Modelling and simulation of induction motors with inter-turn faults for diagnostics

Transcription

1 Electric Power Sytem Reearch 75 5) Modelling and imulation of induction motor with inter-turn fault for diagnotic M. Arkan a, D. Kotic-Perovic b, P.J. Unworth c, a Inonu Univerity, Engineering Faculty, Electrical Electronic Department, Malatya, Turkey b Dana Corporation, Automotive Motion Technology Ltd., Andover, UK c Univerity of Suex, School of Engineering and IT, Brighton BN1 9QT, UK Received April 4; received in revied form 1 Augut 4; accepted 18 Augut 4 Available online 4 May 5 Abtract Thi paper preent two orthogonal axi model for imulation of three-phae induction motor having aymmetrical winding and inter-turn hort circuit on the tator. The firt model aume that each tator phae winding ha a different number of turn. To model horted tator turn, the econd model aume phae a ha two winding in erie, repreenting the unaffected portion and the horted portion. It ue the reult of the firt model to tranfer phae a to qd o that horted portion i tranferred to the q axi. Simulation reult from the model are in good agreement with other tudie and are compared with experiment carried out on a pecially wound motor with tap to allow different number of turn to be horted. The model have been uccefully ued to tudy the tranient and teady tate behaviour of the induction motor with hort-circuited turn, and to tet tator fault diagnotic algorithm operating in real time. 5 Elevier B.V. All right reerved. Keyword: Induction motor; Turn fault; Modelling; Diagnotic; Orthaogonal axi 1. Introduction Becaue of cotly machinery repair, extended proce down time, and health and afety problem, a trend in modern indutry i to focu attention and reource on fault detection and predictive maintenance trategie for indutrial plant [1,]. It i known that approximately 6% of induction motor failure are caued by failure of the tator winding, and it i believed that thee fault begin a undetected turn-to-turn fault in a coil, which progre to catatrophic phae-to-phae or phae-to-ground hort circuit fault [1,]. To achieve prior warning of failure o that an orderly hut-down may be made to avoid catatrophic failure, horted turn within a tator winding coil mut be detected or predicted [1 5]. Correponding author. addree: markan@inonu.edu.tr M. Arkan), dragica.kotic-perovic@dana.com D. Kotic-Perovic), p.j.unworth@uex.ac.uk P.J. Unworth). Modelling of induction motor with horted turn i the firt tep in the deign of turn fault detection ytem []. Simulation of tranient and teady tate behaviour of motor with thee model enable correct evaluation of the meaured data by diagnotic technique. The aymmetrical induction machine ha been a ubject of coniderable interet. Brown and Butler [6] have utilized ymmetrical component theory to etablih a general method of analyi for operation of polyphae induction motor having aymmetrical primary connection. Jha and Murthy [7] have utilized rotating field concept to develop a generalized theory of induction machine having aymmetrical winding on both tator and rotor. Winding-function-baed model preented in Ref. [8,9], and model preented in Ref. [1,] need motor geometrical deign parameter. The generalized theory of electrical machine incorporating orthogonal or qd axi theory i generally accepted a the preferred approach to almot all type of tranient and teady tate phenomena [1]. The analyi of machine i greatly facilitated by the tandard tranformation /$ ee front matter 5 Elevier B.V. All right reerved. doi:1.116/j.epr

