Evaluation and forecasting of solar radiation using time series adaptive neuro‐fuzzy inference system: Seoul city as a case study

IET Renewable Power GenerationVolume 13, Issue 10 p. 1711-1723 Research ArticleFree Access Evaluation and forecasting of solar radiation using time series adaptive neuro-fuzzy inference system: Seoul city as a case study Mohammed H. Alsharif, Corresponding Author Mohammed H. Alsharif malsharif@sejong.ac.kr Department of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, Neungdong-ro, Gwangjin-gu, Seoul, Republic of KoreaSearch for more papers by this authorMohammad K. Younes, Mohammad K. Younes orcid.org/0000-0001-5548-4821 Department of Civil Engineering, Philadelphia University, Amman, JordanSearch for more papers by this author Mohammed H. Alsharif, Corresponding Author Mohammed H. Alsharif malsharif@sejong.ac.kr Department of Electrical Engineering, College of Electronics and Information Engineering, Sejong University, Neungdong-ro, Gwangjin-gu, Seoul, Republic of KoreaSearch for more papers by this authorMohammad K. Younes, Mohammad K. Younes orcid.org/0000-0001-5548-4821 Department of Civil Engineering, Philadelphia University, Amman, JordanSearch for more papers by this author First published: 03 May 2019 https://doi.org/10.1049/iet-rpg.2018.5709Citations: 10AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Given that solar radiation is unpredictable, an accurate solar energy prediction model must be developed. This study aimed to evaluate the changes in solar radiation over the past 37 years in Seoul city. The capability of the adaptive neuro-fuzzy inference system (ANFIS) to forecast solar radiation using chaotic time series inputs was analysed. Results demonstrate the capability of ANFIS to provide a relatively good monthly solar prediction model with a normalised root mean square error of 0.22%, a root mean square error of 55.4, and a coefficient of determination of 0.8. The Jarque–Bera test was implemented as well to test the null hypothesis for the normal distribution of standardised residual. Results support the null hypothesis with P-value = 0.222, which indicates the normal distribution of the standardised residual and its goodness. The standardised residual shows that the model can effectively predict solar radiation on a monthly basis. 1 Introduction Solar radiation is one of the most available power sources in the world. However, the variability of solar radiation limits its usability and reliability as a source of power [1]. Energy security is a key issue all over the world, especially in developed and fuel-importing countries [2], such as the Republic of Korea. The demand for energy has been growing rapidly in the Republic of Korea, thereby placing it among the ten largest energy-consuming countries in the world. Imported non-renewable energy sources, such as oil, gas, and coal, represent 84% of the energy supply in the Republic of Korea and comprise its major import [3, 4]. Thus, energy sources must be diversified by increasing the dependence on renewable energy sources to enhance energy security and protect the environment [5]. The Republic of Korea is the seventh largest emitter of carbon dioxide globally due to its dependence on the burning of fossil fuel to generate the required energy [3]. However, the Republic of Korea has renewable natural resources that can help it pursue a sustainable energy strategy that covers energy, the environment, the economy, and society [6]. The use of non-renewable sources is a growing concern worldwide, and calls have been made for the Korean government to reduce its operational expenditure. Consequently, the strategic vision issued for the energy sector in the Republic of Korea is targeted at increasing the contribution of renewable energy to 11% of the total generated power by 2035 [7]. In this initiative, wind and solar energy play a decisive role in meeting the demand for energy and climate-friendly power sources [8]. The vision of the government is to increase the energy contribution of solar energy by up to 14.2% of the total renewable energy produced by 2035. The strategy is based on (i) increasing investments in the green energy field, (ii) achieving efficient development, and (iii) ensuring the sustainable provision of clean energy with improved planning. Fig. 1 shows the mix of power resources and the final energy consumption in the Republic of Korea for 2017. The current renewable energy is hydropower, which comprises only ∼6.1% of the total energy mix and poses a major challenge for the development of the industrial sector in the country. The industrial sector is the largest consumer of energy (65.2%), followed by the transportation sector (20.4%). Thus, a local renewable power resource is aggressively demanded to maintain the current economic and industrial growth. Fig. 1Open in figure