XXVI. ASR '2001 Semnar, Instruments and Control, Ostrava, Aprl 26-27, 2001 Paper 14 Estmaton of Solar Radatons Incdent on a Photovoltac Solar Module usng Neural Networks ELMINIR, K. Hamdy 1, ALAM JAN, Javed 2, ALI, U. Rahuma 3 & BENDA, Vítězslav 3 1 Ing., Dept. of Electro Technology, FEL, CTU, Techncká 2, 166 27 Praha 6, CZ, ehamdy@hotmal.com 2 Ing., Dept. of Instr. & Control Eng., FSI, CTU, Techncká 4, 166 07 Praha 6, CZ, avedalaman@hotmal.com 3 Dr., Natonal Research Insttute of Astronomy and Geophyscs, Helwan, Caro, Egypt Abstract: As solar energy applcatons ncrease, the need for accurate estmates of avalable solar rradance becomes evermore mportant n the optmal desgn of converson systems. Routne meteorologcal measurements of the beam radaton and the dffuse skylght radaton are generally carred out for a horzontal surface. However, feld-testng carred out for the purpose s costly, tme consumng and depends heavly on prevalng weather condtons. Adequate securty and weather protecton must also be provded at the test ste. Measurement may also suffer because of delays that could be caused by bad weather and system falures. To overcome these problems, models are employed to estmate the radatons. For ths purpose a Neural Network Model s traned aganst some measured data, then ths model can be used to predct the data for varous condtons n dfferent spectral bands. A feed forward neural network consstng of two hdden layers contanng 5 and 6 neurons (both logsg TF) wth 5 nputs and 9 outputs has been used. Levenberg-Marquardt backpropagaton optmzaton functon has been used for tranng. Keywords: Solar radaton, Isotropc model, Neural Network, Estmaton, Optmzaton. 2. Introducton Desgn and performance evaluaton of photovoltac systems usually nvolve an estmaton of rradaton ncdent on the photovoltac module plane. For desgn purpose usually only global horzontal rradaton s avalable, whch s usually publshed by meteorologcal nsttutes. Usng rradaton models, one can calculate the gan n rradaton on tlted plane wth respect to the horzontal rradaton. Concernng a part of ths task, most textbooks [Duffe J. and Beckman W., 1980] recommend that the dffuse component be treated as f t were sotropcally emanatng from the sky vault. However, theoretcal as well as expermental results have shown that ths smplfyng assumpton s generally far from realty. Dave J., 1977 examned the valdty of ths sotropc dstrbuton approxmaton for a sun facng flat surface located at the bottom of plane parallel models of non absorbng homogeneous atmospheres. Even for such dealzed and somewhat unrealstc models, he showed that the use of an sotropc dstrbuton approxmaton results n a systematc underestmaton of the dffuse energy contrbuton to the sun facng surfaces. That study demonstrated the need for testng of ths approxmaton for more realstc, atmospherc condtons. Thus t appears that the sky radance should be treated as ansotropc, partcularly because of the strong forward scatterng effect of aerosols [Bugler J., 1977; Hay J., 1979, 1980; Klucher T., 1979; and Iqbal M., 1983]. - 1 -
In ths work, a new approach usng neural network can carry out ths target wth a very hgh accuracy. Artfcal Neural Networks (ANNs) are composed of smple processng elements called neurons or neurodes that are nterconnected n a network (we use the term neurodes and nodes nterchangeably here) operatng n parallel and are programs desgned to smulate the way a smple bologcal nervous system s beleved to operate. They are based on smulated nerve cells or neurons, whch are oned together n a varety of ways to form networks. These artfcal neurodes receve nputs that are analogous to the electrochemcal sgnals that natural neurons receve from other neurons. We can tran a neural network to perform a partcular functon by adustng the values of the connectons (weghts) between elements. By changng the weghts gven to these sgnals, the network learns n a process that seems smlar to that found n nature. These networks have the capacty to learn, memorze and create relatonshps amongst data. The network s adusted, based on a comparson of the output and the target, untl the network output matches the target. Typcally many such nput/target pars are used, n ths supervsed learnng, to tran a network. For example, neurodes n an ANN receve sgnals or nformaton from other neurodes or from external sources, perform transformatons on the sgnals, and then pass those sgnals