Evolving Radial Basis Function Neural Networks for One-Day-Ahead Hourly Forecasting of PV Power Generation

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1 Proceedngs of the 3rd Internatonal Conference on Indstral Applcaton Engneerng 5 Evolvng Radal Bass Fncton Neral Networs for One-Day-Ahead Horly Forecastng of PV Power Generaton Chao-Mng Hang a* Yann-Chang Hang b, and Kn-Yan Hang b a Department of Electrcal Engneerng, Kn Shan Unversty, No.95, Knda Rd., Tanan 7, Tawan, R.O.C. b Department of Electrcal Engneerng, Cheng Sh Unversty, No.84, Chengcng Rd., Kaohsng 833, Tawan, R.O.C. *Correspondng Athor: h744@ms.hnet.net Abstract Ths paper proposes a novel method to predct one-day-ahead horly photovoltac (PV) power generaton. The proposed method comprses three stages: data classfcaton, tranng and forecastng. In the frst stage, a fzzy -means algorthm s sed to classfy the hstorcal data for daly PV power generaton nto varos weather types. In the second stage, fve tranng models are establshed, accordng to the verbal weather forecast of the Tawan Central Weather Brea (TCWB). Each tranng model s constrcted sng a radal bass fncton neral networ (RBFNN), for whch the parameters of each RBFNN, ncldng the poston of RBF centers, the wdth of the RBFs and the weghts between the hdden and the otpt layers, are optmzed sng a harmony search algorthm (HSA). To select an adeqate forecastng model from the traned models, fzzy nference s sed n the forecastng stage. The proposed approach s tested on a practcal PV power generaton system. The reslts show that the proposed method provdes better forecastng reslts than the exstng methods over one-year testng data. Keywords: PV power forecastng, radal bass fncton neral networ, fzzy nference, harmony search algorthm.. Introdcton To allow effcent plannng for grd-connected PV systems, the forecastng of PV power generaton s very mportant. Accrate forecastng of PV power otpt mproves the PV penetraton level, ncreases system relablty and allows for effcent load management strateges, ncldng demand response (DR), the tme of se rates (TOU) and chargng schedles for electrc vehcle (EV). However, becase t s lmted by amont of solar rradaton, PV power generaton s hghly ncertan and dffclt to predct. To mae effectve se of PV power generaton, accrate forecastng of PV power otpt s necessary. Snce the PV power otpt s affected by varyng solar rradaton, many stdes focs on predctng solar rradaton, sng hstorcal weather nformaton. The forecasted solar rradatons are then converted to PV power otpts, sng the manfactre s data for a solar panel. These technqes nclde tme seres methods [], artfcal neral networ (ANN) methods [], fzzy logc methods [3] and wavelet-based methods [4]. Other stdes drectly forecast PV power otpt, sng hstorcal tme-seres data and assocated weather nformaton. These stdes se statstcal methods [5] and spport vector regresson (SVR) technqes [6]. As prevosly mentoned, most exstng stdes mprove the forecastng accracy for PV power otpt. However, a tme seres method [] cannot effectvely model the hgh varaton n PV power generaton, especally for clody or rany days. The ANN method [] allows good approxmaton for a wde range of nonlnear fnctons, bt t experences slow convergence n tranng and the networ strctre and parameters mst be determned manally. The fzzy logc method [3] expresses the weather nformaton and the herstc rles n mprecse lngstc terms, bt t s dffclt to desgn an effcent nference engne to draw conclsons from a large volme of rle-based nowledge. The wavelet-based method [4] ses mlt-resolton analyss to dvde the orgnal data nto several levels of sbsets. The dsadvantages of ths method are ts complex DOI:.79/cae The Insttte of Indstral Applcatons Engneers, Japan.

