Module G1 Electric Power Generation and Machine Controls

Transcription

1 G1 lecric Power Generion nd Mchine Conrol 115 Module G1 lecric Power Generion nd Mchine Conrol Primry Auhor: Jme D. McClley, ow Se Univeriy mil Addre: Co-uhor: None Prerequiie Compeencie: 1. Sedy-e nlyi o circui uing phor, ypiclly covered in n inroducory circui coure 2. Three-phe circui nlyi nd hree-phe power relionhip, ound in module B. Converion beween hree-phe nlyi nd per-uni nlyi, ound in module B2 Module Objecive: 1. deniy he phyicl rucure nd eenil componen o ynchronou generor. 2. Perorm nlyi o hree-phe ynchronou generor uing he quivlen Circui Model.. Decribe recive operion o ynchronou generor in erm o recive power generion, exciion volge mgniude, power ngle, leding generor operion veru lgging generor operion, cpciive lod veru inducive ld, nd curren ngle. 4. xpre erminl volge, exciion volge, rel nd recive power, nd rmure curren uing phor digrm. G1.0 nroducion Generion o elecricl power i proce whereby energy i rnormed ino n elecricl orm. There re everl dieren rnormion procee, mong which re chemicl, phoo-volic, nd elecromechnicl. lecromechnicl energy converion i ued in convering energy rom col, peroleum, nurl g, urnium, wer low, nd wind ino elecricl energy. O hee, ll excep he wind energy converion proce ke dvnge o he ynchronou AC generor coupled o em, g, or hydro urbine uch h he urbine conver em, g, or wer low ino roionl energy, nd he ynchronou generor hen conver he roionl energy o he urbine ino elecricl energy. i he urbine-generor converion proce h i by r mo economicl nd conequenly mo common in he indury ody. n hi chper, we will udy hi converion proce wih priculr emphi on he ynchronou mchine nd he conrol h re ued o govern i behvior. All meril re under copyrigh o PowerLern projec copyrigh 2000, ll righ reerved

2 G1 lecric Power Generion nd Mchine Conrol 116 G1.1 Generor Operion A urbine-generor i illured in i bic orm in Figure G1.1. Figure G1.1 Block Digrm or Turbine-Generor Syem The governor nd exciion yem re known eedbck conrol yem becue i i he eedbck loop which provide or good conrol o cerin prmeer. The governor nd exciion yem re ypicl eedbck conroller in h he quniie o be conrolled (peed nd volge, repecively) re lo providing he eedbck ignl. We will udy hee conroller more cloely. However, we mu ir ke cloer look he operion o he generor iel. The generor i cliied ynchronou mchine becue i i only ynchronou peed h i cn develop elecromgneic orque. he nominl yem requency i (60 Hz in Norh Americ), ynchronou peed i compued 2 m e p (G1.1) where 2 i he requency in rd/ec nd e 120 peed in RPM cn be compued N. p p i he number o pole on he roor o he mchine. The mchine The ynchronou generor h wo iron rucure. The roor i he revolving pr o he mchine, nd i loced inide he or, which i he ionry pr o he mchine. Hydroelecric generor hve heir roor buil wih liency; he roor pole prorude rom he cenrl xi. Becue hydro-urbine re relively low (600 o 1800 RPM hydro-urbine generor re ypicl ), he number o pole mu be high in order o produce 60 Hz volge (ee eqn. G1.1). Slien pole conrucion i impler nd more economicl when lrge number o pole re required. Sem pln, on he oher hnd, hve very high peed (1800 nd 600 RPM em-urbine-generor re ypicl), nd liency would cree igniicn mechnicl re hee peed. Thereore, mooh or round roor conrucion i employed or hee generor. The wo ype o roor conrucion re illured in Figure G1.2.