on to other neurodes. The way nformaton s processed and ntellgence stored n an ANN depends on the archtecture and algorthms of the ANN (see Fg.1). Lachtermacher and Fuller has mentoned the followng characterstcs of ANN: Quck n response. Self organzed n nformaton and ts representaton. Adaptable and generalzed n dong predcton task. Bult-n procedures for statstcal calculatons. No presumed functonal relatonshp between varables. Easly understandable results through graphc presentaton. Deal wth the nonlneartes. Handle nosy or mssng data. Create ther own relatonshp amongst nformaton no equatons! Can work wth large numbers of varables or parameters. Provde general solutons wth good predctve accuracy. Neural networks yeld statstcally lower forecast errors Fg.1 ANN Predcton Model - 2 -
2. Determnaton of the ANN Structure Determnng structure of ANN s based on underlyng theory about what nfluences the dependent varable. Ths nvolves choosng nput varables, number of nput nodes, number of hdden layers and nodes, the transfer functon type, and the number of output nodes. The number of nput nodes n an ANN equals the number of nput varables. In our case, the number of nput nodes s 5 whle number of hdden layers s two, and output nodes are 9. Dvde the nputs and outputs data nto Tranng and Valdaton Sets Input data s used to tran (.e., ft) the network, whle output data s used to valdate the network n an out-of-sample experment or forecast. It s mportant to tran and valdate ANNs usng two dfferent data sets. The frst data set s used to tran the network and the second data set s used to valdate the model. In our case, we used 240 numbers of data as nput set for tranng. Set ntal weghts and start a tranng epoch The ntal values of the tranng weght can nfluence the requred number of epochs and the fnal soluton. The randomzaton of the ntal tranng weght s done between 1 and 1. An epoch s the calculaton of errors and the adustment of weghts by processng all observatons n the tranng set. Also, n ths step, ntal values are gven to all of the weghts (w s) n the ANN. These ntal values can nfluence the speed and RMS that result from the tranng process. Most programs allow weghts to be ntalzed wth all zeros or random numbers from. Input Varables The nput nodes at I 0, I 1,. receve the nputs or varables after feedng. Dstrbute the scaled nputs The scaled varables are then dstrbuted to each hdden node. Each hdden nodes receves all scaled nput varables, whch results n a parallel processng of all nputs at multple nodes. In ths step, each neurode n the nput layer receves ts value and dstrbute t to every node n the hdden layer. Snce output s equal to nput therefore, O I (1) Weght and sum nputs to recevng nodes The weghts and values n above fgure are determned by many teratons of the tranng process. In a very real sense, the weghts n an ANN contan ts memory & ntellgence. Just as wth the coeffcent n regresson analyss, ANN weghts express the relatonshp between the ANN layers and the fnal output. These weghts mnmze the RMS (Root Mean Square). Thus At each hdden node, the outputs of the nputs nodes (0, 1, ) are weghted and summed. Thus the nput node 3 s: I 3 W0 3 O 0 + W 13 O 1 +.. (2) Transform hdden-node nputs to outputs The relatonshp between the nput and output of a node s expressed by a transfer functon. Here sgmod transfer functon s used. Ths non-lnear transformaton makes t possble to model non-lnear functon. Ths sgmod transfer functon at each hdden node transforms nput to an output level n the range of 0 to 1. For ths we have the expresson as: O 1 (1 + e 3 I 3 ) Where e s the natural number of 2.718282 (3) - 3 -
Durng ths transformaton process, the weghts leadng to the hdden layer neurodes are adusted through back propagaton so as to mnmze the ANN error. Weght and sum hdden node outputs as nputs to output nodes The next step s to sum nputs at the fnal node, the output node. For example, two nodes, node 2 & 3 send sgnals to the output nodes. I 4 W 24 O 2 + W 34 O 3 (4) The output from O 2 & O 3 are weghed and summed and thus gve the result I4. Then ths s passed through a transfer functon. Transform nputs at the ANN output nodes At the output node, the weghted nput I 4 s transformed nto the output of O 4 n the range of 0 to 1. Ths s the fnal output of the ANN: O 1 (5) 4 I 4 (1 + e ) Calculate output errors The output error s smply the dfference between O 4 and the desred value D 4. Ths