Available online at www.sciencedirect.com ScienceDirect Procedia Engineering 154 (2016 ) 1237 1242 12th International Conference on Hydroinformatics, HIC 2016 Estimating Global Solar Irradiance for Optimal Photovoltaic System Sungwon Kim a *, Youngmin Seo b, Vijay P. Singh c a Department Railroad and Civil Engineering, Dongyang University, Yeongju, 36040, South Korea b Department Constructional Environmental Engineering, Kyungpook National University, Sangju, 37224, South Korea c Department Biological and Agricultural Engineering & Zachry Department Civil Engineering, Texas A & M University, College Station, Texas, 77843-2117, USA Abstract The objective this study is to develop the hybrid model for estimating solar irradiance and investigate its accuracy for optimal photovoltaic system. The hybrid model is wavelet-based support vector machines (WSVMs) and wavelet-based adaptive-neuro fuzzy inference system (WANFIS). Wavelet decomposition is employed to decompose the global solar irradiance time series components into approximation and detail components. These decomposed time series are then used as input to support vector machines (SVMs) modules in the WSVMs model and adaptive-neuro fuzzy inference system (ANFIS) modules in the WANFIS. Based on statistical indices, results indicate that WSVMs and WANFIS can successfully be used for the estimation global solar irradiance at Big bend, Carbondale, Champaign, and Springfield stations in Illinois. 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 2016 The Authors. Published by Elsevier Ltd. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review Peer-review under under responsibility responsibility the the organizing organizing committee committee HIC HIC 2016 2016. Keywords: Solar Irradiance, ANFIS, WANFIS, SVMs, WSVMs, Photovoltaic system 1. Introduction Solar irradiance is the important energy supply basis for natural processes, such as snow melt, plant grow-up, evapotranspiration, and crop growth, and is also a variable needed for biophysical models to evaluate risk forest fires, hydrological simulation models and mathematical models. Solar irradiance plays an important role in the design and analysis energy efficient buildings in different types climate. In cold and severe cold regions, passive solar designs and active solar systems help lower the reliance on conventional heating means using fossil fuels. In tropical and subtropical climates, solar heat gain is a major cooling load component, especially in cooling dominated buildings [1, 2]. The effects prevailing climate and local topography would determine the actual amount solar irradiance reaching a particular location. Solar irradiance data provide information on how much the sun s energy strikes a surface at al location on earth during a particular time period. Due to the cost and difficulty in measurement, these data are not readily available. Therefore, there is the need to develop alternative ways generating these data [3]. The objective the present study is to develop wavelet-based support vector machines (WSVMs) and wavelet-based adaptive-neuro fuzzy inference system (WANFIS) models that can be used to estimate daily solar irradiance at four weather stations (Big bend, Carbondale, Champaign and Springfield) in Illinois State, USA. * Corresponding author. Tel.: +82-54-630-1241; fax: +82-54-637-8027. E-mail address: swkim1968@dyu.ac.kr 1877-7058 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility the organizing committee HIC 2016 doi:10.1016/j.proeng.2016.07.446
1238 Sungwon Kim et al. / Procedia Engineering 154 ( 2016 ) 1237 1242 The paper is organized as follows: The second part describes the wavelet decomposition method. Artificial neural networks models, including support vector machines (SVMs) and neuro fuzzy inference system (ANFIS), are described in the third part. The fourth part describes a case study, including study catchment and data. The fifth part describes applications and discussion results. Conclusions and further studies are presented in the last part the paper. 