The fuzzy decision of transformer economic operation

Transcription

1 The fuzzy decs f trasfrmer ecmc perat WENJUN ZHNG, HOZHONG CHENG, HUGNG XIONG, DEXING JI Departmet f Electrcal Egeerg hagha Jatg Uversty 954 Huasha Rad, 3 hagha P. R. CHIN bstract: - Ths paper presets a ew tellget methd f fuzzy ptmzat, abut the le decs-mag f trasfrmer ecmc perat. The methd ca autmatcally dvde the daly lad curve t several mprtat tme perds ad regulate the trasfrmer perat status wth these perds t reduce the lss f eergy trasfrmer t a mmum t acheve the gal f savg eergy ad creasg ecmc beeft. It maes the -le tellget ctrl cme truead t maes up the defect f prevus -le ctrl methds f trasfrmer ecmc perat. The result f smulat shws that the methd s effectve. Key-Wrds: - Pwer Trasfrmer, Ecmc Operat, Fuzzy Decs, Chagg Weght Itrduct The Ecmc Operat f pwer trasfrmer s a mprtat measure f savg eergy pwer etwr perat. Nwadays much lterature prbe t the quest deeply ad wdely, ad the wrs the aspect has bee publshed[]. The geeral methd f trasfrmer ecmc perat s: t calculate the crtcal lad values C ( = ) amg all the perat mdes; t fd ut the best perat mde whe the actual lad value s bgger r smaller tha the crtcal lad values C, t get the lwest eergy lss f trasfrmer; If the actual lad value becme bgger tha C + r smaller tha C, the perat mde f trasfrmers shuld be chaged. Capacty marg s used t avd the frequet chagg the status f swtch. ecause the mst values f lad chage a wde rage, ad frequetly, the effect f capacty marg avdg frequet perat f swtch s lttle. The wr [] presets a methd t dvde the daly lad curve t tw typcal tme perds ad regulate the trasfrmer perat status wth the tw perds t reduce the lss f eergy trasfrmer t a mmum. ut the methd ly taes tw mdes f the cmbat f trasfrmers e day, whle the chages f lads are varus. Thus the advatage f the trasfrmer ecmc perat ca t be fully tae, f the perat status f trasfrmers has bee chaged ly ce a day. Further mre, the advatage f the lad curve f shrt term lad frecastg ca t be fully tae als, fr the methd ly maes use f tw tme pts, the startg pt ad ed pt f the pea lad perd. [3] puts frward a methd f usg hstrcal r the frecast lad data, t aalyze the eergy lss f ma trasfrmers all tme perds f a day ad uder all ds f perat mdes respectvely, accrdgly t arrage the ecmc perat mdes f ma trasfrmer every day. I ths d f stuat, f the lad f substat waves frequetly, the eergy lss curves geerated by all ds f perat mdes wll brg ut t may pts f tersect. Thus, the umber f cmbat amg all ds f perat mdes f all tme perds wll be extremely large, ad t wll tae a great deal f cmputer system resurces t carry ut the cmparatve aalyss f them. If there are may substats pwer dstrbut etwr, the stuat f system resurces csumpt wll be mre serus. I ths paper we mae use f frecast lad data t calculate the eergy lss f all ds f trasfrmer perat mdes, ad get the eergy lss curves. The pts f tersect amg all ths curves culd be fud ut. fter sme smplfcats, the left pts f tersect wll be the tme pts f chagg trasfrmer perat mde crrespdgly. Every day ca be dvded t a umber f tme perds wth these tme pts. Fr every tme perd, the area f relatve eergy lss ad the fluece f the ecmc perat mde eghbr tme perds are csdered as tw dexes t estmate whch perat mde shuld be adpted. The dea that the value f weght chages alg wth the chagg legth f varus tme perds has bee trduced t ths paper. ecause, embarg frm the huma dspatchers vsual agle, the fluece f eghbr tme perds has bee tae t accut, the

