Adaptive Critic Designs for Optimal Control of Power Systems

Transcription

1 Adapv Crc Dsgns for Opmal Conrol of Powr Sysms G. K. Vnayagamoorhy, Snor Mmbr, IEEE, and R. G. Harly, Fllow, IEEE AbsracTh ncrasng complxy of h modrn powr grd hghlghs h nd for advancd modlng and conrol chnqus for ffcv conrol of xcaon, urbn and Flxbl AC Transmsson Sysms FACTS. Th crucal facors affcng h modrn powr sysms oday s volag and load flow conrol. Smulaon suds n h PSCAD/EMTDC nvronmn and ralm laboraory xprmnal suds carrd ou ar dscrbd and h rsuls show h succssful conrol of h powr sysm lmns and h nr powr sysm wh adapv and opmal nuroconrol schms. Prformancs of h nuroconrollrs ar compard wh h convnonal PI conrollrs for dampng undr dffrn oprang condons for small and larg dsurbancs. Indx Trms Approxma Dynamc Programmng, Rnforcmn Larnng, Opmal Conrol, Nworks, Excaon Conrol, Turbn Conrol, SSSC, SCRC, FACTS Dvcs. I. INTRODUCTION OWER sysm conrol ssnally rqurs a connuous P balanc bwn lcrcal powr gnraon and a varyng load dmand, whl mananng sysm frquncy, volag lvls and h powr grd scury. Howvr, gnraor and grd dsurbancs can vary bwn mnor and larg mbalancs n mchancal and lcrcal gnrad powr, whl h characrscs of a powr sysm chang sgnfcanly bwn havy and lgh loadng condons, wh varyng numbrs of gnraor uns and ransmsson lns n opraon a dffrn ms. Th rsul s a hghly complx and nonlnar dynamc lcrc powr grd wh many opraonal lvls mad up of a wd rang of nrgy sourcs wh many nracon pons. As h dmand for lcrc powr grows closr o h avalabl sourcs, h complx sysms ha nsur h sably and scury of h powr grd ar pushd closr o hr dg. Thus, h nd for advancd modlng and conrol chnqus for h ffcv conrol of powr sysm lmns. Adapv crc dsgns ACDs ar nural nwork dsgns Th suppor from h Naonal Scnc Foundaon undr h grans CAREER ECS # 0348, ECS # , ECS # 0363 and ECS # s grafully acknowldgd by h auhors. G. K. Vnayagamoorhy s wh h RalTm Powr and Inllgn Sysms RTPIS Laboraory, Dparmn of Elcrcal and Compur Engnrng, Unvrsy of Mssour Rolla, MO 65409, USA mal: gkumar@.org. R. G. Harly s wh School of Elcrcal and Compur Engnrng, Gorga Insu of Tchnology, Alana, GA 3033, USA mal: ron.harly@c.gach.du. capabl of opmzaon ovr m, undr condons of nos and uncrany. Ths famly of ACDs brngs nw opmzaon chnqus whch combn concps of rnforcmn larnng and approxma dynamc programmng, hus makng hm powrful ools. Th adapv crc mhod provds a mhodology for dsgnng opmal nonlnar conrollrs usng nural nworks for complx sysms such as h powr sysm whr accura modls ar dffcul o drv. Ths papr dscrbs h work of h auhors basd on adapv crcs for dsgnng xcaon and urbn nuroconrollrs for gnraors [][3] and FACTS dvcs SSSCs and SCRCs [4], [5] whch ovrcom h rsk of nsably [6], h problm of rsdual rror n h sysm dnfcaon [7], npu uncrans [8], and h compuaonal load of onln ranng. Th nuroconrollr augmns/rplacs h convnonal PI conrollrs, and s rand n an offln mod pror o commssonng. Two dffrn yps of Adapv Crcs ar dscussd, namly h Hursc Dynamc Programmng HDP yp and h Dual Hursc Programmng DHP yp. Rsuls ar prsnd for a snglmachnnfnbus, as wll as for a mulmachn powr sysm wh and whou FACTS dvcs. II. ADAPTIVE CRITIC DESIGNS A. Background Th smpls adapv crc dsgns larn slowly on larg problms bu hy ar succssful on many ral world dffcul small problms. Complx adapv crcs may sm brahakng, a frs, bu hy ar h only dsgn approach ha shows ponal of rplcang crcal aspcs of human nllgnc: ably o cop wh a larg numbr of varabls n paralll, n ral m, n a nosy nonlnar nonsaonary nvronmn. A famly of ACDs was proposd by Wrbos [9] as a nw opmzaon chnqu combnng concps of rnforcmn larnng and approxma dynamc programmng. For a gvn srs of conrol acons ha mus b akn squnally, and no knowng h ffc of hs acons unl h nd of h squnc, s mpossbl o dsgn an opmal conrollr usng h radonal suprvsd larnng nural nwork. Th adapv crc mhod drmns opmal conrol laws for a sysm by succssvly adapng wo ANNs, namly an acon nural nwork whch dspnss h conrol sgnals and a crc nural nwork whch larns h dsrd prformanc ndx for som funcon assocad wh h prformanc ndx. Ths wo nural nworks approxma h Hamlon JacobBllman quaon assocad wh opmal conrol hory. Th adapaon procss sars wh a nonopmal, /05/$ ISAP. 36

2 arbrarly chosn, conrol by h acon nwork; h crc nwork hn guds h acon nwork owards h opmal soluon a ach succssv adapaon. Durng h adapaons, nhr of h nworks nd any nformaon of an opmal rajcory, only h dsrd cos nds o b known. Furhrmor, hs mhod drmns opmal conrol polcy for h nr rang of nal condons and nds no xrnal ranng, unlk ohr nuroconrollrs. Dynamc programmng prscrbs a sarch whch racks backward from h fnal sp, ranng n mmory all subopmal pahs from any gvn pon o h fnsh, unl h sarng pon s rachd. Th rsul of hs s ha h procdur s oo compuaonally xpnsv for mos ral problms. In suprvsd larnng, an ANN ranng algorhm ulzs a dsrd oupu and, havng compard o h acual oupu, gnras an rror rm o allow h nwork o larn. Th backpropagaon algorhm s ypcally usd