ESTIMATION OF SOLAR RADIATION USING LEAST SQUARE SUPPORT VECTOR MACHINE

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1 ESTIMATION OF SOLAR RADIATION USING LEAST SQUARE SUPPORT VECTOR MACHINE Sthita pragyan Mohanty Prasanta Kumar Patra Department of Computer Science and Department of Computer Science and Engineering CET Bhubaneswar, India. Engineering CET Bhubaneswar, India. Sudhansu Sekhar Sahoo Department of Mechanical Engineering CET Bhubaneswar, India. Abstract The paper presents prediction of solar radiation data of Bhubaneswar by using least square support vector machine. We used the least squares support vector machine (LS-SVM) based algorithm to predict the monthly average solar radiation of Bhubaneswar based upon the input parameters sunshine duration and temperature. A Gaussian Radial Basis Function (RBF) kernel with Epsilon SVR is used for estimation of solar radiation from 2000 to 2004.The model uses 65% of the data for training, and 35% data for testing. The input parameters used in these models are ratio of sunshine hours (S/S 0 ), average temperature ratio (T/T 0 ) and the output parameter is the solar radiation. The monthly average data recorded and mentioned in solar radiation handbook, India during the period has been considered as training data. The performance of the model can be evaluated by comparing the predicted and measured by using different kernel function used for regression and optimization. It has been found that the after using NU-SVM or Epsilon-SVR for regression varying the different kernel function RBF kernel will give better result with lower mse ( ) and higher r%(95.72). Keywords Sunshine duration, Temperature, Solar Radiation, Radial Basis Function, Support Vector Machine Introduction Among all energy sources Solar energy is the most important renewable /nonconventional energy sources which is available almost every part of the earth, providing 99.98% of the heat energy useful for many applications such as architectural design, agriculture, and atmospheric, land, ocean, and hydrologic models. As the conventional energy sources i.e. coal, petrol, Diesel are depleting day by day, so we are going to use nonconventional energy sources such as solar energy, wind energy and biogas. There are many places which are away from conventional energy sources (remote areas) therefore scientist are relying upon nonconventional energy sources. Nonconventional energy sources are pollution free not makes any noise to the environment, and they are available plenty throughout the year. So to improve the efficiency of solar energy prediction of solar radiation is necessary. The solar radiation reaching the earth s surface could be represented in a number of ways i.e. global solar radiation (Direct + Diffuse), Direct (beam) and diffuse radiation. Many developing 175

2 countries solar radiation measurements are not easily available due to the shortage of measurement equipments. Therefore it is necessary to develop some methods to design models for estimating the solar radiation. Estimation of solar radiation was carried out monthly, hourly and daily based on various meteorological and climatological parameters. To estimate the amount of solar energy incident on a horizontal surface, many models have been developed by using either traditional approach or in soft computing approach based upon available geographic and meteorological parameters such as minimum and maximum temperature, sunshine duration, relative Humidity, rainfall, wind speed. This paper presents the use of Least Squares Support Vector Machines (LS-SVM) for estimating and predicting monthly average global solar radiation of Bhubaneswar for a period of five years from , as LS-SVM is the advance version of standard SVM. The first empirical relation of GSR estimation was proposed by Angstrom [1] in 1924 using only one input parameter i.e. sunshine duration.in1940 Prescott modified the Angstrom model named as Angstrom-Prescott model [2]. Traditional statistical methods are very easy to understand and implement, but they are not suitable for complex time series problem. To solve complicated problems/to perform complex function in different fields as conventional or analytical methods are infeasible or too expensive due to limited sets of operational data are available, for this Scientist developed some soft computing approaches i.e. artificial neural networks (ANNs), Adaptive neuro-fuzzy inference system(anfis), support vector machine (SVM), Genetic Algorithm (GA), Particle Swarm optimization (PSO).Now a day s Scientist are going for developing Hybrid models i.e. Solar-wind, Solar-wind-diesel. A. Rahimikhoob [3] estimate global solar radiation of Iran from ( ) for training and from for testing by using Artificial neural network with maximum and minimum air temperature as input. The empirical Hargreaves and Samani equation (HS) is used for the comparison. The comparison result shows the ANN model was superior to the calibrated Hargreaves and Samani equation. Alawi and Hinai [4] used ANN to estimate solar radiation based on input parameters month, averages of pressure, temperature, vapour pressure, relative humidity, wind speed, and sunshine duration. After prediction the model gave a mean absolute percentage error of 7.3%. Mubiru and Banda [5] applied ANN to estimate monthly average daily global solar irradiation on a horizontal surface at four locations in Uganda based on meteorological parameters sunshine duration, maximum temperature, and cloud cover and geographical parameters (latitude, longitude, and altitude).after prediction a correlation coefficient of was obtained with MBE of MJ/m2 and RMSE of MJ/m2. Karoro Angela et al. [6] used five years of global solar radiation data of Uganda to estimate the monthly average of daily global solar irradiation on a horizontal surface based on a single parameter, sunshine hours, using the artificial neural network technique. A correlation coefficient of was obtained with a mean bias error of MJ/m2 and a root mean square error of MJ/m2. Mellit et al. [7] used a neuro-fuzzy model for predicting monthly clearness index (K t ) in isolated areas based on some geographical coordinates (latitude longitude). The model is also applicable for sizing of stand-alone photovoltaic system. Here the model has been tested and compare with ANN architecture (MLPN, RBFN and RNN).After comparison the model shows 176

