Time-domain Analysis Methodology for Large-scale RLC Circuits and Its Applications *

Transcription

1 Tme-domn Anlyss Metodoloy fo Le-sle LC Cuts nd ts Appltons Zuyn Luo Y C Sdon X.-D Tn 3 Xnlon on Xoy Wn Zu Pn Jnn Fu (Deptment of Compute Sene nd Tnoloy Tsnu Unvesty Ben P..Cn; Collee of nfomton Sene nd Tnoloy Ben Noml Unvesty Ben P..Cn; 3Deptment of Eltl Enneen Unvesty of Clfon t vesde vesde CA USA) Astt: Wt son wo fequeny nd desn fetue szes LS uts wt LC pst omponents e moe le nlo uts nd sould e efully nlyzed n pysl desn. oweve te nume of extted LC omponents s typlly too le to e nlyzed effently y usn pesent nlo ut smultos le SPCE. n ode to speedup te smultons wtout eo penlty ts ppe poposes nov metodoloy to ompess te tme-destzed uts esulted fom numel nteton ppoxmton t evey tme step. Te mn ontuton of te metodoloy s te effent stutue-lev ompesson of DC uts ontnn mny uent soues w s n mpotnt omplement fo pesent ut nlyss teoy. Te metodoloy onssts of te follown pts:. An ppo s poposed to dete ll ntemedte nodes of L nes.. An effent ppo s poposed to ompess nd -solve pll nd sel nes so tt tey e eo-fee nd of lne omplexty to nlyze uts of tee topoloy. 3. Te Y to π tnsfomton metod s used to eo-fee edue nd -solve te ntemedte nodes of ldde uts wt te lne omplexty. Tus te wole smulton metod s vey ute nd of lne omplexty to nlyze uts of n topoloy. Bsed on te metodoloy we popose sevel nov lotms fo effently solvn LC-mod tnsent powe/ound (P/) netwos. Amon tem EQU-AD lotm of lne-omplexty s poposed to solve LC P/ netwos wt mes-tee o mes-n topoloes. Expementl esults sow tt te poposed metod s t lest two-ode of mntude fste tn SPCE wle t n sle lnely n ot tme- nd memoy-omplexty to solve vey le P/ netwos. Keywods: LC uts Anlo ut nlyss Tme-domn nlyss P/ netwos Alotm omplexty. As LS tnoloy sles nto nnomete eme C fetue szes ontnue snn nd won fequeny ontnues so up. Tus pst ptnes nd ndutnes ve snfnt mpts on snl nteton [-4] so tt snls of dtl uts eve moe le nlo ones. ently LC mod s een poposed to uty nlyze dtl snls [-3]. As llons of tnsstos e nteted nto -end p tdtonl ut smultos su s SPCE e neffent fo LS snl nlyses own to ts ntolele omplexty. As esult nume of metods e poposed ently fo effent snl nlyss fo nstne wvet nlyss metod [4] nd s-domn ut eduton smulton metods [-3]. Amon tem [] ompts tee-onstuted uts wle [-3] n ompt enel-topoloy uts. n pysl desn powe/ound (P/) netwos e te spl nd of nlo uts tt e vey le n tems of LC omponents due to te ft tt ll tnsstos must et te powe supply fo P/ netwos [5]. Menwle due to son powe onsumpton nd lo fequeny P/ netwos e moe suseptle to uent-ndued lty nd funtonl flues of ps own to exessve dops Ld/dt nose to-mton nd esonne effts [5]. Buse snl nteton of P/ netwos ddes wete tnsstos n et supply volte enou to dve ot lol tnstons lotm study on effent P/ netwo nlyss s vey mpotnt n ot teoy nd pplton. ese lon ts lne omes n ntensve ese e n LS pysl desn [6-]. Mny effent smulton tnques ve een poposed fo fst P/ d nlyss n te pst. Tese metods nlude fequeny-domn nlyss metods [6-7] Ts wo s found y te pot of Ntonl Sene Foundton of Cn (NSFC) No Cnese 973 pot unde nt No. 005CB3604 nd UC Sente ese Fund of Ame.

