Two-step artificial neural network to estimate the solar radiation at Java Island

Received Sep 3, 2020 Revised Jan 13, 2021 Accepted Feb 10, 2021 The availability of information about solar radiation characteristics, particularly solar radiation predictions, is important for efficiently designing solar energy systems. Solar radiation information is not available in Indonesia because official measurements have not been conducted by the Indonesian Meteorological, Climatology, and Geophysical Agency (BMKG). In this study, a new two-step artificial neural network (ANN) is proposed to estimate both the daily average and hourly solar radiation at Java Island, Indonesia. The input parameters for the daily average solar radiation estimation are the location and time required, along with five selected monthly meteorological parameters that BMKG predicts for the subsequent month. The selected meteorological parameters are temperatures, relative humidity, and precipitation. The estimated daily average solar radiation is then used as the input parameter of the hourly solar radiation estimation along with the local time and location. The ANN training was conducted using two years of data, 2018 and 2019, from Surabaya and Jakarta, while the validation was performed in the same cities for January through July 2020. The accuracy of the proposed method is comparable to previous studies with an average R2 of 98.70% for the daily average solar radiation estimate and 97.44% for the hourly solar radiation estimate.


INTRODUCTION
As of November 2019, Indonesia has utilized only 152 MW or 0.028% of its abundant 536 GW solar energy potential through solar energy systems [1]. A lack of official solar radiation measurements could be one of the factors contributing to the slow development of solar energy systems, as optimal designing becomes more difficult without this information [2]. This problem could be overcome by generating an accurate solar radiation estimator for a specific location.
Estimates of solar radiation have been used in various optimal solar energy design. The annual solar radiation calculation has been used to determine the ideal location to build a photovoltaic system [3,4]. The monthly total, or daily average, solar radiation is required for the optimal sizing of solar panels or storage systems [5][6][7], while determining panel installation angles calls for the hourly solar radiation [8].
Various methods have been proposed to estimate either the daily average or hourly solar radiation. The artificial neural network (ANN) method for estimation is one of the most popular methods for the daily average prediction due to its high accuracy [9,10]. While a wider range of methods has been used to estimate hourly solar radiation, ANN-based methods have also been applied with accurate results. Those methods include multilayer perceptron [11], deep learning [12], adaptive neuro-fuzzy [13,14], Jordan recurrent [15] and comparison of various methods [16]. However, those aforementioned methods cannot be used for estimating solar radiation in Indonesia because they require meteorological input parameters that are not measured by Indonesian Meteorological, Climatology, and Geophysical Agency (BMKG). The unavailable input parameters are hourly cloud cover, clearness index, atmospheric pressure, and visibility.
The objective of this study is to build a solar radiation estimator using an ANN-based method and the meteorological data types available in Indonesia. Because no hourly weather information is available, the hourly solar radiation estimator relies on the daily average solar radiation in the same month. Therefore, a two-step ANN is required. The first ANN (ANN-1) predicts the daily average solar radiation using the selected monthly weather parameters, while the second ANN (ANN-2) predicts the hourly solar radiation using the output of ANN-1. Both the training and the validation of the ANNs were performed using data from the cities of Jakarta and Surabaya, which are located on Java Island. The cities were selected because they have the largest electricity demand in Indonesia. The results of this research can be used to help solar energy system designers to build high-efficiency photovoltaic systems in Indonesia, especially on Java Island.

RESEARCH METHOD
In this study, a two-step ANN is proposed to estimate the amount of solar radiation at Java Island. ANN-1 estimates the amount of the daily average solar radiation, which is then used by ANN-2 to estimate the hourly solar radiation in the same month. The configuration of the two-step ANN is depicted in Figure 1. The meteorological data for training both networks were from 2018 and 2019 from the city of Jakarta, which is located in the western part of Java Island, and Surabaya, which is the capital of East Java province. The ANNs were built in MATLAB environment using neural network toolbox. The selection of the input and the number of hidden neurons are explained in the sub-sections. To get the estimation result, the ANN model was added to the Simulink and was executed with the meteorological data of Surabaya and Jakarta for January through July 2020 as the input. The validation of the accuracy of the model was performed by comparing the estimation results with the measured solar radiation in the same period.

