Development of a Symmetrical Multi-Phase Synchronous Machine Model for Real-Time Digital Simulation

Transcription

1 Development of a Symmetrical Multi-Phae Synchronou Machine Moel for Real-ime Digital Simulation A. B. Dehkori Abtract Multi-phae electric machine have the avantage of fault tolerance, reliability an reuction in the torque ripple. Such propertie make them attractive for application uch a electric hip propulion, traction, aircraft ytem, electric vehicle []-[]. Failure of the rive ytem through a few phae coul be tolerate by operating the remaining phae of the machine. Moeling of multi-phae machine for real-time igital imulation i an important tep in enhancing thee imulator for application uch a electric hip propulion an new cheme in win generation. hi paper preent evelopment of a ymmetrical multiphae (three or more phae) ynchronou machine moel for the Real-ime Digital Simulator (RDS ). he paper tart with the introuction an analyi of ymmetrical multi-phae machine. he extenion of two-reaction theory to multi-phae machine i preente. he evelope moel allow the uer to chooe the number of tator phae. he moel i valiate uing off-line numerical imulation. Aitional control component are evelope to enhance the application of thi moel in multi-phae ytem. Keywor: real-time igital imulation, ynchronou machine, ymmetrical component, multi-phae, two reaction theory, igital tranient network analyzer, win generation I I. IRODUCIO n conventional power ytem application, the number of phae i three a it generally reult in a lower tranmiion cot. Hitorically 3-phae ytem are electe for tranmiion an electric machine in both generation an loa. When it come to application where the electric machine i connecte to power electronic converter, there i no nee to be retricte to a ytem with 3 phae []. Hitorically, electric machine with higher number of phae (multi-phae machine) were introuce to lower ripple in electric torque, an alo for their lower current rating. In fact, the later wa a reaon that promote the evelopment of multi-phae machine in early tage of breaker evelopment. Aitionally, lower current rating per phae allow the eployment of power electronic converter with lower rating. In aition to lower torque ripple an lower current rating, multi-phae machine have other avantage uch a higher force enity, reuction in the noie characteritic an the tator copper loe []. Reliability an fault tolerance i another benefit of multi-phae machine. A Few phae can be A. B. Dehkori i with RDS echnologie Inc., Winnipeg, Canaa ( ehkori@rt.com). Paper ubmitte to the International Conference on Power Sytem ranient (IPS7) in Seoul, Republic of Korea June 6-9, 7. lot yet the machine can till be operate utilizing the remaining phae by proviing proper excitation through power electronic converter. For the above reaon, multi-phae machine have application in electric hip propulion, traction, aircraft ytem, electric vehicle []-[3] an new cheme of win turbine. here are variation of multi-phae machine uch a plit-phae, ual tator, higher orer ymmetrical, etc. which can be tuie in literature. A Real ime Digital Simulator (RDS) i a combination of computer harware an oftware eigne pecifically for the olution of power ytem an power electronic electromagnetic tranient in real time. here are many area where thi technology ha been uccefully applie. Moeling of multi-phae machine for real-time igital imulation i an important tep in enhancing thee imulator for the above mentione application. Moeling of multi-phae machine poe a few challenge epecially when it come to real-time igital imulation; one of the main problem i the iverity of thee moel. Even if the phae are iplace in a ymmetric manner, the number of phae may vary between 3 to 8 or even more [4]. Developing an maintaining a large number of machine moel in the library of any commercial oftware i challenging an time-conuming. If the moel are evelope irectly in the phae omain, not only it become a teiou tak to form the inuctance matrix of the machine, but