viewerPowerPoint Summary of energy sources and final consumers in Republic of Korea The availability and variability of solar radiation, which is a source of energy, are the main challenges for solar systems. Solar radiation is extremely variable and is often described as an unreliable source of energy. If the risk and uncertainty levels increase in the expected generation of solar energy, then these factors will inhibit energy security [9]. However, competent forecasting and careful analysis can help reduce these risks and enable assets to be operated in the most cost-effective manner. Complex statistical and artificial intelligence (AI) techniques are widely implemented at present to simulate meteorological phenomena, such as solar radiation [9, 10]. These methods minimise the risk of failure within energy systems and forecast their reliability by modelling or simulating future scenarios. Solar radiation modelling is usually performed using time-series or causal forecasting techniques. Causal forecasting searches for relationships between dependent and independent variables. In [11], artificial neural network (ANN) used wind speed, air temperature, sunshine duration, and relative humidity as independent variables to estimate the mean average daily solar radiation. In [12], the model performance was evaluated using a mean absolute percentage error of 5.2%. Moreover, geographic location, date (latitude, longitude, and altitude), monthly mean temperature, mean sunlight duration, and relative humidity were implemented by ANN model to estimate the mean average daily solar radiation in Nigeria [12]. However, the quality of the developed models depends on the accuracy of the input factors. Causal forecasting is not implemented in the current study due to the high fluctuation of affecting factors of solar radiation, such as the lack of availability and accuracy of metrological data. Given that solar radiation is partially dependent on various factors, such as weather, location, and time [13], it represents a kind of serial correlation. Therefore, time series forecasting is preferable for solar radiation forecasting. Time series forecasting collects observations x(ti) over a designated period before predicting future outputs by depending on the previous ones. Compared with causal forecasting, time series forecasting is flexible and requires fewer input data. Thus, this method can be implemented easily and does not require much effort or cost. The main limitation of time series forecasting is the lack of a deterministic cause [14]. To overcome this limitation, model developers usually depend on several inputs or stochastic events [15]. The implementation of non-linear AI techniques, such as ANNs and adaptive neuro-fuzzy inference system (ANFIS), can overcome similar time series forecasting limitations [16]. ANFIS is a dynamic, data-driven model that does not require knowledge on the internal system parameters to offer a compact solution [17]. This technique is popular for the modelling of environmental systems due to its accuracy, efficiency, and capacity to handle a large amount of stochastic (linear and non-linear) data [18]. In [19], ANFIS was implemented to estimate the solar radiation based on metrological data, namely the minimum monthly mean temperature (Tmin), maximum monthly mean temperature (Tmax), and monthly mean sunshine duration as the input data. The results showed that ANFIS is more capable of estimating solar radiation than empirical models. However, the developed data-driven model is highly dependent on the availability and accuracy of the input data. The performance of several forecasting techniques with no exogenous inputs has also been evaluated and compared with that of the model for solar radiation. The results showed that the ANN-based model performs better than other techniques. However, substantial improvements can be achieved by introducing a genetic optimisation algorithm [18]. This study aimed to investigate the variation in solar radiation over time and represent its behaviour. Thus, a time-series ANFIS model was built to forecast the monthly solar radiation in Seoul city, Republic of Korea. ANFIS is usually used in causal forecasting. This study was the first to use a time series ANFIS model in predicting solar radiation. The performance of the model was evaluated using the root mean square error (RMSE) and standardised residual. The findings of this study can help policymakers frame strong policies in the near future by understanding the overall perspective of solar radiation. The rest of this study is organised as follows: Section 2 presents related work. Section 3 highlights the case study information. Section 4 shows the dataset used in this study and discusses the daily and monthly solar radiation in Seoul for over 37 years. A detail of the forecasting model approach (ANFIS) is given in Section 5. Simulation results and discussion are presented in Section 6. Section 7 draws the conclusion of the study. 