o oban h ncssary drvavs of h rror rm wh rspc o h ranng paramrs and/or h npus of h nwork. Howvr, backpropagaon can b lnkd o rnforcmn larnng va h crc nwork whch has cran dsrabl arbus. Th chnqu of usng a crc, rmovs h larnng procss on sp from h conrol nwork radonally calld h acon nwork or acor n ACD lraur, so h dsrd rajcory s no ncssary. Th crc nwork larns o approxma h cosogo or sragc uly funcon h funcon J of Bllman s quaon n dynamc programmng and uss h oupu of h acon nwork as on of s npus, drcly or ndrcly. In h Dynamc Programmng, or Markov Dcson Procss MDP, Lraur, problms ar dscrbd n rms of fv ssnal characrscs: Epochs Sas Acons Rwards Transon probabls. Mos of h lraur has focusd on fn sa spacs, whr sas ar known wh crany. Acons may hav probablsc ruls assocad wh hm, and rwards and obvously ranson probabls may also b nondrmnsc. Rcn lraur has addrssd h xnson o whr sas ar also nondrmnsc. Ths ar known as Parally Obsrvabl Markov Dcson Procsss POMDP s. I s sraghforward o show ha a POMDP can b ransformd o a rgular MDP wh connuouslyvalud sa varabls. Snc Adapv Crcs ypcally hav bn usd n conrol problms wh connuousvalud sa spacs, hy rvally ar applcabl o POMDP s. Ths obsrvaon, by slf, s suffcn rason for h famly of Adapv Crc approachs o b known and ulzd ousd h confns of h Inllgn Conrol communy. Dffrn yps of crcs hav bn proposd. For xampl, Wakns [0] dvlopd a sysm known as Qlarnng, xplcly basd on dynamc programmng. Wrbos, on h ohr hand, dvlopd a famly of sysms for approxmang dynamc programmng [9]; hs approach subsums ohr dsgns for connuous domans. For xampl, Qlarnng bcoms a spcal cas of AconDpndn Hursc Dynamc Programmng ADHDP, whch s a crc approxmang h J funcon s scon B blow, n Wrbos famly of adapv crcs. A crc whch approxmas only h drvavs of h funcon J wh rspc o s sas, calld h Dual Hursc Programmng DHP, and a crc approxmang boh J and s drvavs, calld h Globalzd Dual Hursc Programmng GDHP, compl hs ACD famly. Ths sysms do no rqur xclusvly nural nwork mplmnaons, snc any dffrnabl srucur s suabl as a buldng block. Th nrrlaonshps bwn mmbrs of h ACD famly hav bn gnralzd and xpland n dal by Prokhorov [, ]. B. Hursc Dynamc Programmng Fg. shows a modl dpndn HDP Crc/Acon dsgn. Th HDP Crc nural nwork s conncd o h Acon nural nwork hrough a Modl nural nwork of h plan. Ths hr dffrn nural nworks ar ach dscrbd n blow and ar akn for h purposs of hs sudy o b a hrlayr fdforward nural nwork wh a sngl hddn layr wh sgmod ransfr funcon. Th npu and oupu layrs hav lnar ransfr funcons. Y J A ACTION Nwork Y rf A Y [A, A, A3] [ Y, Y, Y3] Fg. A modl dpndn HDP crc/acon dsgn. PLANT CRITIC Nwork MODEL Nwork J Y For modl dpndn dsgns s assumd ha hr xss a Modl nural nwork whch s abl o prdc h sas/oupus Y, of h plan a m, gvn a m, h sas/oupus Y and h acon sgnals A. Y fy, A In addon o sgnals a m, dlayd valus of hs sgnals can b usd as wll dpndng of h complxy of h plan dynamcs [3]. For h purposs of hs sudy, h Modl nural nwork prdcs h changs n h oupus Y, a m [3]. In Fg., h npus o h Modl nwork ar mdlayd valus of boh h plan and h Acon nwork oupus. A nural nwork basd chnqu o dvlop a Modl nwork usng suprvsd larnng s shown n Fg. and mor Y J 37

3 dals can b found n [4]. Th convnonal sac backpropagaon algorhm s usd n ranng h nural nwork. Ths Modl nural nwork can undrgo offln or onln ranng, as rqurd by h applcaon. Y Y Y CRITIC Nwork J Y U Y Plan Inpus PLANT MODEL Nwork Plan Oupus Y Y Y CRITIC Nwork J Y E C Targ γ J Y U Y Targ sgnal rror Fg. Dvlopmn of a nural nwork modl of a plan. Hursc Dynamc Programmng has a Crc nural nwork ha smas h funcon J cosogo n h Bllman quaon of dynamc programmng, xprssd as follows: Fg. 3 HDP Crc nural nwork adapaon/ranng. Th Crc nwork rs o mnmz h followng rror masur ovr m E E 3 C k J Y γ UY k k 0 whr γ s a dscoun facor for fn horzon problms 0 < γ <, U. s h uly funcon or h local cos and Y s an npu vcor o h Crc. Th Crc nural nwork s rand forward n m mulm sps ahad, whch s of gra mporanc for ralm opraon. Fg. 3 shows h HDP Crc adapaon/ranng. Th npus o h Crc ar oupus from h Modl nural nwork and s mdlayd valus Fg.. Two Crc nural nworks ar shown n Fg. 3 havng h sam npus and oupus bu a dffrn m nsans. Th frs Crc nural nwork has npus from m sps, and, and h scond Crc nural nwork has npus from m sps, and. Thr corrspondng oupus ar J and J rspcvly. Th scond Crc nural nwork smas h funcon J cosogo a m by usng h Modl nural nwork o g npus on sp ahad. As a rsul s possbl o know h Crc nural nwork oupu J a m. C E J Y γ J Y U Y 4 whr Y s h changs n Y, a vcor of obsrvabls of h plan or h sas, f avalabl. Th uly funcon U s dpndn on h sysm conrolld and a ypcal funcon s gvn n []. I should b nod ha only for h purposs of hs sudy, changs n h sa varabls ar usd rahr han sa varabls. Th ncssary condon for o b mnmal s gvn n 5. W E E E 0 C C C C WC Th wghs upda for h Crc nwork usng h backpropagaon algorhm s gvn as follows: C EC WC η EC W C C W η{ J Y γ J Y U Y } { J Y γ J Y U Y } W whr η s a posv larnng ra and W C ar h wghs of h Crc nural nwork. Th sam Crc nwork s shown n wo conscuv momns n m n Fg. 3. Th Crc nwork s oupu J Y s ncssary n ordr o provd h ranng sgnal γ J Y U Y, whch s h dsrd/arg valu for J Y. 38