comparson s made between O 4 and D 4, whch gve the error. e D 4 O 4 (6) Where s the observaton number n the tranng set. Back propagaton errors to adust weghts Based on the errors, the weghts throughout the network are modfed through a tranng process, so as to move toward mnmzaton of the RMS value (Root Mean Square). Ths s called the Backpropagaton method. Through ths way, the error s reduced to mnmum and we get correct output varable. W ( new) W W δ O I ( new) ηδ O SSE W 1 (1 + e W O ) ( old) + W where η learnng rate (0-1.0), α momentum rate (0-1.0) SEE sum of squared error W weghts SSE O O I I + α W I W ( new) ( old) I nput, O output from node (7) Contnue the epoch Repeat the above steps for all observatons n the nput data set and contnue the process for the tranng. Each nput data pass through tranng s called an epoch. - 4 -
Calculate the epoch RMS We calculate the epoch RMS errors up to the level when t reaches to the lowest level n tranng. When t s reached to requred lowest errors level, t wll stop and gve the results. RMS where e nt ( e ) nt RMS Root Mean Square 2 Errors durng each observaton Numbers of observatons n the epoch/tranng set. (8) 3. Model Evaluaton For ths model, the measured dffuse and horzontal global values were used to calculate the rradance on surfaces tlted at 30 above the horzon. The results were compared wth the rradances montored, on the terrace of research laboratory n the Natonal Research Insttute of Astronomy and Geophyscs n Helwan, Egypt and presented n terms of usual statstcs: Mean Bas Error (MBE), Root Mean Square Error (RMSE) and Correlaton Coeffcent (r). Inspectng the results, t s apparent that the models agree qute well wth the montored data. 500 Global Solar Radaton Intensty n Red Band, W/m 2 450 400 350 300 250 200 150 Estmated Data 100 20 25 30 35 40 45 50 55 60 65 70 75 Data Ponts at Dfferent Condtons (Tme, Temp, Humdty and Cloudness) Fg. 1 Actual and Estmated Data n Red Band for Dfferent Condtons - 5 -
40 Global Solar Radaton Intensty n Ultra Volet Band, W/m 2 35 30 25 20 15 10 5 Estmated Data 0 10 15 20 25 30 35 40 45 50 Data Ponts at Dfferent Condtons (Tme, Temp, Humdty and Cloudness) Fg. 2 Actual and Estmated Data n Ultra Volet Band for Dfferent Condtons 700 Global Solar Radaton Intensty n Infra Red Band, W/m 2 600 500 400 300 200 Estmated Data 100 20 25 30 35 40 45 50 55 60 65 70 75 Data Ponts at Dfferent Condtons (Tme, Temp, Humdty and Cloudness) Fg. 3 Actual and Estmated Data n Infra Red Band for Dfferent Condtons - 6 -
1000 Global Solar Radaton Intensty, W/m 2 900 800 700 600 500 400 300 200 Estmated Data 100 20 25 30 35 40 45 50 55 60 65 70 75 Data Ponts at Dfferent Condtons (Tme, Temp, Humdty and Cloudness) Fg. 4 Actual and Estmated Data for Global Solar Radaton n Dfferent Condtons 4. Conclusons Neural Network Model has been developed for predctng the amount of solar radaton ncdent on horzontal plates n dfferent bands at dfferent condtons. Because of the varety and complexty of sky radaton, a common assumpton made s that the dffuse component of solar radaton (skylght) has an sotropc dstrbuton over the hemsphercal sky. On the bass of the results obtaned from of ths study, we came to ths concluson that Neural Network Model provdes an effcent approach for predcton of solar radatons for dfferent spectral bands at dfferent condtons e.g. Tme, temperature, humdty etc. References BUGLER J., 1977. The determnaton of hourly nsolaton on a tlted plane usng a dffuse rradance model based on hourly measured global horzontal nsolaton, Solar Energy, Vol. 19, No. 5, pp. 477 DAVE J., 1977. Valdty of the sotropc dstrbuton approxmaton n solar energy estmatons, Solar Energy, Vol. 19, pp. 331 DUFFIE J. AND BECKMAN W., 1980. Solar engneerng of thermal processes. Wley, New York HAY J., 1979. Calculaton of monthly mean solar radaton for horzontal and tlted surfaces, Solar Energy, Vol.23, pp. 301 HAY J. AND DAVIES J., 1980. Calculaton of the solar radaton ncdent on an nclned surface, Proceedngs Frst Canadan Solar Radaton Data Workshop, pp.59 IQBAL M., 1983. An ntroducton to solar radaton, Academc Press, Toronto HOWARD D., MARK. B. Onlne manuals (n PDF), 1997: Neural Network Toolbox wth Matlab, The MathWorks Inc. KLUCHER T., 1979. Evaluaton of models to predct nsulatons on tlted surfaces, Solar Energy, Vol. 23, pp.114. STEPHEN A. DELURGIO, 1998, Forecastng prncples and applcatons, Irwn McGraw- Hll, ISBN 0-256-13433-2. - 7 -