A prediction model for wind farm power generation based on fuzzy modeling

Transcription

1 Avalable onlne at Proceda Envronmental Scences (0 ) 9 0 Internatonal Conference on Envronmental Scence and Engneerng (ICESE0) A redcton model for wnd farm ower generaton based on fuzzy modelng Bo Zhu, Mn-you Chen,a, Neal Wade, L Ran,b State Key Laboratory of Power Transmsson Equment & System Securty and New Technology Chongqng Unversty, Chongqng, Chna School of Engneerng, Unversty of Durham,Durham, UK a e-mal: mnyouchen@cqu.edu.cn, b e-mal: l.ran@durham.ac.uk Abstract As a renewable energy source, wnd turbne generators are consdered to be mortant generaton alternatves n electrc ower systems because of ther non-exhaustble nature. As wnd ower enetraton ncreases, ower forecastng s crucally mortant for ntegratng wnd ower n a conventonal ower grd. A short-term wnd farm ower outut redcton model s resented usng fuzzy modelng derved from raw data of wnd farm. Usng wnd data from a wnd farm n Inner Mongola of Chna, an nterretable model whch reveal a useful qualtatve descrton of the redcton system s develoed, and a ower forecastng ma s llustrated. The comaratve study of model redcton wth dfferent erods s conducted. 0 Publshed by Elsever by Elsever B.V. Selecton Ltd. Selecton and/or eer-revew and/or eer-revew under resonsblty under resonsblty of Natonal Unversty of [name of Sngaore. organzer] Oen access under CC BY-NC-ND lcense. Keywords:Renewable energy, wnd farm, redcton, Fuzzy modelng.introducton Wnd s one of the fastest growng energy sources snce t s renewable, abundant and olluton-free. The ower generated by a wnd turbne generator vares randomly wth tme due to the varablty of wnd seed. In Chna, by the end of 009, there were more than,000 Wnd Turbnes (WTs) wth an nstalled caacty of 5,800 MW generated []. Uncertanty of the wnd ower and wnd ower enetraton ncreasng wll affect system stablty and run the rsk of blackouts. Therefore, a new oeratonal strategy based on recse wnd ower forecasts s necessary, and t s mortant for the ower ndustry to have the caablty to estmate ower varatons Publshed by Elsever B.V. Selecton and/or eer-revew under resonsblty of Natonal Unversty of Sngaore. Oen access under CC BY-NC-ND lcense. do:0.06/j.roenv

2 Bo Zhu et al. / Proceda Envronmental Scences ( 0 ) 9 3 The fluctuaton of wnd seed results n rad changes n the electrc ower generated by electrc wnd turbnes; the forecastng model wll nevtably be non-lnear. Many dfferent aroaches have been used to forecast wnd farm ower, such as an Auto Regressve Movng Average Model (ARMA) [], a Kalman Flter Model [3], an Auto Regressve Integrated Movng Average Model (ARIMA) [4], a Tme Seres Analyss Model [5], and Artfcal Neural Networks (ANN) [6]. In ths aer, a wnd ower redcton model s resented by usng fuzzy modelng due to ts advantages of combnng exlct knowledge reresentaton and data-drven modelng. Frst, a modfed Fuzzy C-Means (FCM) clusterng algorthm s used to decde the otmal number of fuzzy rules. Secondly, the arameters of nut and outut membersh functons are adjusted automatcally by a back-roagaton algorthm. Case studes demonstrate that the redcton model has a good agreement wth the measured data and can descrbe nut-outut relatons usng a set of rules n the IF-THEN form.. Wnd farm modelng In ths secton, major factors affectng wnd farm ower are analyzed and a redcton model of wnd farm electrc ower outut s resented...major factors effectng wnd farm ower Wnd farm outut ower comes from wnd ower catured by wnd turbnes. Essentally, wnd energy s knetc energy, and t can be calculated usng ( ) () E mv Joules where m s the ar mass ( kg ) and v s the ar seed n the ustream wnd drecton at the entrance of rotor blades ( m /sec.) Wnd ower can be derved from knetc energy of wnd usng P de dm. v dt dt 3 (. Av). v. Av ( Watts) () 3 where s ar densty ( kg / m ), A s area swet by rotor blades ( m ). Followng the same rncle, the actual ower extracted from wnd turbne blades can be obtaned usng (), where the ar mass flow rate through wnd turbne blades dm has changed; equaton (3) shows dt the new ar mass flow rate: dm v v. A.( 0 ) (3) dt where v s the ar seed n the downstream wnd drecton at the ext of the rotor blades ( m /sec.). 0 So the mechancal ower extracted from wnd turbne blades can be obtaned usng () and (3): where dm dm dm v v0 P0. v. v0. ( v v0).[. A. ]( v v0) dt dt dt v0 v0 ( )[ ( ) ] Av.. v v.. Av.. C ( Watts) C s the rotor effcency, and t s shown by equaton (5)(6) (4)