2 mod eduton metods [8-0] el metods [0-] te pondtoned onute dent metod (PC) [] te ltentn-dton-mplt metod (AD) [3] Mult-d metods (M) [4-6] equvlent ut metods (EQU) [77] nd te lst ndom wl metod (W) [8]. On te ote nd ll te exstn metods ve te dws w lmts te ppltons. Fo nstne PC sed metods [] e senstve to te pe-ondtone used. M metods [4-6] e typlly effent fo mes-stutued uts nd e less memoy effent s moe d stutues e stoed due to te use of multple d ppoxmtons. Mod eduton metods [8-0] eque te uent wvefoms of ll te uent soues efoe te smulton w my not e possle fo P/-deve o-smulton nd e less ute fo uts wt mny (oupled) ndutos due to one-pont expnson. Te ndom wl sed metod n [8] otns ts effeny fom te lolzed wvefom popety n P/ uts wt ente-umped DD/ND pds. But te metod s unle to d wt enel LC ut nlyss. No metod s exploted te spl stutue of typlly lne LC uts esplly fo LS on-p P/ netwos. We ve poposed fou effent tnsent nlyss lotms fo LC P/ netwos to explot te spl topoloes of typlly LS P/ netwos n te pst [9-]. Ppes [9-0] popose two equvlent ut lotms fo eo-fee ompessn LC tees nd ns esptvy. Ppe [] pesents eomet mult-d sed lotm fo P/ netwos of stt mes topoloy. Ppe [] omnes te dvntes of EDU [9-0] nd AD [3] metod nd ten poposes yd lotm EDUAD fo P/ netwos of sevel topoloes. Te ove ppes only pesent spf lotms te wole ptue of te tme-domn nlyss teoy sed on tose lotms fo le-sle LC uts e not ven. Ts ppe systemtlly deses nov tme-domn nlyss metodoloy fo le-sle LC uts. Fst t ntodues tpezodl ppoxmton tnque w s ute (O( )) nd un-ondtonl stle to tnsfom tnsent LC ut nlyss nto qus-stt -only ut nlyss. Ten t poposes te follown metodoloy to eo-fee ompess te DC uts fo nesn te effeny of le-sle LC uts. Te metodoloy onssts of te follown tee pts:. Te ppo s poposed to dete ll ntemedte nodes of L nes.. An effent ppo s pesented to ompess nd -solve pll nd sel nes so tt tey e eo-fee nd of lne omplexty to nlyze uts of tee topoloy. 3. Te Y to π tnsfomton metod s ven to eo-fee edue nd -solve te ntemedte nodes of ldde uts wt te lne omplexty. Tus te wole smulton metod s vey ute nd of lne omplexty to nlyze uts of n topoloy. Afte LC ut dsetzton tee e mny ddtonl equvlent uent soues n qus-stt -only uts. Pesent ut nlyss teoy ls effent metods to fute smplfy tese nds of uts. Tus ou ut-smplfyn metodoloy mes te mpotnt omplements fo pesent ut nlyss teoy. Tee e nume of ppltons ndued fom ou metodoloy [9-]. n ode to sow te enelty nd effeny of ou metodoloy ts ppe only pesents one typl pplton: EDU-AD lotm n []. Te EQU-AD lotm of lne-omplexty s poposed to solve LC P/ netwos of mes-tee o mes-n topoloes fo ASC ps. Te lotm fst ompesses tee nd n uts wt lne omplexty; ten t uses te mpoved AD lotm to solve te emnn mes ut wt lne omplexty; fnlly t solves lef nodes of tee uts nd ntenl (ntemedte) nodes of n uts wt lne omplexty. Te mn dvntes of te poposed EQUAD lotm e te stt lne omplexty nd unondtonl stlty fo onveene. Ts ppe s onzed s follows. Ston deses te tpezodl tnque of ute (O( )) nd un-ondtonl stlty fo tnsent ut ppoxmton. Ston deses te nov tme-domn nlyss metodoloy fo le-sle LC uts. Ston 3 pesents ts ppltons nludn ou lst ese wo te EQUAD lotm. And Ston 4 ves onludes nd futue wos.

