Examination Electrical Machines and Drives Et4-117 Thursday, October 30, 2003 from 9.00 to 12.00

Transcription

1 Exmintion Electricl Mchine nd Drive Et4-117 Thurdy, Octoer 30, 003 from 900 to 100 Thi exmintion conit of 6 prolem The numer efore prolem indicte how mny point cn e erned with thi prolem 15 Prolem 1 c d Sketch cro-ection of dc motor with interpole Indicte the current direction in the excittion winding, the winding round the interpole nd the rmture with dot (for current coming out of the plne of the drwing) nd + (for current going into the plne of the drwing) A vrile-peed drive ytem ue dc motor which i upplied from vrilevoltge ource The drive peed i vried from 0 to 1500 rpm (e peed) y vrying the terminl voltge from 0 to 500 V (rted vlue) with the field current mintined contnt The peed eyond (ove) the e peed i otined y field wekening while the rmture voltge i held contnt t 500 V (rted vlue) The rted vlue of the torque elow 1500 rpm (e peed) i 300 Nm Armture rection, iron loe nd the voltge drop over the rmture reitnce my e neglected Determine the motor rmture current if the torque i held contnt t the rted vlue of 300 Nm elow 1500 rpm (e peed) Determine the torque ville t peed of 3000 rpm if the rmture current i held contnt t the vlue otined in quetion Sketch the mximum torque nd the mximum power function of the peed for peed rnge of 0 to 3000 rpm 11 Prolem c d A three-phe, 500 MVA 08 kv four-pole tr-connected ynchronou mchine h negligile ttor reitnce nd ynchronou rectnce of 08 Ohm per phe t rted terminl voltge The mchine i operted genertor connected to three-phe 08 kv infinite u Note: 08 kv i the line voltge Give the per-phe equivlent circuit of the ynchronou mchine Clculte the phe voltge Sketch the phor digrm when the mchine i delivering rted MVA t power fctor of 08 lgging Determine the excittion voltge nd the power ngle when the mchine i delivering rted MVA t power fctor of 08 lgging

2 I L σ I 4 Prolem 3 R + Thi prolem del with -pole three-phe induction U L R R / mchine connected to 50 Hz upply (& Œ50 rd/) - The figure give n equivlent circuit where the ttor reitnce i neglected Thi equivlent circuit cn e mthemticlly derived from the T-cheme (the IEEE recommended equivlent circuit) Ue thi equivlent circuit to derive n expreion for the torque-peed chrcteritic function of the prmeter of the equivlent circuit, the voltge, the ngulr frequency nd the lip ( L, R R, U, &, ) Mention t let 6 importnt umption ued in the derivtion other thn tht Mxwell eqution nd the power lnce hold c Give n expreion for the lip where the torque i mximum (the derivtion i not required) The prmeter of the equivlent circuit cn e determined from the no-lod tet nd the hort circuit tet In the no-lod tet, the rotor rotte ynchronouly ( & ) t the rted voltge The voltge nd the current re meured U 30 V nd I 50 A d Determine the vlue of L In the hort-circuit tet, the rotor i locked ( 0) nd voltge, current nd power re meured t reduced voltge The reult re U 40 V, I 00 A en P 1500 W (NB the power i meured three-phe) e Determine L nd R R It my e umed tht the current through L i negligile f The mchine work motor t & / Determine the efficiency ccording to the ued equivlent circuit 1 Prolem 4 The Dutch rilwy ytem h DC upply Thi prolem del with the comprion of three type of electricl motor for rilwy trction ppliction, nmely DC motor, three-phe quirrel-cge induction motor nd three-phe permnent-mgnet ynchronou motor We ume the voltge of thi DC upply to e contnt For the three motor type, ketch the power electronic converter (witche nd diode) etween the DC upply nd the motor If you think the me converter cn drive more mchine type, one ketch of tht converter i enough Compre the three motor drive (motor nd converter) for thi ppliction y giving t let 6 dvntge or didvntge per motor type y pying ttention to eg cot, mintennce, rik of filure, ize nd weight, efficiency, complexity of the power electronic converter nd the control, field wekening

3 Prolem 5 The depicted ruhle DC motor h the following chrcteritic The mgnetic permeility of iron i infinite The xil tck length (in the direction perpendiculr to the plne of the drwing) i l The ir gp rdiu i r The ir gp length i l g The mgnet length in the direction of mgnetiztion i l m The mgnet hve remnent flux denity B r nd reltive recoil permeility µ rm nd the BH-chrcteritic i tright line in the econd qudrnt of the BH-plne The ttor winding re concentrted winding with N turn The ir gp length nd the mgnet length my e umed o mll compred to the ir gp rdiu ( l g l m <<r ) tht the flux denity in the ir gp nd the mgnet doe not chnge in rdil direction nd tht the flux my e umed to cro the ir gp perpendiculr In quetion to f, the ttor current re zero c Give Ampère lw nd ketch contour nd urfce where Ampere lw hold Give n eqution decriing the BH-chrcteritic of the mgnet Uing the given chrcteritic, give n expreion for the mximum vlue of the mgnetic flux denity in the ir gp uing Ampère lw Ue further tht the mgnetic flux denity in the gp i d Uing the given chrcteritic, give n expreion for the mximum flux of phe (conductor ) e Sketch the flux linkge of coil function of the rotor poition f g h The mchine rotte with n ngulr peed Clculte the mximum excittion voltge of phe (the voltge induced y the mgnetic field of the mgnet) In prctice, the no-lod (excittion) voltge wveform of ruhle DC mchine re trpezoidl due to kewing The mximum phe current i I Sketch the three-phe trpezoidl no-lod (excittion) voltge wveform nd the idelized current wve form function of time for one cycle Clculte the torque 7 Prolem 6 Sketch cro-ection of hded-pole ingle-phe induction mchine Explin why it trt rotting when it i connected to ingle-phe upply