3 4 Bo Zhu et al. / Proceda Envronmental Scences ( 0 ) 9 C v v 0 0 ( )[ ( ) ] Protor v v (5) Pwnd v0 where x v, so we can get ts maxmum value as follows. Dfferentatng (5) wth resect to x, 3 dc d ( x)( x ) d x x x [ ] [ ] [ 3x x] 0 (6) dx x x From equaton (6), the extremum s found to be C max x, so C max 3 can be derved: Protor ( x ) (7) 3 P wnd The maxmum value of the mechancal ower extracted from wnd turbne blades can be derved usng (4) (7), thus 3 3 Pwnd max Av. C max Av (8) We know that C s a functon of wnd seed, turbne seed and turbne blade arameters, such as tch angle, angle of attack. Therefore, n varable seed wnd turbnes, rotor seed s vared to hold C at ts maxmum value. Therefore, outut ower of a wnd turbne generator, P s roortonal to P. wnd max For a fxed wnd turbne, the area swet by the rotor blades s constant, so P s roortonal to the ar densty, and the ar seed n the ustream wnd drecton at the entrance of rotor blades v, and s determned manly by ar temerature. Therefore, the major factors affectng wnd farm electrc outut are smlfed to ar seed and ar temerature...predcton model of outut ower of sngle wnd turbne generator In ths model, data-drven fuzzy modelng s used to forecast the wnd ower generated by a wnd turbne generator. As mentoned n Secton A, the major factors affectng wnd turbne outut are ar seed and ar temerature, so they can be used as model nuts, and can be obtaned from a Suervsory Control and Data Acquston (SCADA) system nstalled at a wnd farm. Because the forecast s used by the oeratonal deartment of ower system, and n order to mrove the accuracy of redcton, the hstorcal ower outut collected by the Energy Management System (EMS) can be used as nut. The wnd ower can be used as sngle outut. Fgure llustrates data flow. Fgure. The sketch ma of data flow In order to get good redcton recson, the nuts can be exanded nto tme seres of hstorcal data of ar seed, ar temerature and wnd ower. Therefore, the nut arameters of the model

4 Bo Zhu et al. / Proceda Envronmental Scences ( 0 ) 9 5 are vn ( ), vn ( ) tn ( ), tn ( ) n ( ), n ( ) and the model outut s n ( ). So the nut/outut attern can be reresented as P(x, y). The number of fuzzy rules can be confrmed by erformance of fuzzy clusterng n ths model. [7] A fuzzy model s consdered as a set of rules n the IF-THEN form to descrbe nut-outut relatons of redcton model. Based on a collecton of n data onts { P, P,..., Pn }, a mult-nut and sngle-outut fuzzy model s reresented as a collecton of fuzzy rules n the followng form: R : IF x s A and x s A... and x s s where x=, x,..., x ) dscourse ( s x U U... U s A s THEN y z (x), are lngustc varables, A j are fuzzy sets of the unverses of U j R (j=,,,s), R reresents the th rule, =,,..., and y V s the outut of the th rule. Tycally, z (x) takes the followng forms: sngleton,.e. z b Mamdan model, or lnear functon,.e. s bj j j, whch can be reresented as z b 0 x, whch s Takag-Sugeno (TS) model. In ths aer TS models are used to redct the wnd ower snce a Mamdan model can be consdered as a zero order TS model under certan condtons. The fuzzy logc system wth center average defuzzfer, roduct-nference rule and sngleton fuzzfer are of the followng form: y s s z uj ( x j )]/ [ j j [ u ( x )] (9) j j where u j ( x j ) denotes the membersh functon of x j belongng to the th rule,.e. ( x x ) ex( a ) j j j ( j j u ) (0) where j and j are the center and wdth of the jth membersh functon n the th rule. Thus, the relaton between the nut and outut can be rewrtten as y z q ( ) () Frstly, the number of fuzzy rules s determned by a modfed Fuzzy C-Means (FCM) clusterng algorthm. The FCM algorthm dvdes a collecton of n data onts nto c fuzzy clusters such that the followng objectve functon s mnmzed: J m n c k m k u ( x) xk v, <m< () where m s a fuzzy exonent, v s the rototye of the th cluster generated by fuzzy clusterng, [0,] s the membersh degree of the kth data belongng to the th cluster reresented by v, s a cn fuzzy artton matrx whch satsfes the constrants: 0< k n u k <n for =,, c; and k c u k = for k=,,,n. uk uk U, U

