Joint State and Parameter Estimation by Extended Kalman Filter (EKF) technique

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1 Inrnaonal Journal o Engnrng Rsarch an Dvlopmn -ISSN: p-issn: Volum Issu 8 (Augus Jon Sa an aramr Esmaon by En alman Flr (EF chnu S. Damoharao.S.L.V. Ayyarao G Sun Dp. o EEE GMR Insu o chnology Rajam Anhra rash Ina Asssan rossor Dp. o EEE GMR Insu o chnology Rajam Anhra rash Ina Absrac:- In orr o ncras powr sysm sably an rlably urng an ar surbancs powr gr global an local conrollrs mus b vlop. SCADA sysm provs say an low samplng nsy. o rmov hs lmaon MUs ar bng raply aop worlw. Dynamc sas o powr sysm can b sma usng EF. hs rurs l caon as npu whch may no avalabl. As a rsul h EF wh unnown npus propos or nyng an smang h sas an h unnown npus o h synchronous machn. In rms:- Dynamc sa smaon n alman lr sa smaon synchronous gnraor. I. INRODUCION armonc njcon has bn a ncrasng powr ualy concrn ovr h yars. Wh h growng h us o powr lcronc vcs h mannanc o powr ualy has bcom a major problm or h lcrc uly compans [6]. Bu hgh-prormanc monorng an conrol schms can harly b bul on h sng SCADA sysm whch provs only say low-samplng nsy an non synchronous normaon abou h nwor. SCADA masurmns ar oo nrun an non synchronous o capur normaon abou h ynamc sysm. I s o rmov hs lmaons ha w ara masurmns an conrol sysms (WAMAC usng phasor masurmn uns MUs ar bng rarly aop worlw. h w ara masurmn sysm (WAMS vlop raply n mos o h yars. I has bn appl o h monorng an conrol o powr sysms. Bu as a n o masurmn sysm WAMS has h masurmn rror an no convnn aa unavoably []. h say masurmn rrors o WAMS hav bn prscrb n corrsponng IEEE sanar bu h ynamc masurmn rrors now bcom h ocus o scusson. I h ynamc raw aa s appl rcly h unprcabl consunc wll b rsul n whch wll amag o powr sysms. hror h ynamc sa smaon or h sa varabls urng lcromchancal ransn procss s h bacbon or ynamc applcaons an ral-m conrol. A numbr o paprs hav ocus on jus on ynamc sa o h powr sysm a a m ypcally h roor angl or sp whch was sma such as nural nwors an AI mhos. hs AI-bas mol-r smaors gnra h sma roor sp or roor angl sgnal whou rurng a mahmacal mol or any machn paramrs [-]. In h larg-scal powr sysm sably analyss s on prrabl o hav an ac mol or all lmns o h powr sysm nwor nclung ransmsson lns ransormrs Inucon moors an also synchronous machns. hror h physcal mol-bas sa smaor o h gnraor nclung volag sas n aon o roor angl an sp woul b mor nrsng n sysm monorng an conrol. Synchronz phasor masurmn uns (MUs wr nrouc an snc hn hav b-com a maur chnology s us wh many applcaons whch ar currnly unr vlopmn aroun h worl. h occurrnc o major problms n many major powr sysms aroun h worl has gvn a nw mpus or larg-scal mplmnaon o w-ara masurmn sysms (WAMS usng MUs an hasor aa concnraors (DCs [4]. Daa prov by h MUs ar vry accura an nabl sysm analyzng o rmn h ac sunc o vns whch hav l o h problms. As prnc wh WAMS s gan s naural ha ohr uss o phasor masurmns wll b oun. In parcular sgncan lraur alray ss whch als wh applcaon o phasor masurmns o sysm monorng procon an conrol. h mos common chnu or rmnng h phasor rprsnaon o an npu sgnal s o us aa sampls an rom h wavorm an apply h scr Fourr ransorm (DF o compu h phasor masurmn. Snc sampl aa ar us o rprsn h rrnc sgnal s ssnal ha an alasng lrs b appl o h rrnc sgnal bor aa sampls ar an. h an alasng lrs ar analog vcs whch lm h banwh o h pass ban o lss han hal h samplng runcy. 4