2 58 M.Arkan et al./ Electric Power Sytem Reearch 75 5) to qd axi. The ame tranformation proce can be applied to machine in which there are phae unbalance [1]. Hence, it i ueful to extend thi approach to alo incorporate problem encountered with aymmetrical induction motor. The aim of thi paper i to preent a ueful and traightforward method to imulate inter-turn hort circuit for diagnotic purpoe. The fault can be imulated by diconnecting one or more turn making up a tator phae winding [9,14]. Firtly an induction motor model with unequal number of tator turn ha been developed. Then uing thi model, a econd model ha been developed to imulate tator inter-turn hort circuit. Model are imulated in Matlab Simulink and imulation reult are preented. Reult obtained are confirmed with a conventional aymmetrical motor model in a three-phae, non-orthogonal bae, and by experimental reult obtained from a pecially wound motor.. Induction motor model with different number of tator turn The model for a ymmetrical three-phae induction motor i well known [15 18]. To derive equation for aymmetrical tator winding and rotor, the following aumption have been made: = r r1 r 1 where r qd = r1 r r and matrix element r1 r r are given in Appendix A and auming r ar = r br = r cr = r r, r r qd = r r I x. In matrix notation, the flux linkage of the tator and rotor winding may be written in term of the winding inductance and the current a [ ] [ ][ ] λ L i = ) λ r L r where tator and rotor L aa L ab L ac inductance are = L ba L bb L bc, and = L ca L cb L cc L arar L arbr L arcr L brar L brbr L brcr Becaue of ymmetry, tator L crar L crbr L crcr mutual inductance have L ab = L bac, L ac = L ca and L bc = L cb. Similarly rotor elf- and mutual inductance have L arar = L brbr = L crcr, and L arbr = L arcr = L brar = L brcr = L crar = L crbr, repectively. Thoe of the tator-to-rotor mutual inductance are dependent on the rotor angle orientated with repect to tator), therefore L aar co θ r L abr co θ r + π ) L acr co θ r π ) L bar co θ r π ) L bbr co θ r L bcr co θ r + π ) 4) L car co θ r + π ) L cbr co θ r π ) L ccr co θ r i r each tator phae of the motor ha a different number of turn, but uniform patial diplacement i aumed; magnetic aturation i not preent. With the appropriate ubcript a, b, c, ar, br, and cr, the voltage equation of the magnetically coupled tator and rotor circuit can be written a follow: v = r i + pλ, = rr ir + pλr 1) where p = d/dt. Applying a tationary reference frame tranformation to thi equation yield the correponding qd equation and Eq. 1) become v qd = r qd i qd + pλ qd, 1 = r r qd ir qd ω r 1 λ r qd + pλr qd ) and L r = Lr where ) mean the tranpoe of the matrix. The coefficient L aar, L abr, L acr, L bar, L bbr, L bcr, L car, L cbr, and L ccr are peak value of tator-to-rotor mutual inductance. Becaue of rotor ymmetry L aar = L abr = L acr, L bar = L bbr = L ccr, and L car = L cbr = L ccr. The tator and rotor qd flux linkage are obtained by applying tranformation to the tator and rotor flux linkage in Eq. ), that i λ qd = L qd i qd + Lr qd ir qd, λ r qd = Lr where 1 qd i qd + Lrr qd ir qd 5) 1 1 qd =, L qd =, qd =, and

3 L r qd = qd, Lr qd, Lrr qd M.Arkan et al./ Electric Power Sytem Reearch 75 5) Matrix element of, and Lr qd are given in Appendix A. Normally, an induction machine i connected to a threephae upply by a three-wire connection i.e. neutral current doe not flow). Hence, for a quirrel cage induction machine and three-wire connection, the tator and rotor flux linkage in Eq. 5) may be expreed compactly a λ q λ d λ r q λ r d = Determination of inductance In order to define aymmetrical machine inductance, aume tator phae a, b and c have number of winding turn given by N a, N b, and N c, repectively, and that rotor phae ar, br and cr have winding turn given by N ar = N br = N cr = N r. If elf- and mutual inductance are known for a ymmetrical machine with reference number of turn N, new parameter for an aymmetrical machine can be defined from thee inductance value a decribed in [,15,18]. By uing known parameter the tator elf-inductance for phae a, b and c can be calculated a L aa = N a N i q i d i r q i r d 6) L l + ) L m = Na L ml 7) L bb = N b L ml 8) L cc = N c L ml 9) ) where L ml = 1 L l + L m. The tator mutual inductance between phae a and b, b and c, and c and a can be derived a L ab = L ba = 1 ) N an b L m N ) = 1 N a N b L m = N a N b L m 1) Therefore L arar = L brbr = L crcr = L lr + Nr L m = L lr + L mar 1) where L mar = Nr L m. For