3 . Tpezodl Appoxmton Tnque fo LC Cut Dsetzton As fo LC uts lned wt d volte nd uent soues (t) nd (t) e te node volte vto nd n uent vto esptvy. Te tnsent nlyses n e fomulted usn modfed nodl nlyss (MNA) s follows: T C 0 & ( t) A ( t) U( t) l T () 0 L t () & A 0 ( t) 0 l wee C L nd e oeffent mtes fo ptos ndutos nd ondutos wle U(t) s te nput vto eneted y d volte nd uent soues. Sown n ove equton te pstl C nd L ly nese te omplexty of ut nlyss. Up to now TLM-AD metod n [3] s te only metod to dtly solve EQ() wt low omplexty. But te metod n solve only uts of stt mes topoloy w lmts ts pplton. n ode to effently solve LC uts te enel de fst uses numel nteton metods le Bwd Eule [] o tpezodl ppoxmton [5] to tnsfom LC tnsent ut nlyss nto -only qus-stt DC ut nlyss. n te sme wy we lso use tpezodl ppoxmton tnque fo LC ut dsetzton w pves te wy fo desn ou tme-domn nlyss metodoloy to eo-fee smplfy te qus-stt uts of f moe uent soues. Now let s ntodue te tpezodl ppoxmton tnque fo LC ut dsetzton n te follown. Assume s te tme step. We fst use te tpezodl ppoxmton metod fo ptne n dsetzton s follows. C C ( ) () wee denote esptvy te n voltes nd n uents of te pto t step nd step esptvy nd C s te vlue of te pto. EQ() n e tnsfomed nto: ( ) (3) C f s wd o fotwd expnded odn to Tlo Expnson we n et follown equton: & & 3 && O( ) 8 3 && O( ) 8 (4) Te dffeene of ove two equtons s sown n follown C C 3 ( & & ) ( && && ) O( ) 3 3 ( ) &&& O( ) 3 ( ) O ( ) 8 8 (5) Aodn to EQ(5) we n ndue te follown equton to sow te O( ) eo of EQ(). C C O ( ) efeene [3] defnes te tpezodl metod s te snle-step mplt metod nd poves tt te tpezodl metod s unondtonl stle. Fo te ontent lmtton we don t pove te onluson n. n te sme wy we lso popose te tpezodl ppoxmton metod fo ndutne n dsetzton w

4 s te O( ) uy nd unondtonl stle. L L ( L L ) L L (6) wee L L L L denote esptvy te n voltes nd n uents of te nduto t step nd step wle L s te vlue of te nduto. Fue. Dsetzton mods of ptne nd ndutne Wt EQ() nd EQ(6) we use tpezodl ppoxmton fo ptne nd ndutne nes. Sown n F. LC uts ve een tnsfomed nto -only DC uts of so mny equvlent uent soues fo qus-stt ut nlyss. Te follown s te MNA equton fo dsetzed ut nlyss. A B (7) wee A B e ondutne oeffent mtx nodl volte vto nd uent stmul vto esptvy. Te PC lotm n e dtly used to solve EQ(7) fo qus-stt uts. Sown n F. use n of ptne nd ndutne enetes one ddtonl equvlent uent soue fte dsetzton qus-stt uts nlude le nume of uent soues. Pesent ut nlyss teoy s sot of metods to smplfy su uts of mny uent soues. Tus te metodoloy n te ppe fo eo-fee ompessn su uts of so mny uent soues mes te mpotnt omplements fo pesent ut nlyss teoy.. A Nov Tme-Domn Anlyss Metodoloy fo LC Cuts Te metodoloy onssts of te follown tee pts:. A metod s poposed to dete ll medl nodes of L nes odn to Noton teoy.. Aodn to Noton teoy eo-fee nd lne-omplexty metods e poposed to ompess nd -solve pll nd sel nes so tt tey e eo- fee nd lne omplexty to nlyze uts of tee topoloy. 3. Bsed on KCL lw one Y to π tnsfomton metod s used to eo-fee n nd -solve te medl nodes of Y uts wt lne omplexty. As te esult te metod s eo-fee nd of lne omplexty to nlyze uts of n topoloy. t s of eo-fee nd lne omplexty dvntes to use te metodoloy fo smplfyn te ove-mentoned qus-stt uts. Now let s fst dese ow to smplfy te smple ut nes n follown suston.. Smplfton Metod fo Smple Cut Bnes As fo L n sown n f.() tee stll s ntenl nodes etween two esstos fte LC ut dsetzton. n ode to smplfy te n of two essto nd uent fo dete te ntenl node we use Noton teoy to mee two esstos one s te stt nd note s te equvlent essto of L. Ts opeton n e fomulted s follown. L L L L L / L / (8) wee L s te t L n uent wle L s te t ndutne volte otned wt te equton Ld L /dt.