2. Wavelet Decomposition Wavelet analysis is a multi-resolution analysis in time and frequency domains. The wavelet transform decomposes a time series signal into different resolutions by controlling scaling and shifting. It provides a good localization properties in both time and frequency domains [4]. It also has an advantage that it has flexibility in choosing the mother wavelet, which is the transform function, according to the characteristics time series. A fast DWT algorithm developed by Mallat [5] is based on four filters, including decomposition low-pass, decomposition high-pass, reconstruction low-pass and reconstruction high-pass filters. For the practical implementation Mallat s algorithm, low-pass and high-pass filters are used instead father and mother wavelets, which are also called scaling and wavelet functions, respectively. The low-pass filter, associated with the scaling function, allows the analysis low frequency components, while the high-pass filter, associated with the wavelet function, allows the analysis high frequency components. These filters used in Mallat s algorithm are determined according to the selection mother wavelets [6]. A multilevel decomposition process can be achieved, where the original signal is broken down into lower resolution components. 3. Artificial Neural Networks (ANN) 3.1. Support Vector Machines (SVMs) Support vector machines (SVMs) has found wide application in several areas including pattern recognition, regression, multimedia, bio-informatics and artificial intelligence. SVMs is a new kind classifier that is motivated by two concepts. First, transforming data into a high-dimensional space can transform complex problems into simpler problems that can use linear discriminant functions. Second, SVMs is motivated by the concept training and using only those inputs that are near the decision surface since they provide the most information about the classification [7, 8]. The solution traditional ANN models may tend to fall into a local optimal solution, whereas global optimum solution is guaranteed for SVMs [9]. 3.2. Adaptive Neuro-Fuzzy Inference System (ANFIS) Adaptive neuro-fuzzy inference system (ANFIS) is a combination an adaptive neural network and a fuzzy inference system (FIS). Since this system is based on the FIS reflecting vague knowledge, an important aspect is that the system should always be interpretable in terms fuzzy IF-THEN rules. ANFIS can approximate any real continuous function on a compact set to any degree accuracy [10]. There are two approaches for FIS, namely the approaches Mamdani [11] and Sugeno [12]. The differences between the two approaches arise from the consequent part. Mamdani s approach uses fuzzy Membership Functions (MFs), whereas Sugeno s approach uses linear or constant functions. In this study, Sugeno s approach was used for estimating solar irradiance. 3.3. WSVMs and WANFIS WSVMs is a combination wavelet decomposition and SVMs, whereas WANFIS is a combination wavelet decomposition and ANFIS. The wavelet decomposition is employed to decompose an input time series into approximation and detail components. The decomposed time series are used as inputs to SVMs and ANFIS for WSVMs and WANFIS models, respectively. The application WSVMs and WANFIS models in hydrology and water resources can be found from the literature [13, 14]. WSVMs and WANFIS consist a two-step algorithm. The first step corresponds to a multilevel wavelet decomposition. The input data SVMs and ANFIS are decomposed using the wavelet transform. In this study, DWT using Mallat s algorithm was used for decomposing the time series signals. The multiresolution analysis by Mallat s algorithm generates approximations and details for a given time series signal. An approximation holds the general trend the original signal, whereas a detail depicts high-frequency components it. Therefore, the original signal is broken down into lower resolution components. For example, three-level DWT decomposes a signal x(t) into D 1, D 2, D 3, and A 3, where D 1, D 2 and D 3 are details and A 3 is an approximation. D 1, D 2, D 3 and A 3 are used as input to SVMs and ANFIS. The second step corresponds to training and testing phases using SVMs and ANFIS, respectively.
Sungwon Kim et al. / Procedia Engineering 154 ( 2016 ) 1237 1242 1239 4. Case Study 4.1. Study Area and Data In this study, the daily weather data obtained from four weather stations (Figure 1), Big bend (latitude 41.6341 N, longitude 90.0394 W, altitude 182.4 m), Carbondale (latitude 37.6997 N, longitude 89.2433 W, altitude 137 m), Champaign (latitude 40.0840 N, longitude 88.2404 W, altitude 219 m) and Springfield (latitude 39.7273 N, longitude 89.6106 W, altitude 177 m) and operated by the Illinois State Water Survey (ISWS), were used in this study (http://www.isws.illinois.edu/warm/). The ISWS is a division the Prairie Research Institute the University Illinois at Urbana-Champaign and has flourished for more than a century by