2 strctre and the long comptatonal tme reqred. Statstcal methods [5] se the nflence of several weather parameters on the PV power forecastng. For more accrate forecastng, ths method reqres accrate detecton devces to accrately collect the weather parameters. The SVR method [6] has been sccessflly appled to data classfcaton and regresson predcton. However, the ernel fncton, whch determnes the propertes of SVC, s often obtaned throgh operator experence. To allow more accrate forecastng, ths paper proposes an ntellgent method to predct the one-day-ahead horly PV power generaton. The proposed method comprses data classfcaton, tranng and forecastng stages. Compared to the exstng methods, the proposed approach has the followng advantages:. Fve forecastng models are establshed to cover dverse PV power otpts, based on dfferent weather condtons. Ths s more accrate and mch more effectve than a sngle forecastng model.. HSA s a poplaton-based random search algorthm that provdes an effcent scheme to ncrease the varety of the offsprng and has a good probablty of convergng towards the optmal parameter solton for a RBFNN. 3. Fzzy nference s sed to select an adeqate forecastng model from the traned models. Ths avods a large forecastng error, f an naccrate weather forecast s provded by the TCWB.. Characterstcs of PV Power Generaton PV power generaton s senstve to weather condtons, sch as the solar rradance and temperatre, as follows: q Vpv P n V ( I I (exp( ) )) PV p pv ph sat () nt ns K r I ( I ( T T )) S () ph scr r r where P PV s the power otpt of a PV array, n p s the nmber of PV arrays n parallel, n s s the nmber of PV arrays n seres, V pv s the otpt voltage of a PV array, I ph s the otpt crrent of a PV array, I sat s the dar satraton crrent, q s the charge on an electron (.6-9 C), n s an dealty factor, s the Boltzmann constant (.38-3 J/ K) ), T s the absolte temperatre ( K), T r s the reference temperatre( K), I scr s the short-crct crrent at both the reference temperatre and W/m solar rradaton, K r s the temperatre coeffcent of the short-crct crrent and S r s the solar rradance (W/m ). As shown n () and (), the PV power generaton s affected by solar rradance and temperatre. Dfferent weather types reslt n a varaton n PV power otpt patterns. Based on the verbal weather descrptons gven by the TCWB, the weather types can be classfed nto snny, snny and clody, clody, clody and rany and rany. On a snny day, the power otpt of PV generaton system s hgh and stable. On the other weather days, the PV power otpt s low and nstable. In Tawan, there s solar rradance from abot 6: to 9: every day. Snce the power otpt of a PV generaton system s ntrnscally nstable and has an ntermttent natre, provdng an accrate forecast of PV power otpt s mportant for a renewable energy sorce. Ths paper presents a novel method to mae more accrately forecast for PV power otpt. Detals of the proposed scheme are gven n the next secton. 3. The Proposed Approach 3. Data classfcaton The collected hstorcal PV power generaton patterns are classfed sng a fzzy -means clsterng algorthm. K-means clsterng was frst proposed by Lloyd n 98 [7], as a technqe for plse-code modlaton. It s a method of vector qantzaton and s sed for clster analyss n data mnng. Gven a set of observatons (X, X,, X n ), the -means clsterng parttons n observatons nto clsters, as follows: n arg mn w X R (3) where X s the th observaton, R s the th clsterng center, w s a synaptc weght and s the Ecldean dstance. R and w are respectvely expressed as follows: R w n w X (4) w n, f X R X Rm, m (5), otherwse As shown n (3), -means clsterng parttons the n observatons nto clsters ( n), n order to mnmze the wthn-clster sm of the sqares. Ths algorthm assgns sng the least sm of the sqares of the Ecldean dstance and there s no garantee that t gves the global optmm. 387