3 ANFIS is more effective than other ANN architecture. B. B. Ekici [8] proposed a least square support vector machine model for predicting the solar insolation of next day by taking data measured by Turkish State Meteorological Service from ( ).The input parameters used in this model are daily mean temperature, daily maximum temperature, sunshine duration, solar insolation of the day before parameters. A value of for RMS and for R2 value were obtained after estimation using LS-SVM. J. Zeng, W. Qiao [9] uses a leastsquare (LS) support vector machine (SVM)-based model for short-term solar power prediction (SPP). The input of the model includes sky cover, relative humidity, and wind speed. The output of the model is the predicted atmospheric transmissivity, which then is converted to solar power according to the latitude of the site and the time of the day. Benghanem et al.[10]used Radial Basis Function network (RBF) for modeling and predicting the daily global solar radiation data using meteorological parameter such as air temperature, sunshine duration, and relative humidity. The data s were recorded from at Al-Madinah (Saudi Arabia) by the National Renewable Energy Laboratory. After prediction the result shows that the RBF-model which uses the sunshine duration and air temperature as input parameters, gives accurate results as the correlation coefficient in this case is 98.80%. II. MODEL USED FOR PREDICTION SUPPORT VECTOR MACHINE Support Vector Machines are a useful technique used for data classification and regression. SVM is a kernel based Algorithm generally used for solving nonlinear problems. LS-SVM [11] is a modified version of SVM and a more simple technique than the standard SVM [12].The LS-SVM enables to deal with linear and nonlinear multivariable calibration and solves multivariable problems. The p no of input support vectors are in the first layer and the second layer contains a nonlinear operation of N support vectors. Values can be expressed as: ( ) ( ) ( ) ( ) Where P 1, P2 and P n are the input vectors of LS-SVM.The weight values are calculated by Multiplying Q vectors with the nonlinear output of each support vectors. y( x) w ( x) b (2) Where w is a weighed value vector and b is a threshold value. By using this function non linear prediction function is transformed to linear prediction function in a high-dimensional feature space. As LS- SVM is an improved/advanced version of classical SVM the solution process is a group of equations which greatly enhance the solution speed. Optimization can be obtained by using the equation. I 1 2 min L,, w, b c wb, 2 w (3) 2 i 1 177

4 Fig.1. Support vector Machine Q is a saddle point, and differentiating Q gives the formulas as follows, using Lagrangian multiplier method to solve the formulas Q W l i x i 0 (4) i 1 i 1 l Q i 0 ( 5) b Q T W ( x i) b i y i 0 ( 6) The Fig.2 and Fig. 3 depict the different input parameters used for prediction of global solar radiation at Bhubaneswar from These data are collected from Solar radiation Handbook 2008 and National renewable energy source Laboratory. Fig.2 Average Monthly Evolution of Sunshine Duration Fig.3 Average Monthly Solar radiation Estimation and Prediction As LS-SVM time series prediction uses function estimation in the parameter tuning, prediction, to test the function estimation ability, a simple nonlinear model is used to estimate the target function, Y, which can be implemented with a few line of code using MATLAB We generate sample data sets K 7 divided into input x and output k, After using LS- SVM processing type to 'function estimation,' we then tune the coefficients using the tune ls-svm command, then pass the values for x, k, type, and other functions(cost function and different Kernel functions) used for the computation. Two tuning hyper-parameters, gamma and sig2 combining gives the output with the use of tune ls-svm function. After execution the program produce the following output and specific values for the hyper parameters. Coupled Simulated Annealing results: [gam] = [sig 2] = F(X) = e-007 TUNELSSVM: chosen specification 2. Optimization routine Simplex Cost Function Leaveoneout lssvm Kernel Function RBF_Kernel 3. Starting values Figures and Tables 178

