Study on Fuzzy Models of Wind Turbine Power Curve

Transcription

1 Proceedngs of the 006 IASME/WSEAS Internatonal Conference on Energy & Envronmental Systems, Chalkda, Greece, May 8-0, 006 (pp-7) Study on Fuzzy Models of Wnd Turbne Power Curve SHU-CHEN WANG PEI-HWA HUANG CHI-JUI WU Department of Electrcal Engneerng Department of Electrcal Engneerng Natonal Tawan Ocean Unversty Natonal Tawan Unversty of Scence and Technology No., Penng Rd., Keelung 0 No., Sec., Keelung Rd., Tape 0607 TAIWAN TAIWAN Abstract: - Ths paper presents the fuzzy modelng approach to the descrpton of wnd turbne power curve. The fuzzy system model s bascally a collecton of fuzzy IF-THEN rules that are combned va fuzzy reasonng for descrbng the features of a system under study. The method of fuzzy modelng has been proven to be well-suted for modelng nonlnear ndustral processes descrbed by nput-output data. In vew of the nonlnear characterstc of wnd turbne power curve, the method of fuzzy modelng s employed for representng the curve. Based on the Sugeno-type fuzzy model, varous models wth dfferent numbers of modelng rules are used to descrbng the power curve whch depcts the turbne output power under varous wnd speeds. It s found that such fuzzy model offers both quanttatve and qualtatve descrptons for the wnd turbne power curve. Key-Words: - power system, wnd energy, wnd turbne, power curve, fuzzy modelng. Introducton Electrc energy s playng a very mportant role n our daly lfe. It offers the motve power of the economc actvty and has much nfluence on the qualty of lvng envronment. Wth ncreasng envronmental concern, the mpact of conventonal electrcty generaton on the envronment s beng mnmzed and efforts are made to generate electrcty from renewable sources. The man advantages of electrcty generaton from renewable sources are the absence of harmful emssons and the nfnte avalablty of the prme mover that s converted nto electrcty [-5]. One way of generatng electrcty from renewable sources s to use wnd turbnes that convert nto electrcty the energy contaned n flowng ar. A fuzzy system model s bascally a collecton of fuzzy IF-THEN rules that are combned va fuzzy reasonng for descrbng the features of a systematc behavor [6-]. The method of fuzzy modelng has been proven to be well-suted for modelng nonlnear ndustral processes descrbed by nput-output data. The fuzzy model descrbes the essental features of a system by usng lngustc expressons. The fuzzy model not only offers the accurate expresson on the quanttatve nformaton to the nonlnear system, but also can present the qualtatve descrpton for the physcal property of study system. Generaton of electrcal power by a wnd turbne generator system at a specfc ste depends upon the power curve [-6]. The method of fuzzy modelng has been proven to be well-suted for modelng nonlnear ndustral processes descrbed by nput-output data. In vew of the nonlnear characterstc of wnd turbne power curve, the fuzzy model s employed for the purpose of analyss. Ths paper ams to report an applcaton of the Sugeno-type fuzzy modelng method [8-0] to the descrpton of power curve for the wnd turbne generator. Based on the Sugeno-type fuzzy model, dfferent numbers of modelng rules are adopted and compared n constructng the fuzzy models for representng the output power of a wnd turbne generator under dfferent wnd speeds whch s referred to as the power curve [-5]. The data ponts are ftted nto the Sugeno-type fuzzy model by employng the algorthm of ANFIS (Adaptve Neuro-Fuzzy Inference System) [0]. It