NAME: EE 459/559, Exa 1, Fall 2016, D. McCalley, 75 inute allowed (unle othewie diected) Cloed Book, Cloed Note, Calculato Peitted, No Counication Device. The following infoation ay o ay not be ueful fo oe pat of thi exa. ; ; ; 1. (30 pt) A 1.0 MW, 575 v (line-to-line), 60 Hz 2160 p DFG i ued in a wind enegy conveion yte. The paaete of the geneato ae given below. The geneato opeate with an MPPT chee. Auing the a-phae line-to-neutal tato voltage i the efeence, deteine the following when the DFG opeate in the geneato ode at a peed of 2160 p, a toque of T e =4421ntn-, a tato powe facto of 0.95 leading, and a tato cuent agnitude of =874.38 apee. a. Copute the ynchonou peed in electical ad/ec ω and in p n. Thi i a 60 Hz achine; theefoe, ω =2π60=376.99 ad/ec. The p i given by ad ev 60ec 376.99 60 n 1800p p ec 2ad in 2 2 b. Copute the lip, and identify whethe thi achine i opeating ub-ynchonouly o upeynchonouly. n n 1800 2160 0.2 n 1800 The lip i negative; theefoe, the achine i opeating in the upe-ynchonou ode. 1
c. Copute the fequency, in electical ad/ec, of the oto cuent: ω =ω =-0.2376.99=-75.4 ad/ec. d. What i the peed of otation of the oto, in electical ad/ec? One way to get it i to convet fo p, a follow: ad ev 60ec 60 2 n p 2 (2160)2 n 452.39 ad / ec p ec 2ad in p 2 60 60 Anothe way to do it, given we know ω, i to ue the equation at the top of the exa: 376.99 ( 75.4) 452.39 ad / ec e. What i the peed of otation of the otating agnetic field fo the oto, elative to the oto, in electical ad/ec? -75.4 ad/ec f. What i the peed of otation of the otating agnetic field fo the oto, elative to the (fixed) tato, in electical ad/ec? To have a contant toque, the peed of otation of the agnetic field fo the oto and the peed of otation of the agnetic field fo the tato, both given elative to the (fixed) tato, ut be the ae. Theefoe, the anwe i 376.99 ad/ec. One could alo get thi by eaoning that the peed of otation of the otating agnetic field fo the oto, elative to the (fixed) tato, i given by the peed of otation of the oto plu the peed of otation of the agnetic field fo the oto elative to the oto, that i: Speed of otating ag field fo oto elative to tato 452.39 ( 75.4) 376.99 ad / ec g. Give the a-phae line-to-neutal tato voltage phao (agnitude and angle): V =575/qt(3)=331.98 V =331.98/_0. h. Give the tato cuent phao (agnitude and angle): =874.38 apee. pf=0.95 leading aco(0.95)=18.2. Howeve, it i opeating in the geneato ode and o, with V a efeence, geneato ode with leading pf equie that lie in the econd quadant. And o θ i =180-18.2=161.8. Anwe i theefoe =874.38 /_161.8 apee. i. Copute the agnetizing banch voltage phao V (agnitude and angle). Fo the cicuit: V V R 331.98 874.38161.8(0.003654 (376.99)(0.0001304)) 349.916.58. The oto cuent phao (agnitude and angle) Fo the cicuit: 2
V 349.916.58 874.38161.8 (376.99)(0.00412) 990.17 30.`12 k. The oto voltage phao V (agnitude and angle) Fo the cicuit: V V R 73.03 166.1 2. (14 pt) Given T e =3p ag{ }, deive the following elation fo toque: T e 3p Uing ; we have that T 3 e p p 3p 0.2(349.916.58) 990.17 30.`12 ( 0.2)(376.99)(0.0001198) 3 3 But note that i entiely eal, and o ince we ae taking the iaginay pat of what i inide the backet, the econd te can be eliinated. Theefoe: T e 3p 3. (21 pt) The ynchonou peed of a 60 Hz double-fed induction geneato fo a wind tubine i 1800 RPM. While opeating at a peed of 2100 RPM, it ee a echanical input powe of 1 MW fo the dive tain. a. Copute the lip. n n 1800 2100 0.1667 n 1800 b. gnoing loe, copute the powe though the tato and the powe though the oto. We aue poitive diectionality fo P and P a into the achine and poitive diectionality fo P ech a out of the achine. Theefoe: Pech 1 P 0.8571MW 1 1 ( 0.1667) P P ( 0.8571)( 0.1667) 0.1429 c. dentify whethe the diection of flow of oto powe i into the oto fo the gid o into the gid fo the oto. Fo the lat calculation, auing poitive diectionality fo P a into the achine, we ee
