory (NREL) and supported by the US Department of Energy (DOE), provides various meteorological observation data, including hourly irradiance values for more than 2100 sites worldwide [
19]. Using these hourly data and the aforementioned software, such as the SAM, PVWatts, and PVsyst, enables estimating the hourly EPP values (henceforth, EPPs) from the PV system. Most irradiance observation sites operated by EnergyPlus are distributed in the US, China, and European countries. However, there are no abundant irradiance observation systems present in most developing countries in Africa, South America, and South-East Asia. Thus, it is difficult to obtain adequate hourly irradiance data observed over a long time for such countries from the EnergyPlus website [
19].
Conversely, it is relatively easier to secure monthly (mean or accumulated) irradiance data than hourly data in most countries worldwide, including developing countries. This is attributed to the US National Aeronautics and Space Administration (NASA) providing long-term observation data of the monthly worldwide irradiance by analyzing numerous satellite imageries including information of global meteorology [
20]. In the case of Korea, hourly irradiance data are available only in a few major cities equipped with irradiance observation systems. However, monthly irradiance data are available across the entire region from the 1 km-resolution solar-energy resource map provided by the National Institute of Meteorological Research (NIMR) of Korea. If monthly irradiance data could be converted into hourly irradiance data at an appropriate confidence level, it would be possible to accurately estimate the hourly EPPs or the total monthly EPPs from such hourly data by employing the aforementioned software. Accordingly, this would help us evaluate the feasibility of a PV project in developing countries not equipped with an irradiance observation system.
Various researchers have studied methods of hourly irradiance estimation and have tried projecting the amount of available solar energy based on such irradiance data. Goh and Tan [
21] employed probabilistic modeling to estimate future hourly irradiance, and Perez et al. [
22,
23,
24] developed a model to estimate irradiance from global horizontal irradiance data (GHI) or diffuse horizontal irradiance data (DHI). Aguiar et al. [
25] analyzed the association between the daily clearness index (CI) and the hourly CI, and conducted statistical analysis of hourly irradiance data at several sites. Santamouris et al. [
26] performed comparative analysis of irradiance estimation models using cloudiness data. Zhang and Huang [
27] suggested an hourly irradiance estimation model for China, considering meteorological information including local temperature, humidity, wind speed, and cloudiness. Gueymard [
28,
29,
30] assessed the effect of CI on irradiance and proposed an irradiance estimation model. Recently, Benmouiza and Cheknane [
31] modeled the pattern of clustered irradiance data and estimated hourly irradiance using this pattern.
Most previous studies have focused on developing simple models to estimate the future hourly irradiance from existing observed irradiance data. However, little attention has been paid toward examining the universal applicability of these models and, consequently, these models are not directly applicable to developing countries. Furthermore, an approach of solar resources estimation using model-based indicated (or inferred) hourly irradiance data (not measured data), has the limitation of inherent uncertainty owing to the low confidence level of the input data used [
32]. Therefore, it is necessary to obtain hourly irradiance data at an adequate level of confidence to accurately estimate the EPP from a PV system in developing countries or rural areas. Several previous studies have estimated EPPs by using monthly irradiance data or hourly irradiance data obtained by simply dividing monthly or yearly accumulated irradiance by the total sunshine hours of the month or the year [
33,
34,
35]. However, these approaches are limited, as they do not consider either the sunshine hours or the hourly variation of the irradiance value for the estimation of EPP. Moreover, few previous studies have compared the conversion methods for the measured monthly irradiance data and the resulting EPPs from the PV system.