3 G1 lecric Power Generion nd Mchine Conrol 117 Figure G1.2 Slien Pole (le) nd Smooh (righ) Roor Conrucion A mgneic ield i provided by he DC-curren crrying ield winding, which induce he deired AC volge in he rmure winding. For ynchronou generor, ield winding volge re ypiclly much lower in mgniude hn rmure winding volge; in ddiion, rmure volge mu be vilble exernl o he mchine. i hereore impler o loce he rmure winding on he or where here i no roion. The ield winding i lwy loced on he roor where i i conneced o n exernl DC ource vi lip ring nd bruhe or o revolving DC ource vi pecil bruhle conigurion. The rmure coni o hree winding, ll o which re wound on he or, phyiclly diplced rom ech oher by 120 degree. i hrough hee winding h he elecricl energy i produced nd diribued. A ypicl lyou or 2 pole, mooh roor mchine would pper in Figure G1.. Figure G1. Winding Lyou or Two-Pole Smooh Roor Synchronou Mchine A complee heoreicl nlyi o ynchronou mchine operion i beyond he cope o hi coure, bu here re mny good ex on he ubjec; repreenive mple o hee i [2,,4]. will uice here o dicu he bic o edy-e, blnced operion only. G1.2.1 The Revolving Mgneic Field The DC curren in he revolving ield winding on he roor produce revolving mgneic ield. We denoe he lux ocied wih hi ield h link he rmure winding (he ubcrip indice ield winding). By Frdy Lw o nducion, hi roing mgneic ield will induce volge in he hree rmure winding. Becue hee hree winding re phyiclly diplced by 120 degree (or wo-pole mchine), he induced volge will be phe diplced in ime by 120 degree.

4 G1 lecric Power Generion nd Mchine Conrol 118 ech o he hree rmure winding i conneced cro equl impednce, blnced hree phe curren will low in hem. Thee curren will in urn produce heir own mgneic ield. We denoe he lux ocied wih ech ield,, nd. The reuln ield wih ocied lux obined he um o he hree componen luxe b b,, nd c c i he ield o rmure recion. We deigne he ocied lux elecromgneic ield heory nd rigonomeric ideniy, one cn how h roor. Thereore he wo ield repreened by nd r r r. Uing revolve he me velociy he re ionry wih repec o ech oher. The rmure ield i eecively locked in wih he roor ield nd he wo ield re id o be roing in ynchronim. The ol reuln ield i he um o he ield rom he roor winding nd h ocied wih rmure recion:. r r G1.2.2 The Phor Digrm From Frdy Lw o nducion, volge i induced in ech o he hree rmure winding ccording o d v N r d where i he number o winding urn. Becue cpure he c h he induced volge will lg he lux by 90 degree. Leing induced in winding by he luxe r, r, nd beween he vriou quniie uing he phor digrm, illured in Figure G1.4. r i inuoidl uncion o ime, he negive ign, r, nd be he volge, repecively, we cn repreen he relionhip in ime r φ φ r φ r r r Figure G1.4 Phor Digrm or Synchronou Mchine Regrding Figure G1.4, ke noe h All volge lg heir correponding luxe by 90 degree. The curren in winding, denoed by, i in phe wih he lux i produce r 0 (no lod condiion), hen r 0, nd in hi ce, r F, nd r F. All reince hve been negleced. G1.2. The quivlen Circui Model We develop he equivlen circui model or winding only; he me model pplie o winding b nd c wih pproprie 120 degree phe hi in ll curren nd volge, uming blnced operion uch h he loding on ech winding i he me.

5 G1 lecric Power Generion nd Mchine Conrol 119 From Figure G1.4, he componen volge re reled vi However, becue r r (G1.2) r dr N d nd r i direcly proporionl o (uming conn permebiliy), we cn wrie h ( K ). r Auming r i inuoidl, he ngle mu be -90 degree; hereore he conn o proporionliy K recnce, which we will denoe X r. Thee chnge reul in mu be o r ( X r 90 ) or r jx r Subiuion ino eq.(g1.2) yield r jx r We obin he erminl volge by ubrcing rom Thi reinemen reul in r, volge drop cued by o ccoun or he lekge lux. V jx j( X X ) r l l r Deining X X X he ynchronou recnce, we hve h l r V jx The circui model correponding o hi equion i illured in Figure G1.5. Figure G1.5 quivlen Circui Model o Synchronou Mchine The phor digrm correponding o he equivlen circui, when he lod i inducive, i hown in Figure G1.6.

