Journal of Physcs: Conference Seres PAPER OPEN ACCESS Mult-step-ahead Method for Wnd Speed Predcton Correcton Based on Numercal Weather Predcton and Hstorcal Measurement Data To cte ths artcle: Han Wang et al 2017 J. Phys.: Conf. Ser. 926 012007 Vew the artcle onlne for updates and enhancements. Ths content was downloaded from IP address 148.251.232.83 on 08/10/2018 at 17:17
Mult-step-ahead Method for Wnd Speed Predcton Correcton Based on Numercal Weather Predcton and Hstorcal Measurement Data Han Wang 1, Je Yan 1*, Yongqan Lu 1, Shuang Han 1, L L 1, Jng Zhao 2 School of Renewable Energy, North Chna Electrc Power Unversty, Bejng, 102206, Chna 1 Bejng Shenzhou Aerospace Software Technology Co., Ltd., Bejng, 100094, Chna 2 E-mal: yanje_freda@163.com Abstract. Increasng the accuracy of wnd speed predcton lays sold foundaton to the relablty of wnd power forecastng. Most tradtonal correcton methods for wnd speed predcton establsh the mappng relatonshp between wnd speed of the numercal weather predcton (NWP) and the hstorcal measurement data (HMD) at the correspondng tme slot, whch s free of tme-dependent mpacts of wnd speed tme seres. In ths paper, a mult-stepahead wnd speed predcton correcton method s proposed wth consderaton of the passng effects from wnd speed at the prevous tme slot. To ths end, the proposed method employs both NWP and HMD as model nputs and the tranng labels. Frst, the probablstc analyss of the NWP devaton for dfferent wnd speed bns s calculated to llustrate the nadequacy of the tradtonal tme-ndependent mappng strategy. Then, support vector machne (SVM) s utlzed as example to mplement the proposed mappng strategy and to establsh the correcton model for all the wnd speed bns. One Chnese wnd farm n northern part of Chna s taken as example to valdate the proposed method. Three benchmark methods of wnd speed predcton are used to compare the performance. The results show that the proposed model has the best performance under dfferent tme horzons. Key words. Wnd speed predcton, mult-step-ahead, predcton correcton, tme-dependent effects, support vector machne. 1. Introducton As an mportant renewable energy resource, wnd power has been ncreasng dramatcally n the power system worldwde [1]. However, the ntermttence of wnd brngs serous challenges to the securty and stablty of the power system operaton as well as the power qualty [2-3]. Cubc relatonshp between wnd speed and power output means that even tny wnd speed predcton error would trgger very large wnd power forecastng devaton. To mprove the wnd speed predcton accuracy on both short-term and ultra-short-term s one of the effectve ways to reduce the negatve mpact of wnd power ntegraton on the power system [4] Prevous lteratures on wnd speed predcton can be dvded nto two categores [5]. The frst category s based on hstorcal wnd speed measurements to make ultra-short-term predcton, prmarly 1-4h. Its man dea s to mappng the nternal relatonshp between wnd speed tme seres. Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lcence. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal ctaton and DOI. Publshed under lcence by Ltd 1
The commonly used algorthms nclude ARMA [6-7], Kalman flter [8], gray theory [9], etc. However, the accuracy of such methods fall sharply wth the ncrease of predcton tme horzon snce the mpact of prevous wnd seres on the followng wnd condton s weakened. Another category employs the Weather Research and Forecastng (WRF) mesoscale NWP wnd speed [10]. The ntal and the boundary feld of the WRF model s released by the Natonal Centers for Envronmental Predcton at 6 o clock every day. The WRF model s adopted to extract the tme-seral results from 24 o clock a day to 24 o clock the next day as the nput data for the power forecastng. The accuracy of NWP data suffers relatvely small mpacts from the predcton horzons, however, the devaton of NWP s not neglgble and contrbutes largely to the wnd power forecastng error. Therefore, the mprovement and correcton of NWP data n ether physcal or statstcal manner s sgnfcant to serve well for the wnd power forecastng. Many researchers are