Statistical Comparison Between Empirical Models And Artificial Neural Network Method For Global Solar Radiation At Qena, Egypt

Transcription

1 Statstcal Comparson Between Emprcal Models And Artfcal Neural Network Method For lobal Solar Radaton At Qena, Egypt Emad Al Ahmed Physcs department, faculty of scences South Valley Unversty Qena, Egypt Abstract Seven emprcal models and the artfcal neural network model (ANN) are appled and valdated to estmate the daly and monthly global solar radaton on a horzontal surface n Qena, Upper Egypt. Statstcal comparson has been done between all these models. The results demonstrated that ANN model wth MBE, RMSE, MPE, R, NSE and t values of , , , , and respectvely, are superor to the other models. Ths model can be appled as a relable and accurate global solar radaton estmator for Qena and regons wth smlar clmatc condtons. regons, atmospherc parameters at a partcular locaton are beng to predct the global solar radaton n that locaton. Keywords lobal solar radaton; regresson models; statstcal analyss; artfcal neural networ; emprcal models I. INTRODUCTION Egypt has an ntenton for usng further alternatve resources of energy due to several economc reasons and more mportantly other envronmental protecton goals. lobal solar radaton (SR) s consdered as one of the most mportant sources of energy that reach our planet. Egypt has great advantageous poston, belongs to the global sun-belt, as shown n Fgure 1 [1]. Egypt has an ntenton for usng further alternatve resources of energy due to several economc reasons and more mportantly other envronmental protecton goals. lobal solar radaton (SR) s consdered as one of the most mportant sources of energy that reach our planet. Egypt has great advantageous poston, belongs to the global sun-belt, as shown n Fg. 1 [1]. Solar radaton measurements have effect n several applcatons such as solar energy systems, agrculture, and archtecture; but they are not easly avalable n all places because of the cost, regular mantenance and tunng requrements. The avalablty of solar radaton measures s not an easy matter [2]. Thus, suggestng adequate alternatves to estmate such measures based on easly avalable clmatologc data. Assessng global solar radaton s an mportant requrement for feasblty analyss, desgn and mplementaton of solar energy systems. However, because of the unavalablty of the nstrument n many Fg. 1. Egypt s part of the solar belt. There are many models to predct long-term daly and monthly average solar radaton n dfferent regons usng dfferent combnatons of measured weather parameters. The avalablty of a solar radaton model, n a partcular regon, s very useful n estmatng the amount of power that could be generated from a partcular solar energy system [3]. Frst theoretcal model has been ntroduced by Angstrom [4] for estmatng global solar radaton based on sunshne duraton. Page [5] and Prescot [6] reconsdered ths model to calculate monthly average of the daly global radaton, on a horzontal surface from monthly average daly total nsolaton on an extraterrestral horzontal surface. Many models have been developed to estmate the amount of global solar radaton on horzontal surfaces usng varous clmatc parameters, such as sunshne duraton, cloud cover, humdty, maxmum and mnmum ambent temperatures, wnd speed, etc. [7-11] Few papers appeared concernng estmaton of solar radaton over varous places n Egypt [12-14]. An artfcal neural network (ANN) provdes a computatonally effcent way of determnng an emprcal, possbly nonlnear relatonshp between a number of nputs and one or more outputs. ANN has been appled for modelng, dentfcaton, optmzaton, JMESTN