2 Jon Sa an aramr Esmaon by En alman lr (EF chnu Fg. compnsang or sgnal lay nrouc by h an alasng Flr Synchrophasor s a rm us o scrb a phasor whch has bn sma a an nsan. In orr o oban smulanous masurmn o phasors across a w ara masurmn o h powr sysm s ncssary o synchronz hs m ags so ha all hasor masurmns blongng o h sam m ag ar ruly. Consr h marr n Fg. s h m ag o h masurmn. h MU mus hn prov h phasor gvn by usng h sampl aa o h npu sgnal. Furhrmor hs lay wll b a uncon o h sgnal runcy [7]. h as o h MU s o compnsa or hs lay bcaus h sampl aa ar an ar h an alasng lay s nrouc by h alman lr. h synchronzaon s achv by usng a samplng cloc puls whch s phas-loc o h on-puls-pr-scon sgnal prov by a GS rcvr. h rcvr may b bul n h MU or may b nsall n h subsaon an h synchronzng puls srbu o h MU an o any ohr vc. h m ags ar a nrvals ha ar mulpls o a pro o h nomnal powr sysm runcy. II. SINGLE-MACINE INFINIE-BUS OWER SYSEM A gnral powr sysm can b smpl o an uvaln crcu sysm wh a sngl machn connc o an nn bus va ransmsson lns. h so-call sngl machn nn-bus (SMIB sysm shown n Fg. wll b h bass or vlopng an valang our gnraor sa smas. Assumng a classcal synchronous gnraor mol l n as h roor angl by whch h -as componn o h Fg.. Synchronous machn connc o an n n bus va ransmsson lns. Volag bhn ransn racanc las h rmnal bus. I h rmnal volag can b chosn as h rrnc phasor. h phas gnraor can gnra phas volags an currns can b connc o h nn bus hrough h ransormrs an ransmsson lns. h ransormrs can b spp up h volag. h roor angl an roor sp can b sma by h synchronous machn. h gnraor n Fg. can hn b rprsn n h o oman by h ollowng gh-orr nonlnar uaon: h sa varabls an sa vcors ar calcula as: [ ] [ 4 ] u ] [ m E ] [ u u Sa varabls ar scrb by uaons ar: w.. ( u D j. ( u ( ( ( ( (4 (5 4

3 Jon Sa an aramr Esmaon by En alman lr (EF chnu. 5 (7 (8 6 (9 7 ( 8 Whr w s h nomnal synchronous sp (lc.ra/s h roor sp (p.u oru (p.u ( ( 4 4 h ar-gap oru or lcrcal oupu powr (p.u E (6 m h mchancal npu h cr oupu volag or h l volag as sn rom h armaur (pu an h roor angl n (lc.ra. Ohr varabls an consans ar n. Bas on h phasor agram assoca o h nwor h ar-gap oru wll b ual o h rmnal lcrcal powr (or nglcng h saor rssanc s zro: R a whr h -an -as volags can b prss as E V sn V cos V ( ( Also h -as an -as currns ar I V cos V sn ( Usng ( an (4 n ( an ar som mahmacal smpl-caon h lcrcal oupu powr a rmnal bus wh h sa varabls an can b oban as: V V sn ( sn (4 h oupu powrs ( Q ar V V sn sn V cos sn (5 V Q Assumpons ar: V. D.5 J m.6 cos (6.8 E

4 Jon Sa an aramr Esmaon by En alman lr (EF chnu h say sa uaons a o oun h valus o (7 h abov assumpons o n h valus o h ar gap oru (or lcrcal powr can b calcula as:.8 h oupu powrs can b calcula as:.8 Q.5 III. LINEAR AND NONLINEAR MODELS alman Flr En F Unscn F (UF ar mols popularly us or sa smaon procss. h raonal alman Flr s opmal only whn h mol s lnarz. SAE SACE MODELS A sa spac mol s a mahmacal mol o a procss whr sa o a procss s rprsn by a numrcal vcor. A. Non lnar Sa Spac Mol h mos gnral orm o h sa-spac mol s h Non lnar mol. hs mol ypcally consss o wo uncons an h: + = (uw (8 z = h(v (9 Fg: A gnral sa spac mol. 45

