Direct and diffuse solar radiation components estimation based on RBF model: Case study

Transcription

1 Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p Engineering, Environment Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI 1,2*, Mawloud GUERMOUI 1, Redouane MIHOUB 1 1 Unité de Recherche Appliquée en Energies Renouvelables, URAER, Centre de développement des Energies Renouvelables, CDER, 47133, Ghardaïa, Algeria 2 Laboratoire de Micro-électronique Appliquée. Université Djillali Liabès de Sidi Bel Abbés, BP 89, 22000, Sidi Bel Abbés, Algeria. (s): *rab_ehi@hotmail.fr * Corresponding author, phone: 00(213) , fax: 00(213) Received: June 26, 2017 / Accepted: December 02, 2017 / Published: December 30, 2017 Abstract The current study, propose a new application of radial basis functions neural network for estimating direct normal radiation (DNR) and diffuse solar radiation (DSR) components based on different inputs parameters. The proposed methodology was validated and tested on limited data set recorded over three years ( ) in a semi-arid climate in Algeria.The experimental results show that RBF-model was highly qualified for estimating DNR and DSR with high performance accuracy. The obtained statistical parameters of Normalized Root Mean Square Error (NRMSE), Determination Coefficient (R 2 ) and Correlation Coefficient (r) for DNR and DSR are: 0.030, %, 98.60% and 0.044, 94.34%, 97.61%, respectively. Keywords Global solar radiation; Neural network; Regression; Renewable energy; Radial basis function (RBF); Diffuse solar radiation; Direct radiation Introduction Renewable energy is considered as a key source for the future, not only for Algeria but also for the world. This is primarily since renewable energy resources have a lot advantages when compared to fossil fuels. Ghardaïa city is a dry and arid site, characterized by an exceptional sunshine, most 93

2 Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB often, it has a very important rate of insolation (75% on average) and the mean annual of global solar radiation measured on horizontal plane exceeds 20 (MJ/m 2 ). The sunshine duration is more than 3,000 hours per year, which promotes the use of solar energy in various fields [1]. An accurate knowledge of solar radiation distribution at a geographical location is of vital importance for the development of many solar energy devices and for estimates of their performances. Unfortunately, for many developing countries solar radiation measurements are only available for selected stations due to the cost of the measurement equipment and techniques involved. Therefore, it is rather important to elaborate mathematical methods to estimate the solar radiation based on sun position geometry and more readily meteorological data [2]. Over the years, many models have been proposed to predict the amount of solar radiation using various parameters [3-4]. Some works used the sunshine duration [3-5], others used mean daytime cloud cover or relative humidity and maximum and minimum temperature [6-7], while others used the number of rainy days, sunshine hours, and a factor that depends on latitude and altitude [4]. The literature contains more complex models for the solar irradiance, for example Gueymard analysed eleven clear sky irradiance models for predicting beam, diffuse and global radiation on a horizontal surface [8]. Bird and Hulstrom analyzed six atmospheric clear sky models for direct, diffuse sky, diffuse sky/ground and Global Horizontal Irradiance [9]. Badescu looked at five very simple clear sky models for GHI for two cities in Romania [10]. Younes and Muneer evaluated four clear sky models for six locations in UK, Spain and India [7]. Gueymard and Wilcox did a very detailed study on 18 broadband radiative clear sky models that predict direct, diffuse and global irradiances under clear skies from atmospheric data [11-12]. An analysis study of hourly diffuse solar radiation on horizontal surface was presented by Karatasou et al [13], they used data for Athens site for establish relationships between the diffuse fraction and clearness index (Kt). Mustafa G [14] and Oturanc et al [15] performed an analysis of daily total horizontal solar radiation measurement for 9 cities and for Konya city in Turkey. They compared action graph data with pyranometer data of some stations, and developed a nonlinear model between the monthly average daily global solar radiation and the ambient temperature. Sen [16] proposed a nonlinear model for the estimation of global solar radiation from available sunshine duration data. This model is an Angström type model with a third 94