2 predcton, forecastng and control of complex systems. ANN models are type of solar predcton models and there have been several artcles that have used artfcal neural networks for predctng solar radaton [15-19]. The am of the study s the estmaton the global solar radaton by usng artfcal neural network and some emprcal models wth atmospherc parameters of relatve humdty, maxmum temperature, sunshne hours and cloud cover. Varous regresson analyses are performed between the parameters to fnd the relevant coeffcents for establshng the models. Conventonal statstcal ndces such as RMSE, MBE, MABE, R 2, t-statstc, MPE and MAPE are appled to the estmated values for each model and the actual data to evaluate model performance and to determne the most advantageous. II. DATA AND METHODOLOY A. Data In ths study, the comparson process has been completed n Qena ( N, E) whch located n the Upper Egypt about 600 Km south of Caro. The clmate of Qena s very hot dry n summer, cold n wnter and rarely ranng. Also, t receves a large quantty of solar radaton, especally n summer [20]. South valley unversty staton at Qena, whch s one of the statons gudes of the Egyptan Meteorologcal authorty, provdes us wth the relevant data. The data collected cover a perod of thrteen years from 2001 to 2013, as shown Table 1. B. Extraterrestral radaton. Solar radaton ncdent outsde the earth s atmosphere s called extraterrestral solar radaton. The daly extraterrestral radaton o was calculated from the followng equaton [21, 22]. 24 I 0= SC [ cos 360D π 365 ] [cos φ cos δ sn ω s+ πω s 180 snφsnδ] Where: I sc = 1367 Wm -2 s the solar constant [23]. D s the Julan day number; φ s the lattude; δ s the declnaton angle; ω s s the sunset hour. δ and ω are gven from these formulae. δ = 23.45sn ( D 365 ) ω s = cos 1 [ tanφtanδ] The maxmum possble sunshne duraton So was calculated usng the followng equaton. S o = 2 15 ω s A bref descrpton of the mathematcal expresson of the varous models proposed n the present paper s gven below. C. Models used Table 1. The avalable data for each month per year The Angstrom correlaton (1924) [4] has served as a basc approach to estmate global radaton for a long tme. Prescott (1940) [24] put the correlaton n a better form known as the Angstrom-Prescott model as; o = a + b S S o (1) Where s the average daly global radaton, o s average daly extraterrestral radaton, S s the day length, So s the maxmum possble sunshne duraton, and a and b are emprcal coeffcents. Angstrom s calculatons for Swedsh clmatc condtons showed that the sum of the emprcal regresson coeffcents a and b s equal to unty. Also, nvestgatons for varous world geographcal lattudes demonstrated that the value of ths sum ncreases as the lattude ncreases, wth some exceptons. years month Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Total JMESTN

3 lover and McCulloch presented coeffcent a as a functon of the cosne of the lattude, for lattudes under 60 and suggested that [25, 26]. = 0.29 cos( ) S (2) o S o Aknoglu and Ecevt (1990) [27] suggested a quadratc correlaton between the rato of o and n to estmate the values of global solar radaton = a + b S + c ( S ) 2 (3) o S o S o In order to have more precson n the estmaton of the global solar radaton, Ampratwum and Dorvlo (1999) [28] have developed a logarthmc form of lnear model as: o = a + b log S S o (4) Almorox [29, 30] presents the exponental S correlaton between and wth the followng expresson: = a + beso (5) o S o Hargreaves et al. [30-33] were the frst to propose a procedure to estmate the global solar radaton by usng the dfference between daly maxmum and daly mnmum ar temperature and extraterrestral radaton. The proposed equaton has the followng form: S o o = a + b(t max T mn ) 2 (6) Accordng to the opnathan model [10], whch studed the varaton of o as a functon of the lattude and the elevaton of the ste, the fracton of nsolaton, ar temperature, and the maxmum average relatve humdty, Abdalla (1994) [34] propose model correlates o wth the sunshne duraton, maxmum ar temperature, and average relatve humdty, n order to ncrease the accuracy of the estmatng coeffcents, as follow: = a + b S + c T o S max + d RH (7) o Emad (2013) [15] uses Artfcal Neural Network (ANN) method to estmate lobal solar radaton n Qena based on the number of sunshne hours, day number and locaton coordnates. A feed-forward back-propagaton neural network was used n ths study. A typcal neural network conssts of an nput, a hdden, and output layer. Other components nclude a neuron, weght, and a transfer functon as shown n Fg. 2. Fg. 2. Typcal neuron n a feed forward network. D. Comparson and Statstcal technques There are many parameters whch deal wth the assessment and comparson of daly solar radaton estmaton models. Here mathematcal expressons and physcal meanng of some of these parameters. 1. The Mean Bas Error (MBE) n MBE = 1 n (,calc.,meas. ) Ths test helps to calculate the error or the devaton of the calculated value from the measured value and provdes nformaton on long-term performance. A low MBE value s desred. A negatve value gves the average amount of underestmaton n the calculated value. So, one drawback of these two mentoned tests s that overestmaton of an ndvdual observaton wll cancel underestmaton n a separate observaton. 2. The Root Mean Square Error (RMSE) RMSE = [ 1 n n (,calc.,meas. ) 2 The value of RMSE s always postve, representng zero n the deal case. The normalzed root mean square error gves nformaton on the short term performance of the correlatons by allowng a term by term comparson of the actual devaton between the predcted and measured values. The smaller the value, the better s the model s performance [35]. 3. The Mean Percentage Error (MPE) n MPE(%) = 1 n ((,calc.,meas. ) ) 100,meas. Ths s one of the measures used to evaluate forecasts usng forecast errors. Forecast error s defned as actual observaton mnus forecast. The mean percentage error s the average or mean of all the percentage errors. A percentage error between 10% and +10% s consdered acceptable [36]. 4. The Coeffcent of Correlaton (R) n calc. meas. calc. meas R = n ( calc. ) 2 ( calc. ) 2 n ( meas. ) 2 ( meas. ) 2 ] 1 2 JMESTN