workng on the statstcal correcton of wnd speed predcton, and tradtonally to establsh a mappng relatonshp between NWP wnd speed and the measured wnd speed at the same tme slot. Commonly used algorthms nclude neural network [11], SVM [12-13], relevance vector machne [14], and deep learnng [15], etc. These methods acheve the accuracy mprovement by around 1-2m/s on average, and s slghtly affected by the predcton tme horzons. However, ths mappng relatonshp, whch can be nterpreted as NWP devaton pattern, s not always very clear and consequently affects the correctng performance. To solve above problem, ths paper presents a mult-step-ahead wnd speed predcton correcton method consderng the mpacts passng from the wnd speed n the latest tme seres. Both numercal weather predcton and hstorcal measurement data are used as tranng nputs. Addtonal nputs encourage the NWP devaton pattern to be dfferentated under varous wnd condtons durng the tranng process and mprove the correcton performance. The results show that the proposed method outperforms the other three benchmark methods at dfferent tme horzons, and the accuracy degradaton along wth the tme horzons s reduced to some extent. The remander of ths paper s organzed as follows. Secton 2 analyses the probablty densty of NWP devaton. Secton 3 descrbes the proposed wnd speed predcton correcton method constructon. Secton 4 dscusses the predcton results among the proposed method and three benchmark methods. Secton 5 concludes the paper. 2. Probablty Densty of NWP Devaton Numercal weather predcton s the basc nputs of wnd power forecastng and s also the man source of the power forecastng error. Ths secton takes one wnd farm n north Chna as example to analyse the probablty densty of NWP devaton n each wnd speed bn and the dependency of prevous tme seres to the followng wnd speed. The NWP devaton s calculated as eq. (1). v t v t v t (1) where, devaton NWP m vnwp t s the NWP wnd speed at tme of t; m v t s the measured wnd speed at tme of t. Fgure 1. Frequency of the overall NWP devaton 2
Frstly, the overall NWP devaton n ths wnd farm s calculated. The maxmum value of the postve devaton s 15.8 m/s, the average value of the postve devaton s 3.38m/s. The maxmum value of the negatve devaton s 12.5 m/s, the average value of the negatve devaton s 2.54m/s. The frequency of the overall NWP devaton s shown n Fg. 1. Dstrbuton of the NWP devaton can be ftted by usng normal dstrbuton. However, the range of NWP devaton s large, so further study on the devaton of NWP wnd speed s needed. Secondly, the NWP wnd speed s segmented nto several bns, for example, 1 m/s per bn. Accordng to the range of NWP wnd speed and the power curve, four wnd speed bns (0-1m/s, 7-8m/s, 14-15m/s, 21-22m/s) are selected to show the results of NWP devaton. Fg.2 shows the frequences of NWP devaton n several wnd speed bns. Tab. 1 shows the statstcs of NWP devaton n several wnd speed bns, ncludng maxmum postve devaton, average postve devaton, maxmum negatve devaton and average negatve devaton. It can be seen from Fg. 2 and Tab. 1, the frequences of NWP devaton n small bns show dfferent shapes, and cannot be ftted such well by the normal dstrbuton. Also, the range of the NWP devaton s stll large even f a small NWP wnd speed bn s consdered. It means that the relatonshp between NWP wnd speed and the measured wnd speed at the same tme slot s not very clear. That s one mportant dffculty for the tradtonal NWP correcton methods to acheve good performance. Therefore, more mpact factors need to be consdered to be learnng labels durng the tranng of wnd speed predcton correcton. a) NWP wnd speed: 0-1m/s b) NWP wnd speed: 7-8m/s Frequency Frequency Frequency Frequency c) NWP wnd speed: 14-15m/s d) NWP wnd speed: 21-22m/s Fgure 2. Frequences of NWP devaton n several wnd speed bns Table 1. Statstcs of NWP devaton n several wnd speed bns NWP bn postve devaton (m/s) negatve devaton (m/s) (m/s) maxmum average maxmum average 0-1 / / 9.55 4.30 7-8 6.64 1.97 9.91 2.18 14-15 12.7 4.66 5.97 1.55 21-22 13.2 8.11 / / 3