3 Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p parameter appears as the power of the sunshine duration ratio that gives the nonlinear effects in solar radiation and sunshine duration relationship. Recently, the neural-network technique was used to estimate hourly values of diffuse radiation on horizontal surfaces at Sao Paulo city (Brazil) using the global radiation and other meteorological parameters [17]. Models were also proposed for estimating daily diffuse radiation using sunshine fraction, clearness index and cloudiness factor [18]. Rehman [19] estimate the fractions of diffuse solar radiation and direct normal radiation using measured values of global solar radiation, ambient temperature, and relative humidity as input. The authors found that the mean absolute percentage errors (MAPE) for DSR and DNR are and 0.085, respectively. Solanki and Sangani [20] proposed a new method which may be used for estimating daily direct solar radiation on the basis of calculation of the elevation angle constant () for a given location and time. Artificial neural-network using satellite data were also used to estimate monthly mean daily average of horizontal direct and diffuse radiation in different cities of Turkey [21]; where diffuse and direct radiation were calculated as functions of optical air mass, turbidity factor and Rayleigh optical thickness for clear-sky. In this paper, we present a model based on Radial Basis Function (RBF) neural networks for estimating direct normal radiation (DNR) and diffuse solar radiation (DSR) fractions of solar radiation from GSR based on different inputs parameters. We have developed this approach using database consist of three years measured ( , collected in Ghardaïa area, Algeria). The paper is organized as follow: in the first Section, we present the theory of RBF-model. In Section two we deal with site location and the data set collection. Results and discussion are given in section three. Finally, the last section was dedicated to the conclusion of the work. Material and method Artificial neural network Artificial neural networks (ANNs), are no algorithmic and intensely parallel information processing systems. They learn the relationship between the input and output variables by mastering previously recorded data. ANNs have been used in different fields of 95

4 Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB science and technology and in solar radiation modelling [22]. ANNs have been used in computation of beam solar radiation [23], forecasting solar potential [24], prediction of global radiation [25] and solar radiation estimation [26, 27, 28, and 29]. An ANN consisted of parallel elemental units called neurons [30]. The computational capability of ANN is given by connection weights which passes signals or information. Simply, a neuron receives and combines inputs and then generates the final results in a nonlinear operation, during training weights and biases (network parameters) changes in each step to minimize the mean square of output error. The term ANN usually refers to a multilayer perceptron (MLP) network. However, there are many other types of neural networks, including probabilistic neural networks (PNN), general regression neural networks (GRNN), radial basis function networks (RBF), cascade correlation, functional link networks, Kohonen networks, Gram-Charlier networks, learning vector quantization, Hebb networks, Adaline networks, hetero associative networks, recurrent networks, and hybrid networks [31]. In this study, a model based on radial basis function networks (RBF) used to separating daily global solar radiation into direct and diffuses components. Radial basis function theory RBF neural networks have three functionally distinct layers. The input layer is simply a set of sensory units (Figure 1). Figure 1. RBF neural network topology The second layer is a hidden layer of sufficient dimension, which applies a non-linear transformation to the input space generating a (usually) higher-dimensional hidden-units 96

5 Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p space. The third and final layer performs a linear transformation from the hidden-units space to the output space. The topology of a RBF neural network is presented in Figure 1. Its output is given by Eq. (1) [31, 32, 33, and 34]: n j i i j i i 1 f ( x ) b x c (1) Where: f (x j ) - the predicted values; b - is a bias term; n - is the number of neurons; i - are weights for the output linear combiner; φi - represent the activation function (in the RBF model represent the Gaussian function); xj - are the inputs parameters; c i - the centre locations. The function used in the RBF hidden layer units is usually a Gaussian kernel of the form, Eq. (2): φ j x j 1 x j c exp 2 i i 2 (2) Where: φj (xj) - represent the projection of the input data into a higher dimension domain using a Gaussian function; σi - spreads of the Gaussian functions; φj and x j - is one input pattern. The centre of the basis function can be determined by simple heuristic approaches like the k-means clustering method, and the width can be determined using the nearest neighbour method. Training the RBF network can be accomplished by supplying pairs of input and output pattern vectors aimed to minimize the sum-of-squares of error between the actual and the neural network outputs. Radial-Basis Function Networks (RBFN) can be used for a wide range of applications, primarily because they can approximate any function and their training faster compared to Multi-Layer Perceptron s (MLP). Once the network is trained, the next step is to test the ability of the trained network to generalize, or to respond correctly to data that it has not seen before. A common practice is to test the generalization capabilities of neural networks by dividing the data into two parts. One part, the training data set, is used for training, and the second part, the test data set, is used to evaluate the generalization performance of the network [35]. The RBF prediction algorithm is shown on Figure 2. 97

6 Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB Data collection Data processing Split Train data Test data Input selection RBF model Els e If Good performance Estimated outputs RBF-model Model validation Test Figure 2. The RBF prediction algorithm The performance of RBF models is judged by comparing the estimated values with the measured values using different statistical indexes such as Root Mean Square Error (RMSE), Relative Square Error (RRMSE), Determination Coefficient (R 2 ) and Correlation Coefficient (r). 98

