Wind Power Prediction Using a Hybrid Approach with Correction Strategy Based on Risk Evaluation

Transcription

1 M.Essa et al., Vol.7, No.3, 7 Wnd Power Predcton Usng a Hybrd Approach wth Correcton Strategy Based on Rsk Evaluaton Mohammed Essa*, Yu Jla*, Wang Songyan*, Peng Lu* *School of Electrcal Engneerng and Automaton, Harbn Insttute of Technology, Harbn 5, Chna (mohessa83@gmal.com, yupwrs@ht.edu.cn, wangsongyan@63.com, lupeng_ht@63.com) Correspondng Author; Mohammed Essa, IEPS and New T, Post #353 Danj buldng, HIT, Tel: , mohessa83@gmal.com Receved:..7 Accepted:.5.7 Abstract- Wth the rapd ncrease of renewable-energy capactes, the management of grd-connected wnd farms s becomng more and more mportant. In ths paper, a very short-term wnd power predcton (VSTWPP) method wth hybrd strategy based on rsk evaluaton s proposed. The VSTWPP s essental for both producers and consumers n the electrcty market, because t can reduce uncertantes of wnd power fluctuaton and thus mantan power balance, securty and qualty of the system. Ths paper focuses on a hybrd approach wth correcton (HWC) strategy for the VSTWPP method, n whch the Gaussan model s appled to calculate the probablty dstrbutons of wnd power value and ts error durng dfferent tme perods and dfferent methods. The WPP process ncludes: ) Wnd power ratos are predcted usng the hybrd approach of multple lnear regresson and least squares; ) Transformaton of these ratos s performed to obtan predcted wnd power values; 3) Correcton strategy s mplemented to obtan the fnal results of WPP. Besdes, n order to observe the predcton performance, WPP model wth HWC, wth the hybrd approach wthout correcton (HWoC), wth autoregressve movng average (ARMA) and wth autoregressve ntegrated movng average (ARIMA) are examned respectvely. The results confrm the accuracy and valdty of the proposed HWC-based VSTWPP method, and show great promse for the predcton wthn ntrcate tme seres, whch are hghly volatle, rregular and uncertan. The obtaned results confrm an observable accurate for the predcton valdty of the proposed hybrd approach wth correcton strategy. Keywords- wnd power predcton, hybrd approach, normal dstrbuton, correcton strategy. Nomenclature WPP wnd power predcton VSTWPP very-short-term wnd power predcton MLR multple lnear regressons LS least square HWC hybrd approach wth correcton strategy HWoC hybrd approach wthout correcton R rsk evaluaton ndex t length of predcton or tme perod (mnute) T wdth of predcton tme wndow (mnute) ARMA autoregressve movng average ARIMA autoregressve ntegrated movng average ANN artfcal neural network BP back propagaton RBF radal bass functon NWP numercal weather predcton PDF probablty densty functon CDF cumulatve densty functon RMSE root mean square error MAPE MSE. Introducton mean absolute percent error mean square error Wnd power generaton has effects on power system operaton relablty and effcency. These effects are apparent n three aspects of power system: the securty, stablty and power qualty. However, connectng wnd power plants to an exstng electrcty network may lead to ncreased uncertanty n the operaton of the energy system. In ths paper, we evaluate the HWC-based WPP performance by comparng smulaton results usng dfferent methods. Wnd power s consdered as one of the most attractve renewable-energy sources because of ts hgh-effcency and low polluton. However, the penetraton of wnd power n power grd brngs several challenges to system stablty. In terms of power system operaton, accurate predcton of wnd power can reduce the unrelablty of electrcty supply, and

2 M.Essa et al., Vol.7, No.3, 7 ncrease wnd power penetraton [,, 5]. An unexpected varaton of wnd power output may ncrease uncertanty for the electrcty system, whch requres hgh-accuracy predcton of wnd energy propertes. In addton, accurate WPP plays an essental role n the balancng of power system. One of the most mportant prortes of wnd power research s to mprove the performance of predcton method [], such as mprovements of WPP technques by a number of scentfc hypotheses [3]. Connectng wnd power farm to power network ncreases the varablty and uncertanty of power grd. Therefore, applyng accurate predcton technques, such as tme seres predcton, combned predcton, mult-step-ahead and snglestep predcton, s essental to assure system stablty [4, 7]. Nowadays, some other