2 judgmet result reflect a lg tme scpe lad chage stuat. I ther wrds, t s a trasfrmer ptmal perat whch the swtch peratg tme gap has bee csdered. Dvs f Daly Eergy Lss Curve The aalytcal express f cmprehesve eergy lss f sgle trasfrmer wth tw-wdg s P = ( P ) + ( P )( / e ) () where: e = trasfrmer rated capacty (V); = trasfrmer actual lad (V); P = dlg actve lss (W); P = shrt-crcuts actve lss (W); Q = dlg reactve lss (V); ( Q = I e / ad I =dlg electrc curret percetage); Q = shrt-crcuts reactve lss (V); ( Q = U e / ad U = shrt-crcut vltage percetage); = reactve pwer ecmy equvalet. The aalytcal express f cmprehesve eergy lss f parallel trasfrmers wth tw-wdg s P ( ) ( ) ( )( / ) ( )( / ) Σ = P e e where: () = the value f lad dstrbuted t Fg. The daly eergy lss curves ad ther cvers fr 3 perat mdes trasfrmer ( = U /( U + U ) ); = the value f lad dstrbuted t trasfrmer ( = U /( U + U ) ); U =The value f trasfrmer shrt-crcut vltage percetage cverted t the capacty e ( U = eu / e ); Tae a certa substat as the example. There are tw trasfrmers wth duble wdgs the substat. The techcal parameters f the trasfrmers are shw as fllws: e = 63V, e = 5V, U = 7.44, U = 7.39, I =.45, I =.38, P = 8.W, P = 5.495W, P = 39.57W, P = 33.88W, =.. Daly eergy lss curve f trasfrmer, trasfrmer ad parallel trasfrmers( ad ) ca be draw as fg., by the daly frecast lad curve ad the calculatg result f frmula (), (). I fg., x-axs express tme ad

3 y-axs express eergy lss. s we ca see fg., the lad value f trasfrmers s chagg ad the techcal characterstcs f these trasfrmers are dfferet, whch cause the cmprehesve eergy lss f trasfrmers chagg -learly. Therefre, may pts f tersect are created these eergy lss curves. These pts f tersect may be crrespdgly the tme pts t chagg perat mde f trasfrmers. Fr the cveece f aalyss, the eergy lss curves fg.(a) have bee cverted t sme ther frms. The daly eergy lss curve f trasfrmer (gree curve) s csdered as base curve, ad all the curves (clude the gree curve) subtract the base curve t get the curves fg.(b). I the same way, f the daly eergy lss curve f trasfrmer (red curve) s csdered as base curve, ad the daly eergy lss curves f trasfrmer (red curve) ad parallel trasfrmers, (blue curve) subtract the red curve, the curves fg.(c) culd be gtte. There are several areas eclsed by blue curve ad gree curve fg.(b). The chagg pts f pstve area t egatve area r the pts f egatve area t pstve area may be crrespdgly the tme pts t chagg perat mde f trasfrmers. These pts dvde a day t several tme perds. If the abslute value f a certa area s less tha a gve Threshld value, t wll be regarded as zer, ad the crrespdg tme perd wll be merged t the left tme perd. If the abslute value f a certa area has bee regarded as zer, ad the tw sde areas f t have the same symbl, these three tme perds wll be merged t e tme perd. Thus, the tme dvs f a day ca be smplfed, ad a grup f tme pts whch dvde e day t several tme perds ca be btaed. The treatmet f the area eclsed by red curve ad gree curve fg.(b) r the area eclsed by red curve ad blue curve fg.(c) s the same as abve. Thus, 3 grups f tme pts are btaed. These tme pts are all lely t becme the perat mde chagg pt. y dvdg a day t mre tme perds wth the 3 grups f tme pts, the the fuzzy decs f every tme perds ca be executed, ad the ptmal perat mde whch tae t accut bth the ecmc factr, determed by the relatve lss area f a tme perd, ad the legth f swtch peratg tme terval factr, determed by the cmparatvely ecmc perat mde f eghbr tme perds. 3 Fuzzy Decs Every Tme Perds Tw trasfrmers wth duble wdg have three d f peratg mdes e tme perd: perat f sgle trasfrmer ; perat f sgle trasfrmer ; perat f parallel trasfrmers,. Tw factrs have bee csdered: ecmc factr, that s t say that the value f eergy lss a tme perd shuld be as smaller as pssble; the fluece factr f eghbr tme perds, fact, the swtch peratg tmes decreasg wll be tae t accut. The data f abve sect are stll used here. ccrdg t the abve methd, the day f fg. ca be dvded t tme perds. The eergy lss value these tme perds are shw table. The uverse f dscurse s U = V = { Operat f sgle, Operat f sgle, Operat f parallel } { Tme perd, Tme perd,, Tme perd x} Table The eergy lss value f 3 peratg mdes tme perds * Tme perd Tme perd Tme perd Tme perd v Tme perd v tartg ad ed pt mde gle trasfrmer gle trasfrmer Parallel trasfrmers, tartg ad ed pt Tme perd v Tme perd v Tme perd v Tme perd x Tme perd x mde gle trasfrmer gle trasfrmer Parallel trasfrmers, *The terval f frecast s regarded as a tme ut. 3. Fuzzy relatal matrx f factr I