s shown that the model s capable of provdng both quanttatve and qualtatve descrpton for the power curve of a wnd turbne generator. Power Curve of Wnd Turbne The output power generated by a wnd turbne at a specfc ste depends upon many factors. Besdes the mean wnd speed of the ste, a much more sgnfcant one wll be the power curve of the wnd turbne whch reles on varable wnd speeds under dfferent hub heghts [-5]. A typcal wnd turbne power curve s shown n Fgure []. Essentally the wnd turbne power curve has a nonlnear physcal characterstc and the wnd speed has sgnfcant

2 Proceedngs of the 006 IASME/WSEAS Internatonal Conference on Energy & Envronmental Systems, Chalkda, Greece, May 8-0, 006 (pp-7) Fgure. A typcal wnd turbne power curve [] Table. The Beaufort scale Scale Name Wnd speed (m/s) 0 Calm Below 0. Lght Ar Slght Breeze.6-. Gentle Breeze.-5. ModerateBreeze Fresh Breeze Strong Breeze Near Gale Gale Strong Gale Storm.5-8. Volent Storm Hurrcane effect on energy producton. In general, the wnd turbne starts to generate energy under a wnd speed of to 5 m/s whch s referred to as the cut-n wnd speed. When the wnd speed falls between and 5 m/s, the wnd turbne electrcal power arrves at the rated output, and such wnd speed s named the rated wnd speed. As the wnd speed reaches certan ntensty above 5 (m/s), t s necessary to shut down the wnd turbne for avodng damage. Ths s called the cut-out wnd speed or furlng. It s general to desgnate the scale of wnd speed by meter per second (m/s) or accordng to the Beaufort scale shown as Table. Fuzzy Modelng. Fuzzy Set The classcal set notaton strctly assgns each studed object nto a relaton of membershp or non-membershp. On the contrary, a set contanng elements that have varyng degrees of membershp n the set s referred to as the fuzzy set [6]. Based on fuzzy set theory, the fuzzy model [7-], whch conssts of a number of fuzzy IF-THEN rules, s used for descrbng the behavor or characterstc of the studed system. It typcally expresses an nference such that f we know a premse, then we can nfer or derve a concluson. In a general nonlnear system, each of the fuzzy relatonal equatons can be expressed n rule-based form. In modelng nonlnear systems, varous types of fuzzy rule-based system could be descrbed by a collecton of fuzzy IF-THEN rules. The objectve of ths paper s to study an applcaton of the fuzzy model to descrbe the nonlnear wnd turbne power curve. Among varous types of fuzzy models, the Sugeno-type fuzzy model has recently become one of the major topcs n theoretcal studes and practcal applcatons of fuzzy modelng and control [8-0]. The basc dea of Sugeno-type fuzzy model s to decompose the nput space nto fuzzy regons and then to approxmate the system n every regon by a smple lnear model. The overall fuzzy model s mplemented by combnng all the lnear relatons constructed n each fuzzy regon of the nput space. The man advantage of the Sugeno-type fuzzy model les n ts capablty of smoothly nterpolatng lnear functons n dfferent regons of the system.. Model Structure In ths study, the sngle-nput-sngle-output Sugeno-type fuzzy model consstng of n rules, as descrbed n (), =,,, n, s adopted for descrbng the wnd turbne power curve: R : IFvs A THEN P = av+ b, =,,, n. () where v stands for the system nput (the wnd speed) and P (the output power) represents the output n the th subregon. It s noted that the nput doman s parttoned nto n fuzzy subregons (wnd scales), whch s descrbed by a fuzzy set A, and the system behavor n each subregon s modeled by a lnear