Modelling of Induction Motor for Simulation of Internal Faults

Transcription

1 Modelling o Induction Moto o Siulation o Intenal Fault Maciej Wieczoek Intitute o Electical Powe Engineeing Wocław Univeity o echnology 5-37 Wocław, Poland aciej.wieczoek@pw.woc.pl Eugeniuz Roołowki Intitute o Electical Powe Engineeing Wocław Univeity o echnology 5-37 Wocław, Poland eugeniuz.oolowki@pw.woc.pl Abtact Accuate and lexible copute odel o an induction oto i a vey ipotant tool o diagnotic and ault potection algoith invetigation. hi pape conide odelling o an intenal ault in tato winding o an induction oto. Geneal appoach to inte-tun ault odelling in uch achine i dicued and ipleentation o the odel in AP-EMP poga in a o o ype-94 eleent i peented. Included exaple deontate baic chaacteitic o the popoed odel and it application o intenal ault analyi in the coplex yte included oto, load and a upplying netwok. Keywod-coponent; odelling o induction oto; tanient iulation; intenal tun to tun ault I. INRODUCION Daage o tato inulation i the ot euent ailue in electical oto. Potection o the induction oto againt dieent intenal ault would liit the ault duation and pevent oto o ubtantial daage, what i paticulaly ipotant o highe oto ating. Diagnoing o ault in electical oto i a vey ipotant unction, which enable to potect the oto againt the eult o diuption. In ode to deign an algoith, which will eectively eliinate thi kind o diuption, it i neceay to ake a pope odel o the oto. aditional odel o electical achine ae baed on electical cicuit euation and euation o otion (o called echanical cicuit odel). Matheatical odel o induction oto decibed in thi way i copoed o dieential and algebaic euation. Geneally, it i an aangeent o high ode et o euation containing nonlinea unction. Moto paaete that occu in the entioned cae ae had to identiy, which i the eaon that the odel i exteely had to ue diectly [1]. Lo o powe in one o the phae i oten caued by echanical tenion and vibation. Vibation can lead to looening o the cew on the achine teinal o echanical tenion, coneuently leading to the lo o powe in one o the phae. un to tun ault ae caued by dieent acto aecting tato diectly. Fo exaple, echanical tenion duing aebly o while achine i woking, and alo by patial dichage caued by high voltage aong the tun, (in the ituation when tato i poweed by a ouce with PWM) can caue daage to the inulation, and in coneuence the low o hot cicuit cuent. Vaiou olution ae available in liteatue o detection o intenal ault [1], [2], [3], [4], [5], [9], [1]. Eicient oto potection hould detect all poible ault and iolate the oto in ode to iniize the daage ize. Coon ethod o invetigation o the poce involved i baed on application o uitable copute odel. Widely ued copute odel have a cloe connection with atheatical odel. Obtained eult baed on thee odel o copute iulation ae oe and oe eliable and becaue o that, play an ipotant pat in deigning and teting o the device theelve, and alo elating to the autoatic yte. hi aticle peent a atheatical odel by which the tanient behaviou o an induction oto with a winding ault can be ucceully analyzed. he uiel cage oto wa choen o uthe invetigation. he odel wa pepaed in the AP EMP iulation poga [6]. Included iulation eult how it undaental popetie. It can be een that it i a tool handy to ue, enabling an eay way to obtain the iulation eult by any given condition. In the ollowing tage the tun-to-tun ault odel i peented and decibed in detail. Included exaple deontate baic chaacteitic o the popoed odel and it application o intenal ault analyi in the coplex yte included oto, load and a upplying netwok. II. MAHEMAICAL MODEL OF INDUCION MOOR - BASIC CONSIDERAIONS Electical euivalent o aynchonou achine i hown in Fig. 1. Copanion cicuit o induction oto can be decibed by yte o euation (1), whee thee phae o tato and oto ae peented in vecto o [12]. i L i L tato cicuit u L L u oto ciciut Figue. 1.Electical euivalent o aynchonou achine Moden Electic Powe Syte 21, Woclaw, Poland MEPS'1 - pape P29