5 () Men esstos () Men Cuents Fue. Smple Bn nopoton odn to Noton Teoy Sown n f.() tee e usully two uents fo node of dsetzton uts one s te sopton uent eneted y ut equpment nd note s te equvlent uent of ptne lned to te node. Te follown equton n e fomulted fo men two uents. C e C (9). Smplfton Metods fo Sel Bnes nd Pll Bnes BBL floo-plnnn sed lyout lwys ontns nume of LC tees n P/ netwos [79]. Sown n f.3() fte dsetzton P/ uts nlude -only tees of mny uent nes. n ode to dete lef nodes of tees we sould ltentvy mee sel nes nd pll nes s sown n f.3. F.3() nd 3() mee sel nes wle f.3() mees pll nes. oot mddle Lef- Lef-l e mddle oot () Onl se wt two leves e e () te se wt two smplfed leves () te se wt oot-only t e t t (d) te lst smplest se Fue.3 Flowt of Tee Smplfton We te te left tee of te mddle node n f.3() s exmple to expln ow to eo-fee mee two sel nes. n te left tee te lef node Lef-l s ts lod essto nd lod uent wle essto nd uent ln te lef node to ts fte node mddle. Te symol ee mens te t step nd eeps ts men n emnde of ts ppe. Aodn to Noton teoy te follown equton s used to mee two sel es nd otn te equvlent essto nd equvlent uent s te esult.

6 (0) Sown n f.3() te follown equton s fomulted to mee tple esstos nd uents s te equvlent essto nd te equvlent uent odn to Noton teoy. () Buse EQ(0) nd EQ() e fomulted sttly odn to Noton teoy te men opetons of sel nes nd pll nes e eo-fee. Dffeent fom te smplfton opetons of smple nes n ove suston one tt se nodes of tees e nown te wd solvn opeton s equested to ompute voltes fo lef nodes. We te f.3() nd 3(d) s exmple to expln ow to -solve te ntenl node volte of sel nes. Assume te nown volte of te se node oot n f.3(d) s t. Te follown equton s fomulted to ompute e t te uent flown fom te se node nto te tee. t t t t e () Tus we n fute fomulte te follown equton to ompute te mddle node volte nd e te uent flown fom te node. e t e t e t (3) We fute te f.3() s exmple to expln ow to dstute uents mon pll nes. Te follown equton s fomulted to ompute e e uents of left n nd t n. e e e e (4) Buse EQ()-EQ(4) e fomulted sttly odn to ut lws te -solvn opetons n ts ppe e eo-fee. Wt EQ(0)-EQ(4) we n etnly et te onluson tt smplfton nd -solvn opetons fo sel nd pll nes e eo-fee nd of lne omplexty. Tus ts suston ves n eo-fee nd lne-omplexty lotm fo ompessn nd -solvn tee-topoloy uts..3 Eo-fee Cut Tnsfomton Mod fom Y to π Cl-sed lyouts enete le nume of LC ns [70]. Afte detzton tee e le nume of

7 ddtonl equvlent uents n te qus-stt uts. Sown n f.4() Y-se ut ls onsstn of esstos nd uents me up of n n te onstuton style of nd n nd. n ode to dete te mddle node of Y-se l we must tnsfom Y-se ls nto π-sed ls. And f we do n ounds of tnsfomton fom te left temnl of te n to dete ll n ntenl nodes of te n te edued n only onssts of ts two temnl nodes s sown n f.4(). E E E E E () Y-sed l () π-sed l F.4 Tnsfomton fom Y-sed l to π-sed l Sown n f.4() E nd E e uents fom Y-sed l to node nd esptvy. Cuent dtons e med wt ows. Te follown equton s fomulted fo te volte dffeene etween node nd. ( E ) E E ( E ) Aodn to te pesent metod of Y-π tnsfomton te follown equtons e fomulted fo tee equvlent esstos. ( ) ( ) ( ) (6) Te equtons e fomulted fo omputn E nd E esptvy. (5) E E (7) Ten we popose te defntons out tee equvlent uents s follows. (8) Tus E nd E n e fute fomulted n te follown equtons tt extly mt up wt ut expesson n f.4(). E E (9)