4 Th objcv of h Acon nural nwork n Fg., s o mnmz J Y n h mmda fuur, hrby opmzng h ovrall cos xprssd as a sum of all U Y ovr h horzon of h problm. Ths s achvd by ranng h Acon nural nwork wh an rror sgnal J/A. Th gradn of h cos funcon J, wh rspc o h oupus A, of h Acon nural nwork, s oband by backpropagang J/J.. h consan hrough h Crc nural nwork and hn hrough h prrand Modl nural nwork o h Acon nural nwork. Ths gvs J/A and J/W A for all h oupus of h Acon nural nwork, and all h Acon nural nwork s wghs W A, rspcvly. Th wghs upda n h Acon nural nwork usng backpropagaon algorhm s gvn as follows: E C J Y J Y U Y γ Y Y Y 5 whr./ Y s a vcor conanng paral drvavs of h scalar. wh rspc o h componns of h vcor Y. Th Crc nural nwork s ranng s mor complcad han n HDP, snc hr s a nd o ak no accoun all rlvan pahways of backpropagaon as shown n Fg. 4, whr h pahs of drvavs and adapaon of h Crc ar dpcd by dashd lns. In Fg. 4, h dashd lns man h frs backpropagaon and h doddashd lns man h scond backpropagaon. E E 8 A ACTION Nwork Y rf A PLANT Y J whr EA 9 A and J J Y A Y A 0 Wgh chang n h Acon nwork W A can b wrn as: W E Equaon can b furhr wrn as: A WA EA WA α EA W A J J WA α A WA A whr α s a posv larnng ra. 3 Wh 7 and 3, h ranng of h Crc and h Acon nworks can b carrd ou. Th gnral ranng procdur for h Crc and h Acon nworks ar dscrbd n Scon D. C. Dual Hursc Programmng Th Crc nural nwork n h DHP schm shown n Fg. 4, smas h drvavs of J wh rspc o h vcor Y oupus of h Modl nural nwork and larns mnmzaon of h followng rror masur ovr m: E E E s 4 T 3 C C U Y pah 3 pah 8 pah pah 6 [A, A, A3] [ Y, Y, Y3] U pah 5 Ak λ MODEL pah Y Nwork Y # Y pah 4 γ pah 7 pah 9 MODEL Nwork # Y Y Y CRITIC Nwork # E C CRITIC Nwork # λ J Y pah 0 pah pah Fg. 4 DHP Crc nural nwork adapaon. λ J Y Th Modl nural nwork n h dsgn of DHP Crc and Acon nural nworks ar oband n a smlar mannr o ha dscrbd n Scon B abov. In h DHP schm, applcaon of h chan rul for drvavs ylds: n Y J Y λ Yj Y j m n k k j Y Ak λ A Y 6 whr λ J Y Y, and n, m, j ar h numbrs of oupus of h Modl, Acon and Crc nural nworks rspcvly. By xplong 6, ach of n componns of h vcor E C from 5 s drmnd by whr 39

5 E C j J Y J Y γ Y Yj j m U Y U Ak Y A Y j k k j 7 Th sgnals n Fg. 4 whch ar labld wh a pah numbr, rprsn h followng:... v. v. Pah rprsns h oupus of h plan fd no h Modl nural nwork #. Ths oupus ar Y, Y and Y. Pah rprsns h oupus of h Acon nural nwork fd no h Modl nural nwork #. Ths oupus ar A, A and A. Pah 3 rprsns h oupus of h plan fd no h Acon nural nwork. Ths oupus ar Y, Y and Y. Pah 4 rprsns a backpropagad sgnal of h oupu of h Crc nural nwork # hrough h Modl nural nwork wh rspc o pah npus. Th backpropagad sgnal on pah 4 s n λ Y n 6. Y j Pah 5 rprsns a backpropagad sgnal of h oupu of h Crc nural nwork # hrough h Modl nural nwork wh rspc o pah npus. Th backpropagad sgnal on pah 3 s n Y λ n 6. Ak v. Pah 6 rprsns a backpropagaon oupu of pah 5 sgnal v abov wh rspc o pah 3. Th sgnal m n Y on pah 6 s λ n 6. k Ak v. Pah 7 s h sum of h pah 4 and pah 6 sgnals rsulng n J Y Yj, gvn n 6. v. Pah 8 s h backpropagad sgnal of h rm U Ak Fg. 5 wh rspc o pah 3 and s m U Ak k Ak Yj n 7. x. Pah 9 s a produc of h dscoun facor γ and h pah 7 sgnal, rsulng n rm γj Y Yj n 7. x. Pah 0 rprsns h oupu of h Crc nural nwork #, J Y Y. x. Pah rprsns h rm U Y Fg. 5. x. Pah rprsns E Cj gvn n 7 and as follows: Pah E Cj pah 0 pah 9 pah pah 8. Th paral drvavs of h uly funcon U wh rspc o A k, and Y, U Ak and U Y rspcvly, ar oband by backpropagang h uly funcon, U hrough h Modl nwork as shown n Fg. 5. U A k U Y MODEL Nwork U Fg. 5 Backpropagaon of U hrough h Modl nural nwork. Th adapaon of h acon nwork n Fg. 4, s llusrad n Fg. 6 whch propagas λ back hrough h modl nwork o h acon nwork. Th goal of such adapaon can b xprssd as follows [, ]: U Y J Y γ 0 A A 8 Th rror sgnal for h Acon nwork adapaon s hrfor gvn as follows: E A U Y J Y γ A A 9 Th wghs upda xprsson [], whn applyng backpropagaon, s as follows: U Y J Y A WA α γ A A WA T 0 whr α s a posv larnng ra and W A ar wghs of h DHP Acon nural nwork. Y E A ACTION Nwork Y rf A PLANT MODEL Nwork J A γ Fg. 6 DHP Acon nural nwork adapaon. U A λ Y Y Y Y CRITIC Nwork λ J Y D. Gnral Tranng Procdur for h Crc and h Acon Nworks Th ranng procdur s ha suggsd n [] and s applcabl o any ACD. I consss of wo spara ranng cycls: on for h Crc, and h ohr for h Acon. An mporan masur s ha h Acon nural nwork s prrand wh convnonal conrollrs Proporonal Ingral Drvav, PID conrollng h plan n a lnar rgon. Th 40