5 6 Bo Zhu et al. / Proceda Envronmental Scences ( 0 ) 9 So the object of FCM algorthm s to fnd the best value of c to mnmze J m. But the number of cluster c s requred to be redetermned. In ths aer, an alternatve fuzzy artton measure s used as a cluster valdty crteron assocated wth the FCM algorthm, whch s defned as follows: n k c c n [ V ( U, c) max( uk ) mn( uk, u jk )], n K n j k where c K. (3) The rocedure of the FCM algorthm assocated wth the valdty measure s carred out n the roduct sace of nut-outut varables through an teratve otmzaton of J m [8]. After comletng artton valdaton, we can obtan both the number of rules and the rototyes of the outut clusters v ( v, v,..., vs, v, s ), where =,,, c. Let a ( a, a,..., as ) ( v, v,..., vs ), z v, s, then the vector a denotes the rototye of the th fuzzy artton n the nut sace, and t can also be vewed as the center values of Gausson membersh functons n the antecedent of the th rule, whle z s the rototye of the th fuzzy artton n the outut sace, and denotes the fuzzy outut value n the consequent art of the th rule. After confrmng the structure and obtanng the model arameters, we can buld the fuzzy model mlemented by a RBF network wth m nut and c neurons n hdden layer. Each neuron reresents a fuzzy rule: R : IF x s A and x s A... and x s s A s THEN y s z where A j denotes the Gausson membersh functon centered at outut of the model. a j, aj a, and z s the th rule The next ste s to otmze the arameters of the model. In ths aer, we adot the back-roagaton based aroach to otmze the arameters a j, j and z n combnaton under the erformance ndex of root mean square error [9]. After arameter learnng, the fnal redcton model s obtaned..3.predcton model of outut ower of wnd farm Wnd farms consst of several wnd turbne generators (WTGs) and the ower outut of a wnd farm s the total ower of each turbne. In order to redct the electrc ower of wnd farm, we can dvde a wnd farm nto several wnd turbne generaton unts, and the ower of each unt s redcted frst and then the oututs of all of the unts are aggregated to calculate the wnd farm ower [0]. 3.Case study In ths secton, we gve an examle of the wnd ower redcton by means of fuzzy modelng wth real measured data obtaned from a wnd farm n Inner Mongola of Chna. Ths wnd farm conssts of 35 wnd turbne generators wth 9.8 MW. In order to valdate the erformance of ths model, the ower outut of a wnd turbne generator s redcted. Wnd seed data s measured usng the anemometer on the end of the nacelle of a WTG at a heght of about 80 meters and the ar temerature s measured by the thermometer. Data s saved contnuously n the SCADA system. The samlng erod of the data s 0 mnutes, thus 6 data onts are collected er hour.

6 Bo Zhu et al. / Proceda Envronmental Scences ( 0 ) 9 7 In ths examle, the redcton model s used to forecast the wnd outut ower and we can comare the erformance and error wth dfferent redcton erods. The model s desgned usng MATLAB. The measured data from 5 days are used as orgnal data to tran and valdate the model. The data arsng from the frst 0 days are used to tran the model and the data arsng from the last 5 days are used to valdate the traned model. We use the data durng the latest 3 redcton erods as nut to the model to redct wnd ower over the next erod. The erod can be regulated n half an hour, an hour, two hours, etc. The redcton model starts from zero ntal state. The wnd seed varables v (n) v ( n ) v ( n ), temerature varables t (n) t ( n ) t ( n ) and hstorcal ower outut n ( ) n ( ) ( n ) are consdered as nut. The model outut s ( n ). After rule-base generaton and arameter learnng, an 8-rule fuzzy model s obtaned. The fnal fuzzy model s obtaned as shown n Fgure. Fgure. The fnal fuzzy model of redcton modelng Fgure 3 and Fgure 4 show the results of the wnd ower redcton whose erods are hour and 0.5 hour resectvely. Red lne reresents real measured ower outut and blue dots reresent the redcted ower at redcton onts. Comarng Fgure 3 and 4, we fnd the result n Fgure 4 s sueror to that n Fgure 3. In Fgure 4, the redcted and measured values are almost entrely consstent because the redcton erod s shorter than that n Fgure 3, the correlaton of revous weather and current weather s smaller, t wll mrove the redcton accuracy. Therefore, the redcton accuracy and the redcton erod are closely related.