5 Jon Sa an aramr Esmaon by En alman lr (EF chnu B. Sa smaon Fg 4: Mahmacal vw o sa smaon h mos gnral orm o an sa smaon s nown as Rcursv Baysan Esmaon. hs s h opmal way o analyzng a sa p or any procss gvn a sysm an a masurmn mol. IV. ALMAN BASED FILERS A. alman an En alman lr h problm o sa smaon can b ma manpulabl. I w pu cran consrans on h procss mol by rurng boh an h o b lnar uncons an h Gaussan an wh nos rms w an v o b uncorrla wh zro man. u n mahmacal noaon w hn hav h ollowng consrans: ( u w = F +Bu +w ( h ( v = +v ( h consrans scrb abov ruc h sa mol o: + = F +Bu +w ( z = +v ( Whr F B an ar m pnn marcs. Fg: 5 alman lr loop h rcursv Baysan smaon chnu s hn ruc o h alman lr whr an h s rplac by h marcs F B an. h alman lr s jus as h Baysan smaor compos no wo sps: prc an upa. h acual calculaons rur ar: rc n sa bor masurmns ar an: = F +Bu (4 = F F +Q (5 h alman lr s u asy o calcula u o h ac ha s mosly lnar cp or a mar nvrson. I can also b prov ha h alman lr s an opmal smaor o procss sa gvn a uarac rror mrc. 46

6 Jon Sa an aramr Esmaon by En alman lr (EF chnu 47 B. EF Algorhm Dscrpon o rv h scr-m EF algorhm w sar rom h basc non o m rvaon o a varabl : (6 whr s h m sp an nca h m a.an or rspcvly. (7 (8 Whr s h sysm sa vcor s h nown npu vcor o h sysm s hr h procss (ranom sa nos or rprsns naccuracs n h sysm mol s h nosy obsrvaon or masur varabl (oupu vcor an s h masurmn nos. Sps o mprovng h sa smaon:. Inalz sa vcor an sa covaranc mar = [; ; ; ;.9;.4; 8;.]; =ag ([^ ^^.99.97^^]; (9 Q=ag ([.8^.8^.8^.9^.8^.8^.9^.9^]; R= ([.^ ;.^ ;.^];. Compu h paral rvav marcs: (. rc sa vcor an sa covaranc ( 4. Upa rror covaranc ( 5. rorm h gan marcs an upa h sa vcor ( DISCUSSION: F = w u (4 F (5 w u ( (. (. ( ( w u (. w u p F h ( Q F F ] [ ] [ h y

7 Jon Sa an aramr Esmaon by En alman lr (EF chnu F F 4 (4 u w u w 5 6 F F F F6 F7 F F F5 4 4 u w 4 4 F 4 F44 F48 u w F5 F55 (8 6 u w F6 F66 u w (4 F7 F77 8 u w F8 F88 F= F w F V F sn 7 F6 7 V 7 V cos V cos (6 (7 (9 (4 6 7 F m sn V V sn F7 sn 6 7 F 5 F 5 V cos F5 E V cos F4 5 F 44 F48 8 F55= F66= F77= F88= For calculang h y h u v V sn 4 F mar w sam as h h oupu uaon o h sysm s

8 Jon Sa an aramr Esmaon by En alman lr (EF chnu An or calculang h h h = V V cos sn V cos V = D.MAAB/SIMULIN MODEL FOR EF mho sn V sn cos V cos (4 Fg 6: MALAB/SIMULIN or EF E. EF Mho Smulaon Rsuls h EF algorhm was vlop n Smuln usng hn mb uncon bloc jus as w or h EF mho. In h lar cas was h only masurabl oupu sgnal an wr h hr npu sgnals. Bu n h EF mho an ar h hr oupu masurmns an h npu sgnals an ar sll ncssary. h npu s now assum o b accssbl or nown. h nal valus vcor or sas s an or h gan acor mar s. h nal valus rla o h unnown npu ar: an []. [ ^^^^] Also h man an covaranc o h sa an oupu nos marcs ar as: o br rlc ral sysm conons wh nos was a o h sa wh (man covaranc an o h masur oupu wh (man covaranc unr hs assumpons h rsuls o h EF algorhm or onln sa smaon o h ourh orr nonlnar mol o h synchronous gnraor subjc o a sp on ar prsn n Fg. 4(a. h sma oupu sgnals an h unnown npu sma ar also shown n Fg. 4(b an (c rspcvly.. 49

9 Jon Sa an aramr Esmaon by En alman lr (EF chnu A. Roor angl n ra smaon In EF h acual valu o la s.6.obsrvrng rom h sma valu s.59.h ynamc sa o powr sysm a h say sa valu ar applyng h non-lnar sa smaor o g h say sa valu s.598. I s o b g h sysm b sablz. h gur s rawn bwn h roor angl acual o h sma valu. B. Roor Sp ra/sc smaon In EF h acual valu o chang n sp s..obsrvrng rom h sma valu s.8.h ynamc sa o powr sysm a h say sa valu ar applyng h non-lnar sa smaor o g h say sa valu s.8. I s o b g h sysm b sablz. h gur s rawn bwn h roor sp acual o h sma valu. C. E n p.u smaon 5

