HUGO ROSMAN * Gheorghe Asachi Technical University of Iaşi, Faculty of Electrical Engineering, Energetics and Applied Informatics

Transcription

1 BULETNUL NSTTUTULU POLTEHNC DN Ş Pulit d Univrsitt Thniă Ghorgh shi din şi Toul LV L Fs. 0 SŃi ELECTOTEHNCĂ. ENEGETCĂ. ELECTONCĂ THE CTVE ENEGY TNSMSSON EFFCENCY THOUGH LNE NON-UTONOMOUS ND PSSVE TWO-POTS SUPPLYNG NON-LNE NETL ND PSSVE ECEVES N HMONC STEDY-STTE BY HUGO OSMN Ghorgh shi Thnil Univrsity of şi Fulty of Eltril Enginring Enrgtis nd pplid nfortis ivd Jnury 6 0 ptd for pulition: pril 6 0 strt. Using th rsults stlishd in prvious ppr osn 009 th prol of tiv nrgy trnsission ffiiny through linr nonutonoous nd pssiv two-ports is studid in hroni stdy-stt whn th rivr is onstitutd fro th sril onnxion of rsistor oil nd ondnsr ll thr non-linr inrtil nd pssiv. Ky words: tiv nrgy trnsission; ffiiny; linr non-utonoous nd pssiv two-ports; non-linr inrtil nd pssiv rivr.. ntrodution n prvious ppr osn 009 th prol of th tiv nrgy trnsission ffiiny through linr non-utonoous nd pssiv two-port LNPT in hroni stdy-stt ws studid whn th rivr is non-linr -il: di_rotru005@yhoo.o

2 0 Hugo osn inrtil nd pssiv NP. Nly n LNPT is onsidrd Fig. hving th qs. U U whr [ ij i j is th fundntl prtrs trix supplying n NP hving th oplx ipdn Z j rprsnting th plitud of n ritrry hroni urrnt. Fig. t ws tkd in ount th ft tht if non-linr inrtil lnt is supplid with hroni voltg th urrnt whih flows through this lnt is hroni too Philippow 96 whil th urrnt voltg hrtristi of suh n lnt is non-linr in MS vlus ut linr in instntnous vlus. So if hroni voltg is pplid t th input gt of n LNPT Fig. th stlishd stdy-stt is hroni on; onsquntly th stdy-stt of suh n LNPT y prford in this s using th syoli thod of oplx signls nd prtrs. Th in rsults otind y th uthor 009 y surizd s follows: Th funtion whih orrsponds to diffrnt tiv nrgy trnsission stts with xtr vlus of ffiiny for diffrnt vlus of rfrn urrnt s plitud is { C [ } /.

3 Bul. nst. Polit. şi t. LV L f. 0 rng Th NP s quivlnt rsistn hs vlus situtd in th in in C C C C 6 6 { } 8 { } 8 whr C is n intgrtion onstnt. Th rtns whih orrspond to in x rsistns r qul hving th oon vlu ' ''. 5 Th xiu ffiiny s funtion of rsistn is givn y rltion η x [ C grphilly rprsntd in Fig.. 6 Fig. 5 Th intgrtion onstnt C stisfis th inqulity. C 7

4 Hugo osn. Th Studid Prtiulr Cs n wht follows th prtiulr s rprsntd in Fig. is studid th LNPT s rivr ing sril onnxion of rsistor oil nd ondnsr ll thr non-linr inrtil. Th prtrs of suh lnts wr stlishd y Svin & osn 99 nly >0 0 >0 0 >0 0 L C 8 n th s rprsntd in Fig. th NP s prtrs r thrfor. C L L 9 Sustituting xprssions 9 in rltion it rsults th lgri iqudrti q. 0 γ β α 0 whr [ [ [ > > C γ β α Th ov xprssion of γ ws stlishd tkn into ount th idntity osn t l. 965

5 Bul. nst. Polit. şi t. LV L f. 0 [ stisfid y th fundntl prtrs ij i j of ny LNPT s wll s Şor 96 P0 Ps > 0 > 0. U nlysing th lgri q. 0 it y osrvd tht this on hs t th ost two rl nd positiv roots if whih iplis β αγ > 0 nd β ± β αγ > 0 β < 0. 5 t rsults tht in s of n NP suh tht rprsntd in Fig. hrtrizd y prtrs i i i i it xists t ost two diffrnt hroni stdy-stts for whih th tiv powr s trnsfr ffiiny hs xtr vlus. t is possil to dtrin th urrnt plituds whih flow through th NP whn his quivlnt rsistn hs th vlus in x. With this gol th xprssions of in nd x r sustitutd in rltion 9. Prforing th lulus it rsults C 8 C 8 { } C 6 in x 6 6 { }. C 6 6 n siilr nnr n dtrind th urrnt plitud whih ' '' flows through th NP whn his quivlnt rtn is s.

6 Hugo osn rltion 5. long th s lin it is possil to dtrin th tiv powr s trnsfr xiu ffiiny through n LNPT s funtion of urrnt plitud whih flows through th NP. With this nd in viw in xprssion 6 of th xiu ffiiny th rsistn is sustitutd with rltion 9 rsulting δ ε ηx 7 ϕ ψ whr δ > 0 ε C ϕ C ψ. 8 Th urv η x is rprsntd in Fig.. Hving in viw tht η x > 0 for ny vlu of hn for 0 too nd tht δ > 0 it rsults tht φ > 0. nqulity δ ε < 9 ϕ ψ Fig. rprsnts onsqun of rltions. t is nssry to undrlin tht only th urv s r fro Fig. whih orrsponds to vlus of urrnt plitud situtd in th rng [ in x hs s ws provd in prvious ppr osn 009 physil ning.. Conlusions Using th rsults otind in prvious ppr osn 009 th prol of th tiv powr s trnsfr ffiiny in hroni stdy-stt through linr non-utonoous nd pssiv two-port is studid whn th rivr is onstitutd y th sril onnxion of rsistor oil nd ondnsr ll thr non-linr inrtil. Th in onlusions r th following: t is possil to rliz t ost two diffrnt suh rgis. Th xiu ffiiny of tiv powr s trnsfr is funtion of th plitud rprsntd in Fig..

7 Bul. nst. Polit. şi t. LV L f. 0 5 EFEENCES Philippow E. Nihtlinr Elktrothnik. kd. Gs. Gst. u. Portig Lipzig 96. osn H. Brir. Sl C. zonnń în sistl d tip udripol. Bul. nst. Polithni şi V osn H. Th tiv Enrgy Trnsission Effiiny through Linr Non- utonoous nd Pssiv Two-Ports Supplying Non-Linr nrtil nd Pssiv ivrs in Hroni Stdy-Stt. Bul. nst. Polithni şi LV L s. Eltrot. Enrg. Eltron Svin Gh. osn H. Ciruit ltri nlinir şi prtri. Edit. Thniă Buurşti 97. Şor C. Cudripolul ltri. Edit. Thniă Buurşti 96. NDMENTUL TNSMSE ENEGE CTVE PN CUDPOL LN NEUTONOM Ş PSV LMENTÂND ÎN EGM PEMNENT MONC ECEPTOE NELNE NEłLE zut Utilizând rzulttl stilit într-o lurr prdntă osn 009 s studiză prol rndntului trnsisii nrgii tiv printr-un udripol linir nutono şi psiv lintând în rgi prnnt roni un rptor onstituit din grupr în sri unui rzistor uni oin şi unui ondnstor tot tri nlinir inrńil.