anticipating and responding to new challenges and opportunities to serve the citizens Illinois. The weather data consisted ten years (January 2005 to December 2014, N=3652 days) daily records average air temperature (T), total solar irradiance (R), average relative humidity (h r), average dew point temperature (T d), average wind speed (W), total potential evapotranspiration (ET), and average soil temperature at 10 cm (T s) depth. Air temperature and relative humidity have been measured at 2 m above the ground, whereas wind speed has been measured at 10 m above the ground (prior to winter 2011/2012 measurement made at 9.1 m). Soil temperature has been measured under bare soil conditions at 10 cm depth below the ground and under sod condition between 10 cm and 20 cm depths below the ground. Potential evapotranspiration has been calculated using the Food and Agricultural Organization (FAO) the United Nations Penman Monteith equation as outlined in FAO Irrigation and Drainage Paper No. 56 Crop Evapotranspiration [15] since December 1, 2012. Prior to that time, the Van Bavel method was used for calculating potential evapotranspiration [16]. ANN models use a split sample approach to examine the model generalization. To apply the split sample approach, the data used is split into training and testing sets, respectively. The training data is used to train the model to estimate the model parameters; test data is used to test the generalization capability the model. In all these applications, the first 90% data (January 2005 to December 2013, N=3287 days) was applied for training, and the last 10% data (January 2014 to December 2014, N=365 days) for testing. Fig. 1 Schematic diagram four weather stations in Illinois State The estimated daily solar irradiance values were compared with observed values using five different performance evaluation criteria: correlation coefficient (CC), the Nash-Sutcliffe efficiency (NS) [17], the root mean square error (RMSE), the mean absolute error (MAE), and the average performance error (APE). It can be found that the data length does not significantly affect the performance data-driven models. Although CC is one the most widely used criteria for calibration and evaluation
1240 Sungwon Kim et al. / Procedia Engineering 154 ( 2016 ) 1237 1242 hydrological models with observed data, it alone cannot discriminate which model is better than others. Since the standardization inherent in CC as well as its sensitivity to outliers yields high CC values, even when the model performance is not perfect. Legates and McCabe (1999) [18] suggested that various evaluation criteria (e.g., RMSE, MAE, NS, and APE) must be used to evaluate model performance. 5. Applications and Discussion Results 5.1. Estimating Solar Irradiance using SVM and ANFIS The development an optimal model is a major problem in ANN modeling [19, 20]. Since the number input-output neurons is problem dependent, there is no precise way choosing the optimal number hidden neurons. The model architecture, therefore, is generally determined using a trial and error method. Conventional ANN models adopt one hidden layer for model construction, since it is well known that one hidden layer is enough to represent the nonlinear complex relationship [21]. The number hidden neurons ANN models for estimating solar irradiance was determined using a trial and error approach. Figure 2(a) shows the developed architecture SVMs comprising input, hidden, and output layers for estimating solar irradiance in this study. Figure 2(b) shows the developed architecture ANFIS comprising input, layer 1, layer 2, layer 3, layer 4, layer 5, and output layers for estimating solar irradiance in this study. (a) SVM (b) ANFIS Fig. 2 Developed architecture for estimating solar irradiance
Sungwon Kim et al. / Procedia Engineering 154 ( 2016 ) 1237 1242 1241 In the modeling solar irradiance, comparison SVMs and WSVMs models with different mother wavelets indicates that the results WSVMs models are better than those the SVMs model. Comparison ANFIS and WANFIS models with different mother wavelets also indicates that the results WANFIS models are better than those the ANFIS model. Figure 3(a)-(d) shows the comparison the observed and estimated daily solar irradiance values using SVMs and WSVMs_DB10 (WSVMs with DB10 mother wavelet) models (four inputs) for Big bend station. Figure 4 shows the comparison the observed and estimated daily solar irradiance values using ANFIS and WANFIS_DB10 (WANFIS with DB10 mother wavelet) models (four inputs) for Big bend station. (a) SVMs 4 (EDSW, Big bend) (b) SVMs 4 (ETHW, Big bend) (c) SVMs 4 (EDSW_DB10, Big bend) (d) SVMs 4 (ETHW_DB10, Big bend) Fig. 3 Comparison observed and estimated solar irradiance using SVMs and WSVMs (a) ANFIS 4 (EDSW, Big bend) (b) ANFIS 4 (ETHW, Big bend)