alo it create a large computational buren for the imulation tool. A comprehenive analyi in rotor frame of reference eem neceary a it repon to the quetion of general analyi of multi-phae machine. ote that, in practical application, thee machine are riven by power electronic converter, therefore, moel nee to be implemente with a maller imulation time-tep of few microecon. hi make the moeling in rotor frame of reference more attractive. hi paper preent the evelopment of a multi-phae ynchronou machine moel for real-time igital imulation. he paper tart with the introuction an analyi of ymmetrical multi-phae ynchronou machine. Differential equation of a ymmetrical multi-phae ynchronou machine are ecribe an challenge of moeling an analyi in thee machine are outline. wo reaction theory [5]-[6] i reviewe an it extenion for multi-phae machine i ecribe. A general in rotor frame of reference i preente from which a tranient multi-phae (three or more phae) ynchronou machine moel i evelope an incorporate into the network olution of the RDS real-time igital imulator. he moel i valiate through comparion with an off-line phae omain olution. Capabilitie of the

2 moel uch a flexibility in electing the number of phae are ecribe. II. AALYSIS OF SYMMERICAL MULI-PHASE SYCHROOUS MACHIES hi ection briefly ecribe the analyi an moeling metho of ymmetrical multi-phae ynchronou machine. Since the goal i incorporation of the moel into an electromagnetic tranient program, the couple electric approach i ue for moeling of thi type of machine. hi mean that the machine i coniere a an iealize Park machine auming inuoial itribution for the magnetomotive force an permeance. A. General Decription of a Symmetrical Multi-Phae Synchronou Machine Similar to an orinary 3-phae ynchronou machine, a multi-phae ynchronou machine conit of tator wining known a armature, mounte in tator lot an a fiel wining woun on the rotor. Alo, imilar to a 3-phae ynchronou machine, a amper gri or a et of amortieur wining (which conit of copper or bra ro embee in the pole face) i provie to amp pee eviation. In a ymmetrical multi-phae ynchronou machine, magnetic axe of tator wining are iplace by the electrical angle of δ = π/ where i the number of tator phae. here are alternative arrangement uch a ual woun ynchronou machine [7][8] with two et of arbitrarily iplace 3-phae wining which i not the ubject of thi paper. Fig. how the iagram of an iealize -phae ynchronou machine. Wining a, b n with angular iplacement of δ = π/ repreent tator wining. In an iealize ynchronou machine, in the abence of tructural aymmetrie, the behavior of the amper gri can be repreente by wining on rotor - an q-axe. hi i hown by wining k an k in Fig.. he fiel wining i r repreente by a wining on the rotor -axi. Fig.. δ = π ( ) i c v c v b ω r i b qr v fr θ r v a i fr i a kr kqr Diagram of an iealize -phae ynchronou machine. B. Voltage an Flux Linkage Equation Bae on the above ecription of a ymmetrical multiphae ynchronou machine, voltage an flux linkage v n i n equation of thi type of machine are evelope. he following aumption are mae in thi analyi: A multi-pole ynchronou machine i moele a an two pole machine. It i aume that the machine wining prouce a inuoial MMF, an permeance i inuoially itribute; therefore, pace harmonic are ignore. By the efinition of ymmetry, tator wining are iplace with the electrical angle of δ = π/. For all tator wining, phae reitance an leakage inuctance are equal. Voltage an flux linkage equation for a -phae ynchronou machine are preente in (). Equation () how the relation between vector of voltage, current an flux linkage of the machine. Here, vector of tator voltage, current an flux linkage are hown by v ab n, i ab n an ψ ab repectively. A imilar arrangement i mae for rotor n quantitie. v ab n r i ab n ψ ab n v = + q r i r r q t ψ r q r ψ L L ab n r i = ab n ψ q L L r i r rr q r where: () ( f ) = ( f f f ab n a b n) ( f q) = ( f f f f r r qr qr ) r Self-inuctance matrice of tator an rotor are hown by [L ] an [L rr]. [L