2 Related work Notton et al. [20] tested combinations to select the optimum combinations that have been used to forecast global horizontal irradiation (GHI), then ANN was used to estimate global tilted irradiation (GLI). The RMSE = 10.5 wh/m2 with R2 in the range from 0.86 to 0.95 in dependence on the number of inputs. Benali et al. [21] examined the ANN, random forest, and smart persistence models that were assessed to forecast the GHI, diffuse horizontal irradiation (DHI), and normal beam irradiations (NBI). The performance of random forest was the best in comparison with ANN and smart persistence, with nRMSE = 19.7, 35 and 34.1% for GHI, DHI, and NBI, respectively. To enhance ANN solar radiation forecasting, ANN delay, neuron number, transfer function, and input parameters were assessed to forecast GHI. The obtained RMSE was in the range 10–30 based on the implemented ANN characteristic and input parameters [22]. Moreover, in terms of RMSE, the performance of random forest was RMSE = 88.6 for GHI, 189.5 for NBI and 48.5 for DHI. Ghofrani et al. [23] used clustering techniques to improve the performance of time series ANN model in order to forecast hourly normal beam irradiations (NBI) and GHI in the USA. The obtained nRMSE was between 16.9 and 40.5% for NBI and between 5.5 and 11.6% for GHI. Furthermore, the performance of k-nearest-neighbours (kNN) and gradient boosting (GB) machine learning models was compared in term of hourly GHI and NBI forecasting. The GB obtained results were RMSE = 34.4 for GHI and RMSE = 71.3 for NBI, whereas the performance of kNN was RMSE = 35.5 for GHI and RMSE = 74.5 for NBI, respectively [24]. The historical GHI was implemented to forecast annual and seasonal GHI in three French islands using Autoregressive method. The obtained results were nRMSE = 20.43% for annual GHI while the seasonal values were 25, 18.8, 15.8%, and 24.9 for first, second, third, and fourth annual quarter, respectively [25]. However, integrating the satellite image into time series ANN models enhances the GHI day ahead forecasting in Gran Canaria, Pozo, and Las Palmas islands [26]. Ultimately, Table 1 provides a summary of related works that have investigated the univariate solar radiation forecasting approach. Table 1. Summary of the related works Reference Contribution Results Notton et al. 2019 [20] tested combinations to select the optimum combinations that have been used to forecast GHI, then ANN was used to estimate GLI the RMSE = 10.5 wh/m2 with R2 in the range from 0.86 to 0.95 in dependence on the number of inputs Benali et al. 2019 [21] examined the ANN, random forest, and smart persistence models were assessed to forecast the GHI, DHI, and NBI the performance of random forest was the best in comparison with ANN and smart persistence, with nRMSE = 19.7%, 35%, and 34.1% for GHI, DHI, and NBI, respectively Kashyap et al. 2015 [22] enhanced ANN solar radiation forecasting, ANN delay, neuron number, transfer function, and input parameters were assessed to forecast GHI the obtained RMSE was in the range 10–30 based on the implemented ANN characteristic and input parameters Ghofrani et al. 2016 [23] used clustering techniques to improve the performance of time series ANN model in order to forecast hourly NBI and GHI the obtained nRMSE was between 16.9% and 40.5% for NBI and between 5.5% and 11.6% for GHI Pedro et al. 2018 [24] the performance of kNN and GB machine learning models was compared in term of hourly GHI and NBI forecasting the GB obtained results were RMSE = 34.4 for GHI and RMSE = 71.3 for NBI, whereas the performance of kNN was RMSE = 35.5 for GHI and RMSE = 74.5 for NBI, respectively Lauret et al. 2015 [25] the historical GHI was implemented to forecast annual and seasonal GHI in three French islands using Autoregressive method the obtained results were nRMSE = 20.43% for annual GHI, whereas the seasonal values were 25, 18.8, 15.8, and 24.9 for first, second, third, and fourth annual quarter, respectively DHI, diffuse horizontal irradiation; GB, gradient boosting; GHI, global horizontal irradiation; GLI, global tilted irradiation; kNN, k-nearest-neighbours; NBI, normal beam irradiations; RMSE, root mean square error. 