6 Crc s adapaon s don nally wh h prrand Acon nwork, o nsur ha h whol sysm, conssng of h ACD and h plan rmans sabl. Thn h Acon nwork s rand furhr whl kpng h Crc nural nwork wghs fxd. Ths procss of ranng h Crc and h Acon on afr h ohr, s rpad unl an accpabl prformanc s rachd. I s assumd ha hr s no concurrn adapaon of h prrand Modl nural nwork, and W C s nalzd o small random valus. In h Crc s ranng cycl, an ncrmnal opmzaon of 5 and/or 9 s carrd ou usng a suabl opmzaon chnqu.g. backpropagaon. Th followng opraons ar rpad N C ms:. Inalz 0 and Y0. Compu h oupu of h Crc nural nwork a m, J or λ f C Y, W C 3. Compu h oupu of h Acon nural nwork a m, A f A Y, W A 4. Compu h oupu of h Modl nural nwork a m, Y f M Y, A, W M 5. Compu h oupu of h Crc nural nwork a m, J or λ f C Y, W C 6. Compu h Crc nural nwork rror a m, E C from 5a or E C from Upda h Crc nural nwork s wghs usng h backpropagaon algorhm. 8. Rpa sps o 7. Th funcons f C Y, W C, f A Y, W A and f M Y, A, W M rprsn h Crc, h Acon and h Modl nural nworks wh hr wghs W, rspcvly. In h Acon nural nwork s ranng cycl, an ncrmnal larnng s also carrd ou usng h backpropagaon algorhm, as n h Crc nural nwork s ranng cycl abov, and h ls of opraons for h Acon nural nwork s ranng cycl s almos h sam as ha for h Crc nural nwork s cycl abov sps o 7. Howvr, 7b or 3 ar usd for updang h Acon nural nwork s wghs nsad of usng 5a or 0. Th Acon s ranng cycl s rpad N A ms whl kpng h Crc s wghs W C fxd. N C and N A ar h lnghs of h corrspondng ranng cycls. I s mporan ha h whol sysm conssng of h ACD and h plan rmans sabl whl boh of h Crc and Acon nworks undrgo adapaon. III. ACD BASED CONTROL OF EXCITATION AND TURBINE SYSTEMS OF GENERATORS Th mcromachn laboraory a h Unvrsy of Kwa Zulu Naal, Durban, Souh Afrca has wo 3 kw, 0 V, hr phas mcroalrnaors, and ach on rprsns boh h lcrcal and mchancal aspcs of a ypcal 000 MW alrnaor. Th laboraory powr sysm s smulad n h MATLAB/SIMULINK nvronmn and smulaons suds wh nuroconrollrs ar carrd ou pror o hardwar mplmnaons. Th laboraory sngl machn nfn bus powr sysm n Fg. 7 consss of a mcroalrnaor, drvn by a moor whos orqu spd characrscs ar conrolld by a powr lcronc convrr o ac as a mcrourbn, and a sngl shor ransmsson ln whch lnks h mcroalrnaor o a volag sourc whch has a consan volag and frquncy, calld an nfn bus. Th paramrs of h mcroalrnaors, drmnd by h IEEE sandards ar gvn n Tabls I and II [5]. A m consan rgulaor s usd o nsr ngav rssanc n srs wh h fld wndng crcu [5], n ordr o rduc h acual fld wndng rssanc o h corrc prun valu. A hrmachn powr sysm shown n Fg. 8 s s up by usng h wo mcroalrnaors and h nfn bus as h hrd machn. Govrnor 3 S P rf ~ P rf P rf V ω P m ~ V V V V P rf 3 S ω V fld S3 Mcro Mcrourbn alrnaor Excr MODEL/ V Nuro Idnfr HDP/DHP Nuro Conrollr ω AVR PSS ω S4 B B B3 Z 0.0j0.5 Z 0.0j0.5 Z 3 0.0j0.75 V U m V rf S5 INDUCTIVE LOAD V Infn Bus Fg. 7 Th sngl machn nfn bus confguraon wh h convnonal AVR and govrnor conrollrs, and nuroconrollr. 4

7 ω Govrnor P rf Mcro # P m G 0.0 j j0.375 McroTurbn P Excr rf ω S3 V V E pss PSS AVR Govrnor P rf P rf P m V rf ω McroTurbn Excr V rf Mcro # G AVR V E V S 0.0 j j S j Infn Bus V Fg. 8 Mulmachn powr sysm conssng of wo mcroalrnaors G and G whch ar convnonally conrolld by h AVRs, govrnors and a PSS. A. Convnonal Excaon and Turbn Conrol Th praccal sysm uss a convnonal AVR and xcr combnaon of whch h ransfr funcon block dagram s shown n Fg. 9, and h m consans and gan ar gvn n Tabl III [5]. Th xcr sauraon facor S s gvn by S xp0.65 V T v, T v, T v3 and T v4 ar h m consans of h PID volag rgulaor compnsaor; T v5 s h npu flr m consan; T s h xcr m consan; K av s h AVR gan; V fdm s h xcr clng volag; and, V ma and V m ar h AVR maxmum and mnmum clng volags. V st v5 Inpu Flr V rf AVR Kav st v st v st v 3 st v 4 PID Compnsaon and lms V m fd V ma Fg. 9 Block dagram of h AVR and xcr combnaon. Excr V fdm st Excr S Sauraon Th block dagram of h powr sysm sablzr PSS usd o achv dampng of h sysm oscllaons s shown n Fg. 0 [6]. Th consdraons and procdurs usd n h slcon of h PSS paramrs ar smlar o ha found n [6] and hs paramrs ar gvn n Tabl IV. ω K STAB V pssmx st w st st V st w st3 st pss 4 V pssmn Washou Phaslad Fg. 0 Block dagram of h powr sysm sablzr. A sparaly xcd 5.6 kw hyrsor conrolld moor s usd as a prm movr, calld h mcrourbn, o drv h mcroalrnaor. Th orquspd characrsc of h V fld moor s conrolld o follow a famly of rcangular hyprbola o mula h dffrn posons of a sam valv, as would occur n a ral ypcal hgh prssur HP cylndr urbn. Th hr low prssur LP cylndrs nra ar rprsnd by appropraly scald flywhls aachd o h mcrourbn shaf. Th mcrourbn and govrnor combnaon ransfr funcon block dagram s shown n Fg., whr, P rf s h urbn npu powr s pon valu, P m s h urbn oupu powr, and ω s h spd dvaon from h synchronous spd. Th urbn and govrnor m consans and gan ar gvn n Tabl V [5]. ω Govrnor K g st g st g Mcrourbn P rf nrand sauraon srvo moor sam rhar P rf P m sft g 5 st g 3 st g4 st g 5 Fg. Block dagram of h mcrourbn and govrnor combnaon. Th gans K av of h AVR and K g 0.05 of h govrnor n Tabls III and V rspcvly ar oband by suabl chocs of h gan and phas margns n ach cas, as dscrbd n [7]. Transmsson lns ar rprsnd by usng banks of lumpd nducors and capacors. B. Smulaon and Exprmnal Suds wh Dffrn Conrol Schms for Excaon and Turbn Sysms Th dynamc and ransn opraon of h HDP and DHP nuroconrollrs ar compard wh h opraon of h convnonal CONV conrollr AVR and urbn govrnor, xcludng h PSS for sngl machn nfn bus powr sysm n Fg. 7. In addon, h prformanc of a connually onln rand nuroconrollr COT s also shown. Th COT nuroconrollr s dvlopd basd on h ndrc adapv nuroconrol schm [8]. In powr sysms fauls such as hr phas shor crcus occur from m o m, and bcaus hy prvn nrgy from h gnraor rachng h nfn bus, mans ha mos of h urbn shaf powr gos no 4