3 In contrast to hard or crsp clsters, fzzy -means clsterng [8] allows each observaton vector, X, to have a degree of membershp, as follows: w~ X R X Rm I m where I m s a weghtng ndex whose vale s generally set at. Fzzy -means clsterng has the advantage that t more natrally handles statons n whch sbclasses are formed by the degree of membershp, rather than havng to assgn X completely to one clster or the other. In ths paper, a fzzy -means clsterng algorthm s sed to extract the featres for weather type by classfyng the daly PV power otpt patterns nto fve dfferent types of weather days. To cope wth the varaton of PV power otpt for varos seasons, the synaptc weghts of fzzy -means clsterng mst be pdated accordng to the recently collected data. 3. The creaton of tranng models As descrbed n the data classfcaton secton, a fzzy -means clsterng algorthm provdes nformaton on smlar days and ther assocated weather types. A smlar day s defned as havng the same weather type. In ths stage, the RBFNN evolved sng a HSA s sed to tran the collected npt-otpt data sets. Snce the TCWB provdes the verbal weather forecasts for the next day, n terms sch as the snny, snny and clody, clody, clody and rany and rany, the tranng stage s parttoned nto fve dfferent models. Fgre shows the strctre of the tranng stage. The npts for each tranng model contan the actal horly solar rradance on the latest smlar day, a predcton of the maxmm average temperatre for the next day and a predcton of probablty of precptaton for the next day. The otpts are the horly PV power otpt for the next day. The fve tranng models have the same tranng strctre. In ths paper, a HSA-based RBFNN s sed to tran the npt/otpt data sets. The RBFNN and the HSA-based RBFNN model are hereby descrbed. (a) Radal Bass Fncton Neral Networ (RBFNN) [9] Fg. shows the strctre of a RBFNN. The networ conssts of an npt layer, a hdden layer and an otpt layer. The tranng data sets are gven as npt/otpt pars, each consstng of a vector from an npt space and a desred networ response. Usng a stochastc gradent algorthm, (6) the networ adsts ts weghts so that the error between the actal and desred response s mnmzed. Inpt Actal Horly Solar Irradance on the Latest Smlar Day Predcton of Probablty of Precptaton for the Next Day by TCWB Predcton of Maxmm Average Temperatre for the Next Day by TCWB x x 4 x 6 HSA-Based RBFNN Tranng Model : Snny Day Tranng Model : Snny and Clody Day Tranng Model 3: Clody Day Tranng Model 4: Clody and Rany Day Tranng Model 5: Rany Day Fg. Strctre of tranng stage. x c c 6 x 5 x c 6 N x x cn N w w N 4 w 4 w w 4 w N Fg. Strctre of a RBFNN. Otpt One-Day-Ahead Horly Forecast for PV Power Generaton As shown n Fg., the otpt of the RBFNN s calclated as follows: y ˆ w ( x c ), (7) N where w s the weght between the th center node n the hdden layer and the th otpt node, where =,,, N and =,,, m, N s the nmber of hdden nodes and m s the 6 nmber of otpt nodes, x s an npt vector, c s the th center node n the hdden layer, denotes the Ecldean norm and () s a non-lnear transfer fncton for the th center. In ths paper, the RBFNN has 6 npt nodes and 4 otpt nodes, as shown n Fg.. As shown n (7), () s a non-lnear fncton that transforms the otpt of the th center to an adeqate vale. In ths paper, the most wdely sed Gassan fncton s adopted, as follows: ( x r) ( x ) exp, (8) y y 4 388