7 Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p The RMSE represent the difference between the predicted values estimated by the model and the measured values. In fact, RMSE identifies the model s accuracy calculated by, Eq. (3): 1 RMSE H H n 2 (3) n i 1 Where: H - is the estimated value; H - is the measured value. The RRMSE is calculated by dividing the RMSE to the average of measured data as Eq. (4): RRMSE 1 n i 1H H 2 n n H i1 N The ranges of RRMSE define the model performance as: Excellent if: RRMSE < 10% Good if: 10 % < RRMSE < 20% Fair if: 12 % < RRMSE < 30% Poor if: RRMSE > 30% (4) Data and site description The data used to perform the present study have been recorded at the Applied Research Unit for Renewable Energies (URAER) situated in the south of Algeria far from Ghardaïa city of about 18 km. The latitude, longitude and altitude above the sea level of the URAER are respectively , and 450 m above (see Figure 3) [36,37]. They are recorded every 5 minutes and consist in data of temperature, direct, diffuse and global solar irradiance. 99

8 Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB Figure 3. Location of the studied sites The radiometric station used to measure the three components of irradiance (direct, diffuse and global) installed at the rooftop of the URAER, as shown on Figure 4. [38]. Figure 4. Instrumentation station for measuring the global, the direct and the diffuse solar radiation The elements of Figure 4 are: (1) Pyranometer for measuring the global solar irradiance; (2) Pyranometer for measuring the diffuse irradiance component; (3) Pyrheliometer for measuring the direct irradiance component; (4) The ball used to permanently hide the pyranometer (2); (5) The 2-axis solar tracker [38]. The daily mean ambient temperature, mean relative humidity, global solar radiation (GSR), diffuse solar radiation (DSR), direct normal radiation (DNR) and sunshine duration during the years , are shown in Figures (5-10). 100

9 Daily Global Solar Radiation (GSR) Wh/m² Daily Mean Relative Humidity % Daily Mean Air Temperature C Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p Days of the Year Figure 5. Variation of daily mean ambient temperature Days of the Year Figure 6. Variation of daily mean relative humidity Days of the Year Figure 7. Variation of daily global solar radiation (GSR) 101

10 Sunshine Duration (h) Daily Diffuse Solar Radiation (DSR) Wh/m² Daily Direct Normal Radiation (DNR) Wh/m² Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB Days of the Year Figure 8. Variation of daily direct normal radiation (DNR) Days of the Year Figure 9. Variation of daily diffuse solar radiation (DSR) Days of the Year Figure 10. Variation of sunshine duration 102

11 Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p Results and discussion As mentioned before, the main objective of this work is to assess the potential of the RBF for estimate the DSR and DNR based on climatological data. Therefore, The RBF architecture used in this work, shown in Figure 11, has nine inputs and two outputs, which are: the diffuse solar radiation (DSR) and direct normal radiation (DNR). Input nodes Hidden nodes Day of the year Extraterrestrial SR Global solar irradiation Length of the day Solar declination Sunshine duration Mean temperature Mean humidity Mean pressure Output variables DNR DSR Figure 11. The RNF architecture, for 9 input parameters Many experiments were carried out to select the best inputs attributes for prediction DNR and DSR. The list of the RBF models is shown in Table 1. Table 1. RBF models determined Input parameter RBF-1 RBF-2 RBF-3 RBF-4 Extra-terrestrial SR Global Solar Irradiation Length of the day Sunshine duration (SS) Solar declination (δ) Day of the year Mean Pressure Mean Humidity Mean Temperature The collected data are normalizing to [-1, 1] then divided into two subsets the first part (628 values) are used for training the RBF networks, while the remaining (240 values) are used for testing the performance of the studied RBF-models. Table 2 gives the architecture 103

12 Normalised DNR Predicted Direct irradiation Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB and the statistical results obtained for each model after the estimation of the two components (DNR and DSR). The architecture in the third column contains the number of neurons in the input layer, the hidden layer and the output layer. Table 2. The obtained statistical results Components Model Architecture NRMSE RRMSE R 2 % r % RBF DNR RBF RBF RBF RBF DSR RBF RBF RBF From Table 2, we can show that the proposed model was found suitable for the prediction of DSR and DNR from measured values of GSR and other common meteorological parameters, in all models the estimation of DNR is more accurately than DSR. Also we can note that the model RBF-3 with 7 input neurons (without mean temperature and mean relative humidity), 10 neurons in the hidden layer and 2 output neurons give good results compared to other models (RMSE = 0.030, RRMSE=5.64 R² = 97.30%, r = 98.60%) for DNR and (RMSE = 0.044, RRMSE=11.81, R² = 94.34%, r = 97.61%) for DSR, These results enable us to use the model in regions where both components (direct, diffuse) are not available or where deterioration occurs in the reliability of ( DNR, DSR) measurements due to problems in the calibration of pyranometer that occurs after years. measured predicted 0,8 Data Linear Fit 0, Days (a) 0,4 0,8 Measured Direct irradiation (b) 104