6 G1 lecric Power Generion nd Mchine Conrol 120 Figure G1.6 Phor Digrm or quivlen Circui nducive Lod The phor digrm correponding o he equivlen circui, when he lod i cpciive, i hown in Figure G1.7. Figure G1.7 Phor Digrm or quivlen Circui Cpciive Lod When he lod i inducive, he curren When he lod i cpciive, he curren The ngle beween nd V lg he volge V ; he generor i id o be opering lgging. led he volge V ; he generor i id o be opering leding. i i, i.e., i iv V 0. Thi implie h 0 lgging, 0 i i leding xmple G 1.1 A 10 MVA, phe, Y-conneced, wo pole, 60 Hz, 1.8 kv (line o line) generor h ynchronou recnce o 20 ohm per phe. Find he exciion volge i he generor i opering red erminl volge nd upplying () 00 Ampere 0 degree lgging, (b) 00 Ampere 0 degree leding. Soluion V 1.8kV 7.97kV V V V jx () (b) 00 0A (2090)(00 0) kV 00 0A (2090)(00 0) kV

7 G1 lecric Power Generion nd Mchine Conrol 121 Noe h he exciion volge mgniude i much higher in he lgging ce. We omeime reer o he lgging ce overexcied operion; here we hve h co V, where i he ngle beween nd V. The leding ce reul in under-excied operion; in hi ce we hve co V. G1.2.4 Power Relionhip From our equivlen circui in Figure G1.5, we wrie h V jx. Solving or yield V jx Deine he power ngle,, where, V V 0 o h i he ngle which he exciion volge led he erminl volge. Thereore, V0 jx co j jx in V co V jx j jx in in co V j X X (G1. ) Bu co j in co j in. (G1.4) i i ince v nd 0 becue V V 0 i he reerence phor. i v quing rel nd imginry pr o eqn. G1. nd G1.4, we hve in co V X. Muliplying boh ide o he previou equion by V yield in co nd X P ou V in V co (G1.5) X Q ou 2 V co V V in (G1.6) X X n eqn. G1. 6, recive power ou o he mchine i poiive when he mchine i opered overexcied, i.e., when i i lgging implying i 0. i imporn o relize h eqn. G1.5 nd G1.6 re bed on he umpion h or winding reince i zero.

8 G1 lecric Power Generion nd Mchine Conrol 122 xmple G 1.2 Find P ou nd Q ou or he condiion () nd (b) decribed in he previou exmple. Soluion () 25.4, V 7.97kV, kV ( )( ) in 25.4 P ou 6. 21MW 20 2 ( )( ) co 25.4 ( ) Q ou. 59MVAR (b) 46.27, V 7.97kV, 7. 19kV ( )( ) in P ou 6. 21MW 20 2 ( )( ) co ( ) Q ou. 59MVAR The uden hould conider he ollowing queion regrding hi exmple: Why i rel power he me under he wo condiion? When he generor i opering lgging, i i borbing VAR rom or upplying VAR o he nework? Wh bou when he generor i opering leding? For priculr ngle, re he erm lgging nd leding meningul wih repec o rel power? Wih repec o recive power? G1.2.5 Generor Pull-Ou Power From eq.(g1.5), he elecricl power oupu vriion hown in Figure G1.8. P ou cn be ploed gin he power ngle, reuling in inuoidl Figure G1.8 Power Angle Curve

