EE 559, Exa 2, Spig 26, D. McCalley, 75 iute allowed. Cloed Book, Cloed Note, Calculato Peitted, No Couicatio Device. (6 pt) Coide a.5 MW, 69 v, 5 Hz, 75 p DFG wid eegy yt. he paaete o the geeato ae give i the table to the ight. he geeato opeate with a axiu powe poit tackig (MPP) yt o that it echaical toque i popotioal to the quae o the oto peed. he tato powe acto i uity. Fo a oto peed o 75 p, deteie: a. Slip b. (kn-) c. (volt) d. (ap) e. (volt). (ap) g. (ap) h. (volt) i. Z eq (oh) You ae povided with the ollowig elatiohip ad cicuit: 2 4R p 2R a. Slip 2 2 (5) 4.592ad/ec 75ev 2 ad i 8.26 ad / ec i ev 6ec p 2*8.26 66.52 ad / ec 4.592 66.52.667 4.592 b. (kn-) he ated echaical toque i the table i o a peed o 75p which i the peed give i thi pobl. So awe i 8.85 kn. c. (volt) 69 98.7 d. (ap)
2 4R 2 4(.265)(4.592) 98.7 98.7 ( 885.) p (2) 2R 2(.265) 68.2ap e. (volt) R j L j 98.7 68.2(.265 (4.59 ( 4.2 j56.6. (ap) 4.2 j56.6 2.9 j2.2 jx j(.54749)(4.592) g. (ap) (2.9 j2.2) ( 68.2). j2.2 h. (volt) R j L j.667(4.2 56.6) (. j2.4)(.26 j(.667)(4.592)(.7) 65.62 j7.76 i. Z eq (oh) 65.62 j7.76 Zeq.58 j.275. j2.2 2).687)) 2. (22 pt) We developed the below qd voltage equatio o the double-ed iductio geeato. vq iq q vd id d v i vq iq ( ) q v d id d v i We alo developed the ollowig toque expeio. L p qid diq 2 L L Uig the above elatio togethe with the iplicatio o tato-voltage-oieted-cotol (SOC), how that i a uctio o d-axi oto cuet ad d-axi tato voltage oly. Clealy tate how SOC play a ole i thi developet. State ay othe auptio that ae eceay. Extactig the elatio o vq ad vd, we have: v i v i q q d d d q Solvig o λ d ad λ q, epectively, we get 2
vq i q ( vd i d d) q Now ubtitute thee elatio o λ d ad λ q ito the toque elatio: 2 L L L p i L vd id q q qid diq ( ) p id iq 2 L L L p ( v i ) i ( v i ) i p v i i i v i i i L d d d q q q 2 L L 2 L Now ue SOC which iplie that v q =, ad we obtai L p vdid i did i qiq 2 L L Aue that =, the L pvdid 2 L L L v d d d d. (24 pt) Coide a two-level voltage ouce ivete coected to a thee-phae balaced RL load, ad it voltage i 22 volt. he ivete i odulated by pace vecto odulatio ad it iulatio algoith i give i the igue below. he witchig equecy o the covete i 72Hz. At a give itace o tie, the thee-phae eeece voltage v a *, v b *, ad v c *, ae oud to be volt, 487.9 volt, ad -487.9 volt, epectively. Fo thi pobl, you ay eed the atix ad the equatio povided below. 2 2 2 a v e S v i ' e S 2 2 b i ' Deteie: a. he α-β copoet o the thee-phae eeece voltage. b. he peciic witchig equece eceay to achieve the eeece vecto coepodig to you awe i (a). Hee, you eed to peciy a equece o paticula tate. c. he tatioay vecto to be ued i ytheizig the eeece vecto. Hee, you eed to idetiy appopiate vecto k i the pace vecto diaga how below (o coputatio i equied). d. he dwell tie eceay to achieve the eeece vecto. Secto q q Switchig Sequece q q 2 2 2 2 4 4 5 4 4 5 5 6 6 5 6 6
a. he α-β copoet o the thee-phae eeece voltage. va v 2 / 2 / 2 2 / 2 / 2 v b 487.9 v / 2 / 2 / 2 / 2 56.8 vc 487.9 b. he agle o the eeece voltage vecto & it coepodig ecto ube i give by v 56.8 ta ta 9 v t will be i ecto, theeoe the witchig equece i,, 2,, 2,, c. he thee tatioay vecto to be ued i ytheizig the eeece vecto ae 2,, ad. d. hi i i ecto, theeoe: ( k ) o (2 ) So the eeece vecto, with θ=9deg, will have θ =45deg. 72Hz / 72.89 w a ve S i (56.8)(.89) i 6 45 22.28754ec b ve S *56.8*.4 i ' i(45).7854 22 S a b.89.28754.7854.66 4. (8 pt) A 6 Hz powe yt ha MW o covetioal geeatio. Aue: he ietia cotat o all covetioal geeatio i H=6 ecod (o the bae o the geeato); A tip o a MA uit occu with the uit poducig MW. he equecy adi ollowig geeatio tip occu.5 ecod ate the tip. a. Etiate the adi auig all geeatio i covetioal. b. Etiate the adi auig 2 MW o covetioal uit ae diplaced by 5 MW o double-ed iductio geeato. c. Give eted eao why it i ipotat to avoid low equecy deviatio. a. otal capacity o covetioal geeatio ollowig the tip i MW-MW=9MW. Uig a MA bae, the lo o the MW eult i P L =/= pu 4
H i i d dt 9*6 54 PL 2 H i Re i (6) 2*54.5556Hz / ec With t=.5 ecod, the =-.5556*.5=-.84 Hz, o that the adi i 6-.84=59.7Hz. b. otal capacity o covetioal geeatio ollowig the tip i 8MW-MW=7MW. Uig a MA bae, the lo o the MW eult i P L =/= pu H i i 7 * 6 d dt 42 PL 2 H i Re i (6) 2 * 42.74Hz / ec With t=.5 ecod, the =-.74*.5=-.74 Hz, o that the adi i 6-.74=58.9Hz. c. ubie ailue o lo o lie; tubie tip via ude- o ove-equecy elay; ude-equecy load heddig. 5