4 Ths parameter measures the strength and the drecton of a lnear relatonshp between the measured and estmated values. The value of R s between -1 and +1. The + and sgns are used for postve lnear correlatons and negatve lnear correlatons, respectvely. If there s no lnear correlaton or a weak lnear correlaton, R s close to 0. A value near zero means that there s a random, nonlnear relatonshp between the two varables but t should approach to 1 as closely as possble for better modelng. 5. The Nash Sutclffe Equaton (NSE) 1 NSE = 1 n n (,calc.,meas. ) 2 1 n n ( meas.,meas. ) 2 Where,,meas. s the mean measured global radaton. To mprove the results and better comparson ths parameter s also selected as an evaluaton crteron. A model s more effcent when NSE s closer to 1 [37]. The errors that have been estmated help to compare the models but they do not make the model statstcally sgnfcant. 6. t-statstc Test As defned by Student [38] n one of the tests for mean values, the random varable t wth n 1 degrees of freedom may be wrtten here as follows: (n 1) (MBE)2 t = [ (RMSE) 2 (MBE) 2] The t-statstc allows models to be compared and at the same tme t s carred out to determne statstcal sgnfcance of the predcted values by the models. The smaller the value of t the better s the performance. To determne whether a model s estmates are statstcally sgnfcant, one smply has to determne, from standard statstcal tables, the crtcal t value. For the model s estmates to be judged statstcally sgnfcant at the calculated t value must be less than the crtcal value. III. 1 2 RESULTS AND DISCUSSIONS In the study, the daly average of global solar radaton, the day length, temperature and relatve humdty were taken of the average of the values n the correspondng perod from 2001 to 2013 for the ste under consderaton as shown n Fgs Regresson analyss s performed by usng Mcrosoft Excel 2010 and SPSS Statstcs 22 to fnd values of the regresson coeffcents that mnmze the sum of the squared resdual values. The obtaned regresson coeffcents after analyss are gven n Table 2 for each model. Measured global solar radaton ( Mj/m 2.day ) The day length ( Hours ) Temperature ( o C) Fg. 5. Daly average temperature at Qena from 2001 to Relatve Humdty ( % ) Julan day number Fg. 3. Daly average global solar radaton at Qena from 2001 to Julan day number Fg 4. Daly average the day length at Qena from 2001 to Julan day number Julan day number RH max RH mn RH aver. T max T mn T aver. Fg. 6. Daly average relatve humdty at Qena from 2001 to 2013 JMESTN

5 Table 2. Obtaned regresson coeffcents. Regresson coeffcents Model No. a b c d Eq Eq Eq Eq Eq Eq Eq By usng the developed models, the total daly global solar radaton values are estmated throughout the study perod. Also, the monthly average of daly global solar radaton s calculated as shown n Table 3. To determne the daly agreement between the calculated and the measured global solar radaton values, correlaton plots are provded for the models n Fg. 7. For evaluaton of the establshed models, statstcal ndces are appled to the calculated and the measured data; the results are summarzes n Table 4 for each model. Accordng to the calculated values for Qena n table 4 and Fg. 7; the correcton R or R 2 values are very close to one. Hence, these two ndces do not provde sutable nformaton for comparng the performance of the models. By comparng the values of the rest statstcal ndces for all models; the ANN model has the best values whch are superor to these for other models. Table 3. Measured and calculated monthly averages of daly global solar radaton (Mj/m 2.day) at Qena ( ). Calcuated by model No. Month Measured ANN Eq. 1 Eq. 2 Eq. 3 Eq. 4 Eq. 5 Eq. 6 Eq. 7 model Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Table 4. The calculated values of the statstcal ndces for each model at Qena Model No. statstcal ndex MBE RMSE MPE R NSE t Eq Eq Eq Eq Eq Eq Eq ANN model JMESTN

