Online Modern Philosophy for Stability Detection Based on Critical Energy of Individual Machines

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1 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X Ole oder Phloophy for Stablty Detecto Baed o Crtcal Eergy of Idvdual ache Wagdy. ANSOUR Emal: wagdy_brahm2010@yahoo.com ohamed A. ALI Emal: mohamed.mohamed02@feg.bu.edu.eg Nader SH. ABDELHAKEE Emal: eg_ader2011@yahoo.com Faculty of Egeerg (Shoubra), Beha Uverty, Electrcal Egeerg Departmet, 108 Shoubra St., Caro, Egypt. Abtract Th paper troduce a propoed moder phloophy/algorthm for traet tablty aemet baed o crtcal eergy fucto of dvdual mache. The algorthm deped o the creato of eergy fucto for dvdual mache ug the ole meauremet va the Sychrozed Phaor eauremet Ut (SPU). For further peedg up the algorthm for ole aemet, a parallel algorthm for tablty aemet mplemeted. The propoed algorthm make ole calculato the potetal ad ketc eerge for each mache power ytem ad the compare the total ytem eergy to the crtcal eergy of the ytem. A deco baed o the ole comparo produce a output operad accordg to tablty tuato of the power ytem. The propoed algorthm teted by two mache fte Bu tet ytem to eure t effectvee ad valdty. Keyword Traet Stablty, Traet Eergy Fucto, Crtcal Clearg Tme (CCT), O-Le, Sychrozed Phaor eauremet Ut (SPU), Parallel Algorthm, ATLAB/SIULINK Software. I. INTRODUCTION Traet tablty ha bee evaluated ug Tme Doma (TD) approach [1], [2], but t foud that the computatoal tme for evaluatg tablty for large ytem much more tha the real tme. Th ha ecouraged the expao of varou traet tablty aemet, uch a Equal Area Crtero (EAC), Exteded Equal Area Crtero (EEAC) [3] ad Traet Eergy Fucto (TEF) [4]-[6], to calculate Crtcal Clearg Tme (CCT). Traet Eergy Fucto kow to be a very powerful tool of ole aeg CCT of a power ytem wthout olvg the ytem dyamc equato at pot fault. Th method capable of provdg the formato about the degree of tablty (or tablty). The dffculty th method to fd the utable eergy fucto of power ytem [7]. At the tat of fault occurrece, the electrcal power output reduce, accelerate the rotor agle ad the ytem ketc eergy evetually buld up utl t arrve t maxmum value at the clearg tme. At th tat, the exce of electrcal power output decelerate the rotor agle ad the ytem ketc eergy tarted decreag whle potetal eergy tarted growg up. Th dcate that the covero of ytem ketc eergy to potetal eergy takg place. The ucceful covero of accumulated ketc eergy reulted from a partcular dturbace potetal eergy would reult a cotat ytem' eergy toward the ed of the traet perod. PU devce have bee developed to gve ychrozed data from the whole power ytem. Sampled data of threephae voltage ad curret, whch are tme-ychrozed, gve the voltage ad curret magtude ad phae of each meaured value the power ytem to be ued realtme tablty aalye [8], [9]. The cope of th paper to troduce a method a a accurate algorthm to help ole traet tablty aemet for mult-mache power ytem durg plag ad operato (o-le aemet) phae. For th purpoe, the traet eergy fucto baed o dvdual mache eergy fucto offer good ght to the force caug the eparato of a mache (or a group of mache) from the ytem, ad the eergy aocated wth that eparato. Formulato of each mache equato wth repect to the ytem' Ceter Of Ierta (COI) ad mplemetato of the parallel algorthm [11] to detect the Traet Stablty Aemet (TSA) o parallel mcroproceor [10], [11], to acheve ole deco for the eparato of a mache (or a group of mache) are uggeted. II. THE POWER SYSTE ODEL The power ytem repreeted by the o-called clacal model where geerator are repreeted by cotat voltage behd traet reactace [1]. Furthermore, the moto of the geerator expreed wth repect to the ceter of erta (C.O.I.) of the ytem. For a -geerator ytem, let for geerator, E, δ agtude ad agle of voltage behd traet reactace, repectvely. ω Rotor peed relatve to aychroou frame. Geerator erta cotat. 50