approaches are developed to predct wnd power. For nstance, the hourly level of WPP data can be calculated by Gray Correlaton Analyss [5]; a novel of VSTWPP approach based on numercal weather predcton and error correcton method s an effectve way to overcome the challenge n WPP [6]. Whle data of wnd power have very strong non-lnearty and non-statonary, and the tradtonal approach just focuses on solvng the non-lnear problem, the combnng approach of atomc sparse decomposton and artfcal neural network (ANN) could solve the non-statonary problem as well [7]. The proposed works for VSTWPP are generally based on the predcton horzon from several mnutes to one hour. The horzon n ths paper s carred out by the hybrd approach wth correcton strategy, whch s more accurate than other models used n ths work. The applcaton of the hybrd approach based on the combnaton of partcle swarm optmzaton ntended to reduce WPP s error [8, 8]. The accurate predcton can be acheved by a new hybrd technque for VSTWPP wth real-tme [9]. In addton, the predcton accuracy of WPP by the new hybrd short-term WPP based on the combnaton of neural network and mperalstc compettve algorthms are analyzed n []. The hybrd method of WPP, wth novel tme-seres based on K-means clusterng, enhances the value of wnd energy by mprovng the relablty and ncreasng economc feasblty []. The ARMA model s one of the most popular methods for predcton. It can be effectvely used to predct the behavor of a tme seres just from past values, especally n wnd power predcton where t s suggested to be effectve as compared to those obtaned from other models. The ARIMA model s a popularzaton of ARMA model, and s appled n some cases to hstorcal data wth evdence of non-statonary. The statstcal methods used n WPP, ncludng ARMA and ARIMA models, whch are used to fnd out the nherent structure wthn the measured wnd power data [4, 6, 3]. It s mportant to reveal and mprove the fluctuaton of wnd power, by use of the ultra-short WPP based ARMA model []. The hybrd ARIMA-ANN model s to be used to facltate an ncrease n the forecastng accuracy of a lnear and a nonlnear component of a tme-seres data [3, 9]. The ARIMA model and tme seres based on Markov Resdual Correcton to perform accurate WPP and reduce error values [4]. The numbers of the approaches have been ntroduced to mprove WPP, such as ARMA and Generalzed Autoregressve Condtonal Heteroskedastcty [5]. In recent years, some new technologes such as neural networks are often used for WPP. ANN s used to reduce uncertanty from wnd power [6]. Meanwhle, BP neural network s used to mprove the generalzaton ablty of ANN and predcton accuracy [7, 8, 4]. ANN technques were used wth NWP models to get the accurate WPP [9]. Recently, some of WPP approaches that nclude short-term WPP method s based on RBF neural network, mult-layered feed-forward ANN, the new Imperalstc Compettve Algorthm Neural Network (ICA-NN) method wth NWP; wavelet transform are used to predct wnd power [-3]. Ths paper, extendng the applcaton of the rsk evaluaton ndex, ams to show a detaled mathematcal model of the wnd power plant connected to the power grd. The system contans other generatons, whch causes wnd power uncertantes n the power grd. However, the effects of the uncertanty can be reduced by the accurate calculaton. Ths study proposed a new effcent approach wth correcton strategy for pattern feature vector structure, probablstc dstrbuton of power and power error. In ths work, rsk evaluaton ndex for VSTWPP errors has been proposed to acheve stable and economc operaton of the power system. Rsk evaluaton ndex can be drectly accumulated as rsk operatng of VSTWPP error on securty, and economy cost. The contrbuton of ths work s to propose a new hybrd approach, MLR & LS wth correcton strategy, for VSTWPP n Northeast Chna. Meanwhle, ths paper ntroduces several ndexes for HWC accuracy evaluaton, ncludng the root mean square error value (RMSE), the mean absolute percentage error (MAPE), the mean square error (MSE) and the lnear correlaton coeffcent (r). The frst three ndexes are well-known and used to evaluate predcton accuracy wth the smaller but more accurate ndex value. The last one measures, the strength and the drecton of a lnear relatonshp between actual and predcted values wth the hgher r beng of more accurate.. Methods for VSTWPP Ths secton ntroduces