3 Case study information: Republic of Korea Seoul, the capital and largest metropolis of the Republic of Korea, lies between 37°34′ N latitude and 126°58′ E longitude. This study highlights Seoul because the city has the largest energy consumption compared with other cities in the county. Seoul's energy consumption includes roughly half of the population, as well as most industrial and commercial areas [27]. Seoul consumes 15,496,000 tons of oil equivalents of energy per year, which is 7.5% of the Republic of Korea's national total. Of this energy consumption, 56% is attributed to residential and commercial use. In addition, Seoul is dependent on fossil fuels, with oil and liquefied natural gas accounting for 38.9 and 29.7% of the energy mix, respectively. The city has the abundant potential for using solar energy [28]. Byrne et al. [28] described and defined a solar city concept and an evaluation method for estimating solar electric potential on rooftops using distributed photovoltaic (PV) systems with Seoul as a case study and demonstrated a potential equivalent to almost 30% of the city's annual electricity consumption [29]. Through this methodology, ∼66% of the daytime electricity demand in Seoul can be served by solar power systems (PV systems) on a typical day. However, the total renewable energy production contributes merely 1.6% of the city's total energy consumption [30]. Thus, Seoul's municipal government has continuously strived to implement new policies to transform Seoul into a leading solar city save energy in a city with high energy consumption and reduce greenhouse gas emissions, which are the main causes of global warming. To this end, the municipal government has developed a solar map to show areas suitable for solar PVs and quantify the savings rooftop installations can deliver to increase citizen engagement in the programme, shift toward the use of sustainable energy sources, and reduce greenhouse gas emissions [2]. The findings of this study may help policymakers frame strong policies based on their understanding of the overall perspective of solar radiation in the coming future. 4 Data collection Data related to the intensity and temperature of solar radiation for Seoul city over 37 years (1 January 1981 to 31 December 2017) were obtained from the Korea Meteorological Administration. The hourly solar radiation data from 1981 to 2017 were collected. Next, pre-processing was performed to prepare the data for further analysis, for instance, re-estimating a few readings and the average daily solar radiation due to failure of the measuring equipment or regular maintenance, or determining the outliers to be avoided in the modelling process. Then, the daily and monthly average values were calculated to find the average solar radiation for each day, month and year. The data were then processed by MATLAB R2016b software, and a summary is shown in Table 2. Table 2. Summary of hourly solar radiation data descriptive statistics Variables Daily average, Wh/m2 Monthly average, Wh/m2 Annual average, Wh/m2 no of readings 13,513 444 37 min. 9.4 85.6 186.1 max. 676.2 377.0 278.9 mean 244.6 244.0 243.5 median 244.8 244.5 245 standard deviation 117.2 58.6 20.36 range 666.8 291.4 92.8 4.2 ANFIS modelling The ANFIS technique was originally presented by Jang [31]. ANFIS is a simple data learning technique that uses fuzzy logic to transform given inputs into the desired output through highly interconnected neural network processing elements and information connections, which are weighed to map the numerical inputs into an output. ANFIS combines the benefits of two machine learning techniques (fuzzy logic and neural network) into a single technique [31]. An ANFIS works by applying neural network learning methods to tune the parameters of a fuzzy inference system (FIS). Several features enable ANFIS to achieve great success [32]: It refines fuzzy IF–THEN rules to describe the behaviour of a complex system. It does not require prior human expertise. It has simple implementation. It enables fast and accurate learning. It offers desired dataset, great choice of membership functions to use, strong generalisation abilities, and excellent explanation facilities through fuzzy rules. It easily incorporates linguistic and numeric knowledge for problem-solving. Building the fuzzy logic structure requires (i) the selection of the model inputs, (ii) the determination of the membership functions, and (iii) the generation of fuzzy rules. The time series ANFIS was developed to predict the solar radiation after 3 months (Xt+3) for handling variations in the seasons. The FIS implemented in this study had three inputs, namely Xt−6, Xt−3, and Xt. The training data had the format (Xt−6, Xt−3, Xt; Xt+3) for the monthly solar radiation data. The odd numbers of the input data were used for training, whereas the even numbers were used for checking the performance of the model. The first-order Sugeno fuzzy model with two fuzzy rules was used as follows: Rule1:(1) Rule2: (2) where Ai orBj is a linguistic label (grade) such as 'low'or 'less'; p1, q1,p2, and q2 are thedesign parameters determined by the system developer [33]. The generated FIS matrix had 2^3 = 8 rules, and the number of fittingparameters was 104 of 24 non-linear parameters and 80 linear parameters. Fig. 2 shows the ANFIS architecture used to implement thetwo rules. Detailed