9 G1 lecric Power Generion nd Mchine Conrol 12 For impliciy, nd wihou lo o generliy, we neglec ll rel power loe ocied wih windge nd he lo in he urbine nd ricion in urbine nd generor bering. Coninuing wih he umpion h or winding reince re zero, in edy-e operion, he mechnicl power inpu o he mchine i equl o he elecricl power:. (n reliy, in edy-e operion o h P P P.) Conider wh P mech P ou P lo 0 hppen o hi lole mchine opering P ou P mx ( mech 90 ) when he em vlve opening i increed o h 90, nd he elecricl power begin o decree. However, he mechnicl power i only dependen on he em vlve opening, i.e., i i uneced by he decree in P ou. Thi cn only men h Pmech Pou. The dierence Pmech Pou cue he mchine o ccelere beyond i ynchronou peed. When hi hppen, we y h he mchine h pulled ou, gone ou o ep, or lo ynchronim. The generion level which hi hppen i clled he pull ou power. i given by V Pmx X P mech become lighly lrger. n hi ce, he power ngle incree beyond ou lo Thi limi i lower when he generor i under-excied (leding curren) becue i lower. xmple G 1. Compue he pull-ou power or he wo condiion decribed in xmple G1.1. Soluion () Overexcied ce (lgging): ( )( ) Pmx MW 20 (b) Under-excied ce (leding): ( )( ) Pmx 8. 6MW 20 G1. xciion Conrol n exmple G1.1 nd G1.2, we w wo dieren condiion, ummrized ollow: (lgging), kV, Qou. 59MVAR (upplying) b. 000 (leding), kV, Q. 59MVAR (borbing) We recll h in boh condiion, he erminl volge w conn erminl volge i conn, nd ou V 7.970kV. One oberve h lhough Q ou re no. Thee eec re chieved vi conrol o he generor ield curren, which produce he ield lux. Field curren conrol cn be done mnully, bu i i lo done uomiclly vi he exciion conrol yem.

10 G1 lecric Power Generion nd Mchine Conrol 124 The exciion conrol yem i n uomic eedbck conrol hving he primry uncion o minining predeermined erminl volge by modiying he ield curren o he ynchronou generor bed on chnge in he erminl volge. Wihou exciion conrol, erminl volge would lucue reul o chnge in or exernl nework condiion. The conrol i reerred o negive eedbck becue when erminl volge incree, ield curren i decreed, nd when erminl volge decree, ield curren i increed. A impliied block digrm o n exciion conrol yem i hown in Figure G1.9. P ou Figure G1.9 Block Digrm o xciion Conrol Syem There re hree undmenl componen o ny exciion yem. The min excier, or more imply, he excier, i he device h provide he ield curren or he ynchronou generor. The uomic volge regulor (AVR) couple he erminl volge o he inpu o he min excier. The mpliier incree he power o he reguling ignl o h required by he excier. he mpliier i elecromechnicl, i i clled he pilo excier or he roing mpliier. he mpliier i olid e, i i uully conidered pr o he AVR. There re hree bic ype o exciion yem. Thee re: roing DC commuor roing AC lernor ic Thee re illured in Figure G1.10, G1.11, nd G1.12. Figure G1.10 Roing DC Commuor Type xciion Syem

11 G1 lecric Power Generion nd Mchine Conrol 125 Figure G1.11 Roing AC Alernor Type xciion Syem Figure G1.12 Sic Type xciion Syem The DC commuor exciion yem uilize DC generor mouned on he h o he ynchronou generor o upply he ield curren. Thi ype o yem i no longer ued in new ciliie becue i i low in repone, nd becue i require high minennce lip ring nd bruhe o couple he excier oupu o he ield winding. The AC lernor exciion yem ue n AC lernor wih AC o DC reciicion o upply he ield winding o he ynchronou generor. An imporn dvnge over DC commuor yem i h AC lernor yem my be bruhle, i.e., hey do no ue lip ring o couple he excier o he roor-mouned ield winding. For exmple, he Generl lecric Alhyrex ue n invered lernor o upply he ield volge hrough reciier. The lernor i invered in h, unlike he power generor, he ield winding i on he or nd he rmure winding re on he roor. Thereore he lernor ield cn be ed direcly wihou he need or lip ring nd bruhe. Reciicion o DC, required by he ynchronou generor ield, ke plce by eeding he lernor hree-phe oupu o hyrior conrolled bridge. The hyrior or ilicon conrolled reciier (SCR) i imilr o diode, excep h i remin o unil conrol ignl i pplied o he ge. The device will hen conduc unil curren drop below cerin vlue or unil he volge cro i revere. Thi device will be urher dicued in Chper 7. The hird ype o exciion yem i clled ic yem becue i i compoed enirely o olid e circuiry, i.e., i conin no roing device. The power ource or hi ype o yem i poenil nd/or curren rnormer upplied by he ynchronou generor erminl. Three-phe power i ed o reciier, nd he reciied DC oupu i pplied o he ynchronou generor ield vi lip ring nd bruhe. Sic exciion yem re uully le expenive hn AC lernor ype, nd he ddiionl minennce required by he lip ring nd bruhe i ouweighed by he c h ic exciion yem hve no roing device.