4 where and r are the parameters that control the wdth and the poston of the RBF centers, respectvely. The mean-sqared error between the actal and the desred networ otpt s sed to measre the optmzaton crteron, as follows: m m N J(, r, w) ( y yˆ ) ( y w ( x c )) (9) where y s the th desred otpt and ŷ s the th actal otpt. Eqatons (8) and (9) show that three sets of parameters govern the optmzaton performance of the networ: the poston of the RBF centers, the wdth of the RBFs and the weghts, w, between the hdden and the otpt layers. In ths paper, a HSA algorthm s sed to optmze these three sets of parameters. (b) The optmzaton of parameters sng a harmony search algorthm A HSA []-[] operates smlarly to the process for mscal mprovsaton, whereby mscans tne the ptches of ther nstrments to acheve better harmony. Smlarly to other optmzaton algorthms, a HSA ses a poplaton-based random search to acheve a global optmm pont and s sed n many felds. It has been verfed to be more effcent than dfferental evolton (DE) and partcle swarm optmzaton (PSO) methods []. A HSA tnes the poston of the RBF centers, the wdth of the RBFs and the weghts between the hdden and the otpt layers, as follows. ) Intalzaton In ths step, an ntal harmony matrx (HM) s randomly generated as follows: HM H H H H 3 3, H 3 H 3 () where s the poston of the th RBF center, and =,,, H, H s the sze of the harmony matrx, s the wdth of the th RBF, 3 ( w, =,,, m and =,,, N) are the weghts of the th vector between the hdden and the otpt layers. As shown n (), each row ([,, 3 ]) represents a vector solton that s composed of a set of decson varables. In ths paper, 3 s randomly generated n the range to, and are generated as follows: h rand ), () mn ( max mn where h, and,,..., H, mn and max are the lower and pper bonds of and rand s a nform dstrbton vale that ranges between and. Eqaton () shows that there are +N 4 varables n a vector solton, where N s the nmber of center nodes and 4 s the nmber of otpt nodes. ) Calclaton of the obectve fncton For each row vector of HM, the obectve vale s evalated sng (9). The solton wth the lowest obectve vale n HM s regarded as the optmal solton for the RBFNN. 3) The generaton of a new harmony matrx Usng the memory consderaton, the ptch adstment and random selecton processes, a new harmony matrx U [ ', ', '] s generated. The decson varables n ' 3 U ' are pdated by the dfference ( - H ) n the memory consderaton. The harmony memory consderng rate (HMCR) s sed to mprove the dversty of the solton vector, as follows: H ' [,,..., ], ' ' U, f rand HMCR otherwse () where HMCR [,] s set by operators and U [, mn,, max ] s the set of the possble range of vales for each decson varable. If HMCR s set at.9, there s a 9% probablty that the HSA chooses decson vales from hstorcally stored vales and a % probablty that t chooses decson vales from the entre range. The ptch adstment that s sed to mprove the vector solton s checed when a new harmony matrx s obtaned sng memory consderaton, as follows: ' rand BW f rand PAR ' (3) ' otherwse where PAR [,] s the ptch adstng rate and BW s the bandwdth of the varatons. 4) Parameter adstments In the parameter adstment process, PAR and BW are tned to mprove the performance of the HSA, as follows: PARmax PARmn PAR( ter) PARmn ter (4) NI 389

5 ln( BW / BW ) mn max BW ( ter) BW exp ter (5) max NI where PAR mn and PAR max are the lower and pper bonds of PAR, BW mn and BW max are the lower and pper lmts of BW, ter s the nmber of teraton and NI s the nmber of mprovsatons so far n the optmzaton process. The mprovsatons allow the best obectve vale of the offsprng harmony matrx to be better than that of the parent harmony matrx. 