ANN-1 design
ANN-1 estimates the daily average solar radiation by using the inputs of month, geographical position, and meteorological data of daily average minimum, maximum, and average temperature, relative humidity, and precipitation. These meteorological data were selected because BMKG forecasts these data for the subsequent month. Thus, using these meteorological data allows for the estimation of the daily average solar radiation for the following month. The geographical positions of latitude and longitude were included because the position of the sun, and thus the solar radiation, varies for different locations in the same month. The daily solar radiation data for training ANN-1 was taken from the NASA power database. The data was converted into the daily average solar radiation, with each day in a defined month assumed to have equal solar radiation. Detailed information about the input-output parameters is presented in Table 1. The number of hidden neurons in ANN-1 was chosen by comparing the regression value (R) during training for various numbers of neurons in the hidden layer. The candidates for the number of the hidden neurons are determined by the rules [17]: where h is the number of the hidden neurons, i is the number of the inputs, and o is the number of the outputs.
With eight inputs and one output, the number of hidden neurons is between six and 15. ANN-1 was trained ten times for each number of hidden neurons. The comparison of the highest R for each number of hidden neurons is shown in Figure 2. According to this analysis, the preferred number of hidden neurons for ANN-1 is 15. The training regression line of the preferred ANN structure is shown in Figure 3. The feedforward Levenberg-Marquardt method was chosen to train ANN-1 due to its speed and stable convergence [18]. The iteration-stopping criteria were based on the minimum mean squared error (MSE), which is calculated as (3).
where n is the total number of samples of the output parameter, k is the index of the output samples, e is the error of the output, t is the target value of the output from the data, and y is the output value obtained from the calculation of the ANN.

ANN-2 design
ANN-2 estimates hourly solar radiation based on the daily average solar radiation, geographical position, month, and local hour. The advantage of this method is that it does not require any hourly weather parameters as input, which are not measured and recorded by BMKG. The hourly solar radiation data for the ANN-2 training was taken from the commercial Solcast website for the cities of Jakarta and Surabaya in Detailed information about the input-output parameters is listed in Table 2. Using the same method as described in section 2.1, the number of hidden neurons for ANN-2 was also determined by comparing R values for candidates determined using (1) and (2). The range of the number of hidden neurons was between four and nine, and nine was selected as the number of hidden neurons due to having the highest R, as shown in Figure 4. The regression line during the ANN-2 training with nine hidden neurons is depicted in Figure 5.

RESULTS AND DISCUSSION
Validation of the proposed method was completed by comparing the estimated results from each ANN with the measured solar radiation in Jakarta and Surabaya for January through July 2020. Although the comparison was not performed for a full year, the selected months include portions of the rainy season (October-April) and the dry season (May-September) on Java Island. The accuracy of each ANN is measured by coefficient of determination R 2 , which is calculated as (4).
where Gmeas is the measured value of the solar radiation and Gpred is the estimated value of the solar radiation. R 2 is selected as it is one of the most frequently used parameters to measure the accuracy of solar radiation prediction [9]. Therefore, by calculating the R 2 , the accuracy of the proposed method could easily be compared with the accuracy of the methods from previous studies.