8 Te ove equtons e ndued to tnsfom Y-sed l to π-sed l. As te esult te ntenl node of Y-sed l s deted fo uent smplfton. Fo n of n ntenl nodes we only do n ounds of Y-π tnsfomtons to ompess te n nto te smplest ut sown n f.4(). Buse ove equtons e sttly ndued odn to ut teoy te ompesson fo ns s eo-fee. One two temnl nodes e nown we wll dese ow to solve te unnown ntenl nodes of te n n follown pt. Wt te nown nd we n ompute te E odn to EQ(9). Ten te follown equtons e fomulted to ompute fo node nd E te uent flown fom ts t n. E E ( E ) (0) f te n s moe tn one ntenl node we n use EQ(0) to solve ll unnown t-nd node neos. Buse EQ(0) s ndued odn to ut lws te -solvn poess s eo-fee. Teefoe we popose nov metod to ompess nd -solve n uts wtout eos n ts suston. And EQ(68-0) untee tt te ompesson nd -solvn poess of n uts e of lne omplexty. n enel we popose n eo-fee nd lne-omplexty metod to ompess nd -solve n uts nludn mny uent soues. 3. Teoet Appltons n P/ Netwo Anlyss Buse we fous ou ese on P/ netwo desn nd vefton we mnly pply ou metodoloy to speed up P/ d nlyss tou ou metodoloy n e lso ppled n nlo snl nlyss nd lo netwo vefton. Up to now we ve poposed fou effent lotms fo tnsent P/ netwo nlyss s follown [9-]. Bsed on te metodoloy n suston.-. we popose n equvlent ut lotm fo effently nlyzn tnsent P/ netwos of mes-tee topoloy n [9]. Expements demonstte tt ou lotm s one one-ode of mntude fste tn te lotm n [7]. Ou lotm fst uses te metodoloy n suston.-. to eo-fee ompess ll tees plnted on te mes ten uses PC lotm [] to nlyze te edued mes ut lst uses te teoy n suston. to solve te unnown lef nodes fo tee uts. Bsed on te metodoloy n suston..3 we popose n equvlent ut lotm fo effently nlyzn tnsent P/ netwos of mes-n topoloy n [0]. Expements demonstte tt ou lotm s two one-odes of mntude fste tn SPCE. Ou lotm fst uses te metodoloy n suston..3 to eo-fee ompess ll ns ten uses PC lotm [] to nlyze te edued mes ut lst uses te metodoloy n suston.3 to solve te unnown ntenl nodes fo n uts. 3 Bsed on te metodoloy n suston..3 we popose eomet mult-d sed lotm fo effently nlyzn tnsent P/ netwos of stt mes topoloy n []. Expements demonstte tt ou lotm s two one-odes of mntude fste tn SPCE. Ou lotm omnes te mult-d lotm wt ou metodoloy n suston..3 to onstut mult-lev ose ds fo speedn up mes ut nlyss. 4 We popose te EQU-AD lotm of lne-omplexty to solve LC P/ netwos of mes-tee o mes-n topoloes n []. Te lotm s two-mntude fste tn SPCE. t fst ompesses tee nd n uts sed on te metodoloy n suston.-.3. Ten t uses te mpoved AD lotm to solve te emnn mes ut. Fnlly t solves lef nodes of tee uts nd ntenl (ntemedte) nodes of n uts odn to ou metodoloy n suston..3. Te mn dvntes of te EQUAD lotm e uy stt lne omplexty nd unondtonl stlty