the ame reaon, rotor mutual inductance are alo equal to each other and given by L arbr = L arcr = L brar = L brcr = L crar ) 1 N ) r = L crbr = L m = 1 L mar 14) N Previouly defined tator-to-rotor mutual inductance can be defined in term of new parameter. Becaue of rotor ymmetry turn number for each rotor phae are equal) mutual inductance will be L aar = L abr = L acr, L bar = L bbr = L bcr, and L car = L cbr = L ccr. Referring to Fig. 1, we can ee that the rotor phae ar i diplaced from tator phae a by the electrical angle θ r, where θ r i a variable. The correponding mutual inductance will vary with θ r. The variable ine and coine factor are already preent in Eq. 4), o peak mutual inductance will be L aar = L abr = L acr = L bar = L bbr = L bcr = L car = L cbr = L ccr = where L mr = N r L m. N a N r L m = N a L mr 15) N b N r L m = N b L mr 16) N c N r L m = N c L mr 17).. Simulation of the aymmetrical induction motor In thi ubection, equation are rearranged for the aymmetrical induction motor model that ha been developed. The qd-applied voltage in a reference frame fixed to the tator can be obtained from the tator phae voltage v a, v b, and v c by tandard tranformation [17]. The qd voltage will be L ac = L ca = N a N c L m ) L bc = L cb = N b N c L m 1) L m where L m = 1. The rotor elf- and mutual inductance can be found by a imilar way. Becaue the rotor i aumed ymmetric, the total elf-inductance of rotor phae ar, br and cr are equal. Fig. 1. Induction machine winding diplacement.

4 6 M.Arkan et al./ Electric Power Sytem Reearch 75 5) v q = [ v a 1 ] v b + v c ) = [ v ag 1 ] v bg + v cg ), v d = 1 v b + v c ) = 1 v bg + v cg ) 18) where v ag, v bg, and v cg are upply phae voltage. Flux linkage may be obtained from Eq. ) for a threewire ytem to give λ q = v q r i q r 1 i d )dt, λ d = v d r 1 i q r i d )dt, λ r q = ω r λ r d rr r ir q )dt, λ r d = ω r λ r q + rr r ir d )dt 19) The current can be found by inverting Eq. 6). The peed of the machine can be obtained from the torque equation a ω r t) = P T em + T mech T damp )dt ) J T em i the electromagnetic torque impreed on the haft of the machine and can be expreed a T em = P λ d i q λ q i d ) 1) T mech i the externally applied mechanical torque in the direction of the rotor peed, T damp i the damping torque in the oppoite direction of the rotor peed, and J i inertia. By uing Eq. 18) 1) with reitance and inductance that are defined in Appendix A, a motor with aymmetrical winding can be imulated. The compact model for the imulation of the aymmetrical motor i hown in Fig.. Reult of imulation in Fig. are fed to a diagnotic block that ue negative equence current to diplay motor condition. Supply voltage and motor current are decompoed into their poitive and negative equence component by uing a power decompoition technique [19] and the condition of the motor i analyed uing a method that ha been decribed in [,4,].. Induction motor model with inter-turn tator hort circuit In order to develop an induction motor model with a tator inter-turn hort circuit, it ha been aumed that phae a ha two winding in erie compriing N u unhorted turn and N h horted turn), where N a = N u + N h = N, the overall number of turn N. The phae b and c have N b = N c = N. By auming the unequal number of tator turn, the firt model can be ued for induction motor model with inter-turn hort circuit to tranfer motor equation from axe to qd axe. By doing thi, the N h turn horted winding can be introduced in qd axe. The fault everity can be changed by varying the number of horted turn, and by a current limiting reitance acro the hort circuit winding. The ame aumption that were made for the firt model are valid for thi model a well. In the following, the modification of equation for the new model i preented. The elf-inductance for phae a, b, and c in Eq. 7) 9) will be L aa = N u N + N h N L l + ) L m + N u N h L l + ) L m = N u L ml + N u N h L mh ) L m +N u N h L mh + h L ml) = L aa + L ah) + L ah + L hh ) ) where L mh = L m winding). L bb = L cc = N N and ubcript h i ued for horted L l + ) L m = L ml ) A it can be een from Eq. ), the phae a elf-inductance contain the unhorted elf-inductance L aa, the mutual inductance between unhorted and horted turn L ah, and the horted turn elf-inductance L hh. The tator mutual inductance will be ) L ab = 1 N a N L m = 1 N u L m 1 N h L m N N = L ab + L hb 4) L ac = L ba = L ca = L ab + L hb, L bc = L cb = 1 L m 5) Fig.. Simulation of aymmetrical induction motor model. The tator-to-rotor mutual inductance in Eq. 15) 17) will be