4 The pecfcat f the eergy lss data table ca be executed by fllwg Zadeh frmula (3). r j { x } { x } { x } l xj l = (3) l Thus, the membershp matrx f all the tme perds based the 3 perat mdes ca be btaed as fllws: R = The calculat f weght The dea that the value f weght chages has bee trduced t ths paper, that s t say, the dstrbut f weght chages alg wth the chagg legth f dfferet tme perds. tme perd lger, the weght factr I f ths perd wll be bgger. Whle a tme perd shrter, the weght wll be smaller. ecause f a tme perd s very lg, especally whe t s lger tha 4 hurs (5 tme uts), the perat mde f ths tme perd wll be ly determed by ecmc factr I, ad t effected by the cmparatvely ecmc perat mdes f eghbr tme perds, ad f a tme perd s very shrt, especally whe t s ly r tme uts, the perat mde f ths tme perd wll be almst always determed by ts eghbr tme perd. I ths paper, the weght f tw factrs tme perd s a = (4) a The value f a ad a ca be calculated as fllws:.6* ; (5) a =.84*( 7) < ; (.6* ) ( l max ) >. a = a (6) where: l ( = the legth f tme perd ; l max = the lgest tme perd f all. The cstats frmula (5) have bee debugged. Thus, the weght vectr fr the membershp matrx R based factr I ca be calculated by frmula (5), ad the result ca be btaed as fllws: = a, a,, a ) = [ ] ( Fuzzy relatal matrx f factr II If the membershp matrx f eergy lss abut all tme perds s btaed, the fluece frm the cmparatvely ecmc perat mdes eghbr tme perds ca be calculated the. Fr example, If a tme perd s shrt, ad the eghbr tme perd, e sde f t, s cmparatvely lger, but the perat mdes f tw tme perds are dfferet frm the ecmc perat agle, rder t decrease swtch peratg tmes, the perat mde f ths tme perd may stll ccde wth t s eghbr. The lger the eghbr tme perds, the much eergy lss they decrease, that s t say, the bgger the value after pecfcat f the eghbr area eclsed by curve, the bgger the fluece f t s eghbr tme perds. ccrdg t ths d f thught, If the elemets f the membershp matrx R multpled by crrespdg elemets f weght vectr matrx ca be gtte as fllws: = οr = Every rw f elemets plus the largest, the elemets eghbr rw wth 5 tme uts, ad chagg happeed t the pst f le, the matrx ca be btaed. If the elemets f the matrx weght vectr multpled by crrespdg elemets f, the matrx ca be gtte.

5 = = ο = plus, ad after pecfcat, matrx ca be btaed as fllws: = Fr every rw f, the seral umber f the le whch the largest umber ca be gtte s crrespdgly the d f perat mde shuld be adpted. Frm matrx ad table, fllwg result ca be btaed: the st8th tme ut, the secd perat mde, sgle trasfrmer perat mde, shuld be adpted; the 9th44th tme ut, the thrd perat mde, parallel trasfrmers, perat mde, shuld be adpted; the 45th75th tme ut, the frst perat mde, sgle trasfrmer perat mde, shuld be adpted; the 76th9th tme ut, the secd perat mde, sgle trasfrmer perat mde, shuld be adpted. Thus we ca see the result ccdes wth huma dspatcher s thught. Further mre, we have calculated may ther examples wth dfferet lad data ad dfferet trasfrmer parameters. The results f thse examples shw that the methd s effectve. 4 Cclus Ths paper has prpsed a ew tellget methd f trasfrmer ecmc perat. Dfferet frm ther trasfrmer ctrl decs methd, ths methd ca autmatcally tae ttal stuat t accut, ad all the frmat s utlzed adequately. It maes decs just le a huma dspatcher, ad the result f the decs s satsfyg. Refereces: [] HU Jgsheg, Ecmc perat f pwer trasfrmer. ejg:cha Electrc Pwer Press,998. [] XU Jazheg, Wag Ja, artfcal eural etwr based ctrl system fr trasfrmer ecmc perat. Pwer ystem Techlgy, Vl.5,N.9,,pp [3] Zhag Xl, Zhag Fa, Optmal Operat f Ma Trasfrmers wth Tw-wdg[J]. Electrc Pwer, Vl.34. N.,,pp.9-3