6 Calculated global solar radaton (Mj/m 2.day) Measured global solar radaton (Mj/m 2.day) Fg. 7. Correlaton of calculated and measured global solar radaton for each model. JMESTN

7 IV. CONCLUSIONS Assessng global solar radaton s an mportant requrement for feasblty analyss, desgn and mplementaton of solar energy systems. However, because of the unavalablty of the nstrument n many locatons, atmospherc parameters at a partcular locaton are beng to predct the global solar radaton n that locaton. In ths study, seven emprcal models n addton to artfcal neural network model (ANN) are developed and valdated to estmate the daly and monthly global solar radaton on a horzontal surface n Qena, Upper Egypt. These models were studed based on the avalable clmatc parameters of sunshne hour, maxmum and mnmum temperature, and relatve humdty. Accordng to the statstcal comparson between all models, the ANN model s superor to the other models; t could be appled for estmaton of global solar radaton n Qena and other smlar clmatc condtons regons. REFERENCES [1] Comsan, M.N.H, Solar energy perspectves n Egypt, Proceedngs of the 4 th Envronmental Physcs Conference. Hurghada, Egypt. [2] Ass and M. Jama, Estmatng global Solar Radaton on Horzontal from Sunshne Hours n Abu Dhab UAE, Proceedng of the 4 th Internatonal Conference on Renewable Energy Sources (RES 10), Sousse, Tunsa, pp [3] Hassan A.N. and Al H. Ass, Tme- Seres Regresson Model for Predcton of Mean Daly lobal Solar Radaton n Al-An, UAE. Internatonal Scholarly Research Network; ISRN Renewable Energy. Artcle ID , 11 pages. [4] Angstrom A., Solar and terrestral radaton, Q. J. Roy. Met. Soc., 50, , [5] Page J.K., The estmaton of monthly mean values of daly total short wave radaton on vertcal and nclned surfaces from sun shne records for lattudes 400 N-400 S. Proc. U.N. conf. on new sources of energy. vol. 4(598), P [6] Prescott J.A., Evaporaton from water surface n relaton to solar radaton. Trans. Roy. Soc. Austr., 64, 114. [7] Chegaar, M. and A. Chban, lobal solar radaton estmaton n Algera. Energy Converson and Management. 42, [8] Jacovdes, C.P., F.S. Tymvos, V.D. Assmakopoulos, and N.A. Kaltsoundes, Comparatve study of varous correlatons n estmatng hourly dffuse fracton of global solar radaton. Renewable Energy. 31, [9] opnathan, K.K A new model for estmatng total solar radaton n Doha. Energy Converson and Managemen, vol. 28, pp [10] opnathan, K.K., A general formula for computng the coeffcents of the correlaton connectng global solar radaton to sunshne duraton. Solar Energy. 41, [11] Halouan, N., C.T. Nguyen and D. Vo-Ngoc, Calculaton of monthly average global solar radaton on horzontal surfaces usng daly hours of brght sunshne. Solar Energy. 50, [12] El-Seba, A.A. and Trabea, A.A., Estmatng global solar radaton on horzontal surfaces over Egypt. Egyptan Journal of Solds. 28, pp [13] Khall, S.A. and A.M. Fathy, An Emprcal Method for Estmatng lobal Solar Radaton over Egypt. Acta Polytechnca. vol. 48, no. 5, pp [14] Tadros, M.T.Y, Uses of sunshne duraton to estmate the global solar radaton over eght meteorologcal statons n Egypt, Renewable Energy, vol 21, pp [15] Emad A. Ahmed and Adam, M. El-Nouby, Estmate of lobal Solar Radaton by Usng Artfcal Neural Network n Qena, Upper Egypt. Journal of Clean Energy Technologes, Vol. 1, No. 2. [16] Khatb, T., A. Mohamed, M. Mahmoud and K. Sopan, Estmatng lobal Solar Energy Usng Multlayer Percepton Artfcal Neural Network, Internatonal Journal of Energy, Issue 1, Vol. 6. [17] Jang, Y., Computaton of Monthly Mean Daly lobal Solar Radaton n Chna Usng Artfcal Neural Networks and Comparson wth Other Emprcal Models. Energy, 34(9). [18] AbdulAzeez, M.A., Artfcal Neural Network Estmaton of lobal Solar Radaton Usng Meteorologcal Parameters n usau, Ngera. Archves of Appled Scence Research, vol. 3, no 2, pp [19] Mubru, J., Usng Artfcal Neural Networks to Predct Drect Solar Irradaton. Advances n Artfcal Neural Systems, Artcle ID [20] El-Shazly, S.M., Solar radaton component at Qena-Egypt. DOJARAS Quart J. Hungaran Meteorol. Servce, vol. 101, pp [21] Duffe, J. A. and Beckman, W. A., Solar Engneerng of Thermal Processes. 3rd Edton, John Wley & Sons, Inc., New York. [22] Brd, R.E. and Rordan C.J., Smple solar spectral model for drect and dffuse rradance on horzontal and tlted planes at the Earth s surface for cloudless atmosphere. J. Clmate Appl. Meteorol., 25: pp [23] Frohlch and London, J., Revsed nstructon manual on radaton nstruments and measurements. World clmate research program, publcaton seres, no. 7. [24] Prescott, J.A., Evaporaton from Water Surface n Rela- ton to Solar Radaton. Transactons JMESTN