5 M.Arkan et al./ Electric Power Sytem Reearch 75 5) L ar = L aar = L abr = L acr = = N u N r L m + N a N r L m N h N r L m = L aar + L har 6) L br = L bar = L bbr = L bcr = L car = L cbr = L ccr = N N r L m 7) A in the previou ection, auming that tator winding have different number of turn, dq axe inductance can be obtained for an inter-turn hort circuit condition by uing the newly defined elf- and mutual inductance. The tranformation of qd = qd = to L qd and Lr to Lr qd are and 8) where = L q + Lh q ) + Lh q + Lh q ),L = L d,lr = q + Lhr q and = Lr d. Similarly, the reult of tranformation of rotor elf- and mutual inductance can be implified a qd = and L r qd =.5 1 9) where = Lr q and Lrr = Lr d. Matrix element are given in Appendix A. The tator and rotor flux linkage for the new model of a quirrel cage induction motor will be λ h q L h q h q L hr q i h q λ q h q L q q i q λ d = L d d i d ) λ r q L hr q q L r q i r q λ r d d L r d i r d The tator phae reitance are r a = N a r = N u r + N h r = r a N N N + r h 1) r b = r c = r ) Fig.. Motor model with inter-turn tator hort circuit. where r h i the horted winding) reitance. Stator qd reitance for new model will be r h q r h rq = r r1 ) r1 r r d The horted portion of the tator winding h) i een to only appear in the q-axi element. The matrix element are given in Appendix A. Fig. how the motor model with an interturn hort circuit, which only effect part of the q-axi tator winding. r ext i an external hort circuit current limiting reitance. Flux linkage may be obtained from Eq. ) for a threewire ytem in the tationary reference frame to give = λ h q v h q r hi h q )dt, λ q = v q vh q r i q r 1 i d )dt, λ d = v d r 1 i q r i d )dt, λ r q = ω r λ r d rr r ir q )dt, λ r d = ω r λ r q + rr r ir d )dt 4) Note that v h q will be zero if the external reitance r ext i zero. The current can be found by inverting Eq. ). 4. Simulation reult The model developed have been imulated in Matlab Simulink and the following imulation reult are for a hp motor whoe parameter are given in Appendix A. The reult are taken during acceleration from tand till to full peed. Fig. 4 and 5 are reult for acceleration from tand till to full peed at full load under normal condition. Initially, motor current are not ymmetrical becaue of the tarting

6 6 M.Arkan et al./ Electric Power Sytem Reearch 75 5) Fig. 4. Torque and peed variation. tranient. Thi introduce high negative equence current until the motor reache full peed. Fig. 6 and 7 how the imulation reult from tand till to full peed at full load with five turn horted. The upply negative equence current i around 4 ma. Becaue of tator aymmetry, the torque graph in Fig. 6 how the expected pulation at twice upply frequency f ) even at teady tate. Thi i becaue the negative equence current introduce a braking torque in the motor. The hort circuit current of 6 A in the horted turn een in Fig. 7 i.6 time the normal locked rotor current of A. Fig. 8 and 9 are for ame condition but with an external 1.5 reitance to limit hort circuit current to avoid detruction of the motor. Thi limit hort circuit current to nearly A, and upply negative equence current to 7 ma. The torque till ha pulation f but i much maller a een in Fig. 8. Fig. 6. Torque and peed variation with five turn horted. Fig. 7. Poitive equence, negative equence, and hort circuit current for five turn horted. Fig. 5. Poitive and negative equence current rm). Fig. 8. Torque and peed variation with five turn horted with 1.5 reitance.