7 8 Bo Zhu et al. / Proceda Envronmental Scences ( 0 ) 9 ( ) Fgure 3. Real measured and redcted wnd ower (redcton erod= hour) Fgure 4. Real measured and redcted wnd ower (redcton erod=0.5 hour) The maxmal ower outut of the wnd turbne generators s 850kW. Table shows the root-mean-square error (RMSE) of the redcton model for dfferent redcton erods usng the roosed fuzzy model and backroagaton neural network model. It can be seen that the fuzzy model has better erformance. When the redcton erod s 0.5 hour, the fuzzy model attans the hghest redcton recson. Ths erod can meet the needs of oeratonal deartment n ower system. TABLE. Comarson of redcton errors for dfferent redcton erods n each model 4.Concluson Predcton Fuzzy Model NN Model erod RMSE tran RMSE test RMSE tran RMSE test 0.5hour hours hours Based on the hstorcal data of a wnd farm, the alcaton of a fuzzy model for wnd ower redcton s carred out. It has been found that wnd ower can be successfully redcted usng fuzzy model. The redcton by use of the fuzzy model has the smaller error when the erod s 0.5 hour. The model not only mantans good redcton accuracy but also rovdes an nterretable model structure whch contans several rules, from whch t may also reveal a useful qualtatve descrton of the redcton system. Wth more arameters, the model can forecast ower outut better. Further studes wll be carred

8 Bo Zhu et al. / Proceda Envronmental Scences ( 0 ) 9 9 out to mrove ths smlfed model, such as consderng effects of other factors whch are wnd drecton, humdty, etc. 5.Acknowledgement The authors wsh to acknowledge the fnancal suort from Educaton Mnstry of Chna va the Project. Reference [] Kang Jnsong, Zhang Zhwen, Lang Yongqang,Develoment and trend of wnd ower n Chna 007 IEEE Canada Electrcal Power Conference, EPC 007, (007) [] J.L. Torres, A. Garca, M. De Blas, A. De FrancscoForecast of hourly average wnd seed wth ARMA models n Navarre (San), Solar Energy79, 65-77(005) [3] P. Louka, G. Galans, N. Sebert, G. Karnotaks, P. Katsafados, I. Pytharouls and G. Kallos: Imrovements n wnd seed forecasts for wnd ower redcton uroses usng Kalman flterng, Journal of Wnd Engneerng and Industral Aerodynamcs, 96, (008) [4] Fonseca, Inaco, Farnha, Torres, Barbosa, Fernando Macel: On-condton mantenance of wnd generators-from redcton algorthms to hardware for data acquston and transmsson, WSEAS Transactons on Crcuts and Systems, 7, (008) [5] Tanquch Kenqo, Ichyanaq Katsuhro, Yukta Kazuto, Goto YasuyukStudy on forecast of tme seres of wnd velocty for wnd ower generaton by usng wde meteorologcal data, IEEJ Transactons on Power and Energy, 8, (008) [6] Caroln Mabel. M., Fernandez. E.Analyss of wnd ower generaton and redcton usng ANN: A case study, Renewable Energy, 33, (008) [7] D.A. Lnkens, Mn-You Chen,Inut selecton and artton valdaton for fuzzy modelng usng neural network, Fuzzy Sets and Systems, v07, n3, , 999 [8] Mn-You Chen, D.A. LnkensRule-base self-generaton and smlfcaton for data-drven fuzzy models, Fuzzy Sets and Systems, v4, n, 43-65, March, 004 [9] Wang LX, Mendel JM Backroagaton fuzzy system as nonlnear dynamc system dentfers. ST IEEE Int Conf on Fuzzy Systems, San Dego, CA, 99; [0] Andrew Kusak, Hayang Zheng, Zhe SongWnd farm ower redcton: a data-mnng aroach, Wnd Energy,,75-93(009)