9 fo onveene. Tou omnn ou metodoloy wt el metod ndom wl metod nd AD metod we lso ty studyn moe effent lotms fo tnsent P/ netwo nlyss nd me vsle poesses. n ode to sow te enelty nd effeny of ou metodoloy we only ve out one typl pplton te EQU-AD lotm n follown pts. 3. EQU-AD Alotm Due to sote metn yle of ASC p desn dffeent fom CPU s P/ netwos of doule-mes topoloy ASC s P/ netwos ve to e of yd topoloy wose ose uppe-lev d s of mes-topoloy fo lty nd fne low-lev d s of tee o n topoloy fo desn flexlty. To ts nd of P/ netwos of yd topoloy EQU-AD lotm s of lne omplexty. Te flowt of EQU-AD lotm s sown n follows. Bsed on te tpezodl ppoxmton tnque n ston nd te metodoloy n suston 3. EQU-AD efeses ll ut pmetes. Bsed on te metodoloy n suston t eo-fee ompesses tee nd n uts nd tnsfoms te on ut of yd topoloy nto te edued ut of stt mes topoloy wt lne omplexty. Te edue mes ut s sown n follown fue. 3 t uses te mpoved AD metod to solve te qus-stt mes ut wt lne omplexty. Te mpoved AD metod s of te unondtonl stle dvnte nd te low-uy O() dsdvnte. 4 Bsed on te metodoloy n suston t eo-fee -solves te unnown lef nodes of tee uts nd te unnown ntenl nodes of n uts wt lne omplexty. Fom te lotm flowt EQU-AD lotm s of stt lne omplexty w mens t s te sp-ede tool to effently nlyze ue P/ netwos fo vey le-sle ASC ps. Altou t s unondtonl stle t needs te sot tme step own to ts low uy O(). n ts ppe we ssn /500T fo ute esults. 3. mpoved AD Metod Afte te ompesson poess fo tee uts nd n uts te onl P/ uts of yd topoloy ve een edued nto te stt mes topoloy s sown n f.5. Te AD metod ws poposed to solve PDE equtons fomulted fom te LC-mes P/ ds. Sne we dtly wo essto-only qus-stt mes ut t tme step wt foementoned eduton te TLM-AD metod n [3] n t e dtly used to solve te essto-only mes ut. n te follown we popose nov mpoved AD metod fo qus-stt mes ut nlyss. Fue.5 Te edued P/ ut of stt mes topoloy n f.5 e te nown ut pmetes fte ut ompesson. n ode to

10 use te mpoved AD to solve te qus-stt mes ut te ozontl mplton opeton t te t step uses t uents fo ozontl nes nd t uents fo vetl nes to fomulte te follown equton odn to KCL lw.. δ δ () wee 5 0. e te volte of node () nd te equvlent uent lned to te node t t step. Menwle δ δ e two uent dffeenes etween two nes n ozontl dton t te t step nd etween two nes n vetl dton t te t step. As te vlues t te t step e nown we only need to ompute te vlues t te t step nd te t step s follows. ( ) ( )... () ( ) [ ] ( ) [ ] ( ) ( ) δ (3) wee e te ondutne oespondn to te esstos s sown n F.5. Wt EQ(-3) EQ() n e tnsfomed nto te follown equton. ( ) ( ) ( ) 5 0. δ (4) Ten EQ(4) n e fute smplfed nto te follown equton. ( ) ( ) ( ) δ (5) Te t tem of EQ(5) s te nown uent wle tee left tems e unnown. Wt EQ(5) ll nodes of ow ompose of t-donl donl-domnnt mtx tt n e solved n lne omplexty. Ten t te.5 t step we ne te mplton dton fom ozon to uptness. n ode to use te mpoved AD to solve te qus-stt mes ut te vetl mplton opeton t te.5 t step uses t uents fo vetl nes nd t uents fo ozontl nes to fomulte te follown equton odn to KCL lw δ δ (6) Smlly EQ(6) n e tnsfomed nto te follown equton. And ll nodes of olumn lso ompose of t-donl mtx so tt tey n e solved wt lne omplexty. ( ) ( ) ( ) δ (7) Wt EQ(5) nd EQ(7) we popose te mpoved AD metod of te lne omplexty to qus-sttlly smulte te emnn ut of pue mes topoloy sown n F.5. At te sme tme te mpoved AD metod s lso unondtonl stle s te essto-only netwo mtx s symmet postve defnte w s unondtonl stle nd AD lotm s lwys onveent [3].