7 M.Arkan et al./ Electric Power Sytem Reearch 75 5) Fig. 9. Poitive equence, negative equence and hort circuit current for five turn horted with 1.5 reitance Comparion of experimental with imulated reult In order to validate the reult from the dynamic model developed, an experimental invetigation wa alo conducted. The reult in Table 1 compare experimental reult with imulation reult obtained for a pecially wound hp motor with up to four turn horted. Experimental and imulated hort circuit current have been limited by uing an external. r ext reitance. I n i motor negative equence current, and I r ext i hort circuit current in the external current limiting reitance. 4.. Relation between horted turn and negative equence current Reult have alo been obtained by imulation for different number of directly horted turn r ext = ). For r ext = negative equence current I n i proportional to the number n of horted turn Fig. 1. Short circuit current v. horted turn for different external reitance value r ext ). circuit current i almot independent of the number of horted turn when external reitance i zero, at.6 time locked rotor current. Thi mean that for a hort circuit fault involving only few turn, the motor will run for a coniderable time, from a few minute to an hour, ince the horted turn can diipate heat into adjacent turn. In addition, a their temperature rie, their reitance increae, and Fig. 1 how that the current reduce quite rapidly with additional reitance within the hort circuit path r ext in the experimental tudy). Fig. preent relation between the number of horted turn, external current limiting reitance, and negative equence current. 4.. Effect of unequal winding temperature If a motor i operated from an unbalanced voltage upply, the heating effect of unequal phae current will caue I n n or I n = kn 5) where k i contant. Fig. 1 how I r ext current in the external reitance and number of horted turn relation with and. external current limiting reitance. A it can be een from figure hort Table 1 Experimental and imulation reult for different number of horted turn with hort circuit current limited externally n Experimental reult Simulation reult I n ma) I r ext A) I n ma) I r ext A) Fig.. Negative equence current v. horted turn for different external reitance value r ext ). Short circuit current limited by,.1,. and.5 reitance.

8 64 M.Arkan et al./ Electric Power Sytem Reearch 75 5) With the motor parameter ued in the imulation ee Appendix A) at rated voltage 4 V and full-load current.7 A, Eq. 4) can be implified to r unb =.69n 41) From imulation reult, r unb =.6n i obtained, which i cloe to the theoretical relation Eq. 41)). Hence a thermal increae in reitance of one phae due to current unbalance) by.69 relative to the other winding will give the ame effect a a ingle turn hort circuit. For the motor ued, thi i a 17% increae, which i equivalent to a 4.5 C increae in temperature in one winding over the other winding. Fig. 1. Negative equence current v. extra erie reitance r unb. reitive unbalance to develop between the phae, whoe contribution to negative equence current could be confued with a tator fault. Thi i now conidered. Auming an additional temperature rie in only one motor phae, it effect may be obtained by conidering an unbalance reitance r unb in erie with tator phae a. The maximum added reitance r unb i 1 which i equivalent to a 61.5 C temperature rie. I n i linearly proportional to r unb ee Fig. 1). I n r unb 6) The relation between r unb and negative equence current can be defined [] a I n = r unb I p Z n + r unb /) 7) where I p i poitive equence current, Z n = r + r r p + jx + X r ), and if Z n r unb the above equation can be implified to I n = r unb I p Z n 8) under balanced upply condition. The relation between negative equence and the number of horted turn n i preented in [] a I n = n V p 9) 8 N Z where V p i the applied poitive equence voltage, N the total number of turn, n the number of horted turn, and Z = r + jx. The relation between r unb and n to give the ame negative equence current can be defined from Eq. 8) and 9) r unb n = 9 1 Z n V p 4) 8 N Z I p 5. Concluion Two model have been developed for analying an aymmetrical induction motor. The model are baed on general machine parameter o that it i not neceary to know detailed motor geometry or phyical layout of the winding. New parameter for aymmetrical condition have been preented. The model have alo been confirmed againt imulation reult obtained from a conventional aymmetrical motor model in a three phae non-orthogonal bae, which require even differential equation. It ha not been preented becaue of pace. Inter-turn fault can be eaily imulated by the model. Fault everity can be controlled by the number of horted turn and an optional current limiting reitance to hort circuit the winding. Simulation reult have been ued in [,4,,1] to check fault detection algorithm for tator fault. The model have been ued to tudy the relation between the number of horted turn and negative equence current, the effect of reitive unbalance between the phae due to the heating effect of unbalanced phae current, and temperature effect on horted turn reitance. Reult confirm that negative equence current and horted number of turn are linearly dependant, and that reitive unbalance can produce comparable negative equence current, o that fault detection algorithm hould be able to ditinguih between the effect of turn hort and thermal unbalance [,4,]. The reult obtained for hort circuit under limited hort circuit current by external reitance) reveal that enitivity depend on number of horted turn and hort circuit current. Acknowledgement The author thank Dr. Peter Lindon for providing a conventional aymmetrical motor model in a three-phae nonorthogonal bae to validate the developed model, and for hi valuable dicuion.