5) The selecton of the best vector solton After adstng the parameters, the sze of HM s mantaned at H. H sets of the better row vector n the harmony matrx are then selected. Processes 3 and 4 are repeated, ntl the maxmm nmber of teratons s reached. The best vector solton n HM s regarded as the optmal solton for the RBFNN. (c) Model selecton for forecastng sng fzzy nference Fzzy nference ses If-Then statements to nvoe each fzzy rle, where If s the premse and Then s the conseqence. The basc form of fzzy nference s as follows: R :If x s A and x s A and and x n s A n, Then y f () (6) where R s the th fzzy rle, x,, x n are the premse (or npt) varables, A,, A n are the lngstc vales related to the npts for the th rle and f () s the conseqent (or otpt) varable of the th rle. In general, f () s a nonlnear transfer fncton of the premse varable. In ths paper, fzzy nference s sed to select an adeqate model for accrate forecastng. The npt varables of fzzy nference comprse the maxmm PV power otpt on the latest smlar day, the predcton of the maxmm average temperatre for the next day by the TCWB and the predcton of the probablty of precptaton for the next day by the TCWB. The otpt varables are the models of the dfferent weather days. Fgres 3-5 show the fzzy npt varables and ther assocated membershp fnctons whch are tned by tral-and-error experments to acheve the best performance. Fgre 6 shows the otpt varables for dfferent weather types. As prevosly descrbed, each fzzy npt varable s parttoned nto three regons. Therefore, there are 7 (3 3 3) fzzy rles n the nowledge base. The reslts for the rles that fre are de-fzzfed to a crsp otpt vale n the de-fzzfcaton stage. In ths paper, the poplar centrod method [3] s sed to ntegrate the fzzy otpt. Grade L M H n n n 3 L:low M:medm H:hgh [n,n,n 3 ]=[5,3,38] Max. PV power otpt (Wp) Fg. 3 The npt varable of maxmm PV power otpt. Grade L M H m m m 3 m 4 [m,m,m 3,m 4]=[4,7,9,3] Temperatre ( C) Fg. 4 The npt varable of maxmm average temperatre. Grade L M H 3 4 [,, 3, 4 ]=[,,3,4] Probablty of precptaton(%) Fg. 5 The npt varable of probablty of precptaton. Fg. 6 The otpt varables of dfferent weather types. 4. Data collecton 4. Nmercal Reslts The proposed method s sed to forecast the one-day-ahead horly PV power otpt for a 5 Wp system. To verfy the sperorty of the proposed approach, the tradtonal RBFNN and ANN methods are also tested sng the same database. The practcal PV power generaton data 39

6 and the rradance vales sed were from 3 May st to 4 Aprl 3 th. The data was sampled every 5 mntes. The horly PV power otpt and the rradance data are then obtaned by averagng the data collected over one hor. To verfy the proposed approach, the data for the last fve days of each month was sed for testng and that for the other days are for tranng. For comparson prposes, the tradtonal RBFNN and ANN also se the same npt/otpt strctre, whle the nmber of ntermedate layers remaned to be determned ndependently. 4. Evalaton crtera To evalate the performance of each method, the crtera for the mean relatve error (MRE) and root mean sqare error (RMSE) are sed, as follows [4]: N f P P fore tre MRE % (8) N P f N f total ( P P ) fore tre RMSE (9) N f where P fore s the forecastng vale, P tre s the real vale, P total s the capacty of the PV system, and N f s the nmber of forecastng ponts. 4.3 Forecastng reslts Fgre 7 shows the forecastng reslts for Ag. 7 to Ag. 3 of 3. The weather on Ag. 9 was rany, so there was a very low PV power otpt. The MRE vale s.3688% for the proposed method and the RBFNN and ANN gve vales of.436% and.6496%, respectvely. For the RMSE vale, the proposed method gves a vale of 468. (W), the RBFNN gves a vale of 54.8 (W) and the ANN gves a vale of (W). The proposed method gves a better forecast for PV power otpt. Fgre 8 shows the forecastng reslts for Nov. 6 to Nov. 3 of 3. Nov. 6 and Nov. 7 were rany and the other days were snny. The RBFNN and the ANN methods gve a worse forecast for Nov. 6 and Nov. 7. The proposed method prodces a better forecast than the other methods, except for Nov. 8. Fgre 9 shows the forecastng reslts for Feb. 4 to Feb. 8 of 4. These days were snny and the PV power otpts were stable. However, the RBFNN and ANN methods prodce lower forecasts from Feb. 4 to Feb. 7. Fg. shows the