The transfer relatonshp wthn the wnd speed sequence s the bascs for tme-seres method to predct wnd speed. Therefore, the range of NWP devaton can be reduced when the measured wnd speed at prevous tme s also consdered as an nput label. And the correspondng relatonshp between nputs and outputs of the predcton correcton model wll be much clearer under ths condton. For example, the frequency of NWP devaton s shown n Fg. 3 when NWP wnd speed at tme of t and the measured wnd speed at tme of t-1 are both lmted n 7-8m/s. Compared wth Fg. 2. b), the frequency of NWP devaton s more concentrated, and the range of NWP devaton s reduced obvously, only between -1 m/s to 1 m/s. Frequency Fgure 3. Frequency of NWP devaton (Wnd speed of NWP at tme of t and HMD at tme of t-1 are both lmted n 7~8m/s) 3. The Proposed Wnd Speed Predcton Correcton Method Ths secton descrbes the proposed wnd speed predcton correcton method constructon. The results from secton 2 show that even f NWP wnd speed s wthn very small bns, the correspondng relatonshp between NWP and the measured wnd speed at the same tme slot s stll obscure. Therefore, the tme-ndependent predcton correcton methods cannot largely mprove the accuracy of NWP. In order to further mprove the correcton performance, as mentoned before, the mpacts passng from the wnd speed n the latest tme seres should be consdered. A mult-step-ahead wnd speed predcton correcton method s proposed n ths paper. The man dea of ths work s to take the passng effects from wnd speed at the prevous tme slot nto account by addng the hstorcal measurement data as another nput varable. The proposed model s a rollng predcton correcton model, the model and nput varables of the model are updated n real-tme. In ths paper, SVM s employed to valdate the proposed modellng strategy, and any AI-based algorthm, such as neural network, relevance vector machne, deep learnng, etc. can be easly appled to mplement the proposed strategy. The man modellng process of the proposed wnd speed predcton correcton method s shown n Fg. 4. 4
Fgure 4. Modellng process of the proposed wnd speed predcton correcton method 1 To collect the tranng samples, and to separate the samples nto several groups accordng to NWP wnd speed segments. In ths case, the segment s 1 m/s for each. 2 To tran the model for mappng the relatonshp between NWP wnd speed and the wnd speed measurements. NWP wnd speed at tme of t and the wnd speed measurement at tme of t-1 are all mported as tranng nputs. And the measured wnd speed at tme of t s mported as tranng targets. 3 In ths case, SVM s used to establsh the wnd speed predcton correcton model for every wnd speed segment, and the model parameters n each wnd speed segment are stored to the future correcton. 4 The predcton correcton model s determned and updated n real-tme accordng to the NWP wnd speed. And then the correspondng model s appled to the wnd speed predcton correcton. Except for the frst wnd speed correcton pont, the measured wnd speed s substtuted by predcted wnd speed for nput varables durng the predcton n the proposed method. The modellng process of SVM s as follows. SVM [16] s proposed by Vapnk. Ths algorthm not only has the ablty to deal wth nonlnear regresson problems, but also has the global optmal soluton. It s sutable for solvng small sample, nonlnear and hgh-dmensonal pattern recognton problems. To solve the nonlnear regresson problem of wnd speed predcton, a nonlnear mappng functon s used to map the orgnal sample space nto a hgh dmensonal space, and then the lnear regresson method s appled to analyss. The regresson lnear functon s shown as eq. (2). f x w x b (2) x s the nonlnear mappng functon; b s the threshold. So the soluton of the regresson problem s converted to search for optmal w and b. The where, w s the weght vector; expresson of mathematcal programmng problem s shown as eq. (3). 5