The objective of this study is to compare the methods that convert the monthly accumulated irradiance data that are easily obtainable into hourly irradiance data. Toward this aim, three different conversion methods were applied to the irradiance dataset relevant to 11 sites in the US and Korea. These conversion methods are the sunshine hour mean, the SOLPOS algorithm [
36], and the Duffie and Beckman algorithm [
37]. Each converted hourly irradiance dataset was entered into the SAM to estimate the monthly EPPs from the PV system. The resulting EPPs were compared with the true EPPs analyzed from the measured hourly irradiance data in order to calculate the errors and to examine which method would be appropriate for data conversion. This is because, from the perspective of the feasibility of a PV project, it is more important to predict EPP in a monthly level than the hourly irradiance value. It is reasonable to apply the conversion method for the purpose mentioned above to the region where hourly data are unavailable, but monthly data are abundant. However, in this study, the region for which hourly data are available was selected because reference values (true irradiance or true EPPs) are necessary for error analysis in order to compare the conversion methods. This study did not compare the hourly irradiance data, converted from satellite-based monthly irradiance data, and the observed hourly irradiance data.
3. Methods
The flowchart employed to determine the most suitable method for converting the monthly accumulated irradiance data into hourly irradiance data is shown in
Figure 2. First, the hourly irradiance data measured (code HD0) at each site and acquired from the TMY dataset were summed to produce the monthly accumulated irradiance data. Second, three different methods were applied to convert the monthly accumulated irradiance data into hourly irradiance data (HD1, HD2, and HD3). Third, the capacities of the PV system were designed by selecting the proper model of the PV modules and inverters and setting the parameters (e.g., direct current (DC) to alternating current (AC) ratio, tilt, azimuth, tracking), and the converted data were subsequently entered into the SAM software to estimate the monthly EPPs from the PV system (R1, R2, and R3). Fourth, for a quantitative comparison of the accuracy of the four estimated EPPs, the hourly measured irradiance data were entered into the SAM software to analyze the monthly EPPs from the identical-capacities PV system mentioned above (R0). The monthly EPPs from the identical-capacities PV system were regarded as true EPPs (reference values) in this study. Subsequently, the three conversion methods were compared in terms of the errors between the EPPs estimated from the converted hourly irradiance data and those from the measured hourly irradiance data.
3.1. Construction of Monthly Accumulated Irradiance Data
Hourly irradiance values for each month in the US and Korea were summed separately to produce each monthly accumulated irradiance dataset. This was done because the measured monthly accumulated irradiance data were not provided by the NREL NSRDB. In this study, the produced monthly accumulated irradiance data will be converted into hourly irradiance data to estimate the monthly EPPs.
3.2. Conversion of Monthly Accumulated Irradiance Data into Hourly Irradiance Data
As already mentioned, this study employed three different methods to convert the monthly data into hourly data, namely sunshine hour mean, the SOLPOS algorithm, and the Duffie and Beckman algorithm. These three methods commonly follow the equations:
where m is the month and h is the time (e.g., m = 3 and h = 10 refers to the month of March and the time 10 AM); GHI
C indicates the converted global horizontal irradiance (GHI) at a specific month and hour (unit: W/m
2); DNI
C indicates the converted direct normal irradiance (DNI) at a specific month and hour (W/m
2); A(m) indicates the formula for the monthly mean value; and F(m, h) indicates the formula for irradiance at a specific month and hour. Therefore, both A(m) and F(m, h) vary according to the conversion methods used. The DHI was not considered, as only two values (GHI and DNI) were required to simulate EPP using the SAM software. In order to calculate GHI
C and DNI
C, the observed accumulated GHI value for a specific month (∑GHI(m)) and the observed accumulated DNI value for a specific month (∑DNI(m)) were usually employed, respectively, for all three methods.
Although the sunshine hour mean method is a simplified way of upscaling the irradiance data and performing the EPP analysis, it was used in this study as a means of comparing the results against those estimated using the other approaches. The simple arithmetic mean method (which defines the converted hourly irradiance value as the ratio of the monthly accumulated irradiance to the total hours of the month) was not considered in this study since it is obviously not compatible with the SAM software. The irradiance values assigned in the non-sunshine hours (night time) were ignored in the simulation process by the SAM software.