several methods wth the wdth of predcton tme wndow h. Frstly, the proposed approach, HWC, s generally explaned; then, the detals of the HWC algorthm steps and HWoC model are ntroduced; lastly, ARMA and ARIMA approaches are presented. In addton, the evaluaton of the predcton performance s also dscussed... Descrpton dataset and the regon Wnd power data s collected by SCADA systems of wnd farm; the data n ths paper s averaged nto tme ntervals, 5 mnutes, whch are sutable for varous applcatons. The data used n ths study was collected at every one-mnute ntervals (called s data) at a wnd farm for a perod of hour, day, and month up to one year. The proposed approach s tested on 5- mnute mean wnd power data provded by the Northeast Chna of wnd farm power generaton at eght wnd farms. 353

3 M.Essa et al., Vol.7, No.3, 7 Data from one year are avalable comprsng at each ste. The wnd farm locaton n Northeast Chna. Some of the data are used as a tranng set on whch the mplementaton of the fttng procedure s optmzed by cross valdaton, and usng data processng step s chosen. The other data are then used to evaluate the performance of the predcton approach, and the results confrmed that... HWC model The proposed approach s based on the hybrd of multple lnear regressons and least square (MLR & LS) wth correcton strategy (HWC). The MLR & LS are used to calculate the coeffcents for mnmzng the error and to mprove the performance of the HWC. It can be used to predct wnd power of a tme seres from hstorcal values alone. The HWC s most accurate wth lower expected error. The general form of the MLR models s as follows: w ( k) W ˆ ( k) () Where, W ˆ ( k ) s the predcted varable; w (k) s the hstorcal wnd power (predctor varables); s regresson coeffcent to be computed; s the maxmal order of regresson; k=~n, N s the length of the predcton varable; s regresson error. In order to estmate regresson coeffcents, we take the least squares approach n smple lnear regresson case that t s mnmzed as: L N [ Wˆ ( k) w ( k)] () k To mnmze L, should be as Eq. (3): ˆ ( w w) w Wˆ For the proposed approach, the rato to total wnd power s used n the followng steps for mprovng the performance of WPP: - Rato to total WPP s defned as followng: (3) X w w (4) Where, w s the wnd power from the th wnd farm, and w s the total wnd power of the farm cluster ncludng the th wnd farm. - After gettng rato X and total wnd power w, the WPP of th wnd farm s as followng: W X w (5) 3- Use correcton strategy to calculate the correcton ratos as followng: X Corr X n X (6) 4- Fnally predct wnd power by usng correcton ratos and total wnd power from the wnd farm cluster: Wˆ Corr X Corr w Algorthm steps of the proposal approach for WPP n Matlab code are as follows: Input data: () w a ( w (), w (), w (3),..., w ( n)) tme seres of sample data; (7) () X ( X (), X (), X (3),..., X ( n)) tme seres of ratos; () T ( t (), t (), t (3),..., t ( n)) sample tme (per mnute). Output data: ˆ () ˆ ˆ ( (), (), ˆ (3),..., ˆ X X X X X ( n)) tme seres of predcton ratos; () W p ( wˆ (), wˆ (), wˆ (3),..., wˆ ( n)) sequence of predcton values. Coeffcents: n number of tme seres data; w a actual wnd power; X rato of wnd power; W p predcted wnd power. Procedure of the HWC code: : Read the hstorcal data; : Evaluate the transformaton of the tme seres data to ratos; 3: Check the ratos from = up to n (, n) = where ==w sze; 4: End of ths, and start loop of WPP (, n) = where ==W sze; 5: Check the predcton wnds, and then go through correcton; 6: Start for =: correcton sze; 7: End of that, and calculate the sum of correcton must be equal to, then; 8: Calculate WPP accordng to the correcton values. In vew of the uncertanty resultng from wnd energy, we ntroduced the method of multple lnear regressons and the least square analyss based on the correcton process. Calculaton steps are as follows: prelmnary analyss of data processng; observaton of the change n the behavor of the data or graphcally shape; comparson of results; reprocessng of the abnormal values. Therefore, the hstorcal wnd power data sequence tends to be stable, as llustrated n Fg.. 354