y w x b (3) wxb y st.. 0 0 where, C s the penalty factor to equlbrate the model complexty and error term; s the estmated * accuracy;, are relaxaton varables, whose purpose are to deal wth data that cannot be estmated; x are the nputs of tranng samples; y are the outputs of tranng samples. Gaussan radal bass kernel functon s selected as kernel functon n ths paper, as shown n eq. (4). x x Kx (4), x exp 2 2 where, s the nuclear parameter. The mnmzaton form s transformed nto dual form by Lagrange functon. Thus, the wnd speed predcton model (regresson functon) can be expressed as eq. (5). N f x K x, x b (5) * where,, are Lagrange multplers. 1 mn w 2 4. Case Study In ths secton, the NWP and measured wnd speed of the wnd farm n north Chna s taken as example to analyss. Temporal resoluton of the data s 10 mnutes. Data of the frst 20 days each month are taken as the tran samples, and the rest data of each month are taken as the test samples. Based on two wdely acknowledged crtera, three conventonal benchmark methods are compared wth the performance of the proposed model, and followed by the error analyss for dfferent tme horzons. 4.1. Performance Crtera In order to evaluate the accuracy of wnd speed predcton models, two error ndexes are used as evaluaton crtera. One s root mean square error (RMSE), formulated n eq. (6), to evaluate the overall error. Another s mean absolute percentage error (MAPE), formulated n eq. (7), to evaluate the real-tme error. RMSE 2 C N t 1 v 2 p t vm t (6) 100 N vpt vmt MAPE (7) N t 1 vm t where, vm t s the measured wnd speed at tme of t; vp t s the predcted wnd speed at tme of t; N s the length of predcton. 4.2. Results and Analyss In ths case study, three wdely used methods are selected as the benchmark, whch are ARMA, SVM and SVM n all wnd speed bns (SVM-bns). ARMA s a typcal tme-seres method workng well for the ultra-short-tme predcton, t s manly used to valdate the performance of 1-4h predcton. SVM s one of manstream algorthm for establshng the mappng relatonshp between NWP and the N 1 N 1 6
measured wnd speed at the same tme slot. SVM-bns method s to establsh typcal SVM model for each wnd speed bn, n ths case 1 m/s per bn. Fg. 5 compares the error of raw NWP data, and corrected NWP data by the proposed method and the other three benchmarks. The NWP represents orgnal NWP. The NWP & HMD represents the results of the proposed wnd speed predcton correcton model. RMSE and MAPE of the proposed model are compared wth those of the orgnal NWP as well as the other three conventonal models under dfferent tme horzons. The percentage of the accuracy mprovement s calculated, and the comparson results to the orgnal NWP and the second-rankng benchmark are shown n Tab. 2 and Tab. 3. It can be seen that, the proposed wnd speed predcton correcton model has the hghest accuracy comparng wth the three benchmarks under dfferent tme horzons for both evaluaton crtera. For 1h and 4 h, ARMA s n the second-rankng of ths comparson. Compared wth ARMA, the predcton accuracy of the proposed model s ncreased 8.15% and 1.76% of RMSE and MAPE under 1h tme horzon, 8.66% and 0.80% of RMSE and MAPE under 4h tme horzon. For 12h, SVMbns and ARMA are the second-rankng of ths comparson when usng RMSE and MAPE as the evaluaton crteron respectvely. The mprovement accuracy of the proposed model s 16.67% of RMSE comparng wth SVM-bns, 15.26% of MAPE comparng wth ARMA under 12h tme horzon. For 24h, SVM-bns s n the second-rankng of ths comparson. Compared wth SVM-bns, the predcton accuracy of the proposed model s ncreased 13.41% and 20.87% of RMSE and MAPE under 24h tme horzon. Fgure 5. Comparson of wnd speed predcton error usng two evaluaton crtera Table 2. Improvement compared wth orgnal NWP 1h 4h 12h 24h RMSE 69.22% 54.91% 45.59% 43.46% MAPE 70.06% 52.69% 40.81% 39.12% Table 3. Improvement compared wth the second-rankng method 1h 4h 12h 24h 8.15% 8.66% 16.67% 13.41% RMSE (ARMA) (ARMA) (SVM-bns) (SVM- bns) 1.76% 0.80% 15.26% 20.87% MAPE (ARMA) (ARMA) (ARMA) (SVM- bns) To further valdate the adaptablty of the proposed method, RMSE n dfferent months are compared for the four models under ultra-short-term and short-term tme scales. The results are shown n Fg. 6. It can be seen that n each month the proposed method outperforms the other benchmarks under varous tme horzons. And, for the ultra-short-term (1 and 4 hours ahead) the performance of the proposed method s smlar to that of ARMA at around 1-2m/s and 1.5-2.5m/s; whle for the shortterm (12 and 24 hours ahead) the proposed method seems to have larger advantages comparng to the rest methods, and the devaton range of the proposed method for 12h and 24h s around 2-3m/s. Also, the degradaton of the proposed method from 1h to 24h s not as large as that of ARMA. Fg. 7 shows the accuracy degradaton of the proposed method wth the ncrease of the predcton horzons. As 7