5 Y Y Proceedings of International Interdisciplinary Conference On Engineering Science & Management Svmtype TABLE I OPTIMIZATION AND MAXIMUM FUNCTION EVALUATION AFTER SIMULATION Itera Funccoungamm Min f(x) Log- Logsig2 tion a e e e e e e e e e e-007 Epsilon- SVR Kernel Used Iterat ion RBF LS-SVM 2 and its 95% (2 ) error bands =6.9642, = Fig.4 LS-SVM function estimation X MSE r% Linear RBF Polynomial Sigmoidal Nu-SVR Linear RBF Polynomial Sigmoidal Optimization terminated successfully (Max Fun Evals) Simplex results: X= , F(X) = 4.257e-007 Obtained hyper-parameters:[gamma sig2]: The trainlssvm command is used to generate alpha and b which are taken as both the input to the plot lssvm function. The estimated function Y in terms of X shown in Fig. 3 to Fig. 4. TABLE II MEAN SQUARE ERROR (MSE) AND REGRESSION VALUE USING SVM X Results and Discussion Fig.5 Plot of Y vs X After several iteration and using different kernel function for training and testing of data the Best

6 Performance is obtained by the model having input sunshine duration and temperature. By using RBF kernel function and for both the case of regression with Epsilon-SVR and nu-svr the model will give highest correlation coefficient with least mean square error between measured and Predicted data. A Comparison between measured and predicted solar radiation based upon the input sunshine duration and temperature is shown in the Fig. 6. Fig.6 predicted vs measured solar radiation IV. CONCLUSION The least squares support vector machine (LSSVM) based algorithm used to predict the future data. A Gaussian Radial Basis Function (RBF) kernel function was used on the data set to optimize the tuning parameters and to obtain the moderated output. The training process of LS-SVM was designed to select both kernel and other meteorological parameters. The solar radiation of Bhubaneswar data collected from meteorological department (IMD Bhubaneswar) and renewable energy source laboratory were used for prediction.60% of the data were used for training, and remaining 40% were used for testing. The experimental results demonstrated that the proposed LSSVM based predictive model and the training algorithm gives an accurate prediction. This algorithm could be very useful for developing a resource efficient prediction model for any quantifiable data set, i.e. Global warming, glacier melting, and wind solar prediction, global energy budget, weather forecasting etc. Feasibiltity study of Solar thermal collectors and solar PV applications may be done with the output of solar data with this present method. V. REFERENCES [1] Angstrom, Solar and terrestrial radiation, Quart. J. Roy. Met. Soc, pp , [2] J. A. Prescott, Evaporation from water surface in relation to solar radiation, Trans. Roy. Soc. Aust, [3] A. Rahimikhoob, Estimating global solar radiation using artificial neural network and air temperature data in a semi-arid environment, Renewable Energy, vol. 35, pp ,2010. [4] S. M. Alawi and H. A. Hinai, An ANN-based approach for predicting global radiation in locations with no direct measurement instrumentation, Renewable Energy, vol. 14, pp , [5] J. Mubiru and E. J. K. B. Banda, Estimation of monthly average daily global solar irradiation using artificial neural networks, Solar Energy, vol. 82, pp , [6] K.Angela, S. Taddeo, and M. James, Predicting Global Solar Radiation Using an Artificial Neural Network Single-Parameter Model, Advances in Artificial Neural Systems, pp. 1-7, [7] Mellit.et.al, An ANFIS based prediction for monthly clearness index and Daily solar radiation: Application for sizing of a stand alone photovoltaic system, journal of Physical Science, vol.18, pp.15 35,

7 [8] B. Ekici, A least squares support vector machine model for prediction of the next day solar insolation for effective use of PV systems, Measurement, vol.50, pp , [9] J. Zeng, and W. Qiao, Short-term solar power prediction using a support vector machine, Renewable Energy, vol.52, pp , [10] M. Benghanem, A. Mellit, Radial Basis Function Network-based prediction of global solar radiation data: Application for sizing of a stand-alone photovoltaic system at Al-Madinah, Saudi Arabia, Energy, vol.35, pp , [11] Support Vector Machines Toolbox, [12] J. Suykens, and A. Vandewalle, J. Least squares support vector machine classifiers, Neural Processing Letter, vol.9, pp ,