3.2.1. Sunshine Hours Mean Method
The sunshine hours mean conversion method calculates the hourly irradiance value by dividing the monthly accumulated irradiance by the total sunshine hours in a month (Equations (3) and (5)). Originally, the term “sunshine hours” represented the duration (in hours) of direct solar irradiation that exceeded a DNI of 120 W/m
2, and was closely associated with the EPP [
39]. However, in this method, “sunshine hours” is defined as the total hours during the period from sunrise to sunset.
For DNI,
where ∑ST(m) is the total sunshine hours of a specific month. This method differs from the simple arithmetic mean method, as it considers only the total hours during the period of sunshine hours. The formula for the irradiance value of F(m, h) or F’(m, h) equals zero for non-sunshine hours (irradiance value = 0) or one for sunshine hours (irradiance value > 0) in this method (Equations (4) and (6)). As such, ∑ST(m) is smaller than ∑T(m), and the value of A(m) is larger in the sunshine hours mean method than in the simple arithmetic mean method. Consequently, the converted hourly irradiance is assigned only to sunshine hours, whereas the hourly irradiance value of zero is assigned to the non-sunshine hours.
The resulting converted hourly irradiance (GHIC or DNIC) is a constant value for every sunshine hour, as this method is unable to take into account the variation of irradiance within the duration period of sunshine hours. This method enables entering the monthly mean irradiance, with a consideration of both sunrise and sunset times, into the PV software that uses hourly data to analyze the EPP.
3.2.2. SOLPOS Algorithm
The SOLPOS algorithm provides estimation results of hourly irradiances GHI
S(m, h) and DNI
S(m, h)) by calculating the apparent solar position and intensity based on the date, time, and location in clear-sky conditions. This is done by considering the extraterrestrial radiation, earth radius vector [
36], and the refracted solar zenith angle [
40]. The converted hourly irradiance values can be obtained by using the following equations:
For DNI,
where GHI
S(m, h) indicates GHI at a specific month and hour, DNI
S(m, h) indicates DNI at a specific month and hour, and both values are calculated by the SOLPOS algorithm. For further details of the theories and calculation processes pertaining to the SOLPOS algorithm, please refer to Iqbal [
36].
3.2.3. Duffie and Beckman Algorithm
The Duffie and Beckman algorithm is used for the RETScreen software, which employs monthly accumulated irradiance values as input data to simulate monthly total EPP. This algorithm calculates the hourly irradiance on the horizontal surface relevant to all the hours of an average day with the same daily global radiation as the monthly mean [
37]. This algorithm provides the estimation results of hourly irradiances (GHI
DB(m, h) and DNI
DB(m, h)) by breaking down the monthly mean daily radiation using the Collares-Pereira and Rabl model for global irradiance [
41] and the sunset hour angle (solar hour angle corresponding to the time when the sun sets) in the clear-sky condition. The converted hourly irradiance values can be obtained by using the following equations:
For DNI,
where GHI
DB(m, h) indicates GHI at a specific month and hour, DNI
DB(m, h) indicates DNI at a specific month and hour, and both values are calculated by the Duffie and Beckman algorithm. As both the numerator and the denominator in Equations (11) and (13) are constant values, the resulting A(m) is a constant value. However, F(m, h) depends on the specific month and hour and, therefore, the resulting converted hourly irradiance value (GHI or DNI) varies according to the time change. For further details of the theories and calculation processes pertaining to the Duffie and Beckman algorithm, please refer to Duffie and Beckman [
37].
3.3. Simulation of PV Electricity Power Generation
In this study, PV-based EPPs were simulated with SAM software to determine the accuracy of the converted hourly irradiance data. The PV module of SAM software simulates the performances of a PV system by combining the module and the inverter sub-models to calculate the hourly output of the PV power system. Such calculation takes into account the weather file and the data describing the physical characteristics of the module, inverter, and array. As the SAM PV module employs hourly irradiance as the input data, it enables an hourly simulation of EPPs and a detailed design for the PV system. For further details on the PV module of SAM software and the system design process, please refer to Choi and Song [
35].
