Avalable onlne at www.scencedrect.com Proceda Envronmental Scences 11 (201 1308 1315 An ANN-based Approach for Forecastng the Power Output of Photovoltac System Mng Dng, Le Wang, Ru B Research Center for Photovoltac System Engneerng, Mnstry of Educaton Hefe Unversty of Technology Hefe, Anhu Provnce, Chna mngdng56@126.com, wang_le_1987@126.com, bruzz@126.com Abstract Wth the ncreasng use of large-scale grd-connected photovoltac system, accurate forecast approach for the power output of photovoltac system has become an mportant ssue. In order to forecast the power output of a photovoltac system at 24-hour-ahead wthout any complex modelng and complcated calculaton, an artfcal neural network based approach s proposed n ths paper. The mproved back-propagaton learnng algorthm s adopted to overcome shortcomngs of the standard back-propagaton learnng algorthm. Smlar day selecton algorthm based on forecast day nformaton s proposed to mprove forecast accuracy n dfferent weather types. Forecastng results of a photovoltac system show that the proposed approach has a great accuracy and effcency for forecastng the power output of photovoltac system. Keywords: Photovoltac system; 24-hour-ahead forecastng; Artfcal neural network; Improved back-propagaton learnng algorthm; Smlar day selecton algorthm 1. Introducton In recent years, photovoltac (PV) technology has been rapdly developed due to the mantenance free, long lastng, and envronment frendly nature of PV as well as government s support [1]. However, power output of PV system s a non-statonary random process because of the varablty of solar rradaton and envronmental factors. Any grd-connected PV system n the publc power grd, s regarded as a noncontrolled, non-schedulng unt, ts power output fluctuatons wll affect the stablty of power system [2]. As the use of large-scale grd-connected PV system s ncreasng, t s mportant to strengthen the predcton of PV system power output, whch can help the dspatchng department to make overall arrangements for conventonal power and photovoltac power coordnaton, schedulng adjustment, operaton mode plannng. To forecast the power output of PV system, partcularly the short term forecast (say 24-hour-ahead), applcatons can be grouped nto two categores: one s the predcton model based on solar radaton ntensty. Frstly obtan the predcted value of solar radaton based on solar radaton model, then use PV 1878-0296 2011 Publshed by Elsever Ltd. Open access under CC BY-NC-ND lcense. Selecton and/or peer-revew under responsblty of the Intellgent Informaton Technology Applcaton Research Assocaton. do:10.1016/j.proenv.2011.12.196
Mng Dng et al. / Proceda Envronmental Scences 11 (201 1308 1315 1309 output formula to calculate the power output of PV system [3]. Another method s to predct the power output of PV system drectly [4]. Although the predcton model based on solar radaton ntensty has been consdered to be an effectve method n the practcal applcaton, t takes a lot of meteorologcal and geographcal data to solve complex dfferental equatons [5]. Artfcal neural network (ANN) has been vewed as a convenent way to forecast solar radaton ntensty and power output of PV system, whch can be traned to overcome the lmtatons of tradtonal methods to solve complex problems, and to solve dffcult problems whch are hard to model and analyze [6]. In ths paper, an ANN-based approach for forecastng the power output of PV system at 24-hour-ahead s proposed. Instead of the predcton model based on solar radaton ntensty, the proposed ANN-based approach uses feed-forward neural network (FNN) to predct the power output of PV system drectly by reference to hstorcal data of PV system. The mproved back-propagaton (BP) learnng algorthm s adopted to overcome shortcomngs of standard BP learnng algorthm, such as slow convergence and easy to fall nto local mnmum. In order to mprove forecast accuracy n dfferent weather types, smlar day selecton algorthm based on forecast day nformaton s proposed, and weather nformaton s added as nput of ANN. The valdty of proposed ANN-based approach s verfed by comparng the predcted value and actual value of PV system. It shows that the proposed ANN-based approach has a wde applcablty. 2. Artfcal Neural Network 2.1 Feed-forward Neural Network Schematc dagram of a multlayer feed-forward neural network archtecture s shown n Fg.1. The outputs of neurons n each layer are fed forward to ther next level, untl the entre output of network s obtaned. It usually conssts of an nput layer, multple hdden layers and an output layer. Through adaptable synaptc weghts, each sngle neuron s connected to other neurons of a prevous layer. Knowledge s usually stored as a set of connecton weghts [7]. Neural networks workng process s dvded nto two steps: the frst step s called learnng (or tranng) process, connecton weghts are modfed by learnng, connecton weghts matrx changes adaptvely wth the external envronment ncentves essentally. The second step s called network operatng process, connecton weghts are fxed at ths tme, and the correspondng output s obtaned............. Input Layer Hdden Layers Output Layer Fgure 1 Schematc dagram of a multlayer feed-forward neural network archtecture 2.2 Back-propagaton Learnng Algorthm The learnng step s an mportant subject of neural networks; supervsed learnng and unsupervsed learnng are two types of learnng models [8]. The back-propagaton (BP) algorthm s one of the most powerful supervsed learnng algorthms [9]. But t s dscovered that BP algorthm has the followng