12 G1 lecric Power Generion nd Mchine Conrol 126 G1.4 Turbine Speed Conrol We hve lredy een h he mechnicl peed o ynchronou generor m (rd/ec) i reled o he elecricl requency hrough m 2 (2/ p) where i he number o pole. Thi implie h conrol o peed lo men conrol o requency. Bu wh cue requency o devie rom i nominl vlue o 60 Hz? p you conider your own dily ue o elecriciy, you will relize h he lod level een by upplying generor i connly chnging, nd le one generor mu compene or hee chnge. n dicuion o pullou power, we w h when, he generor ccelered. n he me wy, i i greer hn he lod,, he P mech P ou generor will lo ccelere, reuling in requency incree; i reuling in requency decree. P ou P ou i le hn P L P L, he generor will decelere, The eec o generion-lod imblnce on requency, nd he relion beween generor peed nd requency, oer n elegn wy o minin generion-lod blnce: ue deviion rom red urbine peed ( 2 (2 / p), 60 ) conrol ignl o cue pproprie cion regrding djumen o he energy m, re upply vlve. Pou P L, cuing m m, re, he dierence ignl m m, re m i ed bck o n cuor, which dju he energy upply vlve o o reduce he energy upply nd hu reduce P ou. Likewie, i Pou P L, cuing, he dierence ignl m m, re m i ed bck o n cuor, which dju he energy upply vlve o o incree he uel inke nd hu incree. The cuor, which ccomplihe m m, re hee cion, i clled he peed governor. A impliied block digrm o he complee peed governing conrol yem i hown in Figure G1.1. P ou Figure G1.1 Block Digrm o Speed Governing Conrol Syem The purpoe o requency conrol i no only o minin power blnce, bu lo o proec requency-eniive lod rom experiencing lrge requency excurion. Some ype o lod re deigned o opere be nominl requency, nd he perormnce o hee lod my degrde ubnilly when requency devie rom i nominl vlue. Frequency eniive lod include ome ype o moor drive, elecronic lod (including compuer), nd clock. n Norh Americ, requency i normlly reguled o remin wihin 0.04% ( Hz), bu hi i conidered igh; mny power yem in oher region o he world re opered under looer regulion. ndeed, here i ongoing debe in he U.S. ody regrding looening he requency conrol crierion. Becue peed-governor c o minin lod blnce nd requency conncy, he overll conrol yem o which hey re pr i oen reerred o lod-requency conrol. The peed-governor coniue wh i known he primry conrol; he higher level pec o lod requency conrol re known econdry conrol nd coniue uomic generion conrol (AGC). We will no dicu AGC here. Speed governing equipmen or em nd hydro urbine re concepully imilr. Mo peed governing yem re one o wo ype; mechnicl-hydrulic or lecro-hydrulic. lecro-hydrulic governing equipmen ue elecricl ening ined o mechnicl, nd vriou oher uncion re implemened uing elecronic circuiry.