equaton P = av+ b of whch s the coeffcent of wnd varaton and b s a constant. Let m ( x) denote the membershp functon of the fuzzy set A. 0 If the system nput v attans a readng v then the overall system output P s obtaned by computng a weghted average of all the outputs P 's from each rule as shown n () and (). a n n P ( wp)/( w) = () = = 0 0 ( ),. w = m v P = av + b (). Model Identfcaton Model dentfcaton can be defned as a process of recognzng structure n data by comparsons wth known structure. The am of model dentfcaton s to fgure out all the parameters of the model. The

3 Proceedngs of the 006 IASME/WSEAS Internatonal Conference on Energy & Envronmental Systems, Chalkda, Greece, May 8-0, 006 (pp-7) tasks of model dentfcaton for the Sugeno-type fuzzy model are usually dvded nto two categores: structure dentfcaton and parameter dentfcaton. () Structure dentfcaton: Set the number of model rules accordng to the system characterstcs. Dfferent numbers of model rules wll yeld dfferent ways of descrpton for the power curve. () Parameter dentfcaton: Frst select the type of membershp functons dependng on the shape descrbed n each fuzzy set. Then the parameters of the lnear functon n each rule are to be dentfed. In ths study, the Gaussan type membershp functon n (5) s employed for the fuzzy set n the IF-part of the rule: f ( x c) x) = exp[ ] (5) σ ( where the parameters c and σ defne the shape of each membershp functon. Then the parameters a and b n the THEN part of the rule can be dentfed by the method of ANFIS (Adaptve Neuro-Fuzzy Inference System) [0]. Example The wnd turbne power curve shown n Fg. [] s selected for study n ths paper. From Fgure, the wnd turbne starts to generate electrc energy at ths moment of wnd speed m/s,.e. the cut-n wnd speed. When the wnd speed s m/s, namely the v I rated wnd speed v R, the wnd turbne output power P max arrves at the rated output as 660 kw. As the wnd speed reaches the ntensty around 5 m/s,.e. cut-out wnd speed v O or furlng, the wnd turbne should be shut down for avodng damage. The wnd turbne power curve can be represented as (6) where v s the wnd speed n meter per second and P s the output power of wnd turbne n kw. 0, v< vi or v> v P = FM(), v vi v v Pmax, vr < v vo O R (6) As the wnd speed falls between the cut-n speed and the rated wnd speed, the output power FM() v s to be descrbeded by the Sugeno-type fuzzy model. Note that FM() v s the nonlnear part of the power curve. To better understand the performance of the Sugeno-type fuzzy model, comparatve studes are conducted under condtons of dfferent numbers of modelng rules. As an llustraton, fuzzy models wth two, four, fve and sx rule are shown as follows. All parameters for models wth dfferent numbers of modelng rules are shown n Table to Table 5. The mean-squared errors under dfferent numbers of modelng rules are tabulated as Table 6. () Two-rule model: R : IF v s slght breeze THEN P =0. v -5. (kw); R : IF v s fresh breeze THEN P =0. v +660 (kw). () Four-rule model: R : IF v s lght ar THEN P =0.7 v -5. (kw); R : IF v s moderate breeze THEN P =0. v +0 (kw); R : IF v s fresh breeze =0. v +650 (kw); R : IF v s strong breeze THEN =0. v +660 (kw). P () Fve-rule model: R : IF v s calm THEN P =-0. v -. (kw); R : IF v s slght breeze THEN P =0.7 v -5. (kw); R : IF v s moderate breeze =0. v +50 (kw); R : IF v s fresh breeze THEN P =0. v +660 (kw); 5 R : IF v s strong breeze THEN =0. v +655 (kw). P 5 () Sx-rule model: R : IF v s calm THEN P =-0.5 v -.06 (kw); R : IF v s slght breeze THEN P =0. v -0. (kw); R : IF v s gentle breeze =0.7 v +50 (kw); R : IF v s moderate breeze THEN P =0. v +655 (kw); 5 R : IF v s fresh breeze THEN P 5 =0. v (kw); 6 R : IF v s strong breeze THEN =0. v +660 (kw). P 6