4 M.Essa et al., Vol.7, No.3, 7 Generaton unt sde Processng sde Analyss of the data from the generaton sde Usng statstcal analyss for data prmary sources are dversfed and renewable-energy resources are avalable locally. However, the penetraton level of renewable energy n the system can brng operatonal securty concerns and rsks. The challenges can lead to a varety of nstablty and operatonal securty problems, and the proposed rsk evaluaton procedure can be summarzed n the followng. 3.. Dfferent evaluaton rsk of error values else Forecastng program (ultra-short-term): realtme grd operaton Comparson results to the actual Stable Accuracy output power Fg..The process of the dagram on proposal approach..3. HWoC model Multple lnear regressons and least square are used wthout correcton strategy as Eq. (4) and (5). In ths case, the output power of WPP wll be determned by hstorcal data, drectly through hybrd tme seres model..4. ARMA model The predcted wnd power tme seres {W t } s modeled usng the ARMA model as shown n Eq. (8): W t p q wt jat j at (8) j Where, p s the order of autoregressve parts; q s the order of movng average; s the autoregressve part of the parameters model (=~p); j s the model parameters of the movng average (j=~q); w s the hstorcal wnd power tme seres; a s error terms..5. ARIMA model The ARIMA model s one of the most popular and frequently used stochastc tme seres model n predcton. ARIMA model usng for non-statonary tme seres becomes statonary values, however, ARIMA model s the general form of ARMA model. 3. Rsk evaluaton of WPP method wth dfferent t The power grd ntegraton of renewable resources can sgnfcantly mprove energy securty of power systems as A- Suppose that t ( n ) n the nput data s the current tme and tˆ ( ) n the output s future tme nstant to be predcted. Wth the measured value of wnd power () w as the crteron for a comparson, the error e of the predcton value Wˆ before p usng correcton strategy s defned as: e Wˆ p w () a Wnd power s overrated when e s greater than zero whle t s underestmated when e less than zero n dfferent tme perods. The postve or negatve error values have dfferent mpact on the relablty of the power grd. B- Assume (n) as the number of output WPP values wthn range of nvestgaton, and then the error value after usng correcton strategy s E that conssts of every relevant error e as t appears n the Eq. (). E [ e,,..., n] (9) () The total E reflects the predctve qualty. The above Eq. can be extended to wde range statstcal results. The probablty ( p j ( e j )) of predct error e whose probablty j dstrbuton functon s P (e) can be obtaned from statstcs methods. A normal PDF and CDF probablstc method s proposed to coordnate the WPP between predct values and rsk events wth hgh error's probablty. The rsk evaluaton ndex R for the wnd power s defned as an ntegraton of the probablty of a power nstable status caused by WPP error s defned as R P( t) e( t) dt () The applcaton of the rsk evaluaton ndex can be expanded from the post-evaluaton of WPP to selecton the accurate VSTWPP method usng for the wnd power connected to the power grd. The framework of the rsk evaluaton based VSTWPP method s shown n Fg.. The process evaluaton s dvded nto four parts: frst processng data and checkng the software method; second usng techncal model and smulaton values; then arrangng output of the smulaton and fnally comparng output results wth dfferent methods. Our am n the present secton s to focus on the wndpower predctablty only. For ths purpose, we ntroduce predcton rsk evaluaton ndces that can be used as skll 355

5 M.Essa et al., Vol.7, No.3, 7 forecasts, the forecasts of the dstrbutons of expected predcton wnd power values and errors. In the power system wth wnd farm connecton, the proposed process computes frst data ntalzaton, then usng techncal smulaton to checked data, and fnally comparson results through probablty dstrbuton. In ths case, the predcton perod and horzon wll have a sgnfcant mpact on the wnd power predct error. For T = 6, t = 5-mnute scales, wnd power varaton and predct error s smallest and can be seen nto the followng Fg. (3, 5 and 4), t confrms that larger tme perod and horzon up to several hours can lead to hgher predcton errors due to the hgher probablty of wnd power output changes for longer predct horzon. The rsk evaluaton ndex for wnd power predcton s proposed n Fg.. Ths ndex can be used for quanttatve evaluaton of the largest wnd power predcton error at any confdence level. Smulaton the system for varous operaton condtons Orgnal power data Data preprocessng Software methods Data