that the diection of flow of oto powe ut be into the gid fo the oto. t i actually unneceay to keep tack of the ign of the vaiou quantitie (although it i helpful) becaue we know that the achine i opeating in the upeynchonou ode, and in thi cae, the oto i AWAYS deliveing powe to the gid. 4. (15 pt): n the cla note, we developed the following elation: 2 1 Q Te 1, V, 3V 3, pv Auing λ a the efeence, how that V Q Te 3V 3pV Equate the two expeion fo : Q Te 1 3V 3pV (i) Expe λ a a function of V : V But given that λ i the efeence, we obtain V V 0 (ii) Subtitute (ii) into (i): Q Te 1 V 3V 3pV Solve fo the te in λ : 1 V Q Te 3V 3pV Divide though by the coefficient of λ : V Q Te 3V 3pV Siplifying: V Q Te (iii) 3V 3pV The above anwe the exa quetion, and no oe wok i needed o expected. But ut to coplete the developent, we alo obtain an expeion fo, confiing elation on lide 22 of DFG et 2. Fo the flux-linkage equation, we ay deive 1 (iv) Subtituting (ii) and (iii) into (iv), we obtain: V 1 V Q Te 3V 3pV 4
a. F b. T c. T d. F e. F f. T g. F h. T i. T. F Ditibuting the 1/σ : V 1 V Q Te 3V 3pV Siplifying within the backet: V 1 V Q Te 3V 3pV Factoing V / σω fo the fit two te: 2 V Q Te 1 3V 3pV Noting that the te in the backet i σ, we have: V Q Te 3V 3pV 5. (20 pt) Tue/fale: a. The electic geneation technology with the laget hae of new capacity (MW) built in the US duing the 2015 yea wa ola-photovoltaic. b. Fo any US wind plant built in 2016, the fedeal poduction tax cedit povide an additional $22 fo evey MWh poduced ove the fit 10 yea of the plant life. c. The unubidized levelized cot of enegy fo wind plant i aong the lowet of all electic geneating technologie in 2016 ainly becaue, elative to othe technologie, (i) it ha vey low opeation & aintenance cot (fixed and vaiable, including fuel), and (ii) it invetent (capital) cot ha teadily declined ove the pat few yea. d. COE i the ight indicato fo deciding whethe to build a wind plant o not. e. The ain eaon why ot wind tubine ae built with a vetical axi i that vetical axi wind tubine (VAWT) have a highe wind enegy conveion efficiency than hoizontal axi wind tubine (HAWT). f. The video of the wind enegy laboatoy included illutation and dicuion of a tabletop wind tubine, a load box, the gea box, the pitch oto, the hub aebly, the haft and beaing, eveal diffeent type of geneato, and data acquiition equipent. g. The Betz liit equie that the powe of the wind downtea fo a wind-tubine ut be le than 59.26% of the powe of the wind uptea fo the tubine. h. A type 1 geneato, i.e., a quiel-cage induction geneato, ut opeate upeynchonouly when in geneato ode; it ha alot contant peed; it ha a wide toque ange and o wind gut ae paed on diectly a vaying powe inection to the gid. i. When a DFG geneate powe in the ub-ynchonouly ode, the haft ut eceive powe fo the oto.. The pape titled A tutoial of wind tubine contol fo uppoting gid fequency though active powe contol, povide the following deciption: n tandad Region 3 contol, blade pitch i typically held contant at the value β that poduce the peak C p. The goal i then to aintain the TSR at the optial level λ ; hence, the tip-peed, and theefoe oto peed, ut vay popotionally to the wind peed. Thi i achieved by vaying the geneato toque. 5
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