1310 Mng Dng et al. / Proceda Envronmental Scences 11 (201 1308 1315 shortcomngs: easly fallng nto local mnmum by usng gradent-descent algorthm to converge the error between actual output and expected output; slow convergence rate; tranng process prone to oscllatons and so on. 3. Factors that Affect PV Power Output For PV system wth fxed orentaton, the maxmum DC power output can be descrbed by the followng emprcal formula [10]: Ps = ηsi[1 0.005( t0 + 25)] 2 Where, η s the converson effcency of solar cell array (%), S s the array area ( m ), I s the nsolaton ( kw m 2 ), t 0 s the outsde ar temperature ( C ). As can be seen from the above formula,for the PV system, there are many factors that affect ts power output, such as the converson effcency, the array area,the solar radaton ntensty, the nstallaton angle, pressure, temperature, etc. Snce all of the tme seres of power output are from the same set of power generaton system, an obvous feature of PV system s that the tme seres of power output have hgh correlaton; t solves the mpacts of nstallaton locaton and use of tme on converson effcency of PV system [11]. Converson effcency and array area have been mpled n the hstorcal data of power output, but the ntensty of solar radaton and atmospherc temperature changes should be taken nto account. The ntensty of solar radaton vares greatly n dfferent seasons, dfferent weather types. Power output comparson of dfferent weather condton s shown n Fg.2 and Fg.3, and the weather can be seen n TableⅠ.It s clear that power output of a PV system vares wdely n dfferent weather types. There s a huge dfference n power output between sunny day and rany day, sunny day and snowy day. The power output curve of sunny day s smooth; the power output curve of rany day or snowy day s fluctuant relatvely. The power output of dfferent seasons s not very dfferent on condton that the weather type s all sunny, but the temperature wll also affect the output. Table 2 Weather Condton Date Weather Hgh Average Low Type Temperature Temperature Temperature 2010.10.01 Sunny 33 22 11 2010.10.23 Rany 17 12 7 2010.10.27 Snowy 14 7 0 2010.04.18 Sunny 26 15 4 2010.07.07 Sunny 38 27 14 2010.09.20 Sunny 23 17 11 2010.11.25 Sunny 7 1-6 16000 14000 Power Output Ps[W] 12000 10000 8000 6000 4000 2000 2010.10.01 2010.10.23 2010.10.27 0 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 Tme t[hour] Fgure 2 Power output comparson of dfferent weather types
Mng Dng et al. / Proceda Envronmental Scences 11 (201 1308 1315 1311 Power Output Ps[W] 16000 14000 12000 10000 8000 6000 4000 2000 2010.04.18 2010.07.07 2010.09.20 2010.11.25 0 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 Tme t[hour] Fgure 3 Power output comparson of dfferent seasons 4. Algorthm 4.1 Improved Back-propagaton Learnng Algorthm Search route of the standard back-propagaton algorthm s shown n Fg.4. It can be seen that the standard BP learnng algorthm uses a constant learnng step length. In the early stages of network tranng, t wll reduce error of the network output f approprate learnng step length s adopted. When the network s constantly n the tranng process, learnng step length can not meet the requrements of smaller and smaller error of the network output, resultng n network oscllatons durng the tranng. Fgure 4 Search route of the standard back-propagaton algorthm Set E as the network output error, W as connecton weghts, n as the number of tranng teraton, η as the learnng rate, as the number of computng network output error n each tranng teraton. The flow chart of mproved BP learnng algorthm [12] s shown n Fg.5. ( When E ( n) and W ( n) are determned, compute the network output error E ( n + : ( If E ( n + 1 ) < En ( ), ncrease the learnng rate accordng to the formulaη = 1.1η, and modfy the correspondng weghts to get W (2) ( n+.assumng that the new network output (2) ( error E ( n+ < E ( n+, repeat the above steps untl the new network output error s not reduced. ( If E ( n + 1 ) En ( ), decrease the learnng rate accordng to the formula η = 0.5η, and modfy the correspondng weghts to get W (2) ( n+.assumng that the new network output (2) ( error E ( n+ > E ( n+, repeat the above steps untl the new network output error s not ncreased.