2 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X The poto δo ad peed ωo of the C.O.I. are defed by: 1 1 o, o (1) Where: t t 1 t 1 1 The geerator moto the C.O.I. frame defed a: o o Aume that the effect of dampg eglected the ytem; the geerator equato of moto are gve by the followg dfferetal equato: P Pe PCOI t (3) 1,2,, The expreo for P, Pe ad PCOI are gve by: P P E G 2 m P C D co e j j j j j1 j P P P COI e 1 Where: C E E B, D E E G P m G j j j j j j C j, B j (2) (4) echacal power put. Real part of the th dagoal elemet of the etwork Y-matrx. Real ad magary compoet of the jth elemet of the etwork Y-matrx, repectvely. III. The Traet Eergy Fucto for Idvdual ache Rearrage (3) for each mache at the pot-fault codto ad multplyg t by θ, the followg equato ca be obtaed: P Pe PCOI 0, t 1,2,, (5) Itegrate (5) wth repect to tme, ug to a lower lmt, where ( t o ) 0 ad ( to ) 0 whch called the Stable Equlbrum Pot (SEP), yeld 1 2 ( ) j j 2 j1 j V P C d j1 j Dj cojd PCOI d t The table equlbrum pot of the pot fault ytem foud by olvg the followg olear algebrac equato by the teepet decet method [12]. P Pe PCOI 0, 1,2,, (7) t The oluto of uch equato deped o the tal value of δ, = 1, 2,,, whch ca be choe to be the teady-tate value of the prefault ytem. Eq. (6) evaluated ug the pot fault etwork cofgurato. The frt term (6) repreet the KE of mache wth repect to the ytem COI. The remag term are codered to be the PE. Thu, Eq. (6) ca be expreed a: V V V (8) KE PE Eq. (8) cot of two part: ketc eergy ad potetal eergy. Both eerge eed to be olved umercally. After rotor agle are foud umercally, the eerge ca be repreeted by: 1 2 KE (9) 2 co( ) PE P C co( ) j ( ) j j1 j j j1 j ( ) j Dj P COI d ( j) t COI 1 P d P ( ) co( ) co( ) j Cj 1 j1 j j ( j) D ( ) j 1 j1 j j (6) (10) (11) By mulatg a utaed fault (or a fault of log durato), the potetal eergy term of (10) are computed V PE, = 1, 2,, for each tat of tme. The value of V PEmax are oted for the dfferet mache (or group of mache). Thee repreet the value of V crtcal for each mache. VCrtcal _ y max ( VPE max_ ) (12) V V (13) Crtcal _ PE max_ 51

3 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X The value of V PEmax- (12) repreet the eergy aborbg capacty for each mache. It gve a meaure of the amout of ketc eergy coverted to potetal eergy. To determe whether tablty occur, the total traet eergy at the tat of fault clearg compared wth the value of V Crtcal-y. The mode of tablty the gve by each mache whoe traet eergy at clearg tat exceed t crtcal eergy. IV. PARALLEL ICROPROCESSORS The adaptato of parallel mcroproceor utable ug the parallelzed algorthm [10], [11], [13]-[16]. The ytem cot of Cetral cro-proceor (CP) ad De-Cetralzed cro-proceor (DCP) for each mache. The CP receve the output varable from each mache mcroproceor DCP the CP traferrg the requred varable to each mache DCP whch wll be ued to compute the updated parameter of the mache. Schematc dagram to repreet the adaptato of parallel mcroproceor ug the parallelzed algorthm how Fg.1. Where: V t I t Geerator termal bu voltage va the PU. Geerator termal bu curret va the PU. Smlarly, EV t Pe ( ) X d 1,2,, 2 E E Vt Qe co( ) Xd X d (15) Accordg to (14) ad (15), the geerator rotor agle of mache ca be deduced a follow; 1 Pe ta 2 ( E / X d ) Q (16) e Alo, the geerator rotor peed of mache ca be gve by: ( ) ( 1) (17) t The the above calculated value wll be ued to the pre-cotructed TEF ad plot the maxmum eergy, tate trajectory. The protecto relay (mcro-cotroller baed) ued to compare the reult. If the ytem eergy approache or to border the maxmum eergy, the algorthm provde a output tate a ytem dturbace but the ytem wll tay ychrozed (Alarm meage tate ormal power wg codto). Fg.1. Schematc Dagram Repreet the Parallelzed Algorthm. V. ONLINE TRANSIENT STABILITY ALGORITH BASED ON PU TECHNOLOGY The propoed algorthm ue the ole meauremet va SPU the make rotor agle motorg ad cotrol tat by tat. The algorthm ue the meauremet of curret ad voltage va the talled SPU located at geerator termal bue to calculate the electrcal actve power Pe ad reactve power Qe. The expreo for Pe ad Qe for dvdual mache are gve by: Pe REAL ( Vt It ) (14) Qe IAG ( Vt It ), 1,2,, Fg.2. Protecto Algorthm for ult-mache Sytem. 52