2 Vecto u, i and epeent tato voltage, cuent and lux. i and ae cuent and lux o oto. A a yetical achine i conideed, it i aued: = I and = I, whee I i diagonal atix. Relation (1) can be tanoed with the atix, to coodinate a in (6) and (7), whee u = [u d u ], i = [i d i ] and i = [i d i ] ae adeuately voltage and cuent atix o tato and cuent atix o oto [7]. i = i i + L ( θ ) i ( θ ) i + L i (1) whee lux ae given by: = i i + z ω K p (6) Eleent o atix L, L, and L ae decibed by euation (2). l l and l l ae el inductance o tato and oto, and l i utual inductance whee L ( θ ) = l L L = l = l co( θ ) 2 co θ + π 2 co θ π l l I + L I + L () () 2 co θ π co( θ ) 2 co θ + π 2 co θ + π 2 co θ π co( θ ) Mechanical pat o induction oto can be decibed by (3) and (4), whee ω i angula oto velocity, J oent o inetia, - echanical toue, e electoagnetic toue, z p nube o pole pai. dω ( t) J = e = z p e L ( θ ) ( i ) i θ Model decibed by the above euation i exceptionally diicult o diect application. anoation o to yte i caying out by uing o tanoation atix (5). (2) (3) (4) 2 2 co( θ ) co θ π co θ + π = in( θ ) in θ π in θ + π 3 (5) i i + L + L i i,, L, L and L and ae diagonal atix at the ize o 1 (2 x 2), and K =. 1 III. SIMULAION OF URN O URN FAULS IN SAOR WINDINGS Let u conide tun-to-tun ault on phae A. Winding in thi phae i divided on two pat un-aulted tun winding ection μ u and hoted tun winding μ h, a in Fig. 2. un u μu and μh i oveall nube o tun tato in phae A (μ u + μ h =N ). Phae B and C have the ae nube o tun eual N. I the nube o tun in all thee tato phae ae the ae, we can apply baic odel (with peciic odiication) to decibe a atheatical odel o induction oto with tun-totun ault. he odel o a aulty oto can be deived o tandad elation (1). Flux euation o induction oto with tun-totun ault in yte take the ollowing o [11]: = i ( i μ i ) ( i μi ) + L( θ ) i ( θ )( i μ i ) + L i whee μ = [μ h ] i a vecto epeenting poition o tunto-tun ault in the tato cicuit. (7) (8)

3 A i a u d d μ u μ h i R u d u ( 1 μ h ) L ( μ h ) 1 μ h L μ h C i c i b B i u u i Figue. 3. Moto odel with tun to tun tato hot cicuit Figue. 2. hee phae tato winding with tun to tun ault in phae A he lux in cicuited pat o winding A can be calculated accoding to the ollowing euation: h a = R i μ h ( ia i whee i hot-cicuit cuent. anoing (5) into coodinate, with taking into conideation o (9), one can obtain: ) (9) Intenity level o tun to tun ault in thi odel can be adjuted though the change o nube o hoted tun and eitance ( ), liiting hot cuent. IV. EMP SIMULAION MODEL he conideed odel i ipleented in AP-EMP poga a the ype-94 iteative eleent (Figue 4). In the iulation coue the odel pocee o the input voltage and geneate o the output cuent accoding to the ollowing geneal iteative elation [6]: 1 I ( k) = G ( k) U ( k) + I hit (13) h = R = whee lux ae given by: h = μ i i ( i μ i ) + z ω K μ p h ( i i ( i μi ) + Li ( i μi ) + Li 2 l ( i i ) + μ L i + i μ i h l h ) 3 h (1) (11) whee μ = [μ h ]. Detailed odel o the conideed cicuit i hown in Fig. 3. Mechanical pat o induction oto in yte i decibed by (3) and (12), e 3 = z 2 p ( di id ) z pμhdi (12) whee: 1 1 I( t) G ( k) = i the Jacobian atix, I hit U( t) t= tk epeent the hitoy cuent (depending on the applied integation ethod), U(k) vecto o input voltage, I(k) vecto o output cuent, k iulation tep nube, iteation nube. In the analyzed odel cuent and voltage vecto have the tuctue: U = [ u u u ω ] I = [ i i i ] a b c a b c e. he lat poition ae elated to the odel o the echanical pat. In the tanoation atix (5) alo the yte euency need to be known. Coneuently, the conideed odel i o 4 th ode and the conductance atix G ha 4 4 ize [8]. he elation (13) i applied o iteative olution o the whole odel in the conecutive tie tep. hat i euivalent to the known Newton iteation outine o AP, ued o inding a olution point o nonlinea coponent o the cicuit. Howeve, eal eaction o the intenal induction oto odel to given voltage i calculated accoding to the above deived odel: o peault and ate-ault condition epectively. In the geneal cae when the odel i nonlinea the atix G (tane conductance) hould be upgaded in each iteative tep. In a linea odel a in the conideed cae thi atix et unchanged and need to be ecalculated only at the beginning and duing ault inception due to the topology and algoith changing.