Accuracy of daily average solar radiation estimation
The accuracy of the proposed method was validated by a minimum value of R 2 of 97.86%, as shown in Table 3. A higher value of R 2 indicates that the estimated value is more accurate; a 100% value can be achieved if all the estimated values are equal to the measured values. The graphical comparisons of the daily average solar radiation are shown in Figures 6 and 7. The estimation accuracy for Surabaya is higher than for Jakarta, which indicates that the solar radiation in Surabaya is more predictable and is more strongly correlated with the input parameters than in Jakarta. In both cases, the estimations for January and February produces higher error than for the other months. Considering the error distribution, an improvement for estimation during rainy season is recommended for the future research.  The estimated values of daily average solar radiation tend to be higher than the measured values. This is due to that the measured solar radiation in 2020 is considerably lower than in 2018-2019, while the values of input parameters tend to be equal. The accuracy of the daily average solar radiation estimation on Java Island might be increased if other meteorological parameters are involved. Previous studies have indicated that sunshine duration and cloud cover percentage significantly correlate with the amount of solar radiation [19,20]. However, while the daily sunshine duration is measured, the predicted value is not recorded by BMKG. Therefore, this parameter could not be included as an input for an estimate of the daily average solar radiation for the following month. Compared with the R 2 of the daily average solar radiation estimates from previous studies, the accuracy of the proposed method is comparable, as shown in Table 4.

Accuracy of hourly solar radiation estimation
The measured and estimated hourly solar radiation was compared on an hourly basis for an entire day from 12 AM to 11:59 PM. However, in Surabaya, the earliest sunrise is between 5 AM and 6 AM and the latest sunset is between 5 PM and 6 PM for the entire year. Jakarta has a wider range of sunrise and sunset times, with the earliest sunrise occurring between 5 AM and 7 AM and the latest sunset occurring between 5 PM and 7 PM.
The graphical comparisons between the estimated and measured values are presented in Figures 8 and 9. The horizontal axis is the number of data points, which represents the number of the hour for each month. For example, data point number 1 represents 1 AM in January, while data point number 25 represents 1 AM in February. Although the lines are not perfectly equal, the shapes tend to be similar. Unlike in daily average estimation, the results on hourly estimates are more varied. The estimated values in Surabaya tend to be higher, while the estimated values in Jakarta tend to be lower than the measured values. Since both of daily average estimates in Surabaya and Jakarta are higher than the measured values, the results of hourly estimation indicate that there is limitation of the estimation accuracy when the meteorological input is limited to the daily average radiation only. Figures 8 and 9 also indicate that like in the daily average estimation, the error are higher for the estimation on rainy season. The R2 for the estimated hourly solar radiation for each month are listed in Table 5. The values are lower than for the daily average solar radiation because the estimation of hourly solar radiation is more difficult. For the hourly solar radiation, the estimation accuracy for Jakarta is higher than Surabaya, meaning that the correlation between the daily average solar radiation and hourly solar radiation in Jakarta is higher than in Surabaya. A comparison of the R2 achieved in previous studies with the proposed method is shown in Table 6. This comparison suggests that the accuracy of proposed method is higher than that of previous studies.

CONCLUSION
The goal of this study was to propose a method to accurately estimate both the daily average and hourly solar radiation in Indonesia, where the official measurements are not available from BMKG. The proposed method not only estimates the radiation profile for each month based on the previous history but also can be used to predict daily average and hourly solar radiation for the subsequent month, using meteorological parameter inputs available from BMKG. Due to the unavailability of hourly weather parameter measurements, the estimation of hourly solar radiation is only based on the daily average solar radiation and the time and location in which the estimation is required. The proposed method is also capable Int J Elec & Comp Eng ISSN: 2088-8708  Two-step artificial neural network to estimate the solar radiation at Java Island (Adi Kurniawan) 3565 of estimating the solar radiation for multiple cities, at least on Java Island, by employing latitude and longitude as input parameters. The accuracy of the proposed method has been validated by calculating the R2 and comparing it with the results from previous studies in the same field of study. The comparisons show that the proposed method generates better accuracy than most of the references with average R2 of 98.91% for daily average estimation and 97.44% for hourly estimation. Because the proposed method produced a greater error in the peak of the rainy season than in the dry season, it may be possible to improve the proposed method by using a clustering method that treats the dry and rainy seasons separately.