1242 Sungwon Kim et al. / Procedia Engineering 154 ( 2016 ) 1237 1242 (c) WANFIS 4 (EDSW_DB10, Big bend) (d) WANFIS 4 (ETHW_DB10, Big bend) Fig. 4 Comparison observed and estimated solar irradiance using ANFIS and WANFIS 6. Conclusions SVMs and ANFIS models are used to estimate solar irradiance. Wavelet decomposition is employed and sub-components are used as input to SVMs and ANFIS for obtaining WSVMs and WANFIS models, respectively. Comparison SVMs and WSVMs models with different mother wavelets indicates that the results WSVMs models with different mother wavelets are better than those SVMs model. Comparison ANFIS and WANFIS models with different mother wavelets indicates that the results WANFIS models with different mother wavelets are better than those the ANFIS model. The results SVMs and WSVMs models with different mother wavelets are found to be better than those ANFIS and WANFIS models with different mother wavelets, respectively. References [1] R. Mahmood, K.G. Hubbard, Effect time temperature observation and estimation daily solar radiation for the Northern Great Plains, USA, Agron. J. 94(4) (2002), 723-733. [2] R. Kumar, L. Umanand, L. Estimation global radiation using clearness index model for sizing photovoltaic system, Renew. Energ. 30(15) (2005) 2221-2233. [3] A.S. Dorvlo, J.A. Jervase, A. Al-Lawati, Solar radiation estimation using artificial neural networks, Appl. Energ. 71(4) (2002) 307-319. [4] V. Nourani, A.H. Baghanam, J. Adamowski, O. Kisi, Applications hybrid wavelet Artificial Intelligence models in hydrology: A review, J. Hydrol. 514 (2014) 358-377. [5] S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Trans. Pattern. Anal. Mach. Intell. 11(7) (1989) 674-693. [6] M., González-Audícana, X., Otazu, O. Fors, A. Seco, 2005. Comparison between Mallat s and the à trous discrete wavelet transform based algorithms for the fusion multispectral and panchromatic images, Int. J. Remote Sens. 26(3) (2005) 595-614. [7] V.N. Vapnik, An overview statistical learning theory, IEEE Trans. Neural Network 10(5) (1999) 988-999. [8] S. Tripathi, V.V. Srinivas, R.S. Nanjundish, Downscaling precipitation for climate change scenarios: a support vector machine approach, J. Hydrol. 330(3 4) (2006) 621 640. [9] S. Haykin, Neural networks and learning machines 3 rd Edition, Prentice Hall, New Jersey, 2009. [10] J.S.R. Jang, C.T. Sun, E. Mizutani, Neuro-fuzzy and st computing: a computational approach to learning and machine intelligence, Prentice-Hall, New Jersey, 1997. [11] E.H. Mamdani, S. Assilian, An experiment in linguistic synthesis with a fuzzy logic controller, Int. J. Man Mach. Stud. 7(1) (1975) 1-13. [12] T. Takagi, M. Sugeno, Fuzzy identification systems and its application to modeling and control, IEEE T. Syst. Man Cyb. SMC-15(1) 116-132. [13] O. Kisi, M. Cimen, A wavelet-support vector machine conjunction model for monthly streamflow forecasting, J. Hydrol. 399(1-2) (2011) 132-140. [14] O. Kisi, M. Cimen, Precipitation forecasting by using wavelet-support vector machine conjunction model, Eng. Appl. Artif. Intell. 25(4) (2012) 783-792. [15] R.G. Allen, L.S. Pereira, D. Raes, M. Smith, Crop evapotranspiration. Guidelines for computing crop water requirement, Irrigation and Drainage Paper no. 56. FAO, Rome, Italy, 1998. [16] CHM. Van Bavel, Estimating soil moisture conditions and time for irrigation with the evapotranspiration method, USDA, ARS 41 11, U.S. Dept. Agric., Raleigh, NC, 1 16. 1956. [17] J.E. Nash, J.V. Sutcliffe, River flow forecasting through conceptual models part 1 A discussion principles, J. Hydrol. 10(3) (1970) 282 290. [18] D.R. Legates, G.J. McCabe, 1999. Evaluating the use goodness--fit measures in hydrologic and hydroclimatic model validation, Water Resour. Res. 35 (1) (1999) 233 241. [19] O. Kisi, Evapotranspiration modeling from climatic data using a neural computing technique, Hydrol. Process. 21(14) (2007) 1925-1934. [20] S. Kim, H.S. Kim, Neural networks and genetic algorithm approach for nonlinear evaporation and evapotranspiration modeling, J. Hydrol. 351(3-4) (2008) 299-317. [21] S. Kim, J. Shiri, O. Kisi, Pan Evaporation using neural computing approach for different climatic zones, Water Resour. Manage. 26(11) (2012) 3231-3249.