4 1 Figue 4. Stuctue o the EMP ype 94 induction oto odel he ype-94 pocedue i witten in MODELS code and, theeoe, the odel tat at t = and initial teady-tate condition could not be autoatically calculated. Howeve, the eleent ha additional echani o ineting the teady-tate initial condition (voltage and cuent Figue 4) to the intenal pocedue. hi enable tat o the iulation o dieent initial tate. V. SIMULAION RESULS he uiel cage induction oto wa ued in the iulation tet. hat wa the oto o 2MW powe with upply voltage 1kV and electical paaete: tato eitance R =.367Ω, tato inductance X l =.11482Ω, oto eitance, R = Ω, oto inductance X l =.11482Ω, utual inductance X =.494Ω. Stuctue o iulation odel i peented in Fig. 5. M cable - 2k 1kV 11kV Figue. 5. Stuctue o iulation odel he ai o iulation wa to veiy the given auption and to check the obtained eult with a iila data available o the liteatue. It i conideed to uthe ue o thi odel o invetigation o potection algoith. Selected waveo obtained duing iulation ae peented below. Figue 6 peent typical waveo elated to tat-up o the oto. Moto tat unde no-load condition and next, at t = 2.8 additional load with noinal value wa added. hee waveo wa copaed with the eult obtained o tet with tandad EMP odel. Both eult ae vey cloe each othe. In the econd pat o iulation the inte-tun ault wa conideed. Soe eult can be tack at Fig he ault included 5% o tato phae A winding wa intoduced at t = 3.5. It can be een that the ault cuent take geat agnitude and the negative euence cuent alo appea. It i well Z U g known that appeaance o the negative euence cuent at the upplied cuent i a good detecto to eveal an intenal ault. a) 12 tato cuent [A] tie [] b) 12 oto cuent [A] tie [] c) 7 poitive, neative euence o tato cuent [A] d) 16 angula velocity o oto [ad/] tie [] tie [] I 1 I electoagnetic toue [kn] Figue 6. Siulation o induction oto (without a ault) a - tato cuent, b oto cuent, c poitive and negative euence o tato cuent, d - angula oto velocity an electoagnetic toue.

5 It in t had to ee, that intoducing an additional eito into the hot cicuit chee caue the educing o ault cuent and alo the negative euence o tato cuent. b) ault cuent [A] tie [] c) 15 poitive, neative euence o tato cuent [A] d) angula oto velocity [ad/] tie [] ω e tie [] Figue 7. Siulation o induction oto with tun to tun ault (5% hoted tun and = ) a - tato cuent, b ault cuent, c poitive and negative euence o tato cuent, d - angula oto velocity an electoagnetic toue. I 1 I electoagnetic toue [kn] he potection ha to be deigned in uch a way o that it doen t wok duing the tat - up when the tating cuent i eveal tie bigge o ated cuent. Howeve, it ha to wok when in the poce o tat - up hot cuent occu. In ode to identiy uch a tate, it i vey handy to ue inoation caied in theelve by yetical coponent. In can be een a well that tun-t-tun ault have big inluence on echanical value, epecially on angula peed o oto and the echanical toue, which with doubled netwok euency change both the value o itel and diection Siulation eult o thi cae i hown in Fig. 7d. and Fig. 9e. a) 25. tato cuent [A] tie [] b) 1.5 ault eitance [ Ω ] tie [] c) 2 ault cuent [A] tie [] Figue 8. Siulation o induction oto with tun to tun ault (5% hoted tun and - nonlinea) a - tato cuent, b- ault eitance, c ault cuent.