4 Anwer to the exmintion of Octoer 30, Prolem 1 4 ee figure 410 The flux due to the current round the interpole h to oppoe the flux due to the rmture current 4 The rmture reitnce i neglected, therefore, V t E 500 V E K-, therefore T K-I, therefore I T K- 945 A K- E 60 E V/rd ŒN 3 c E K-, therefore T K-I 150 Nm 4 d See figure 453 d K- E 60 E V/rd ŒN 11 Prolem See figure E63, genertor convention i ued, ut motor convention i lo llowed V t 080 kv 101 kv 3 c See figure E63 5 d I S 1388 ka 3V t The power fctor i 08 lgging Therefore, if the terminl voltge phor i choen in the rel xi ( V t 101 kv), the phor for the current cn e written I 1110 j833 ka Therefore, the phor for the excittion voltge cn e written E f V t jx I j888 kv 1867j888 kv E f kv 068 kv The power ngle cn e clculted / rctn rd 543( Prolem 3 7 The expreion i derived from the power lnce nd the Thevenin equivlent circuit According to thi equivlent circuit, the rotor current i given y I R U R R & L A tedy-tte condition i umed, which men tht - the rotor peed i contnt - the tored mgnetic energy doe not chnge Therefore, ll power i diipted in the rotor reitnce or delivered mechnicl output power According to the per-phe equivlent circuit, the three-phe ttor input

5 power i given y R P 3I R R 3I R R R 3I 1 R R R The power diipted in the rotor reitnce i P di 3I R R R The ret i the electromechnic output power P em Therefore, the torque cn e written T e P 3I 1 R R R em R 3I R R (1 )& & Sutitution of the expreion for the rotor current give: T e 3 R R & U & L R R 6 Ued umption: - ttor winding re inuoidlly ditriuted - ttor winding hve xi which re 10 hifted with repect to ech other - the ttor voltge (nd the reulting current) re inuoidl (with contnt mplitude nd frequency, tedy tte) - the ttor voltge (nd the reulting current) hve phe hift of 10 with repect to ech other - the mechnicl peed i contnt (tedy tte) - the tored mgnetic energy i contnt (tedy tte) - ttor copper loe re neglected, - iron loe re neglected - mechnicl (friction nd windge loe) re neglected c Tmx R R & L d L U & I 4 e R R P 3I 1464 mh 150 m The voltge cn e written U (& L I ) (R R I ) Therefore L U (R R I ) & I mh 3 f In the ued equivlent circuit, only the reitnce tke ctive power P P I diipted in the rotor winding, while (1 )P i converted into electromechnicl power Therefore, 1 1 Prolem 4

6 6 For DC motor: ee fig 1034 of Sen For induction motor nd permnent-mgnet ynchronou motor: ee fig 1043 of Sen 15 DC motor IM PMSM cot - expenive due to commuttor + chep - expenive due to mgnet mintennce - commuttor nd ruhe need regulr mintennce + low mintennce no mechnicl contct with rotor + low mintennce no mechnicl contct with rotor rik of filure - commuttor filure re rik + extremely rout - demgnetiztion of the mgnet due to high temperture or high current i rik ize nd weight - lrge nd hevy + more compct ++ mllet efficiency - not very high due to loe in rotor, ttor nd commuttor - not very high ecue of loe in ttor nd rotor -not very high due to low power fctor + et: no loe in rotor complexity control + chopper impler thn inverter, le witche - complex inverter, more witche - complex inverter, more witche field wekening + poile + poile - more difficult

7 Prolem 5 3 3H#d3l 3J #d 3A or Q Cm PSm Q Cm 3H#3d PSm 3J #3ndA where 3 i the unit vector prllel to the pth C m nd 3n i unit vector perpendiculr to the urfce S m B m µ 0 µ rm H m B r 5 c Applying Ampère lw reult in (l m H m l g H g ) 0 In the ir gp: µ 0 H g q 3B#d 3A 0 P S therefore Sutitution give B m l m l m µ rm l g B r d mx N - N A N l Œr e tringulr f E mx d dt 4f mx N l r My lo e derived from E Blv λ 0 π π θ 4 g ee figure 639 nd 640 h T E mx I 4N & l r I m My lo e derived from T rf rbli i e e i e c 0 π i c π ωt 7 Prolem 6 3 See figure 713 of Sen 4 The winding round the pole reult in pulting flux in the ir gp There i hortcircuited ring round prt of the pole When the flux through thi ring i chnging, current i induced in the ring Thi current oppoe the chnge of the flux Therefore, the flux through thi prt of the pole i delyed with repect to the flux through the ret of the pole Thi give rotting component in the pulting flux Thi rotting component of the flux induce voltge in the rotor r The rotor r re hort-circuited o tht current flow The comintion of thee current with the rotting component of the flux reult in torque which i enough to trt the mchine