8 acclrang h gnraor durng h faul. Ths rprsns a svr ransn s for h conrollr prformanc. Fgs. and 3 show h rspons of all four conrollrs for h hr phas mporary shor crcu for 50 ms wh h nw ransmsson ln mpdanc Z. Hr, s obvous ha h DHP conrollr clarly bas h ohr hr conrollrs n rms of offrng h gras oscllaon dampng spcally n h roor angl. Th DHP conrollr provs s robusnss o changs n h sysm confguraons. Trmnal volag n pu DHP HDP COT CONV Tm n sconds Fg. Trmnal volag of h mcroalrnaor for a mporary 50 ms hr phas shor crcu ransmsson ln mpdanc Z. Basd on h rsuls for h sngl machn powr sysm n abov, h DHP conrollr has h bs prformanc, hnc, h DHP nuroconrollr s h only on ha s now mplmnd on h mulmachn powr sysm. Th prformanc of h DHP nuroconrollr s now compard wh ha of h convnonal conrollrs, on of whch s quppd wh a powr sysm sablzr. Fg. 4 shows h mulmachn powr sysm of Fg. now quppd wh wo DHP nuroconrollrs. Th DHP nuroconrollrs wr mplmnd on DSPs and allowd o conrol h laboraory mulmachn powr sysm [3]. Th purpos of hs ss s o confrm va praccal masurmns h ponal of adapv crc basd nuroconrollrs whch hav bn dmonsrad durng h P rf Mcro # smulaon suds for a sngl machn and a mulmachn powr sysm. Howvr, h laboraory mplmnaon on mcromachns s also nndd o form a bass for possbl fuur nvsgaons no us of such nuroconrollrs on larg mulmgawa szd powr plans n a ralworld powr saon. Load angl n dgrs DHP HDP COT CONV Tm n sconds Fg. 3 Roor angl of h mcroalrnaor for a mporary 50 ms hr phas shor crcu ransmsson ln mpdanc Z. Th DHP nuroconrollrs ar sd for dynamc and ransn opraon for an ncras n h ransmsson ln mpdanc by opnng swch S n Fgs. and 4. Four dffrn conrollr combnaon suds ar carrd ou for h abov dsurbancs and a dffrn oprang condons for G and G: Cas a convnonal conrollr on boh G and G Cas b convnonal conrollr wh a PSS on G and convnonal conrollr on G Cas c DHP nuroconrollr on G and convnonal conrollr on G Cas d DHP nuroconrollrs on boh G and G. 7 S 4 3 P rf P rf P m McroTurbn DHP Nuroconrollr # P m V G Excr V E V ω V Mcro # G 0.0 j j j0.75 S Load 0.0 j Infn Bus P rf McroTurbn Excr 0.0 j j0.50 V V E DHP Nuroconrollr # ω V V Fg. 4 Mulmachn powr sysm wh wo DHP nuroconrollrs. 43

9 A h oprang condon P 0. pu, Q 0 pu on boh gnraors, h srs ransmsson ln mpdanc s ncrasd a m 0 s from Z 0.0 j0.75 pu o Z j.50 pu by opnng swch S. Fg. 5 shows h load angl rspons of gnraor G for hs s wh h four dffrn conrollr combnaons. Clarly h DHP nuroconrollrs cas d agan xhb supror dampng and nsur lssr ovrshoos compard o h prformanc of h convnonal conrollrs vn whn quppd wh a PSS. Th load angl rspons of gnraor G for h sam dsurbanc s shown n Fg.6. I s clar h DHP nuroconrollrs xhb h bs dampng of h conrollrs. h SSSC. Th plan consss of h synchronous gnraor 60 MVA, 5 kv LL, urbngovrnor sysm, auomac volag rgulaor AVRxcr sysm, ransmsson ln conncd o an nfn bus, and h SSSC conncd n srs wh ransmsson ln. Th paramrs of h synchronous gnraor and ransmsson ln ar gvn n [0]. Th EXACA IEEE alrnaor suppld rcfr xcaon sysms and H_TUR/GOV IEEE yp hydro urbngovrnor modls n PSCAD/EMTDC sofwar packag ar usd as h AVR/xcr sysm and urbn/govrnor, rspcvly. v s s v x v c v r Load angl n dgrs Tm n sconds Cas a Cas b Cas c Cas d Fg. 5 Load angl rspons of gnraor G for srs ransmsson ln mpdanc ncras by opnng swch S for P 0. pu and Q 0 pu. Turbn Govrnor AVR Excr r Synchronous Gnraor CONVC x SSSC Conrol DHPNC V GTO Srs VSI Inf. bus Load angl n dgrs Cass c & d Cas b Cas a Tm n sconds Fg. 6 Load angl rspons of gnraor G for srs ransmsson ln mpdanc ncras by opnng swch S for P 0. pu and Q 0 pu. IV. ACD BASED CONTROL OF FACTS DEVICES Currnly, h conrol of FACTS dvcs ar carrd ou usng lnar PI conrollrs wh fxd paramrs. Th PI conrollr paramrs ar slcd o gv som dsrabl prformanc for a parcular rgon of opraon and condons; ousd whch h prformanc of h conrollr dgrads. Thus, h nd for h dsgn of a nonlnar robus/adapv conrollr for FACTS dvcs ars o car for a wd rang of oprang condons and, o handl small and larg dsurbancs. Th followng subscons dscrb h SSSC and SCRC FACTS dvcs and h conrol schms. A. Sac Synchronous Srs Compnsaor SSSC and s Convnonal Conrol Schm Th sac synchronous srs compnsaor SSSC convrr can conrol h racv and/or acv powr on an ac sysm by changng boh phasor angl and magnud of h convrr s oupu volag wh a fas conrol acon. Espcally, h xchang