4 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X If the ytem eergy exceed the maxmum eergy, the algorthm wll top ad ed a output tatg OOS (warg meage, the ytem OOS). Selectvty algorthm hould be adopted to clear the faulted area oly by electg the approprate crcut breaker to be trpped. VI. CASE UNDER STUDY The tet ytem ued cota two geerator wth fte erta ad a fte bu, a how Fg.3.. Fg.3. Network Cofgurato of the Tet Sytem. The ytem parameter ad the prefault load flow data are gve Appedx. The ytem ha bee mulated wth a clacal model for the geerator. The dturbace tatg the traet a three-phae fault occurrg ear bu 4 at the ed of le 4 5. The fault cleared by opeg le 4 5 VII. SIULATION RESULTS Oce the Y matrx for each etwork codto (pre-fault, durg ad after fault) calculated, we ca elmate all the ode except for the teral geerator ode ad obta the Y matrx for the reduced etwork. A ATLAB/SIULINK model how Fg.4 cotructed baed o the propoed method to obta rotor agle (δ), agular peed (ω) ad eergy (V Eergy ) of the two mache. Alo, ATLAB/SIULINK model how Fg.5 cotructed baed o covetoal method to obta the ame parameter ad detcal tme repoe. Fg.4. ATLAB/SIULINK odel for Traet Stablty Study Cojucto wth Parallel croproceor. 53

5 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X Fg.5. ATLAB/SIULINK odel Ug Covetoal ethod. Fg.6. Tme Repoe wth Fault Cleared at t c < t cc, t c =0.4 ec of δ, ω, P e, ω Veru δ ad Eergy. 54

6 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X Fg.7. Tme Repoe wth Fault Cleared at t c = t cc =0.405 ec of δ, ω, P e, ω Veru δ ad Eergy. Fg.8. Tme Repoe wth Fault Cleared at t c > t cc, t c =0.41 ec of δ, ω, P e, ω Veru δ ad Eergy Each mache wg curve, the phae trajectory ω-δ plot ad Eergy fucto for dvdual mache uder pot-fault codto are plotted at clearg tme of 0.4 ec, ec ad 0.41 ec a how Fg. 6, 7 ad 8. Fg.6 how a table cae where the rotor agle ocllate, ad reach aother table equlbrum pot toward the ed of the traet ad tablty could be aured f the traet eergy V 1 (δ cl, ω cl ) < V crtcal1. The ytem crtcally table wth fault cleared at ec, correpodg to a crtcal clearg agle δ cr1 of mache 1 (crtcal mache) of degree, crtcal eergy V crtcal1 of mache 1 ad the ytem vetgated are , repectvely. Whe the fault cleared at 0.41 ec, ytem tablty reulted ad V 1 (δ cl, ω cl ) > V crtcal1 a dcated Fg.8. The crtcal clearg tme (t cc ) ca alo be obtaed from the P e veru tme curve. That mea whe P e touch P m the frt wg, the t cc obtaed. Fg.6 where t c < t cc, the P e hgher tha P m the frt wg. Fg.7 where t c t cc, P e touch P m. Whe t c > t cc, the ytem wll be utable a how Fg.8. 55