8 of the Royal Soc- ety of South Australa, Vol. 64, pp [25] lover, J. and Mculloch J, The emprcal relaton between solar radaton and hours of sunshne. Q J R Meteorolog Soc., 84: pp [26] Tymvos, F. S., Jacovdes CP, Mchaeldes SC and Scoutel C, Comparatve study of Angstrom's and artfcal neural networks' methodologes n estmatng global solar radaton. Sol Energy, 78, pp [27] Aknoglu,. and Ecevt, A., A Further Comparson and Dscusson of Sunshne Based Models to Estmate lobal Solar Radaton. Solar Energy, Vol. 15, No. 10, pp [28] Ampratwum, B. and Dorvlo, A.S.S., Estmaton of solar radaton from the number of sunshne hours. Appled Energy, vol. 63, no. 3, pp [29] Almorox, J. and Hontora, C lobal solar radaton estmaton usng sunshne duraton n Span. Energy Converson and Management, vol. 45, no. 9-10, pp [30] Kacem. and Yaha B., A Comparatve Study of Some Regresson Models to Estmate the lobal Solar Radaton on a Horzontal Surface from Sunshne Duraton and Meteorologcal Parameters for harda\a Ste, Algera. Hndaw Publshng Corporaton; ISRN Renewable Energy, Artcle ID [31] Hargreaves.H and Saman, Z.A., Reference crop evapotranspraton from temperature. Transactons of the ASAE, vol. 1, pp [32] Hargreaves,.H. and Allen, R.., Hstory and evaluaton of hargreaves evapotranspraton equaton. Journal of Irrgaton and Dranage Engneerng, vol. 129, no. 1, pp [33] Saman, Z., Hargreaves,.H., Tran, V. and Bawazr, S., Estmatng solar radaton from temperature wth spatal and temporal calbraton. Journal of Irrgaton and Dranage Engneerng, vol. 137, no. 11, pp [34] Abdalla, Y New correlaton of global solar radaton wth meteorologcal parameters for Bahran. Internatonal Journal of Solar Energy, vol. 16, pp [35] Namrata, K., Sharma, S.P. and Saksena, S.B.L., Comparson of Estmated Daly lobal Solar Radaton Usng Dfferent Emprcal Models. Internatonal Journal of Scence and Advanced Technology (ISSN ), Vol. 2, No 4. [36] Muzathk, A.M., Nk, W.B.W., Ibrahm, M.Z., K.B. Samo, K. Sopan and M.A. Alghoul, Daly global solar radaton estmate based on sunshne hours. Internatonal Journal of Mechancal and Materals Engneerng (IJMME), Vol.6, No.1, [37] Chen R., Ers K., Yang, J. Lu S. and Zhao W., Valdaton of fve global radaton models wth measured daly data n Chna. Energy Converson and Management, 45, [38] Bevngton P.R., Data reducton and error analyss for the physcal scences. frst ed. Mcraw Hll Book Co., New. JMESTN