Processng Wnd power state as obtaned from state estmaton Gaussan functon wth the mn average wnd power, the varance of the wnd power and mean densty. The man purpose of ths paper s to calculate the accurate wnd power n Northeast Chna: ) dentfcaton of the hstorcal records of wnd power data (usng statstcal characterstc of wnd power); ) Gaussan probablty dstrbuton nvestgated by examnng the effect of the assumed shape of the wnd power value probablty dstrbuton on the predcted wnd power; and 3) calculatng the wnd power densty by the proposed method and evaluatng dfferent methods to fnd, whch has the smallest error. The data set s comprsed of a dfferent length of the predcton whch wll be assgned to 5 and mnutes wth tme wndow beng wthn an hour. The hstorcal records of wnd power from an offshore regon are the nput, and the target output s total WPP. Correcton strategy performance was estmated by PDF between the actual and predcted wnd power values wth the dfferent tme perod. For an ndependent evaluaton of the HWC method, the results of the verfcaton are presented n Fg.3. The comparson results are also shown graphcally n Fg.3. Start the wnd power flow for the real tme operaton Techncal and smulaton Formulate the pattern feature vector for the algorthm steps Output pattern feature vector for the algorthm Output Layout Performance of statc securty assessment method Output vector pattern of statc securty Fg.3. Comparson of PDF of smulated wnd power value at dfferent t wth HWC method. Dstrbuton of the output Dstrbuton of the error values by PDF and CDF values by PDF and CDF Comparson Results Fg.. Process of rsk evaluaton. The power generated from wnd power farm depends on many factors, such as wnd speed, drecton, temperature and pressure. These factors lead to the generaton of random fluctuatons. It needs accurate methods to predct wnd power for a dfferent tme. Ths paper proposes a correcton method n hybrd wth multple lnear regressons and least square for VSTWPP n Northeast Chna takng as an example. 3.. Comparson of predcton PDF wth dfferent t The wnd-power varablty was represented by the normal (Gaussan) probablty dstrbuton, a PDF of two parameters ( &). The parameters were used to correlate the Fg.4. Comparson of PDF of smulated wnd power value at dfferent t wth HWoC method. 356

6 M.Essa et al., Vol.7, No.3, 7 Accordng to the hybrd approach wth and wthout correcton strategy for the above PDF shapes at two dfferent samplng ntervals of wnd power predcton, the predcton values of two knds of methods wth dfferent t =5, mnutes and the same T = 6 mnutes. The numercal values of WPP are shown n Table. Fg.3 and 4 show results of predcton wnd power n dstrbuton by normal PDF. Clearly, the two groups of predcton value show the stable result, but the frst one by proposal method shows more accurate and closer to the actual value wth dfferent tme perods Comparson of HWoC and HWC errors wth dfferent t From Table, the results show that the 5-mnutes tme perod of HWC model have the best performance for WPP than -mnutes tme perod at the same model. r assessment ndexes by HWC predcton results decreases values wth the ncreasng of the tme perod, and the evaluaton rsked based ndex (R), HWC model shows more accuracy than HWoC model. Table. rs for dfferent methods and tme perods Tme Perod 5 mnute mnute r/model HWoC HWC HWoC HWC RMSE MAPE MSE For more accurate evaluaton of the HWC and HWoC methods, the followng absolute percentage error s used: Wa Wp r * W a () The maxmum percentage errors of WPP at T = 6, t =5 mnute are 8.57% for HWoC method and.97% for HWC method. Fg.6. r of WPP for HWC at (T = 6, t = 5 mnute). Fg.7 llustrate the comparson error of WPP for HWoC and HWC at T= 6, t= 5 mnute. It s shown that the proposed method reduced maxmum percentage error comparng wth another method. Fg.7. Comparson error of WPP for HWoC and HWC at (T= 6, t= 5 mnute). 4. Smulaton and results of WPP In ths part, smulatons are carred out for the VSTWPP usng a tme seres wth a hybrd approach. The test of WPP values ncludes three parts and dvded nto two ssues: The frst one s the result comparson, and the second one s the result confrmaton. 4.. WPP values by HWC wth dfferent t Fg.8 and 9 respectvely are WPP results wth the HWC at dfferent t. The predcton accuracy n Fg.8 wth t= 5 mnute s hgher than that n Fg. 9 wth t= mnute, and ts overall predct the curve s closer to the actual curve. Obvously, the HWC approach can predct the wnd-power output more accurately than HWoC approach n Fg. &. Fg.5. r of WPP for HWoC at (T = 6, t = 5 mnute). 357