1312 Mng Dng et al. / Proceda Envronmental Scences 11 (201 1308 1315 E( n ), W ( n) =1, W ( n+ = W( n), compute E ( n+ ( ( E ( ( n+ < En ( ) Y N () =+1, η = 1.1 η, compute W ( n+ () =+1, η = 0.5 η, compute W ( n+ () compute E ( n+ () compute E ( n+ ( ) ( E n E n ( + < ( + ( ) ( E n E n ( + > ( + Y N Y N ( En ( + = E ( n+ ( W( n+ = W ( n+ Fgure 5 The flow chart of mproved BP learnng algorthm 4.2 Smlar Day Selecton Algorthm Smlar day selecton algorthm s proposed to fnd the closest hstorcal record whch has the smlar weather condton wth the forecast day, and normalzed nformaton of ths record s set as nput of the network. Selectng approprate tranng set accordng to forecast day nformaton has the followng benefts: Makng the tranng process carred out based on forecast day nformaton. 2) Improvng the forecast accuracy. 3) Havng ablty of forecastng the power output of PV system n non-sunny days. Although ths wll sacrfce some tme, t s acceptable due to 24-hour-ahead forecast beng dscussed n ths paper. Smlar day selecton algorthm can be summarzed as follows: Calculate Eucldean dstance of temperature between forecast day and days before forecast day. 1 3 2 2 j j j = 1 d = ( Y X ), = 1,2,..., n Where, Y1, Y2, Y3 are hgh temperature, low temperature and average temperature of forecast day, X 1, X2, X 3 are hgh temperature, low temperature and average temperature of days before forecast day. 2) If the weather type of days before forecast day s dfferent from forecast day, set d to maxmum. 3) Fnd the mnmum value n D = { d, d,..., dn} and set t as the smlar day of forecast day. 1 2
Mng Dng et al. / Proceda Envronmental Scences 11 (201 1308 1315 1313 5. Feed-forward Neural Network Desgn 5.1 Data Source The hstorcal power data was obtaned from a PV system located n Ashland, Oregon (Lattude: 42.19; Longtude: 122.70; Alttude: 595 m) of Unted States of Amerca [13]. The Ashland staton s part of Ashland's Solar Poneer project, and t has 5 kw array and 15 kw array. We choose the 15 kw array to study. Ashland s hstorcal weather data and forecasted weather data was from a publc weather forecast webste [14]. 5.2 Input Layer As power output of the PV system s zero n 19:01-05:59, study perod s from 06:00 to 19:00 wth the nterval of half-hour, a total of 27 ponts per day. Input data x1 x33 are shown n Table Ⅱ. Table 2 Input Data x x x x 1 27 28 30 27 ponts of power output n smlar day from 06:00 to 19:00 wth the nterval of half-hour x Hgh, low, average temperature value n smlar day x Forecasted hgh, low, average temperature value n forecast day 31 33 5.3 Hdden Layers Smply, t has only one hdden layer n the feed-forward neural network. A tral-and-error method [15] has been used to determne the approprate number of hdden neurons n ths paper. 5.4 Output Layer Snce the objectve of ths paper s to forecast PV power output at 24-hour-ahead wth the nterval of half-hour, a total of 27 ponts of power output from 06:00 to 19:00 n forecast day are taken as the output. 5.5 Assessment Method There are many ways to assess the predcton model; the most common one s the Mean Absolute Percentage Error (MAPE) whch s adopted n ths paper. N 100 P f P a MAPE = % N P = 1 a Where, N s the total number of data, P f s the forecasted value, P a s the actual value, s the ndex of data. In order to avod P P / P approachng to nfnty, P wll be dscarded f t s close to zero. f a a 6. Forecast Results and Dscusson In order to valdate the accuracy of predcton model of PV power output, the PV power output of a sunny day and a rany day were forecasted usng hstorcal power data and weather data, the curves of a
1314 Mng Dng et al. / Proceda Envronmental Scences 11 (201 1308 1315 actual value and forecasted value are shown n Fg.6 and Fg.7. Predcton for the sunny day s shown n Fg.6, the MAPE s 10.06%, and predcton for the rany day s shown n Fg.7, the MAPE s 18.89%. The predcton for the sunny day s more accurate, because the PV power output n sunny day s relatvely stable, the fluctuaton s small. Although there s some dstant between the forecasted and the actual power output, t stll has a hgh reference value. Through the effectve analyss of nfluencng factors of PV power output, combned wth the mproved BP learnng algorthm and smlar day selecton algorthm, an ANN-based approach for forecastng the power output of photovoltac system s proposed. The beneft of the proposed approach s that t does not requre complex modelng and complcated calculaton, forecast under dfferent weather types can be carred out usng only hstorcal power data and weather data. The test results proved valdty and accuracy of the proposed approach; the proposed approach can be used to forecast the power output of photovoltac system precsely. 16000 14000 Power Output Ps[W] 12000 10000 8000 6000 4000 2000 Actual Value Forecasted Value 0 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 Tme t[hour] Fgure 6 Comparson between actual value and forecasted value 16000 14000 Power Output Ps[W] 12000 10000 8000 6000 4000 2000 Actual Value Forecasted Value 0 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 Tme t[hour] Fgure 7 Comparson between actual value and forecasted value 7. Acknowledgment Ths work was supported by the Natonal Hgh Technology Research and Development of Chna under Grant 2007AA05Z240, Natonal Natural Scence Foundaton of Chna under Grant 50837001, and the Fund of Hefe Unversty of Technology under Grant 2010HGXJ0061. References [1] Md.H. Rahman and S. Yamashro, Novel dstrbuted power generatng system of PV-ECaSS usng solar energy estmaton, IEEE Trans. on Energy Converson, vol. 22, pp. 358-367, June 2007. [2] A. Woyte, V. Van Thong, R. Belmans, and J. Njs, Voltage fluctuatons on dstrbuton level ntroduced by photovoltac systems, IEEE Trans. on Energy Converson, vol. 21, pp. 202-209, March 2006.
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