4 Proceedngs of the 006 IASME/WSEAS Internatonal Conference on Energy & Envronmental Systems, Chalkda, Greece, May 8-0, 006 (pp-7) Table. The parameters of two-rule model Parameters (σ,c ) Parameters (a,b ) (.68,.5) (0., -5.) (., 8.55) (0., 660) Table. The parameters of four-rule model Parameters (σ,c ) Parameters (a,b ) (.7,.) (0.67, -5.) (., 6.76) (0.8, 0) (.8, 9.6) (0., 650) (.09,.) (0., 660) (a) Membershp functon Table. The parameters of fve-rule model Parameters (σ,c ) Parameters (a,b ) (., 0) (-0., -.) (.8,.89) (0.67, -5.) (., 6.7) (0.8, 50) (.8, 8.) (0., 660) 5 (.56,.) (0., 655) Fgure. Two-rule model Table 5. The parameters of sx-rule model Parameters (σ,c ) Parameters (a,b ) (.88, 0) (0.5, -.057) (.,.) (0., 0.) (.8, 5.) (0.67, 50) (.65, 7.9) (0.8, 655) 5 (.5, 8.6) (0., 659.5) 6 (., 0.8) (0., 660) Table 6. The mean-square error under dfferent numbers of modelng rules numbers Mean-square error (%) (a) Membershp functon The membershp functons as well as data ponts wth fuzzy models are drawn n a sngle fgure for the purpose of comparson as shown from Fg. to Fg. 5. From Table 6 and Fg. to Fg. 5, t s observed that more modelng rules wll yeld a model wth hgher degree of fttng accuracy. Fgure. Four-rule model

5 Proceedngs of the 006 IASME/WSEAS Internatonal Conference on Energy & Envronmental Systems, Chalkda, Greece, May 8-0, 006 (pp-7) (a) Membershp functon Fgure. Fve-rule model (a) Membershp functon Fgure 5. Sx-rule model 5 Concluson The man purpose of ths paper s to present the descrpton of wnd turbne power curve by fuzzy modelng. In vew of the nonlnear characterstc of wnd turbne power curve whch depcts the turbne output power under varous wnd speeds, the method of fuzzy modelng s employed for representng the curve. Based on the Sugeno-type fuzzy model, varous models wth dfferent numbers of modelng rules has been dentfed to descrbe the power curve It s found that such fuzzy model offers both quanttatve and qualtatve descrptons for the wnd turbne power curve. The valdty of the Sugeno-type fuzzy model n the analyss of wnd turbne power curve has been verfed n ths study. References: [] T. Burton, D. Sharpe, N. Jenkns, and E. Bossany, Wnd Energy Handbook, Wley, 00. [] J. Manwell, J. McGowan, and A. Rogers, Wnd Energy Explaned, Wley, 00. [] Z. Lubosny, Wnd Turbne Operaton n Electrc Power Systems, Sprnger, 00. [] N. Mller, W. Prce, and J. Sanchez-Gasca, Dynamc Modelng of GE.5 and.6 Wnd Turbne-Generators, Verson.0, General Electrc Company, 00. [5] G. Masters, Renewable and Effcent Electrc Power Systems, Wley, 00. [6] L. A. Zadeh, Fuzzy sets, Informaton and Control, Vol. 8, 965, pp [7] B. Bezdek, Fuzzy models-what are they, and why, IEEE Trans. on Fuzzy Systems, Vol., 99, pp. -6. [8] M. Sugeno and G. Kang, Structure dentfcaton of fuzzy model, Fuzzy Sets and Systems, Vol. 8, 988, pp. 5-. [9] R. Yager and D. Flev, Essentals of Fuzzy Modelng and Control, John Wley & Sons, 99. [0] J. Jang and C. Sun, Neuro-fuzzy modelng and control, Proceedngs of the IEEE, Vol. 8, 995, pp [] P. H. Haung and Y. S. Chang, Fuzzy rules based qualtatve modelng, Proc. of the Ffth IEEE Internatonal Conference on Fuzzy Systems, 996, pp [] P. H. Huang and Y. S. Chang, Qualtatve modelng for magnetzaton curve, Journal of Marne Scence and Technology, Vol. 8, No., 000, pp [] Vestas wnd system A/S Ltd., Denmark. (