Four different monthly EPPs (R1–R3) were estimated by separately incorporating the three differently converted hourly irradiance datasets into a PV system with identical capacity in order to compare the conversion methods. Different optimal installation angles for the fixed-tilt PV array were set for each observation point based on the latitude (e.g., 40.983° N for Arcata Airport). The cell temperature of each observation point was automatically estimated using ambient temperature and wind speed data of the TMY weather data in the simulation process of the SAM software, assuming that the temperature of the cells in all of the modules in each subarray was uniform [
42]. The parameter values of the module, inverter, and system design are listed in
Table 2. To evaluate and compare the accuracy of the converted data, the measured hourly irradiance values, as true irradiance values (reference values), were entered into the system to analyze the EPP under the identical conditions indicated above.
3.4. Comparison of Errors in PV Electricity Power Generation
An error test was conducted to quantitatively evaluate and validate the four conversion methods. Errors were calculated by subtracting the true EPPs (R0) from the EPPs estimated from the converted hourly data (R1–R3). Smaller errors indicate that the converted hourly data are accurate and the conversion method is appropriate. The study employed the root mean square error (RMSE), mean bias error (MBE), and mean absolute percentage error (MAPE) statistical test methods using the following equations:
where
n indicates the number of data used, and
et indicates the difference between the EPP estimated from the converted hourly irradiance data (
xt) and the EPP analyzed from the measured hourly irradiance data (
yt). The errors relevant to the US and Korea were calculated separately in this study.
5. Conclusions
This study used the sunshine hour mean method, SOLPOS algorithm, and Duffie and Beckman algorithm to convert monthly irradiance data into hourly irradiance data, and to estimate the monthly EPPs from the PV system at seven sites in the US and four sites in Korea. Three estimated monthly EPPs were compared with those analyzed from the measured hourly irradiance data. Similar results were derived for both countries. In the sunshine hours mean method, the estimated monthly EPPs data were spread out over the graph line of the true EPPs. The result from the SOLPOS algorithm showed that the monthly EPP patterns were highly similar to those of the true EPPs, and low error-value ranges (1.78–2.71%) were generated. This is ascribed to the fact that the SOLPOS method takes into consideration the variation of irradiance within the period of sunshine, based on the position of the sun. The prediction accuracy of the SOLPOS algorithm was approximately 1.05 times and 1.11 times that of the Duffie and Beckman algorithm and sunshine mean hour method. However, as regards the Duffie and Beckman algorithm, the EPPs were overestimated compared with the true EPPs, and the errors were larger than those of the SOLPOS algorithm. Therefore, it could be concluded that it is reasonable to adopt the SOLPOS algorithm to convert the monthly data into hourly data in a feasibility study or the initial design of a PV system in the US and Korea, rather than use the sunshine hour mean method or the Duffie and Beckman algorithm (RETScreen software).
It should be noted that the ranking of the estimation results of the EPPs could change if the metric of interest was alignment during certain key times rather than monthly average EPP. Even though the results for the US and Korea were similar in this study, it is still necessary to conduct additional case studies for other countries in low latitude to ensure the universal applicability and reliability of the conversion methods (e.g., to check whether the estimation of the EPPs may vary according to the latitude of the country). Furthermore, with regard to utilizing the Sandia Array model in the SAM software, it would be interesting to alternatively employ the CEC module with its commonly used database (given its large library), to calculate hourly efficiency values in future studies. The SOLPOS algorithm can be utilized to estimate the monthly EPPs accurately and to assess the feasibility of the PV system reasonably. This can be easily done by converting the acquirable monthly irradiance data into hourly irradiance data in developing countries where measured hourly data and observation systems are unavailable.
The suggested approach may not yield the accurate estimation of EPP at peak hours or hours of interest. In addition, the converted hourly irradiance data cannot substitute for measured hourly irradiance data to estimate hourly EPP toward designing a solar PV project owing to reasons such as unpredictable weather conditions and uncertainties, as seen in
Figure 3c. As such, ideally, reliable measured hourly (not monthly) data should be utilized to design hourly based metrics and activities such as net metering and battery/storage implications for smart grid systems in the initial stage of solar PV projects, if hourly data are available.