forecastng reslts for Apr. 6 to Apr. 3 of 4. Drng these days the weather was nstable. Althogh the proposed method gves a better forecast than the other methods, the forecastng errors are hgher than those for the other months. Table smmarzes the forecastng reslts for each method. The average MRE, sng the one-year testng data, s.348% for the proposed method and the RBFNN and ANN gve vales of.48% and.5968%, respectvely. For the average RMSE, the proposed method gves a vale of (W), the RBFNN gves a vale of (W) and the ANN gves a vale of (W). The reslts show that the proposed method gves a better forecastng reslt than the exstng methods. PV Power Otpt (W ) PV Power Otpt (W ) PV Power Otpt (W ) Actal ANN RBFNN Proposed Fg. 7 Forecastng reslts for Ag. 7 to Ag. 3 of Actal ANN RBFNN Proposed Fg. 8 Forecastng reslts for Nov. 6 to Nov. 3 of Actal ANN RBFNN Proposed Fg. 9 Forecastng reslts for Feb. 4 to Feb. 8 of 4. 39

7 PV Power Otpt (W) Actal ANN RBFNN Proposed Fg. Forecastng reslts for Apr. 6 to Apr. 3 of 4. Table Smmary of forecastng reslts for each method. Month MRE(%) RMSE(W) ANN RBFNN Pro. ANN RBFNN Pro. May, Jne, Jly, Ag., Sep., Oct., Nov., Dec., Jan., Feb., Mar., Apr., Max Mn Ave Conclsons Ths paper presents a novel approach for the one-day-ahead horly forecastng of PV power otpt. The proposed approach comprses data classfcaton, tranng and forecastng stages. The data classfcaton stage ses a fzzy -means clsterng algorthm to classfy the daly PV power otpt patterns nto dfferent weather types. In the tranng stage, fve tranng models, representng dfferent weather types, are created sng a HSA-based RBFNN. The forecastng stage ses fzzy nference to nvoe an adeqate model for accrate forecastng, accordng the weather predctons of the TCWB. For one complete whole year data, the proposed approach acheves better forecastng accracy than the RBFNN and ANN methods, n terms of MRE and RMSE crtera. Althogh only fve models are consdered to establsh the forecastng model, extenson of the proposed approach to consderaton of more models s feasble to ncrease the forecastng accracy. Acnowledgment Fnancal spports from the Mnstry of Scence and Technology, Tawan, R.O.C. nder the Grant No. 3--E-68-5 and -63-E-3--MY3 are acnowledged. References () L. Martín, L. F. Zarzaleo, J. Polo, A. Navarro, R. Marchante, and M. Cony, Predcton of global solar rradance based on tme seres analyss: applcaton to solar thermal power plants energy prodcton plannng, Solar Energy,, vol. 84, pp () G. Capzz, C. Napol, and F. Bonanno, Innovatve second-generaton wavelets constrcton wth recrrent neral networs for solar radaton forecastng, IEEE Trans. Neral Networ and Learnng Systems,, vol. 3, no., pp (3) K. Tanaa, K. Uchda, K. Ogm, T. Goya, A. Yona, T. Seny, T. Fnabash, and C. H. Km, Optmal operaton by controllable loads based on smart grd topology consderng nsolaton forecasted error, IEEE Trans. Smart Grd,, vol., no. 3, pp (4) P. Zhang, H. Taano, and J. Mrata, Daly solar radaton predcton based on wavelet analyss, SICE Annal Conference, Waseda Unversty, Toyo, Japan, Sep., pp (5) M. G. De Gorg, P. M. Congedo, and M. Malvon, Photovoltac power forecastng sng statstcal methods: mpact of weather data, IET Sc. Meas. Technol., 4, vol. 8, no. 3, pp (6) J. Sh, W. J. Lee, Y. L, Y. Yang, and P. Wang, Forecastng power otpt of photovoltac systems based on weather classfcaton and spport vector machnes, IEEE Trans. Indstry Applcatons,, vol. 48, no.3, pp (7) S. P. Lloyd, Least sqares qantzaton n PCM, IEEE Trans. Inform. Theory, 98, vol. 8, no., pp (8) Z. Hang, A fzzy -modes algorthm for clsterng categorcal data, IEEE Trans. Fzzy Systems, 999, vol. 7, no. 4, pp (9) F. M. Ham and I. Kostanc, Prncpal of Nerocomptng for Scence and Engneerng,, 39

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