of acv powr, whch s h parcular characrsc of h SSSC, s accomplshd by conrollng h volag nsd h SSSC [9]. Th sngl machn nfn bus SMIB sysm shown n Fg. 7 s usd o compar h dampng conrol capabls of h Dual Hursc Programmng basd nuroconrollr DHPNC and h convnonal PI conrollr CONVC for Fg. 7 Plan: 60 MVA, 5 kv LL SMIB s sysm. For h mahmacal modl of h SSSC, h assocad quaon can b rprsnd wh h lumpd srs ransmsson ln racanc x ransmsson ln x plus lakag racanc of srsconncd ransformr and ransmsson srs rssanc r h nvrr s rgardd smply o hav no conducon losss n pr un as follows. d d sa sb sc r ωs x rω s x 0 ωs 0 vsa vca v x sa ωs 0 sb v sb vcb v x r sc ω s ωs vsc vcc v x x ra rb rc whr ω s s h synchronous spd of h powr sysm, v s s h sndngnd volag rmnal volag n pracc, s s h currn n ransmsson ln, v r s h rcvngnd volag n h nfn bus, and v c s h njcd srs compnsaon volag. Usng h synchronously roang rfrnc fram basd ransformaon [] n whch h daxs s always concdn wh h nsananous volag vcor v and h qaxs lads h daxs by 90, h hrphas crcu quaons n can b ransformd o h followng dq axs vcor rprsnaon. d d rω s d x q ω ωs ω vs vcd v d x rω s q ωs vcq vrq x x rd 3 44

10 Nglcng h srs nvrr harmoncs, h ac sd njcd volag v c n Fg. can b xprssd wh rlaon o h capacor volag V on h lnk as follows. v mv cos α, v mv sn α 4 cd whr α s h phas angl dffrnc bwn h volags v c and v s h v c lads h v s, and m s h modulaon ndx of h srs nvrr. Th dynamcs of h capacor volag ar dscrbd by dv d P C V C V C V [ m { cos α sn α }] d cq C v q cd d V v cq q 5 Th man goal of h SSSC s o njc h srs volag n quadraur wh h ln currn and o manan h volag V. For hs purpos, h PQ ral and racv powr auomac powr flow conrol mod [9] n Fg. 8 s usd. B. Smulaon Suds wh Convnonal and Nuroconrol for a Sac Synchronous Srs Compnsaor SSSC To valua h dampng prformanc of h proposd nuroconrollr for h conrol of h SSSC, 00 ms and 0 ms hr phas shor crcus ar appld o h nfn bus rcvng nd a s. Th gnraor opras wh a roor angl of 53.6 P.0 pu, Q 0.59 pu n a sadysa oprang pon. Th rsuls ar shown n Fgs. 9 o, whr Uncompnsad and CONVC dno h rspons of gnraor conrolld whou SSSC and wh a PI conrolld SSSC, rspcvly. From h Fgs. 9 and 0, h DHPNC dampng conrol s mor ffcv compard o h CONVC. Also, s clar from Fg. ha h gnraor conrolld whou h SSSC gos unsabl and loss synchronsm whn h faul duraon s 0 ms. In conras, h DHPNC and CONVC rsor h gnraor o a sabl mod, and h DHPNC dampng conrol s mor ffcv compard o h CONVC, whch mans ha h DHPNC allows h gnraor o b oprad closr o s sably lm. Dald rsuls and xplanaons ar gvn n [4]. V * q q * k p s vˆcq q PI q V d p d * k k p d s vˆcd V V' PI p V kp θ k s PIV k Synchrnously roang rfrnc ransformaon vˆ ˆ cd v m V vˆ cq α an vˆ Vcor phaslockd loop cd cq v a v b v c δ [Dgr] DHPNC Uncompnsad CONVC Ral and racv currn compuaon P* Q* V r a b c GTO ga conrol of srs VSI α Fg. 8 PQ auomac powr flow conrol dagram for h nrnal conrol of h SSSC. In Fg. 8, an nsananous hrphas s of ln volags, v a, v b, and v c s usd o calcula h ransformaon angl, θ provdd by h vcor phaslockd loop for synchronous opraon of h srs volag sourc nvrr VSI shown n Fg. 7. As shown n 3, h hrphas s of masurd ln currns a h ac rmnal of h SSSC s dcomposd no s ral/drc componn, d, and racv/quadraur componn, q. Ths acual sgnals d and q and h rfrnc dq currn sgnals * d and * q ar compard, rspcvly. Th rror sgnal q for h racv powr xchang s passd hrough h PI rgulaor PI q. Th sgnal p for h ral powr xchang and mannanc of a consan V, s passd hrough h PI p. Th p consss of h d and rror sgnal V whch passs hrough h PIV. Th V * s h dsrd valu for V. Th valu of V * s drmnd by slcng a suabl valu of h modulaon ndx whn s rang of 0 o. m Tm [s] Fg. 9. A 00 ms hr phas shor crcu s: δ [ ]. V [pu] DHPNC CONVC Uncompnsad Tm [s] Fg. 0. A 00 ms hr phas shor crcu s: V [pu]. C. Srs Capacv Racanc Compnsaor SCRC and s Exrnal and Inrnal Conrol For h srs capacv racanc compnsaor SCRC FACTS dvc, Oo al. [], [3] frs proposd makng us of a sandalon nvrr boh o manan capacor volag of h nvrr and o nsur h srs racanc condon a

11 h nvrr s ac rmnals. Rgby and Harly [4] xndd h orgnal work proposd by Oo al. no a workng laboraory prooyp of a srs capacv racanc compnsaor SCRC, and mprovng h prformanc of h orgnal SCRC schm by modfyng h volag rgulaor srucur. Basd on hs work, hy also rpord [5] on h analyss of a powr oscllaon dampng schm by applyng an xrnal lnarconrollr wh h ad of proprly dsgnd supplmnary conrols [6] o h SCRC, and hy also consdrd h mpac of h SCRC s own nrnal dynamcs on h prformanc of an xrnal dampng conrollr. I s mporan o no ha h sudy of h xrnal conrol calld scondary or funconal opraon conrol [9] for h FACTS dvc maks possbl o progrss furhr owards hrarchcal conrol and possbl global dynamc opmzaon n largscal powr nworks. δ [Dgr] Uncompnsad CONVC DHPNC Tm [s] Fg.. A 0 ms hr phas shor crcu s: δ [ ]. Th hory and opraon of h SCRC as wll as s convnonal xrnal lnarconrollr CONVEC ar dscrbd n [5] and brfly