APPENDIX H CONSTANT VOLTAGE BEHIND TRANSIENT REACTANCE GENERATOR MODEL

Transcription

1 APPNDIX H CONSAN VOAG BHIND RANSIN RACANC GNRAOR MOD h mprov two gnrator mo uss th constant votag bhn transnt ractanc gnrator mo. hs mo gnors magntc sancy; assums th opratng ractanc of th gnrator s th transnt ractanc, th votag bhn transnt ractanc to b a constant., an consrs hs appn scusss th accuracy wth whch th constant votag bhn transnt ractanc gnrator mo mos th actua gnrator votag an th actua gnrator ractanc. H.1 ACCURACY OF H GNRAOR VOAG In th skom ntwork out-of-stp trppng happns urng th frst sp cyc. Hnc, to trmn whthr a constant votag gnrator mo cou b us t shou b shown that th votag, stays constant urng th frst sp cyc. j, bhn transnt ractanc h votag bhn transnt ractanc cays accorng to [45, p114]: t o (H.1-a) t o (H.1-b) ypcay o s arg an o s sma. Hnc, t s sma an t s arg (fgur H.1). 240

2 For norma stay stat opraton Hnc, a rap chang n s argr than os not mak (Appn F, fgur F.1). chang rapy. o show th cay n s sma w trac th Kobrg gnrator votag for th frst sp cyc (fgur H.1). h cas consr s whr Mpumaanga an th Wstrn-Cap ar sppng pos. ab H.1 sts th vaus us for o an o. Fgur H.1 shows t s rasonab to assum s constant for at ast th frst sp cyc. hrfor, whn ony th frst sp cyc s consr t s accptab to assum a constant gnrator votag. FIGUR H.1 Dcay n an masur at Kobrg ab H.1 o an o of th Kobrg gnrator o IM CONSAN o scons scons

3 H.2 ACCURACY OF H GNRAOR RACANC h constant votag bhn transnt ractanc gnrator mo computs armatur racton,, usng (Appn D, scton D.7-a): (H.2) 2 hs scton shows th accuracy wth whch rprsnts armatur racton pns on th ang th gnrator currnt forms wth th -as. H.2.1 Armatur racton Armatur racton rprsnts th votrop u to th armatur,.. stator, currnt. h votrop s obtan by groupng a th stator currnt trms n th uaton us to comput th trmna votag. h cas consr s whr th gnrator s n th transnt stat. h fu nkng th - an -as of th gnrator whn n th transnt stat s shown n fgur H.2. It foows from fgur H.2 that to obtan th uaton us to comput th trmna votag shou b wrttn n trms of th stator currnts, an ; th - as fu nkag, 1, an th f fu nkag, f. 242

4 FIGUR H.2 h - an - as uvant crcuts of a gnrator n th transnt 1 2 stat [1, p184]. Whn n th transnt stat 0 o obtan th uatons us to comput th trmna votag, w not th pr unt stator votag uatons ar [1, p86]: p w R r a (H.3-a) p w r R a (H.3-b) 0 p 0 Ra0 (H.3-c) h transformr votag trms, p an p, can b gnor [1, p170] an th pr unt vau of wr w r can b st ua to 1 p.u. (hnc wr an ) [1, p174]. hrfor, whn 0 th stator trmna votag can b comput usng: 0 R a (H.4-a) R a (H.4-b) o prss an n trms of,, 1 an f w appy Krchhoff s votag aw to th uvant crcuts shown n fgur H.2. W obtan: 243

5 a a a f (H.5-a) a (H.5-b) f a f f (H.5-c) a a a1 (H.5-) a (H.5-) 1 a 1 1 (H.5-f) From uaton H.5-f, w obtan: 1 1 a (H.6) 1 Substtuton nto uaton H.5-, gvs: a a a 1 1 a a a a 1 a a 1 1 a a a 1 1 a a a 1 1 a 1 ( ) 1 a 1 1 a a 1 1 whr: a 1 a (H.7) a 1 244

6 h substtuton of uaton H.7 nto uaton H.5- gvs: a 1 1 (H.8) h substtuton of uaton H.8 nto uaton H.4-a gvs ( w 1 p.u.) ( ) 1 a Ra a 1 (H.9) h rotor bas fus nuc th sp votag. hrfor, by groupng th rotor bas fus of uaton H.9 th uaton for s obtan. h uaton s: a 1 1 a a (H.10) h smarty btwn th - an -as n fgur H.2 aows wrtng: a a f f (H.11) Whr: a a a f f By usng mathmatca manpuaton smar to th manpuaton us to obtan uaton H.9, t can b shown ( w 1 p.u.): ( (H.12) [ ] f a ) Ra a f 245

7 hrfor, prss n trms of th f an -as fu w hav ( w 1 p.u.): a a 1 1 R a a a (H.13-a) a a f f R a a a f f f f (H.13-b) Armatur racton rprsnts th votrop u to armatur currnt. Hnc, by groupng th trms n uaton H.13 contanng armatur currnt th - an -as componnts of th armatur racton ar obtan. Hnc: armatur a a 1 1 R a (H.14-a) armatur a a f f R a (H.14-b) Whn rsstanc s ngct, w hav [1, p146 an p185]: armatur a a 1 1 (H.15-a) armatur a a f f (H.15-b) Whn mong th gnrator as a votag, hav:, bhn th ractanc,, w 246

8 armatur 2 (H.16-a) armatur 2 (H.16-b) Form uaton H.15 an uaton H.16 t foows for gnrators wth w hav: armatur 2 (H.17-a) armatur 2 (H.17-b) H.2.2 Armatur racton an uaton H.17 shows that uaton H.2 scrbs armatur racton accuraty whn. Whn th accuracy wth whch uaton H.2 scrbs armatur racton pns on th ang that vops btwn th gnrator -as an th stator currnt. o ustrat, consr th cas whr I s poston wth rspct to th -as such that 0 an 0. h armatur racton s thn armatur. Whn I s poston wth rspct to th -as such that 0 an 0 th armatur racton s armatur. Whch on of th two amps s bst appromat by ( ) 2 whthr t s or pns on that s numrcay th cosst to ( )