9 M.Arkan et al./ Electric Power Sytem Reearch 75 5) Appendix A A.1. Matrix element for induction motor with different number of tator turn The qd reitance element are: r = r a r b + 1 ) 4 r c 4) r 1 = 6 r b r c ) 4) r 1 = 1 r a r b r c ) 44) r = 1 r b + r c ) 45) r = 1 r a + r b + r c ) 46) r1 = r 1, r = 1 r 1, r 1 = 1 r 1, and r = r 1, where r a = N a r, r b = N b N r, and r c = N c N r, when N a = N b = N c = N, r = r = r = r and r1 = r 1 = r 1 = r = r1 = r =. A.. The tator qd elf- and mutual inductance qd matrix element are: = L aa +.5L bb +.5L cc L ab L ac +.5L bc ) 47) 1 = 1 L bb L cc L ab + L ac ) 48) 1 = L aa.5l bb.5l cc +.5L ab +.5L ac L bc ) 49) 1 = 1.5L bb.5l cc L ab + L ac ) 5) = 1 L bb + L cc L bc ) 51) = 1 L bb + L cc L ab + L ac ) 5) = 1 L aa + L bb + L cc + L ab + L ac + L bc ) 5) and 1 = 1 L 1, and L = 1 L. When N a = N b = N c, N aa = N bb = N cc and N ab = N ac = N bc. By uing Eq. 7) 1) it can be hown that 1 = L 1 = L 1 = L 1 = L = = and L = L = L l + L m, A.. The tator-to-rotor qd mutual inductance = L l. Becaue of rotor ymmetry, the coefficient of tator-to-rotor mutual inductance can be implified a N aar = N abr = N acr = N ar, N bar = N bbr = N bcr = N br, and N car = N cbr = N ccr = N cr, and the tranformation reult i = L ar +.5L br +.5L cr 54) 1 = 4 L br L cr ) 55) = 4 L br + L cr ) 56) 1 =.5L ar.5l br.5l cr 57) 1 = Lr 1, and Lr = Lr 1. When N a = N b = N c = N, L aar = L abr = L acr = L bar = L bbr = L bcr = L car = L cbr = L ccr and mutual inductance will be = Lr = N r N L m and 1 = Lr 1 = Lr 1 = Lr =. A.4. The rotor qd elf- and mutual inductance The rotor elf- and mutual inductance are = Lrr = L lr + L mar = L lr + N r L m 58) = L lr 59) A.5. Matrix element for induction motor with inter-turn tator hort circuit The tator qd elf- and mutual inductance: From 49) and 5), the tator qd elf- and mutual inductance can be defined a follow = L aa +.5L bb L ab +.5L bc ) = [ L aa +.5L bb + L bc ) L ab ) + L ah L hb )] + [L hh + L ah L hb )] = L q + Lh q ) + Lh q + Lh q ) 6) = 1 L bb + L cc L bc ) = L bb L bc = L l + L m = L d 61) The tator-to-rotor qd mutual inductance: From 54) and 55), the tator-to-rotor qd mutual inductance can be defined a follow: = L ar +.5L br +.5L cr = L ar +.5L br = L ar +.5L br) + L har = q + Lhr q 6)

10 66 M.Arkan et al./ Electric Power Sytem Reearch 75 5) = 4 L br + L cr ) = L br = d 6) The rotor elf- and mutual inductance and reitance will be the ame a before. A.6. Motor parameter Reliance motor parameter: Line voltage 46 V Total number of turn per 5 phae Full load line.7 A Stator winding reitance 4.5 current Hore power hp Stator leakage inductance 1.97 mh Rated peed at 175 rpm Rotor reitance tator.6 6 Hz referred) Number of pole 4 Rotor leakage inductance 1.97 mh tator referred) Power factor.815 Magnetiing inductance mh Service factor 1.15 Rotor inertia.6 kg m Reference [1] W.T. Thomon, A review of on-line condition monitoring technique for three-phae quirrel-cage induction motor pat preent and future, in: Proceeding of the 1999 IEEE International Sympoium on Diagnotic for Electrical Machine, Power Electronic and Drive, IEEE SDEMPED 99, 1999, pp. 18. [] M. Arkan, Stator Fault Diagnoi in Induction Motor, Univerity of Suex, Ph.D. Thei,. [] R.M. Tallam, T.G. Habetler, R.G. Harley, Tranient Model for Induction Machine with Stator Winding Turn Fault, in: Proceeding of the IEEE Indutry Application Conference 5th Annual Meeting- World Conference on Indutrial Application of Electrical Energy, Rome, Italy, October,. [4] M. Arkan, D. Kotic-Perovic, P.J. Unworth, Online tator fault diagnoi in induction motor, IEE Proceeding: Electric Power Application 148 6) 1) [5] G.B. Kliman, W.J. Premerlani, R.A. Koegl, D. Hoeweler, A New Approach to On-Line Turn Fault Detection in AC Motor, in: IAS Annual Meeting, October 1996, 1996, pp [6] J.E. Brown, O.I. Butler, A general method of analyi of three phae induction motor with aymmetrical primary connection, Proc. IEE 1 195) 5 4. [7] C.S. Jha, S.S. Murthy, Generalied rotating-field theory of woundrotor induction machine having aymmetry in tator and/or rotor winding, Proc. IEE 1 8) 197). [8] X. Luo, Y. Liao, H.A. Toliyat, T.A. Lipo, Multiple coupled circuit modelling of induction machine, IEEE Tran. Ind. Appl. 1 ) 1995) 17. [9] H.A. Toliyat, T.A. Lipo, Tranient analyi of cage induction machine under tator, rotor bar end ring fault, IEEE Tran. Energy Conver. 1 ) 1995) [1] G.M. Jokimovic, J. Penman, The detection of inter-turn hort circuit in the tator winding of operating motor, IEEE Tran. Ind. Electron. 47 5) ) [] S. Williamon, K. Mirzoian, Analyi of cage induction motor with tator winding fault, IEEE Tran. Power Apparatu Syt. PAS-14 7) 1985) [1] A. Conoli, T.A. Lipo, Orthogonal axi model for aymmetrically connected induction machine, IEEE Tran. Power Apparatu Syt. PAS-11 1) 198) [1] A.K. Wallace, E.S. Ward, A. Wright, Source of harmonic current in lip-ring motor, Proc. IEE 11 1) 1974). [14] M.Y. Chow, Methodologie of Uing Neural Network and Fuzzy Logic Technologie for Motor Incipient Fault Detection, World Scientific Publication, 1997, ISBN [15] D.W. Novotny, T.A. Lipo, Vector Control and Dynamic of AC Drive, Clarendon Pre, Oxford, [16] P. Kraue, O. Waynczuk, S.D. Sudhoff, Analyi of Electric Machinery, IEEE Inc, 1995, ISBN [17] P. Va, Vector Control of AC Machine, Oxford Science Publication, [18] C.M. Ong, Dynamic Simulation of Electric Machinery, Prentice Hall PTR, 1998, ISBN [19] S.P. Huang, Active Main Supply Harmonic Filtering, Univerity of Suex, Ph.D. Thei, [] M. Arkan, P.J. Unworth, Stator fault diagnoi in induction motor uing power decompoition, in: Phoenix, USA, October, Proceeding of the IEEE Indutry Application Conference 4th Annual Meeting, 1999, vol., pp [1] D. Kotic-Perovic, M. Arkan, P.J. Unworth, Induction motor fault detection by pace vector angular fluctuation, in: Proceeding of IEEE Indutry Application Conference 5th Annual Meeting-World Conference on Indutrial Application of Electrical Energy, Rome, Italy, October,.