11 3.3 Expementl esults Te EDU-AD lotm s een mplemented n C. All te expementl esults e ollted on SUN 880 wostton wt 750Mz Ult Sp CPU nd B memoy. Te nume of tme steps s ssned 500 fo one lo yle nd DD s.5. Altou EDQ-AD n lne-omplexty solve P/ netwo of mes-tee mes-n nd mes-(ten) yd topoloes lmted y ontent we te P/ netwos only of mes-tee topoloy s test ses to sow te lne omplexty popety of EQU-AD lotm. Also lmted y ontent we ve out only expementl esults on omplexty nd omt ote esults on stlty nd uy. n ft te esults on stlty nd uy e sml to te ountepts n [3]. () Tme Complexty Compson () Memoy Complexty Compson Fue.6 Complexty ompsons etween EQU-AD nd SPCE n f.6() ozontl unt s 00K nodes of P/ uts wle vetl unt s 500 sonds of unnn tme. Altou SPCE s enel mn-stem ommel softwe en onstntly optmzed y Synopss ompny t tes ntolele lon unnn tme (nely 5000S) to smulte P/ ut of less tn00k nodes w mens SPCE n not mne le-sle ptl uts of moe tn M nodes. Tus n study on P/ ut smulton SPCE s used to test te uy nd effeny of nov lotms. f n lotm s two-mntude fste tn SPCE t n e eded s suessful one. Sown n f.6() te EDU-AD lotm n two-mntude speedup te P/ ut smulton. Menwle te stt lnety on tme omplexty of te EDU-AD lotm demonsttes te teoet otness of ou metodoloy. n f.6() vetl unt s 50M yte of memoy. Sown n f.6() SPCE s of le memoy omplexty nd onsumes ntolele memoy (moe tn 00M) to smulte P/ ut of less tn00k nodes. On te ote nd ou EDU-AD lotm s of stt lne memoy omplexty nd n sve mu moe memoy onsumpton w demonstte te otness of ou metodoloy. Summn up esults of two ove fues te EQU-AD lotm does e of low-oeffent lne omplexty w sows ou metodoloy n ompess P/ uts fo effent smulton. Buse te EQU-AD lotm n lne smulte P/ uts of mes-tee mes-n nd mes-ten topoloes te lotm n effently solve ue ptl P/ netwos fo vey le-sle ASC ps. 4. Conluson n ts ppe we ve poposed nov tme-domn nlyss metodoloy fo enel le LC uts nd ve ppled te new metodoloy fo te tnsent le-sle LS on-p powe dvey netwo nlyss. We dese

12 tpezodl ppoxmton tnque fo LC ut dsetzton wt uy nd unondtonl stle dvntes. A le nume of uent soues n dsetzton uts me tem dffult to fute edue te qus-stt uts. We poposed nov tme-domn nlyss metodoloy to edue su qus-stt uts lnely n n eo-fee mnne w e mpotnt omplement to pesent ut nlyss teoy. Aodn to ts ppltons n P/ netwo smulton ou metodoloy s vey mpotnt n ot teoy nd ppltons fo smultn le-sle LC netwos. Te EDU-AD lotm te only detl desed pplton lso sow te supeoty of ou metodoloy. n futue we wll extent te metodoloy to ote ese fds su s lo netwo smulton nd stt tmn nlyss. n P/ netwo desn nd vefton we wnt to omne te metodoloy wt te el metod fo fute speedn up te smulton nd optmzton opetons fo vey le-sle P/ netwos wt omplex topoloes. efeenes. Yn X D Cen C K Ku W et l. uwtz stle edued ode modn fo LC nteonnt tees. EEE Jounl