7 M.Essa et al., Vol.7, No.3, 7 Fg.8. Actual and predcted total wnd power values by HWC at (T = 6, t = 5 mnute). Fg.9. Actual and predcted total wnd power values by HWC at (T = 6, t = mnute). 4.. WPP values by HWoC wth dfferent t Fg. and shows the actual and predcted outputs of wnd power by HWoC approach at T = 6 and t = 5, mnutes. The shape clearly shows that the performances of the HWoC approach are not close to the actual values at dfferent t when compared wth HWC at the same perod. Table. Comparson between actual, predcted and error values wth dfferent methods Tm e Mn Wthout correcton Actua l Predc t r (%) Wth correcton Actua l Predc t r (%) Fg. llustrates a comparson between WPP values wth correcton and wthout correcton approach. For better comparson, the shape of depctng the WPP by HWoC before usng correcton strategy, and the shape of depctng the WPP by HWC after usng correcton strategy are llustrated. It s clear that the proposed approach (HWC) followed the actual wnd power data better than HWoC approach. Addtonally, the errors of both approaches are lsted n Table. The error of HWC s smaller than that of HWoC. Fg.. Actual and predcted total wnd power by HWoC at (T = 6, t = 5 mnute). Fg.. Comparson of WPP wth and wthout correcton at (T = 6, t = 5 mnute). Fg.. Actual and predcted total wnd power by HWoC at (T = 6, t = mnute) Comparson between HWC and HWoC of WPP values, PDF, CDF dstrbuton Table lsts the comparson between actual, predcted WPP and error values by HWoC and HWC, whch s from one hour. The numercal results confrm the accuracy of the proposed method Varablty of WPP It s very mportant to take the varablty of wnd power value nto account n a rght way whle connected to the power grd. Generally, the varablty of wnd power decreases as there are more wnd turbnes and wnd power plants dstrbuted over the area. Larger areas of wnd power also decrease the number of hours of zero output power, n ths work usng eght wnd power plants. The varablty as well decreases as the tme perod scale decreases; n ths paper, we used mnute scale (t = 5& mnute) that's why t was varablty of large-scale wnd power s generally small. However, the most mportant varablty and uncertanty 358

8 M.Essa et al., Vol.7, No.3, 7 occurrng n the mnma tme wndow scales (T = mnute up to an hour). In case of ths work, Fg. 3. shows an example of the varablty and uncertanty of wnd power predcton by HWC proposed approach and comparson wth HWoC method. The contrbutons of ths paper are n two man parts: accurate predcton of wnd power for the power system grd and evaluaton of the system securty rsk wth wnd power predcted errors; ths also reduces the varablty and uncertanty of wnd power. 7% n T = 6, t = 5 mnutes, and for HWoC method, the larger percentage of WPP errors s concentrated between -48 and 48. Fg. 3. Example of wnd power predcton varablty and uncertanty wth dfferent approach Comparson of PDF, CDF dstrbuton of WPP error The normal dstrbuton descrbes a specal class of the dstrbutons that are symmetrc and can be descrbed by two parameters, whch are, the mean () and the standard devaton (). The probablty densty functon (PDF) of the normal dstrbuton s called Gaussan. The PDF s a very common contnuous dstrbuton n wnd power. Normal dstrbutons are mportant to descrbe the natural and characterstcs to represent real-valued predcted varables whose dstrbutons are not known, usng the PDF as shown n Eq. (3) as the followng: ( e ) f ( e) exp( ) (3) The cumulatve dstrbuton functon (CDF) returns the cumulatve probablty of WPP error from up to nput value of predcted varable error. Techncally, t returns the percentage of area under a contnuous dstrbuton curve from large negatve values to large postve error values. The below formula for the CDF of the standard normal dstrbuton as Eq. (4) used n ths work: f ( e) ( t ) exp e dt (4) PDFs of the normalzed WPP errors for two models are shown n Fg. 4. Clearly error dstrbutons, dependng on the predcton approach are sgnfcantly dfferent. Obvously, the uncertanty for these varous predcton methods must be dfferent. As shown, for proposed method (HWC), the percentage of WPP errors s concentrated