dscrbd by h auhors n [5]. Th dals of h dsgn of a nw xrnal opmal nuroconrollr EC for h SCRC usng h dual hursc programmng DHP opmzaon algorhm [], [4] s proposd as an alrnav o h CONVEC n ordr o mprov h dampng of low frquncy acv powr oscllaons n [5]. Th fasbly of h DHPEC s valuad on h mulmachn powr sysm shown n Fg. quppd wh SCRC. Ths powr sysm modl has bn usd for h sudy of volag sably on a praccal largscal powr sysm n [7] and [8]. In Fg., h sndng nd n AREA has wo gnraors Gn and Gn ransmng powr o h rcvng ara AREA hrough fv 500 kv, 00 km long, ransmsson lns. Gn s gvn a larg nra so ha funcons as h slack bus. Howvr, s rlavly small lcrcally 5000 MVA n ordr o provd only lmd volag suppor or racv powr suppor for h load ara n AREA. Th paramrs of Gn and Gn 3 ar dncal and gvn n h Appndx D Un F8 of [0]. Also, Gn and Gn ar quppd wh an auomac volag rgulaor AVR/xcr and a urbn/spd govrnor sysm. Th prformanc of h DHPEC s valuad by applyng a larg mpuls yp dsurbanc, a 300 ms hr phas shor crcu o bus 0 n Fg., a 0.5 s. Th Gn and Gn 3 ar oprang wh roor angls of 50.4 and 5. wh rspc o buss and 3 rspcvly durng h prfaul sady sa oprang pon. Th rsuls ar shown n Fgs. 3 and 4 for h spds ω and ω 3 of Gn and Gn 3. Thy clarly show ha h DHPEC sll mprovs dampng of low frquncy oscllaons mor ffcvly, compard o h SCRC whou an xrnal conrollr. 3. kv Gn 5000 MVA T4 AREA AREA 500 kv 500 kv 500 kv Z Ln Ln Ln 3 FACTS SCRC DHPEC ω 3, P S3 500 kv 3. kv 6 T kv Gn MVA Indusral load 3. kv Ln 4 Ln 5 T Gn T5 00 MVA 00 km 5 kv 7 5 kv 3.8 kv T3 8 9 T Z Rsdnal load Fg. Largscal mulmachn powr sysm quppd wh SCRC. 46

12 ω [rad/s] SCRC prformanc n comparson o h convnonal lnar conrollrs whch us mor xnsv lnarzd modls. Ths bnf of a nurodnfr agrs wh h conclusons on h comparson of usng approxma and xac modls n adapv crc dsgns whch was xplcly shown n [7]. All hs faurs ar dsrabl and mporan for ndusral applcaons whch rqur a nuroconrollr chnology ha s nonlnar, robus and sabl Tm [s] DHPEC Fg. 3. A 300 ms hr phas shor crcu s a bus 0: ω [rad/s] SCRC VI. APPENDIX TABLE I MICROALTERNATOR # PARAMETERS T d s X d 0.05 pu Rs pu T d0 33 ms X d 0.64 pu H 5.68 s T q0 0.5 s X q.98 pu F 0 X d.09 pu X q 0.3 pu p pol pars TABLE II MICROALTERNATOR # PARAMETERS T d s X d 0.05 pu Rs pu T d0 33 ms X d 0.64 pu H 5.68 s T q0 0.5 s X q.98 pu F 0 X d.09 pu X q 0.3 pu p pol pars ω 3 [rad/s] DHPEC TABLE III AVR AND EXCITER TIME CONSTANTS T v 0.66 s T v s T v.66 s T 0.47 s T v s K av T v s Tm [s] Fg. 4. A 300 ms hr phas shor crcu s a bus 0: ω 3 [rad/s]. V. CONCLUSION Ths uoral papr has prsnd h nvsgaons on h dsgn and mplmnaon of Adapv Crc basd nuroconrollrs o rplac/augmn h convnonal PI conrollrs on gnraors and FACTS dvcs, n boh snglmachnnfnbus and mulmachn powr sysm. Ths nuroconrollrs xhb br dampng han h convnonal conrollrs. Th Adapv Crc Dsgn basd nuroconrollrs hav h gra advanag ha onc rand, hr wghs/paramrs rman fxd and hrfor avod h rsk of nsably assocad wh connual onln ranng. Th convrgnc guaran of h Crc and Acon nural nworks durng offln ranng was shown n [6, 9]. In addon, h havy compuaonal load of onln ranng only arss durng h offln ranng phas and hrfor maks h onln ral m mplmnaon cos of h nuroconrollrs chapr. Th procssng hardwar cos s a small fracon of h cos of urbognraors and hrfor hs s no a bg ssu. Th Adapv Crc Dsgn basd nonlnar opmal rollrs dsgnd n hs chapr ar all basd on approxma modls oband by nurodnfrs, bu nvrhlss xhb supror TABLE IV PSS TIME CONSTANTS AND GAIN T W 3 s T s T 0. s T s T 0. s K STAB TABLE V GOVERNOR AND MICROTURBINE CONSTANTS Phas advanc compnsaon, T g 0.64 s Phas advanc compnsaon, T g s Srvo m consan, T g3 0.5 s Enrand sam dlay, T g s Sam rha m consan, T g5.66 s pu shaf oupu ahad of rhar, F 0.3 Gan K g 0.05 VII. ACKNOWLEDGMENT Th auhors acknowldg h Unvrsy of KwaZulu Naal, Durban, Souh Afrca for allowng h usag of h mcromachns laboraory. REFERENCES [] G. K. Vnayagamoorhy, R. G. Harly, D. C. Wunsch, "Comparson of Hursc Dynamc Programmng and Dual Hursc Programmng Adapv Crcs for Nuroconrol of a Turbognraor", IEEE Transacons on Nworks, Volum: 3, Issu: 3, May 00, Pags:

13 [] G. K. Vnayagamoorhy, R. G. Harly, D. C. Wunsch, Dual Hursc Programmng Excaon Nuroconrol for Gnraors n a Mulmachn Powr Sysm, IEEE Transacons on Indusry Applcaons, Volum: 39, Issu:, March/Aprl 003. [3] G. K. Vnayagamoorhy, R. G. Harly, D. C. Wunsch, "Implmnaon of Adapv Crc Basd Nuroconrollrs for Turbognraors for Turbognraors n a Mulmachn Powr Sysm", IEEE Transacons on Nworks Spcal Issu on Hardwar Implmnaons, Spmbr 003. [4] J. W. Park, R. G. Harly, G. K. Vnayagamoorhy, "Nw nrnal opmal nuroconrol for a srs FACTS dvc n a powr ransmsson ln", Nworks, vol. 6, no. 56, July 003, pp [5] J. W. Park, R. G. Harly, G. K. Vnayagamoorhy, Nw Exrnal NuroConrollr for Srs Capacv Racanc Compnsaor n a Powr Nwork, IEEE Transacons on Powr Sysms, vol. 9, no. 3, Augus 004, pp [6] D. Prokhorov, L. A. Fldkamp, Analyzng for Lyapunov Sably wh Adapv Crcs, Procdngs of h Inrnaonal Confrnc on Sysms, Man and Cybrncs, 998, Vol., pp [7] T. T. Shannon, G. G. 