6 d) 15 poitive, neative euence o tato cuent [A] e) angula oto velocity [ad/] tie [] ω I 1 I 2 e tie [] Figue 9. Siulation o induction oto with tun to tun ault (5% hoted tun and - nonlinea) d poitive and negative euence o tato cuent, e angula oto velocity an electoagnetic toue. Poitive and negative euence tato cuent ae popotional to pecent nube o hoted tun. he cuent at the oto teinal inceae along with gowing nube o hoted tun. Relation between poitive and negative euence cuent v. hoted tun i peented in Fig. 1. poitive, negative euence o cuent in the oto teinal [A] Figue 1. Poitive and negative euence cuent v. hoted tun ( = ) electoagnetic toue [kn] VI. CONCLUSIONS he poble elated to odelling o induction oto, and paticulaly tun-to-tun ault in tato winding ae peented in the pape. he odel wa pepaed by uing o the AP EMP poga. Included iulation eult how it undaental popetie duing tanient. It can be concluded that the popoed ethod give a handy to ue tool which enable to analye the ault induced tanient in induction achine. he utue wok will ocu on wide analyi o the intenal tuctue o oto and pat o the netwok, which enable to conduct a eie o eeach and iulation o the ange o phae to phae ault and gound ault in induction oto, that on the baic o an analyi o the accopanying powe yte potection. REFERENCES [1] M. Akan, D. K. Peovic, and P. J. Unwoth, Modelling and iulation o induction oto with inte-tun ault o dignotic, Electic Powe Syte Reeach 75, 25, pp [2] M. Akan, D. K. Peovic, and P. J. Unwoth, Online tato ault diagnoi in induction oto, IEDEE poceeding on electical powe application, Vol. 148, No. 6, 21, pp [3] F. Biz, M. W. Degne, A. Zaaon, and J. M. Gueeo, On-line tato winding ault diagnoi in invete-ed ac achine uing high euency ignal injection, 37th IAS Annual Meeting and Wold Coneence on Indutial application o Electical Enegy, 22, pp [4] S. M. A. Cuz, and A. J. M. Cadoo, Stato winding ault diagnoi in thee-phae ynchonou and aynchonou oto, by extended pak vecto appoach, IEEE anaction on Indutial Application, Vol. 37, No. 5, 21, pp [5] M. A. Cah,. G. Habetle, and G. B. Klian, Inulation ailue pediction in induction achine uing line-neutal voltage, IEEE Induty Application Coneence, hity-second IAS Annual Meeting, IAS 97, 1997, pp [6] H. W. Doel, Electoagnetic anient.poga. Reeence Manual. BPA, Potland, Oegon, [7] L. Dubé, How to ue MODELS-baed Ue-deined netwok coponent in AP. EEUG New, No. 1, vol. 3, Feb. 1997, pp [8] J. Eztegalyo, D. Koteev, and L Dubé, he application o ue deined induction achine odel in EMP, IPS 99 Intenational coneence o powe yte tanient, Budapet Hungay 1999, pp [9] P. Gacia, F. Biz, M. W. Denge, and A. B. Diez, Diagnotic o induction achine uing the zeo euence voltage, Poceeding o the IEEE 39th IAS Annual Meeting, Seattle, Wahington, 24, pp [1] S. B. Lee, R. M. alla, and. G. Habetle, A obut, on-line tunault detection techniue o induction achine baed on onitoing the euence coponent ipedance atix, IEEE anaction on Powe Electonic, Vol. 18, No. 3,23, pp [11] R. M. alla,. G. Habetle, and R. G. Haley, anient odel o induction achine with tato winding tun ault, IEEE anaction On Induty Application, Vol. 38, No 3 22, pp [12] J. S. hoen, and C. S. Kalleoe, Stato ault odelling o induction oto Intenational Sypoiu on Powe Electonic, Electical dive, Autoation and otion, Speeda 26, pp.6 11.