13 Normalised DSR Predicted Diffuse irradiation Normalised DNR Predicted Direct irradiation Normalised DSR predicted Diffuse irradiation Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p measured predicted Data Linear Fit Days measured Diffuse irradiation (c) (d) Figure 12. Comparisons and correlations between measured and predicted for DNR (a), (b) DSR (c), (d). For the RBF-1 (From 19-may-2016 to 31-Dec-2016) measured predicted 0,8 Data Linear Fit 0, ,4 0,8 (a) Days Measured Direct irradiation (b) measured predicted Data Linear Fit Days Measured Diffuse irradiation (c) (d) Figure 13. Comparisons and correlations between measured and predicted for DNR: (a), (b); DSR: (c), (d). For the RBF-2 (From 19-may-2016 to 31-Dec-2016) 105

14 Normalised DNR Predicted Direct irradiation Normalised DSR Predicted Diffuse irradiation Normalised DNR Predicted Direct irradiation Direct and diffuse solar radiation components estimation based on RBF model: Case study Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB measured predicted Data Linear Fit Days (a) measured predicted Data Linear Fit Measured Direct irradiation (b) Days Measured Diffuse irradiation (c) ( d) Figure 14. Comparisons and correlations between measured and predicted for DNR: (a), (b); DSR: (c), (d). For the RBF-3 (From 19-may-2016 to 31-Dec-2016) measured predicted 0,8 Data Linear Fit 0, (a) Days Measured Direct irradiation (b) 106

15 Normalised DSR Predicted Diffuse irradiation Leonardo Electronic Journal of Practices and Technologies ISSN Issue 31 July-December 2017 p measured predicted Data Linear Fit Days Measured Diffuse irradiation (c) (d) Figure 15. Comparisons and correlations between measured and predicted for DNR: (a), (b) DSR: (c), (d). For the RBF-4 (From 19-may-2016 to 31-Dec-2016) Figures (12-15) suggests the good fitness between measured and predicted irradiation (DNR and DSR) for the RBF models. We see that the gaps between the measured data and the predicted values are very low, except for a few days when the solar radiation is strong, probably due to a few gusts of sand wind. Conclusions In this study, we used: day of the year, Length of the day, daily mean temperature, daily mean relative humidity, Mean Pressure, Extra-terrestrial solar radiation, Solar declination, sunshine duration, global solar radiation measurements data from radio determination stations in Ghardaia city between 2014 and 2016 to estimate fractions of diffused solar radiation and direct normal, the conducted examination showed the appreciable effect of input parameters on the precision of RBF-models. It has been demonstrated that RBF-3{SS, GSR, P Mean, δ, Extra-terrestrial SR, length and day of the year} provides better accurate precision than the other proposed RBF-models (RMSE = 0.030, RRMSE=5.64 R² = 97.30%, r = 98.60%) for DNR and (RMSE = 0.044, RRMSE=11.81, R² = 94.34%, r = 97.61%) for DSR, These results enable us to use the RBF-3 model in regions where both components (direct, diffuse) are not available or where deterioration occurs in the reliability of ( DNR, DSR) measurements due to problems in the calibration of pyranometer, that occurs after years. 107

16 Direct and diffuse solar radiation components estimation based on RBF model: Case study Acknowledgements Abdelaziz RABEHI, Mawloud GUERMOUI, Redouane MIHOUB We would like to thank and acknowledge the support of the team at the Research Unit on Renewable Energies of Ghardaïa who collected the data used in the present study. References 1. Gairaa K., Bakelli Y., An overview of global solar radiation measurements in Ghardaïa area, south Algeria, International journal of Energy and environment, 2011, 2, p Iqbal M., An introduction to solar radiation, Academic Press, Canada, Canada J., Global solar radiation in Pais Valenciano using sunshine hours, International Journal of Ambient Energy, 1988, 4, p Canada J., Global solar radiation in Valencia using sunshine hours and meteorological data, Solar & Wind Technology, 1988, 5, p Ibrahim S.M., Predicted and measured global solar radiation in Egypt, Solar Energy, 1985, 35 (2), p Supit I., Van Kappel R.R., A simple method to estimate global radiation, Solar Energy, 1998, 63 (3), p Ododo, J.C., Sulaiman, A.T., Aidan, J., Yuguda, M. M., Ogbu, F.A. The importance of maximum air temperature in the parameterization of solar radiation in Nigeria. Renewable Energy; (1995), 6 (7), p Gueymard C.A., Critical analysis and performance assessment of clear sky solar irradiance models using theoretical and measured data, Solar Energy, 1993, 51, p Bird R.E., Hulstrom R.L., Simplified clear sky model for direct and diffuse insolation on horizontal surfaces (No. SERI/TR ), Solar Energy Research Inst, 1981, Golden, CO (USA). 10. Badescu V., Verification of some very simple clear and cloudy sky models to evaluate global solar irradiance, Solar Energy, 1997, 61, p Younes S., Muneer T., Clear-sky classification procedures and models using a worldwide data-base, Applied Energy, 2007, 84, p Gueymard C.A., Assessment of spatial and temporal variability in the US solar 108

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