10 Jon Sa an aramr Esmaon by En alman lr (EF chnu In EF h acual valu o E n p.u s.. obsrv rng rom h sma valu s.7.h ynamc sa o powr sysm a h say sa valu ar applyng h non-lnar sa smaor o g h say sa valu s.7. I s o b g h sysm b sablz. h gur s rawn bwn h E acual o h sma valu D. ED IN.U ESIMAION FIG 7:EF SAE ESIMAION WI RESULS (A ROOR ANGEL (B ROOR SEED (C EQ ESIMAION(D ED ESIMAION In EF h acual valu o E n p.u s.4. obsrv rng rom h sma valu s.99.h ynamc sa o powr sysm a h say sa valu ar applyng h non-lnar sa smaor o g h say sa valu s.99. I s o b g h sysm b sablz. h gur s rawn bwn h E acual o h sma valu. F.JOIN SAE AND ARAMEER ESIMAION: (8.a D n p.u smaon In EF h acual valu o D n p.u s.5. obsrv rng rom h sma valu s.49.h ynamc sa o powr sysm a h say sa valu ar applyng h non-lnar sa smaor o g h say sa valu s.4. I s o b g h sysm b sablz. h gur s rawn bwn h D acual o h sma valu. h sas ar obsrv by h scop o b jon o h n alman lr. h subsysm whch consss o h SMIB o h alman lr. h rrors o D J an o can b obsrv. 5

11 Jon Sa an aramr Esmaon by En alman lr (EF chnu (8.bo n p.u smaon Fg 8: Jon sa an paramr smaon rsuls(a(b In EF h acual valu o o n p.u s.. obsrv rng rom h sma valu s.44.h ynamc sa o powr sysm a h say sa valu ar applyng h non-lnar sa smaor o g h say sa valu s.4. I s o b g h sysm b sablz. h gur s rawn bwn h D acual o h sma valu. h sas ar obsrv by h scop o b jon o h n alman lr. h subsysm whch consss o h SMIB o h alman lr. h rrors o D J an o can b obsrv V. CONCLUSION In hs papr ynamc sa smaon o a powr sysm nclung h synchronous gnraor roor angl an roor sp. h approach was h raonal nonlnar sa smaor h EF mho whch nclus lnarzaon sps n s algorhm. Smulaon rsuls o h EF smaor show appropra accuracy n smang h ynamc sas o a saura ourh-orr gnraor connc o an nn bus unr nosy procsss. h vlop EF-bas smaors wr cv as wll unr nwor aul conons wh procss an masurmn nos nclu. h jon sa an paramr smaon rsuls wr som nos. REFERENCES []. Esmal Ghahrman an Innocn amwa Dynamc Sa Esmaon n owr Sysm by Applyng h En alman Flr Wh Unnown Inpus o hasor Masurmns IEEE ransacon on S VOL.6Fb. [].. unur owr Sysm Sably an Conrol []. aohu Qn Bang L an Nan Lu owr Sysm Dparmn Chna Elcrc owr Rsarch Insu Dynamc Sa Esmaor Bas on W Ara Masurmn Sysm Durng owr Sysm Elcromchancal ransn rocss IEEE Nural Nwor Con. (IJCNN 4. [4]. Jam D La R Vrglo Cnno Jams S. horp an A. G. ha Synchronz hasor Masurmn Applcaons n owr Sysms IEEE rans. owr App. Sys. vol.4 pp [5]. ngyangzhaoan IEEE Am Wsl Mmbr owr Sysm Sa Esmaon Usng MUs Wh Imprc Synchronzaon [6]. n. C. Yu N. R. Wason an J. Arrllaga An Aapv alman Flr or Dynamc armonc Sa Esmaon an armonc Injcon racng roc. 9 owr & Enrgy Socy Mng (ES9MAY 995. [7]. G. Valr an V. rzja Unscn alman lr or powr sysm ynamc sa smaon IE Gn. ransm. Dsrb. vol. 5 no. pp [8]. J. Chang G. N. arano an J. Chow Dynamc sa smaon n powr sysm usng ganschul nonlnar obsrvr n roc. 995 IEEE Conrol Applcaon Con pp. 6. [9]. S. Gllan s an B. D Moor Unbas mnmum-varanc npu an sa smaon or lnar scr-m sysms Auomaca vol. no. 4 pp []. Y. Chng. Y Y. Wang an D. Zhou Unbas mnmum-varanc sa smaon or lnar sysms wh unnown npu Auomac vol. 45 no. pp