discussion and the mathematical models of Fig. 2 are provided in the following paragraphs. Fig. 2Open in figure viewerPowerPoint ANFIS architecture model In Fig. 2, a circle indicates a fixed node, whereas a square indicates an adaptive node. ANFIS has five-layer architecture. Each layer is explained in detail below. In layer 1, all the nodes are adaptive nodes. The outputs of layer 1 are the fuzzy membership grade of the inputs, which are given by the following equations: (3) (4) where x and y are the inputs to node i. Ai and Bi are the linguistic labels (high or low) associated with this node function. μAi(x) and μBi−2(y) can adopt any fuzzy membership function. The bell-shaped membership function is used, and μAi(x) is given by (5) where ai, bi, and ci are the parameters of the membership function. In layer 2, the nodes are fixed nodes. This layer involves fuzzy operators and uses the AND operator to fuzzify the inputs. They are labelled with π, thereby indicating that they perform as a simple multiplier. The output of this layer can be represented as (6) In layer 3, the nodes are fixed nodes labelled by N to indicate that they play a normalisation role in the firing strengths from the previous layer. The output of this layer can be represented as (7) In layer 4, the nodes are adaptive. The output of each node in this layer is simply the product of the normalised firing strength and a first-order polynomial (for a first-order Sugeno model). The output of this layer is given by (8) where is the output of layer 3. pi, qi, and ri are the consequent parameters. In layer 5, only one single fixed node is labelled with ∑. This node performs the summation of all incoming signals. The overall output of the model is given by (9) ANFIS is used to achieve the best performance possible. Fig. 3 summarises the ANFIS system training methodology. ANFIS training begins by creating a set of suitable training data to train the neuro-fuzzy system. The obtained training data must include as many solar radiation situations as possible. ANFIS training uses the anfis function. Evaluation of the system compared with the desired output is conducted using the evalfis function. Fig. 3Open in figure viewerPowerPoint Flowchart of the ANFIS training methodology The first step is to prepare the training data to work with ANFIS in MATLAB. The dataset used as the input to the anfis function must be in a matrix form. The last column in the matrix is the output, and the matrix contains as many columns as needed to represent the inputs to the system. The rows represent all the existing data situations. This work uses the genfis1 command to create membership functions. After the initial membership functions are created, system training begins. The command provided by MATLAB to train an ANFIS system is anfis. We input the training data we defined, the membership functions we created using the fismat command, and some training options to produce the most acceptable output. When the training process is completed (trn-fismat), the final membership functions and training error from the training dataset are produced. The checking dataset can be used in conjunction with the training dataset for enhanced accuracy. ANFIS can function with only one training dataset, but the input of checking data increases the possibilities to be understood by the system and thus the effectiveness of the system. 5 Results and discussion Republic of Korea is located between latitudes 34°N and 38°N. Thus, it has excellent potential for solar energy generation. However, the variation in the average hourly solar radiation is relatively large from one month to another due to its location. These variations are due to shifts in the elevation angle of the sun. Fig. 4 shows the average monthly solar radiation throughout the year. The solar radiation varies around the year (164.6–318.8 Wh/m2) due to variations in the duration of daylight and the clearness index. The clearness index, i.e., the ratio of terrestrial global radiation on a horizontal surface W/m2 to the extra-terrestrial radiation W/m2 on that surface is a fundamental factor that affects solar radiation [34]. This factor has low values during the summer months (June–August) and presents the lowest value in July (0.34). The highest value is during the winter months, particularly in December. However, the global horizontal irradiance and clearness index decrease in June and July due to the long spell of rainy weather in early summer. Fig. 4Open in figure viewerPowerPoint Average monthly solar radiation The daylight duration is considered to be the main driver of solar irradiance [35]. As shown in Fig. 4, the highest average monthly solar radiation with an average value of 318.8 Wh/m2 is in May. The lowest value is in December (164.6 Wh/m2). This condition is due to the duration of sunshine hours