13 G1 lecric Power Generion nd Mchine Conrol 127 Some lecro-hydrulic governing yem lo incorpore digil (compuer owre) conrol o chieve necery rnien nd edy e conrol requiremen. The mechnicl-hydrulic deign, illured in Figure G1.14, i ued wih older generor uni. Figure G1.14 Mechnicl-Hydrulic Governor Deign Bic operion o hi eedbck conrol yem or urbine under-peed i indiced by movemen o ech componen indiced by he rrow. A decree, he bevel ger decree heir roionl peed, nd he roing lyweigh pull ogeher due o decreed cenriugl orce. Thi cue poin B nd hereore poin C o rie. Auming, iniilly, h poin i ixed, poin D lo rie cuing high preure oil o low ino he cylinder hrough he upper por. The oil cue he min pion o lower, which open he em vlve (or wer ge in he ce o hydro mchine), increing he energy upply o he mchine in order o incree he peed. m rod CD w no conneced poin, he previou cion would provide conn requency, long no more hn one mchine in he yem w reguling. However, i wo or more mchine were reguling, ech mchine would coninuouly correc requency chnge mde by he oher, i.e. hey would igh ech oher. The connecion poin olve hi problem. Thi connecion orce poin D o move down lighly poin move down. Thi cion provide or nonzero edy e requency deviion ccording o RP where R i clled he edy e droop or regulion conn, nd pu 1 nd P pu pu re he per uni edy e deviion in requency nd power, repecively. The o-clled edy e droop chrceriic i illured in Figure G1.15. pu Figure G1.15 Sedy-Se Droop Chrceriic 1 Per uni requency deviion i given by / 77 / 60 when 60 Hz i he nominl requency. pu

14 G1 lecric Power Generion nd Mchine Conrol 128 xmple G 1.4 Two mchine on peed-governor conrol re inerconneced nd upplying he me lod when he lod uddenly incree uch h he edy e requency deviion i 0.01 Hz. boh mchine hve droop o 5% ( R 005), mchine A i red 100 MW nd mchine B i red 200 MW, compue he edy e deviion in power or ech mchine.. Soluion A udden incree in lod will decelere he mchine nd hereore requency mu decree pu Ppu, A 0.00 R 0.05 P A pu, B RB P A ( 0.00)(100) 0. MW P B ( 0.00)(200) 0. 66MW 0.00 The uden hould nwer he ollowing queion: 1. Why i edy e requency deviion he me or boh mchine? 2. Why i he edy e chnge in per uni power he me or boh mchine?. Bic inuiion migh ugge h, or given lod chnge, we would like ll mchine o repond, bu bigger mchine hould repond more hn mller mchine. By udying he bove exmple, you hould be ble o e imple requiremen regrding coordinion o governing yem h would provide or hi. A key poin i h he droop chrceriic doe reul in nonzero edy e requency deviion. Thi requency deviion mu be correced o h he yem requency reurn o 60 Hz. Thi i he uncion o he econdry lod-requency conrol loop, o be dicued in Chper 5. G1.5 Summry The opering co o genering elecricl energy i deermined by he uel co nd he eiciency o he power pln. The eiciency depend on generion level nd cn be obined rom he he re curve. We my lo obin he incremenl co curve rom he he re curve. n Module i i illured how hi very imporn generor chrceriic i ued o ind opiml (le co) llocion o demnd mong ll o he inerconneced generor. The AC ynchronou mchine i he mo common echnology or genering elecricl energy. i clled ynchronou becue he compoie mgneic ield produced by he hree or winding roe he me peed he mgneic ield produced by he ield winding on he roor. We ue impliied circui model o nlyze edye opering condiion or ynchronou mchine. The phor digrm i n eecive ool or viulizing he relionhip beween inernl volge, rmure curren, nd erminl volge. The exciion conrol yem i ued on ynchronou mchine o regule erminl volge, nd he urbine-governor yem i ued o regule he peed o he mchine.