between -7% and Fg. 4. PDFs of WPP error wth and wthout correcton at (T = 6, t = 5 mnute). The Gaussan dstrbuton n Fg.5 represents the WPP errors by HWC and HWoC respectvely. HWC has more pronounced peak and slmmer shoulders than HWoC. It s also seen that the dstrbuton of the WPP error by HWoC covers for most of the plot. Smlar phenomenon can also be seen from the CDF dstrbuton and plot n Fg. 5. The dstrbuton of HWC mrrors the observed errors very carefully and small devatons. On the contrary, the error dstrbuton of HWoC has large devatons. Fg.5. CDFs of WPP error wth and wthout correcton at (T = 6, t = 5 mnute). The numercal results and shapes ndcate that n every case, the proposed approach s better than the other models,.e., the predcton error s the smallest. 5. Evaluaton ndexes Three ndexes are used to evaluate the hybrd approach wth correcton strategy. These ndexes are descrbed as follows. 5.. The Root Mean Square r (RMSE) 359

9 M.Essa et al., Vol.7, No.3, 7 The root means square error value (RMSE) can be used for a varety of statstc s applcatons. It can be expressed as the followng: r Wa m Wp m (5) RMSE 6 6 m ( Wa m Wp m ) (6) Where, m s the flowed mnutes of the hour, Wa s the m measured value (actual), and Wp s the predcted value of m the mnutely predct. The smaller RMSE ndcates more accurate. 5.. The mean absolute percentage error (MAPE) The mean absolute percentage error (MAPE) can be defned as: 6 Wa * 6 m Wpm MAPE m Wa (7) m A smaller MAPE ndcated that the forecasted values are close to the actual values and the method s more accurate The mean Square error (MSE) Negatve correlaton: f actual value w and predcted value W have a strong negatve lnear correlaton, r s close to -. Negatve values ndcate that the predcton method not accurate and a relatonshp between actual and predcted varables such that as values for actual w ncreases, values for predcted W decreases, and vce versa. Table 3. Comparson between errors wth dfferent models Model rs Predcton Models HWoC ARMA ARIMA HWC RMSE MAPE MSE r Table 3 shows a comparson between the HWC and three other approaches (HWoC, ARMA, and ARIMA), regardng the RMSE, MAPE, MSE, crteron and lnear correlaton coeffcent. The proposed HWC approach presents better predcton accuracy wth RMSE =5.65. MAPE and MSE of HWC are as so less when compared to other methods. The correlaton coeffcent of HWC s hgher than those of other methods. All ndexes show that HWC s the most accurate predcton method. The mean square error (MSE) can be wrtten as the followng: 6 MSE 6 (8) Wa m Wp m m MSE s the always non-negatve. Values of MSE closer to zero are better and perfect accuracy Lnear correlaton coeffcent (r) The mathematcal formulaton for computng the lnear correlaton coeffcent r s: r N w ww W N N w w W W (9) Where, N s the number of pont data, w, w s the actual and means power values, and W, W s the predct and means power values, r [-, ], means postve and negatve lnear correlatons. Postve correlaton: f actual value w and predcted value W have a strong postve lnear correlaton, r s close to +. Postve values ndcate the good predcton method and a relatonshp between actual and predcted varables such as values for actual w ncreases, values for predct W also ncreases General comparson A general comparson of four methods (HWoC, ARMA, ARIMA and HWC) s carred out for total power predcton. Ther actual and predcted values and error values are computed n Table 4. Predcton s done for one hour. Table 4. Comparson between predcted values and errors for 4 methods Tm e Mn HWo C Predc t r (%) ARM A Model r (%) ARIM A Model r (%) HWC Predc t r (%) Table 4 shows the effcency of the proposed method (HWC) and ndcates that the proposed method can predct the VSTWPP better than other methods. 6. Conclusons 36