shown, the RMSE and MAPE of the proposed method ncrease sharply before 8-hour tme horzon, and stays constant when the tme horzon s over 12h. a) 1 hour b) 4 hours c) 12 hours d) 24 hours Fgure 6. RMSE of four predcton models n dfferent months Fgure 7. RMSE and MAPE of the proposed model under dfferent tme horzons Devaton of the wnd speed predcton can be dvded nto two parts, one s the statstcal devaton, whch mght be able to elmnate by the statstcal method and mappng algorthm to capture ts pattern, for example, devaton grows wth the wnd speed ncreases; another s the random devaton, whch mght not be easy to capture ts pattern. The correcton of wnd speed predcton ams to elmnate the statstcal devaton and to leave the random devaton to the corrected NWP wnd speed. Fg. 8 shows the corrected results for dfferent wnd speed bns. For the tme horzon of 1h, the RMSE of each wnd speed bn roughly ranges from 1m/s - 1.5m/s, whch s dfferent from the orgnal NWP devaton pattern. For the rest tme horzons, the results show smlar but not such apparent features. 8
Fgure 8. RMSE of the proposed model n dfferent NWP wnd speed bns 5. Concluson In ths paper, a mult-step-ahead wnd speed predcton correcton method s proposed wth consderaton of the mpacts passng from the wnd speed n the latest tme seres. Both numercal weather predcton and hstorcal measurement data are used as tranng nputs. One Chnese wnd farm n northern part of Chna s taken as example to valdate the proposed method. The conclusons of ths paper are as follows. 1) Through the probablstc analyss, the NWP devaton pattern s not very clear when only the NWP wnd speed nterval s consdered. The actual wnd speed vares wdely even f the NWP wnd speed s wthn a very small range. The nvolvement of wnd speed at prevous tme slot enhances the capture of a clearer devaton pattern. Ths motvates to present a tme-dependent method to correct the wnd speed predcton n ths paper. 2) In ths case study, the proposed method can mprove the accuracy of NWP wnd speed to a large extent at dfferent tme horzons. Compared to the second-rankng benchmark method, the proposed method outperforms by 8.15%, 8.66%, 16.67% and 13.41% at the tme horzons of 1h, 4h, 12h and 24h n terms of RMSE. Also, the accuracy degradaton of the proposed method s not as large as the tradtonal tme-seres based method especally. Acknowledgments Ths paper s supported by Natonal Natural Scence Foundaton of Chna (Project No. 51376062) and the project of system development of the optmzaton and evaluaton of the wnd farm stng and wnd turbne selecton from Unted Power. Reference [1] Du P, Wang J Z, Guo Z H and Yang W D 2017 Research and applcaton of a novel hybrd forecastng system based on mult-objectve optmzaton for wnd speed forecastng Energy Converson and Management 150 90-107 [2] L H B, Lu Z X, Qao Y and Zeng P L 2015 Assessment on operatonal flexblty of power grd wth grd-connected large-scale wnd farms Power System Technology 39 1672-78 [3] Ren G R, Lu J F, Wan J, Guo Y F and Yu D R 2017 Overvew of wnd power ntermttency: mpacts, measurements, and mtgaton solutons Appled Energy 204 47-65 [4] Gebel G, Clne J, Frank H, Shaw W, Pnson P, Hodge B.-M, Karnotaks G, Madsen J and Mo hrlen C 2016 Wnd power forecastng: IEA Wnd Task 36 & future research ssues Journal of Physcs: Conference Seres 53 032042-10 [5] Lazarevska E 2016 Comparson of Dfferent Models for Wnd Speed Predcton IECON 2016-42nd Annual Conference of the IEEE Industral Electroncs Socety (IEEE, Pscataway, NJ, USA: Elsever) 5544-9 [6] Kavasser R G and Seetharaman K 2009 Day-ahead wnd speed forecastng usng f-arima models Renewable Energy 34 1388-93 9
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