15 G1 lecric Power Generion nd Mchine Conrol 129 Reerence A. Bergen, Power Syem Anlyi, Prenice-Hll, New Jerey, V. Del Toro, lecric Power Syem, Prenice-Hll New Jerey, P. Kundur, Power Syem Sbiliy nd Conrol, McGrw-Hill, New York, W. Sevenon, lemen o Power Syem Anlyi, 4h ediion, McGrw-Hill, New York, D. Fink nd H. Bey, edior, Sndrd Hndbook or lecricl ngineer, 1h ediion, 199, Grw-Hill, nc., New York. L. Mch, lecromgneic nd lecromechnicl Mchine, 2nd ediion, Ahrper nd Row, new York, A. Fizgerld, C. Kingley, nd A. Kuko, lecric Mchinery, rd ediion, McGrw-Hill, New York, V. Mbleko, lecric Mchine Theory or Power ngineer, Hrper nd Row, Cmbridge, S. Dewn nd A. Srughen, Power Semiconducor Circui, John Wiley nd Son, New York, P. Anderon nd A. Foud, Power Syem Conrol nd Sbiliy, The ow Se Univeriy Pre, Kimbrk, Power Syem Sbiliy, Synchronou Mchine, Dover Publicion, 1956.

16 G1 lecric Power Generion nd Mchine Conrol 10 P R O B L M S Problem 1 A hree-phe, 60 Hz generor h ynchronou recnce o 0.9 / nd negligible reince. The generor i delivering 50MW 0.8 power cor lgging. The erminl volge remin conn 0kV line o line hroughou hi problem. () Deermine he exciion volge per phe (ngle nd mgniude ) nd he recive power ou o he mchine. (b) Wih he ield curren held conn he level o pr (), he mechnicl power ino he mchine i reduced o 25MW. Deermine he recive power ou o he mchine. (c) Wih he mchine iniilly genering 50MW 0.8 power cor lgging, in pr (), chnge i mde o h he exciion volge i reduced o 79.2% o i vlue. Deermine he recive power ou o he mchine. Problem 2 A hree-phe, 6-pole, 60 Hz, Y-conneced ynchronou generor h ynchronou recnce o X S 2 / opering o h he erminl volge i conn 1.8kV line-o-line. The hree-phe rel power oupu o he mchine i 6MW. Aume he line-o-neurl erminl volge i he reerence (ngle = 0 degree) or ll clculion below.. Wh i he ynchronou peed o hi generor in RPM? b. The exciion volge mgniude i 19kV line-o-line. Wh i he power ngle del (he ngle beween he exciion volge nd he erminl volge)? Bed on hi nwer, indice wheher he generor i opering leding or lgging nd how you cn ell. c. Wh i he mgniude nd ngle o he curren opering leding or lgging nd how you cn ell. d. Compue he hree phe recive power ou o he mchine. Bed on hi nwer, indice wheher he generor i opering leding or lgging nd how you cn ell.? Bed on hi nwer, indice wheher he generor i. i Problem n ech o he ollowing queion circle he nwer h i mo likely o be correc bed only on he inormion or h queion nd he ollowing wo enence. n ll ce ingle generor i direcly conneced o ingle lod. All volge re line o neurl. i) A generor i upplying 20 MVAR o lod. The ngle 'he' o he lod impednce i. ) negive b) zero c) poiive d) no enough inormion ii) The erminl volge o generor i 4.50 kv. The exciion volge i 5 0 kv. Thi generor i opering wih power cor h i. ) leding b) uniy c) lgging d) no enough inormion iii) A generor h n rmure curren o 5020 A when he erminl volge i 50 kv. The generor i. ) overexcied b) under-excied c) neiher d)no enough inormion iv) The exciion volge o generor i very lrge in mgniude. The lod i. ) reiive b) inducive c) cpciive d) no enough inormion v) The rel power oupu o generor i poiive. The curren i he erminl volge. ) leding b) in phe wih c) lgging d) no enough inormion