10 M.Essa et al., Vol.7, No.3, 7 Ths paper evaluates the mpacts of wnd power predcton by usng a hybrd approach wth correcton strategy. By usng the hstorcal wnd power data, the numercal values are determned usng 4 methods, and comparson were determned usng methods wth dfferent tme perods. Performance comparson for the WPP has been done wth fve statstcal tools. Rsk evaluatons based correcton strategy for VSTWPP framework s detaled n ths paper to check mproved predcton approaches and reflect dfferent preferences on WPP methods of a practcal operaton system. The effcacy of the proposed method s verfed by smulaton's results. The smulaton results show that the HWC s the most accurate method for WPP whle compared to HWoC, ARMA and ARIMA. The HWoC s suggested to provde less accurate predcton and s not effcent for the longer tme perod (t). In contrast, the HWC s wth less error and s applcable for dfferent tme perods. Other methods such as ARMA and ARIMA are the least accurate methods to ft the numercal values n ths paper. An HWC based power predcton wth nput hstorcal data selected by a hybrd MLR & LS method s able to produce a good predcton and constantly wth correcton values. The developed HWC approach mproves the predcton, especally after usng the correcton ratos n the nput values to predct total wnd power. Ths study wll be the frst step to evaluate the hgh penetraton of wnd power dstrbuton connected wth power system mpact on the stablty system. The future study ncludes determnng the mpact of the dstrbuted total power generaton and load provdng voltage, and how ths wll mpact transmsson system and outage. Acknowledgment Ths work s supported by the Natonal Natural Scence Foundaton of Chna under Grant References [] W.-Y Chang, A lterature revew of wnd forecastng methods, Journal of Power and Energy Engneerng, vol., pp. 6-68, 4. (Artcle) [] H. Madsen, P. Pnson, G. Karnotaks, H. A. Nelsen, and T. S. Nelsen, Standardzng the performance evaluaton of short-term wnd power predcton models, Wnd Engneerng, vol. 9, pp , 5. (Artcle) [3] X. Wang, P. Guo, and X. Huang, A revew of wnd power forecastng models, Energy proceda, vol., pp ,. (Artcle) [4] Y. Jang, X. Chen, K. Yu, and Y. Lao, Combned approach for short-term wnd power predcton: A case study of the east coast of Chna, n 5 IEEE Power & Energy Socety General Meetng, pp. -5, 5. (Conference Paper) [5] Y. Tao and H. Chen, A hybrd wnd power predcton method, n 6 Power and Energy Socety General Meetng (PESGM), pp. -5, 6. (Conference Paper) [6] X. Peng, D. Deng, J. Wen, L. Xong, S. Feng, and B. Wang, A very short term wnd power forecastng approach based on numercal weather predcton and error correcton method, n 6 Chna Internatonal Conference on Electrcty Dstrbuton (CICED), pp. -4, 6. (Conference Paper) [7] M. Cu, X. Peng, J. Xa, Y. Sun, and Z. Wu, Short term power forecastng of a wnd farm based on atomc sparse decomposton theory, n IEEE Internatonal Conference on Power System Technology (POWERCON), pp. -5,. (Conference Paper) [8] H. M. I. Pousnho, V. M. F. Mendes, and J. P. d. S. Catalão, A hybrd PSO ANFIS approach for short-term wnd power predcton n Portugal, Energy Converson and Management, vol. 5, pp ,. (Artcle) [9] R. M. Per, P. Mandal, A. U. Haque, and B. Tseng, Very short-term predcton of wnd farm power: An advanced hybrd ntellgent approach, 5 IEEE n Industry Applcatons Socety Annual Meetng, pp. -8, 5. (Conference Paper) [] M. J. Ghad, S. H. Glan, H. Afrakhte, and A. Baghraman, Short-Term and Very Short-Term Wnd Power Forecastng Usng a Hybrd ICA-NN Method, Internatonal Journal of Computng and Dgtal Systems, vol. 3, pp. 6-68, 4. (Artcle) [] R. Azm, M. Ghofran, and M. Ghayekhloo, A hybrd wnd power forecastng model based on data mnng and wavelets analyss, Energy Converson and Management, vol. 7, pp. 8-5, 6. (Artcle) [] J. Zhang and C. Wang, Applcaton of ARMA model n ultra-short term predcton of wnd power, 3 Internatonal Conference on Computer Scences and Applcatons (CSA), pp , 3. (Conference Paper) [3] G. Chang, H. Lu, L. Hsu, and Y. Chen, A hybrd model for forecastng wnd speed and wnd power generaton, Power and Energy Socety General Meetng (PESGM), 6, pp. -5, 6. (Conference Paper) [4] L. Ljuan, L. Honglang, W. Jun, and B. Ha, A novel model for wnd power forecastng based on Markov resdual correcton, 5 6th Internatonal Renewable Energy Congress (IREC), pp. -5, 5. (Conference Paper) [5] H. Chen, Q. Wan, F. L, and Y. Wang, GARCH n mean type models for wnd power forecastng, n 3 IEEE Power & Energy Socety General Meetng, pp. -5, 3. (Conference Paper) [6] A.S. Kumar, T. Cermak, and S. Msak, Short-term wnd power plant predctng wth Artfcal Neural Network, n Proceedngs of the 5 6th Internatonal Scentfc Conference on Electrc Power Engneerng, pp , 5. (Conference Paper) [7] J. L and J. Mao, Ultra-short-term wnd power predcton usng BP neural network, n Proceedngs of the 4 9th 36

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