and weather. As reported in [29], the highest ever monthly solar radiation reading is 377 Wh/m2. The spring and early summer months (April–June) represent the highest solar radiation, after which it decreases due to clouds and the long spell of rainy weather in early summer. As reported in [36], clouds reduce solar irradiance to consequently affect the total solar radiation. The month of December shows the lowest solar radiation with an average value of 166.1 Wh/m2. However, the lowest ever monthly solar radiation of 85.6 Wh/m2 was reported in January 1982. The largest variation in monthly solar radiation is in September. The general trend shows that solar radiation is increasing. Fig. 5 shows the behaviour of the monthly average solar radiation over 37 years. The largest increase is between the months of May and August, which represent the summer months. This condition indicates that Seoul is experiencing hotter summers than before. Meanwhile, the lowest increase in the rate is in winter between the months of January and February. The recent years have recorded the largest increase in the rate of solar radiation. Fig. 5Open in figure viewerPowerPoint Monthly average of solar radiation in the last 37 years Fig. 6 shows the average annual solar radiation. Although the annual average solar radiation sometimes decreases, such as in 1998 or 2007, the general trend is increasing. The lowest recorded annual solar radiation was in 1990, whereas the highest recorded solar radiation was in 1988 with a value of 279.0 Wh/m2 and in 2009, with a value of 275.3 Wh/m2. Since the end of the 1990s, the average annual solar radiation has been increasing (Fig. 6). Fig. 7 shows the average daily solar radiation for the past 37 years. Fig. 6Open in figure viewerPowerPoint Annual average solar radiation in the last 37 years Fig. 7Open in figure viewerPowerPoint Daily average solar radiation in the last 37 years Fig. 7 shows the increasing trend of solar radiation with the increase in time. However, most of the readings are within the range of 333.0–155.0 Wh/m2. This relatively small range of recorded data indicates the consistency of solar radiation over Seoul city. Furthermore, these data help solar power plants build their models, measure the risks, and take the required mitigation measures [37]. 5.1 ANFIS model To capture the seasonal variation in solar radiation, a time series ANFIS model using the average monthly solar radiation was developed. The solar radiation in the Republic of Korea has seasonality and a monthly cyclic nature [38]. Thus, data clustering on a monthly basis can improve the modelling result. However, the model tried to predict the average monthly solar radiation every three months to mimic the four seasons in Seoul City. Fig. 8 shows a comparison between the training and checking errors for 100 epochs. The RMSE was in the range of 54–56, whereas R2 for the training phase was 0.81. Training error was lower than the checking error. However, the difference between the training and checking error was relatively small until the completion of the training phase. Fig. 8Open in figure viewerPowerPoint Training error vs. checking error The minimum checking error is at epoch number 37 with RMSE = 55.4 Wh/m2, normalised RMSE (nRMSE) = 0.22%, and coefficient of determination (R2) = 0.80. nRMSE and RMSE are usually used to evaluate model performance by implementing a term-by-term comparison between actual and forecasted values. According to [16], an nRMSE value between 0.2 and 0.5 is an indication of excellent model performance. A low value of RMSE is ideal, and a value of R2 that is close to 1 represents excellent model performance. The obtained results are comparable with the reported results by [16], that is, nRMSE = 0.3 for ARMA model and nRMSE = 0.19 for a hybrid model of k-means and NAR network with RMSE = 60.24 Wh/m2. ANN with exogenous inputs model was used to predict the solar radiation. The reported results vary independent of location, but the average nRMSE is ∼1%. Fig. 9 shows the performance evaluation of the model. As shown in the figure, the ANFIS model performs well in predicting the fluctuation of the average solar radiation. Moreover, the actual and predicted data fluctuate ∼250.0 Wh/m2. However, the ANFIS model prediction has a smaller fluctuation range than the actual reading. Fig. 9Open in figure viewerPowerPoint Actual output vs. forecasted output To check the goodness of the model, the standardised residual was estimated. Fig. 10 shows the results. The negative and positive standardised errors indicate that the model has neither a negative nor a positive bias. Therefore, the predicted values lie below and above the original readings. Given that nearly all the residual errors fall within ± 2, the error of the model is normally distributed. Therefore, a conclusive judgment can be m