17 G1 lecric Power Generion nd Mchine Conrol 11 vi) The lod i inducive. The ngle o he erminl volge i 0 degree. The ngle o he curren i. ) poiive b) negive c) zero d) no enough inormion vii) The DC curren o he ield winding i very mll. The generor i recive power. ) upplying b) borbing c) neiher d) no enough inormion viii) The ngle o he exciion volge nd he erminl volge re boh 0 degree. The rel power o he mchine i. ) poiive b) negive c) zero d) no enough inormion ix) The rel power conumed by he lod uddenly incree. The yem requency will. ) incree b) decree c) y he me d) no enough inormion x) The yem requency incree. The peed o he mchine mu hve. ) increed b) decreed c) yed he me d) no enough inormion Problem 4 Drw rough kech o hree-phe wo-pole mooh-roor ynchronou generor. Lbel he or, roor, ield winding, nd rmure winding. Problem 5 Why re he rmure winding in hree-phe wo-pole ynchronou generor pced 120 degree pr? Problem 6 n Germny norml pplince ue 50 Hz AC power. Wh i he idel peed (in RPM) o he roor in hree-phe our-pole ynchronou generor upplying hi power? Problem 7 Why i i necery o conrol he peed o he urbine? Wh would he problem be (or power conumer) i he urbine peed were no conrolled? n brod ene, how i conrol o urbine peed ccomplihed? Problem 8 A hree-phe ynchronou generor i opering wih erminl volge (line-o-neurl) o V. perphe inernl exciion volge i V. The ynchronou recnce i X 2. ) Compue he hree phe rel power ou o he generor. b) Compue he hree phe recive power ou o he generor. c) Compue he ol curren upplied by he generor. d) Drw he phor digrm or hi opering iuion. Show erminl volge, inernl volge, nd curren. e) ndice wheher hi opering condiion i leding or lgging. ) Compue he ngle o (denoed del) required i he opering condiion were chnged o h he mgniude o remin unchnged, bu he recive power being produced by he generor i zero (i.e. uniy power cor).

18 G1 lecric Power Generion nd Mchine Conrol 12 Problem 9 A hree-phe ynchronou generor, hving red erminl volge (line-o-line) o 220 vol, i opering o h i per-phe inernl (exciion) volge i V. Aume conn erminl volge red volge. The ynchronou recnce i X 2. ) Compue he recive power ou o he generor. b) The ield curren i now chnged o h he recive power upplied by he mchine i 600 VAR. The rel power ou o he mchine i kw. Find he exciion volge (mgniude nd ngle). Problem 10 A hree-phe ynchronou generor i upplying lod over rnormer conneced o rnmiion line. The circui i illured below. mpednce d (in per-uni) re: X 0.06, R 0.01, X 0.10, X x g + V 1 = V - + V - + V L - Opering inormion: Be Volge: Be Power: V 1.00, P 0.80, Q 0.20, L L g V , kV, 20kV 100MVA ) Drw he vecor digrm, howing V, nd, g or hi opering condiion. Alo, redrw he phor digrm or he ce when QL 0. 20per-uni. i unnecery o do clculion, bu he lengh nd ngle o he hree vecor relive o ech oher hould be pproximely correc. deniy ech phor digrm eiher leding, lgging, or neiher. b) Compue he rel nd recive power upplied he generor erminl ( bu 1), in MW nd MVAR. c) Compue he rel nd recive power lowing ino he rnmiion line rom bu, in MW nd MVAR. d) Are he nwer o (b) nd (c) dieren? Why or why no? Problem 11 A Y-conneced hree-phe ynchronou generor h ynchronou recnce o volge o he generor i X S / V 1. 8kV (line-o-line) nd he rmure curren i The erminl (reerenced o line-o-neurl erminl volge). () Compue he inernl volge phor o he mchine, (line-o-neurl). (b) Deermine he mgniude o hi phor, necery o provide 0 vr recive power ou o he mchine erminl, uming h he ngle o hi phor,, i held conn he vlue obined in your clculion o pr ().

19 G1 lecric Power Generion nd Mchine Conrol 1 Problem 12 A ynchronou generor hving ynchronou recnce o X S=2 ohm i opering wih n 18.0 line-o-line erminl volge. The power ou o he mchine erminl i P ou=140 MW, Q ou=0.. Compue he mgniude nd ngle o he inernl (exciion) volge. b. A lrge recor (e.g., inducive elemen) i uddenly conneced in prllel wih he lod R L, nd he ield curren i djued. ndice wh would hppen o ech o he below by checking he pproprie pce: Field curren incree decree Recive power ou o he generor incree decree no chnge Curren led lg neiher