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Parhasarahy, Idnfcaon and Conrol of Dynamcal Sysms usng Nworks, IEEE Trans. on Nworks, Vol., No., March 990, pp. 47. [5] D. J. Lmbr, R. G. Harly, S. M. Schuck, Subsychronous Rsonanc of h Kobrg Turbognraors and of a Laboraory McroAlrnaor Sysm, Trans. of h SA Insu of Elcrcal Engnrs, Novmbr 979, pp [6] P. Kundur, M. Kln, G. J. Rogrs, M. S. Zywno, Applcaon of Powr Sysm Sablzrs for Enhancmn of Ovrall Sysm Sably, IEEE Trans. on Powr Sysms, Vol. 4, No., May 989, pp [7] W. K. Ho, C. C. Hang, L. S. Cao, Tunng of PID Conrollrs basd on Gan and Phas Margn Spcfcaons, Procdngs of h h Trnnal World Congrss on Auomac Conrol, 993, pp [8] G. K. Vnayagamoorhy, R. G. Harly, A Connually Onln Trand Nuroconrollr for Excaon and Turbn Conrol of a Turbognraor, IEEE Trans. on Enrgy Convrson, Vol. 6, No.3, Spmbr 00, pp [9] N. G. Hngoran, L. Gyugy, Undrsandng FACTS: Concps and chnology of flxbl AC ransmsson sysms, Sponsord by IEEE Powr Engnrng Socy, IEEE Prss, 999, ISBN [0] P. M. Andrson, A. A. Fouad, Powr sysm conrol and sably. Nw York: IEEE Prss, 994. [] T. Makomb, N. Jnkns, Invsgaon of a unfd powr flow conrollr, IEE Proc.Gnraon, Transmsson and Dsrbuon, 999, 464, [] X. Wang, S.Z. Da, and B. T. Oo, A Srs Capacv Racanc Compnsaor Basd on Volag Sourc PWM Convrr, n Proc. of IEEE IAS Annual Mng, pp. 9894, 99. [3] B. T. Oo, S.Z. Da, and X. Wang, SoldSa Srs Capacv Racanc Compnsaors, IEEE Trans. on Powr Dlvry, Vol.7, pp. 9499, Aprl 990. [4] Bruc S. Rgby and R.G. Harly, An Improvd conrol Schm for a SrsCapacv Racanc Compnsaor Basd on a VolagSourc Invrr, IEEE Trans. on Indusry Applcaons, Vol.34, No., pp , March/Aprl 998. [5] Bruc S. Rgby, N.S. Chonco, and R.G. Harly, Analyss of a Powr Oscllaon Dampng Schm Usng a VolagSourc Invrr, IEEE Trans. on Indusry Applcaons, Vol.38, No.4, pp. 053, July/Augus 00. [6] F.J. Swf and H.F. Wang, Applcaon of h conrollabl srs compnsaor n dampng powr sysm oscllaons, IEE Proc.Gnr. Transm. Dsrb., Vol.43, No.4, pp , July 996. [7] Carson W. Taylor, Concps of Undrvolag Load Shddng for Volag Sably, IEEE Trans. on Powr Dlvry, Vol.7, No., pp , Aprl 99. [8] Carson W. Taylor, N. J. Balu, and D. Maraukulam, Powr sysm conrol and sably, McGrawHll Compans, EPRI Powr Sysm Engnrng Srs, 993, ISBN [9] D. V. Prokhorov, D. C. Wunsch, Convrgnc of CrcBasd Tranng, Procdngs of h IEEE Inrnaonal Confrnc on Sysms, Man, and Cybrncs, Vol. 4, 997, pp Gansh Kumar Vnayagamoorhy M 97, SM 0 rcvd h B.Eng. Honors dgr wh a frs class honors n Elcrcal and Elcroncs Engnrng from h Abubakar Tafawa Balwa Unvrsy, Bauch, Ngra, and h MScEng and PhD dgrs n Elcrcal Engnrng from h Unvrsy of Naal, Durban, Souh Afrca, n March 994, Aprl 999 and Fbruary 00, rspcvly. H was a Snor Lcurr a h Durban Insu of Tchnology, Souh Afrca pror o jonng h Unvrsy of MssourRolla UMR, USA as an Asssan Profssor n h Dparmn of Elcrcal and Compur Engnrng n May 00. H s h Drcor of h RalTm Powr and Inllgn Sysms Laboraory a UMR. Hs rsarch nrss ar n compuaonal nllgnc, powr sysms, volvabl hardwar and sgnal procssng. Dr. Vnayagamoorhy has aracd n xcss of $ mllon n rsarch fundng from xrnal sourcs snc jonng UMR. H has publshd ovr 30 paprs n rfrd journals and nrnaonal confrncs. Dr. Vnayagamoorhy s h 005 IEEE Indusry Applcaon Socy IAS Ousandng Young Mmbr award rcpn, a 004 NSF CAREER award rcpn, h 004 IEEE S. Lous Scon Ousandng Young Engnr, h 003 Inrnaonal Nwork Socy INNS Young Invsgaor award rcpn, a 00 rcpn of h IEEE Compuaonal Inllgnc Socy CIS W. J. Karplus summr rsarch gran and h rcpn of fv prz paprs wh h IEEE IAS and IEEE CIS. H s an Assoca Edor of h IEEE Transacons on Nworks. H s a Snor Mmbr of h Souh Afrcan Insu of Elcrcal Engnrs, a Mmbr of INNS and h Amrcan Socy for Engnrng Educaon. H s currnly h IEEE S. Lous CIS and IAS Chapr Char, h Char of h ask forc on Inllgn Conrol Sysms and h Scrary of h Inllgn Sysms subcomm of IEEE Powr Engnrng Socy. Ronald G. Harly M 77SM 86F 9 was born n Souh Afrca. H rcvd h BSc.Eng. cum laud and MScEng cum laud dgrs from h Unvrsy of Prora, Prora, Souh Afrca, and h Ph.D. dgr from London Unvrsy, London, U.K., n 960, 965, and 969, rspcvly. In 970 h was appond o h Char of Elcrcal Machns and Powr Sysms a h Unvrsy of Naal n Durban, Souh Afrca. H s currnly a h Gorga Insu of Tchnology, Alana, USA. H has coauhord som 350 paprs n rfrd journals and nrnaonal confrncs. Aloghr 9 paprs aracd przs from journals and confrncs. Ron s a Fllow of h SAIEE, a Fllow of h IEE, and a Fllow of h IEEE. H s also a Fllow of h Royal Socy n Souh Afrca, a Fllow of h Unvrsy of Naal, and a Foundr Mmbr of h Acadmy of Scnc n Souh Afrca formd n 994. H has bn lcd as a Dsngushd Lcurr by h IEEE Indusry Applcaons Socy for h yars 000 and 00. Hs rsarch nrss ar n h dynamc and ransn bhavor of lcrc machns and powr sysms, and conrollng hm by h us of powr lcroncs and modrn conrol algorhms. 48