7 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X VIII. CONCLUSION The paper preet a compreheve ole modelg for traet tablty aemet of a mult-mache power ytem cojucto wth Parallel Algorthm [10], [11]. The algorthm developed ug ATLAB/SIULIK. Acheve ole deco due to ug parallel proceg techology cojucto wth modfed eergy fucto for dvdual mache. The algorthm detect the CCT ole operato that ca be ued for crcut breaker trppg/blockg acto a per fault evet. Alo a ATLAB/SIULIK model cotructed baed o the covetoal tme doma method ad detcal repoe due to varou fault clearg tme are obtaed. The algorthm valdated for ole tablty detecto baed o crtcal eergy of dvdual mache. From Bu APPENDIX Le ad traformer data* To Bu Sere Z Shut Y R X B (1) (2) Geerator data of tet ytem* Parameter G1 G2 Rated VA KV Xd` H Prefault load flow data* Bu Voltage Geerato Load P Q P Q º º º º º *All value are per ut o 100VA bae. REFERENCES [1] P.. Adero, A. A. Fouad, Power Sytem Cotrol Ad Stablty, Joh Wley & So, Ic., [2] D. J. Hgham, A algorthmc troducto to umercal oluto of tochatc dfferetal equato, SIA Rev., Vol. 43, No. 3, pp , [3] A. Y. Abdelazz, Amr. Ibrahm, Zeab G. Haa: Traet tablty aaly wth equal-area crtero for out of tep detecto ug phaor meauremet ut I JEST, Vol. 5, No. 1, pp.1-17, [4]. K. Khedkar, G.. Dhole, V. G. Neve, Traet Stablty Aaly by Traet Eergy Fucto ethod: Cloet ad Cotrollg Utable Equlbrum Pot Approach, IE (I) Joural EL, Vol 85, pp , September [5] W. Zhag, H. Zhag, ad B.-S. Che, Geeralzed Lyapuov equato approach to tate-depedet tochatc tablzato/detectablty crtero, IEEE Tra. Autom. Cotrol, Vol. 53, No. 7, pp , Aug [6] Samta Padh, Bhu Praad hra: Numercal ethod Baed Sgle ache Aaly for Traet Stablty IJETAE, Vol. 4, February [7] L. F. Alberto, F. H. J. R. Slva, ad N. G. Breta, Exteded Lyapuov fucto for detaled power ytem model, I Proc. of 14th PSCC, [8] A. Phadke, J. Thorp, Htory ad applcato of phaor meauremet, : Power Sytem Coferece ad Expoto (PSCE 06), pp , [9] S. Skok, I. Ivakovc, Z. Cera, Applcato baed o PU techology for mproved power ytem utlzato, : IEEE Power Egeerg Socety Geeral eetg, pp. 1 8, [10] ohamed A. Al, Wael R. A, Wagdy. aour, Fahmy. Bedary Novel Real-Tme Stablty Aemet Algorthm Baed O Sychro-Phaor eauremet Ad Parallel Algorthm For ultmache Network, Iteratoal Joural of Emergg Electrc Power Sytem (IJEEPS) 2012, Volume 13, ue 3, artcle 7. [11] ohamed A. Al, Wagdy. aour, "Real-Tme Traet Stablty Aaly/Aemet Baed Propoed Parallel Algorthm", Iteratoal Joural of Electrcal ad Power Egeerg, 2012, Volume: 6, Iue: 4, Page() : , DOI : / jepe [12] A. D. Booth, "A applcato of the method of teepet decet to the oluto of ytem of o-lear multaeou equato," Quart. J. ech. Appl. ath., vol. 2, pp , December [13] achado Ferrera, C.; Beleza Carvalho, J.; Da Pto, J.A.; acel Barboa, F.P.; O-le traet tablty aemet of a electrc power ytem ug a parallel proceg tate etmator, Electro techcal Coferece, ELECON th edterraea Volume 3, Iue, 29-31, pp.: , vol.3, ay [14] Hog, C.; She, C..; Implemetato of parallel algorthm for traet tablty aaly o a meage pag multcomputer, Power Egeerg Socety Wter eetg, IEEE Volume 2, Iue, pp.: , [15] Aloo, G.; Bochccho,.A.; La Scala,.; Sbrzza, R.; A dtrbuted computg approach for real-tme traet tablty aaly, Power Sytem, IEEE Traacto o volume 12, Iue 2, pp.: , ay [16] Wag, F.Z. Geerato; Parallel--tme relaxed Newto method for traet tablty aaly, Tramo ad Dtrbuto, IEE Proceedg- Volume 145, Iue 2, pp.: , ar

8 Iteratoal Joural of Scetfc Reearch Egeerg Techology Volume 1, Iue 4, July-2015, ISSN (Ole): X AUTHOR PROFILE Prof. Dr.-Eg. Wagdy. aour Receve the B.Sc. degree electrcal egeerg from aoura Uverty I 1974 he receved h.sc. from Helwa Uverty ad 1980 a Ph.D. cotrol egeerg from the Techcal Uverty of Brauhweg Germay. Sce 1990 he ha bee a profeor of cotrol of power ytem at the faculty of egeerg, Beha Uverty, Caro (Egypt). (Beha Uverty, Faculty of Egeerg, Elec. Eg. Dep., 108 Shoubra Street, Caro/Egypt). At. Lecturer-Eg. Nader Sh. Abd El-Hakeem Receve the B.Sc. degree electrcal egeerg from Beha Uverty 2006 ad 2012 he receved h.sc. from Beha Uverty. Sce 2009 he ha bee a Admtrator at the faculty of egeerg, Beha Uverty, Caro (Egypt). (Beha Uverty, Faculty of Egeerg, Elec. Eg. Dep., 108 Shoubra Street, Caro/Egypt). 57