of Anlo nteted Cuts nd Snl Poessn 00 3(3): -8. Qn Z nd Cen C K. CLK-J netwo eduton wt uwtz polynoml ppoxmton. n: Po EEE As nd Sout Pf Desn Automton Conf (ASPDAC) 03EX67.Pstwy: EEE Pess Tn X D. A enel s-domn el netwo eduton lotm. n: Po EEE/ACM nt Conf Compute Aded Desn New Yo: ACM Pess L X Zen X Zou D et l. Bevol modn of nlo uts y wvet olloton metod. n: Po EEE/ACM nt Conf Compute Aded Desn New Yo: ACM Pess Douduy A Pnd Bluw D et l. Desn nd nlyss of powe dstuton netwos n powe PC mopoessos. n: Po EEE/ACM Desn Automton Conf New Yo: ACM Pess B Bo S N. Smulton nd optmzton of te powe dstuton netwo n LS uts. n: Po EEE/ACM nt Conf Compute Aded Desn New Yo: ACM Pess 000.: Su l K nd Sptne S S. Fst nlyss nd optmzton of powe/ound netwos. n: Po EEE/ACM nt Conf Compute Aded Desn New Yo: ACM Pess Wn J M nd Nuyen T. Expended Kylov suspe metod fo edued ode nlyss of lne uts wt multple soues. n: Po EEE/ACM Desn Automton Conf New Yo: ACM Pess Odsolu C M nd Plle L T. PME: pssve eduton-ode nteonnt mo-modn lotm. EEE Tns Compute Aded Desn (8): Co Y Lee Y Cen T et l. PME: el nd pssvty eseved nteonnt momodn enne fo LKC powe dvey. n: Po EEE/ACM Desn Automton Conf 4770.New Yo: ACM Pess Zo M Pnd Sptne S S et l. el nlyss of powe dstuton netwos. n: Po EEE/ACM Desn Automton Conf New Yo: ACM Pess Cen T Cen C C. Effent le-sle powe d nlyss sed on pondtoned Kylov-suspe tetve metod. n: Po EEE/ACM Desn Automton Conf 4770.New Yo: ACM Pess Lee Y M Cen C P. Powe d tnsent smulton n lne tme sed on tnsmsson-lne-modn ltentn dton mplt metod. n: Po EEE/ACM nt Conf Compute Aded Desn New Yo: ACM Pess Nssf S nd Kozy J.N. Fst powe d smulton. n: Po EEE/ACM Desn Automton Conf New Yo: ACM Pess Zu Z Yo B Cen C K. Powe netwo nlyss usn n dptve le multd ppo. n: Po EEE/ACM nt Conf Compute Aded Desn New Yo: ACM Pess Su Sn E A Nssf. Powe d eduton sed on le multd pnples. n: Po EEE/ACM Desn Automton Conf New Yo: ACM Pess Tn X D. S C J. Fst powe-ound netwo optmzton usn equvlent ut modn. n: Po EEE/ACM Desn Automton Conf

13 4770.New Yo: ACM Pess Qn F Nssf Sptne S S. ndom wls n supply Netwo. n: Po EEE/ACM Desn Automton Conf New Yo: ACM Pess C Y C Pn Z Luo Z Y et l. Fst eduton nd onstuton sttey n nlyzn powe/ound netwo wt mes nd tee stutue. Jounl of Compute Sene nd Tnoloy 005 0(): Pn Z C Y C Luo Z Y et l. Tnsent nlyss of on-p powe dstuton netwos usn equvlent ut modn. n: Po ACM nt Symposum On Qulty Elton Desn P088. Pstwy: EEE Pess C Y C Pn Z Luo Z Y et l. eomet multd sed lotm fo tnsent LC powe/ound (P/) ds nlyss. Jounl of Compute-Aded Desn & Compute ps (n Cnese) 005 7(4): Wn X Y Luo Z Y Tn X D et l. EQUAD: A lne omplexty lotm on tnsent powe/ound(p/) netwo nlyss fo ASCs. n: Po EEE nt Conf on Sold-stte nteted Cut Tnoloy 04EX863.Pstwy: EEE Pess Ye un Jnln Cen. Dtl Computn Metodoloy. st Ed 990 Ben: Qnu Unvesty Pess 45-46