r] i the matrix for the mutual inuctance between the tator an rotor wining. he value of thee inuctance are function of rotor poition θ r an aturation. A an example, the tator inuctance matrix [L ] i hown in (). Here, L l i the tator wining leakage inuctance an i the number of tator wining. Inuctance value M an L are function of wining itribution, effective number of turn, effective air-gap length an aturation. A mentione previouly, higher orer pace harmonic of the machine are ignore. Similarly, equation for rotor inuctance an mutual inuctance between tator an rotor can be evelope which i not mentione here. aking into account thee time-varying inuctance matrice, the et of ifferential equation in () can be olve irectly in the phae-omain an incorporate into the network olution of electromagnetic tranient program [9][]. Although thi approach i numerically uperior, it ha the rawback of being computationally extenive. he phae omain inuctance matrix of the machine nee to be inverte every time-tep an conuctance matrix of the machine continuouly nee to be compute an pae to the network olution [9][]. ormally thee machine are inverter riven an becaue of high frequency PWM witching, the imulation nee to be performe with the timetep of ~3 µ. Furthermore, it woul be very ifficult for

3 orinary uer of imulation package to acquire enough eign ata to calculate contant uch a M an L. Uually, ata for rotating machine i available in the form of for rotor - an q-axe. hu, it i neceary to analyze the ymmetrical multi-phae ynchronou machine in the q frame of reference. L L L L = l + oh + h where: L i k L = l l = ik i k () L ( ) M co ( k i) δ = h ik L = ( ) L co θ ( i+ k ) δ h ik r π δ= ( ) ik,, he two-reaction theory for the analyi of ymmetrical 3- phae ynchronou machine [5] wa propoe by R. H. Park in 99. In thi work, Park generalize the work of Blonel, Dreyfu, Doherty, an ickle an provie a complete analyi for 3-phae machine with multiple rotor. Park tranformation in it non-orthogonal form i hown in (3). π 4π coθ co( θ ) co( θ ) r r 3 r 3 4 P( r) in r in( π r ) in( π θ = θ θ θr ) (3) hi tranformation ha been ue by reearcher to analyze an moel multi-phae machine with triple number of phae (e.g. 3, 6, 9, etc.) [7]-[8]. Alternative tranformation have been propoe for 5-phae machine coniering the thir harmonic of the air-gap MMF []. At the ame time that R. H. Park preente the two reaction theory on 3-phae machine, Yu H. Ku analyze 3-phae machine [] uing operational calculu an Fortecue ymmetrical component []. he avantage of the two reaction theory over Ku metho i that it ue real tranformation wherea Fortecue ymmetrical component tranformation an forwar-backwar tranformation propoe by Ku are complex tranformation. hi coul have been one of the reaon that Ku metho i not a popular toay. he avantage of hi metho, however, i the fact that ymmetrical component tranformation i applicable to a ytem with any number of phae. hi allowe Ku to exten the two reaction theory to ymmetrical multi-phae machine [5]. If one applie the ymmetrical component tranformation to the magnetizing part of the tator elf-inuctance matrix (i.e. [ L oh ] an [ L h ] hown in ()), the reulte matrice will be iagonal with non-zero element only on the poition correponing to poitive an negative equence. hi i true for ymmetrical ynchronou machine with any number of phae. From the equence omain, ifferential equation of machine can be brought up to the general tator two-phae quantitie (αβ) an ultimately to the rotor two reaction component (q). Appenix II provie the neceary tranformation. hi proce of calculation i lengthy an it i not outline in thi paper. An i provie in Fig. which ecribe the ifferential equation of the ynchronou machine in rotor two reaction component (q). v vq i ωψ r q ωψ i r q i r r L l Ψ t r L l Ψ t q v L i u t Ψ r v L u u u Fig.. t Ψ L m Lmq L lfkr L lfr i fr L lkr r fr Ψ r kr :af t fr :ak v fr L lkqr r kqr -axi u-axi v fr i kqr Ψ :ak t kqr v kqr L lkqr r kqr vw i kr Ψ t kr v kr i kqr Ψ :ak t kqr v kqr i w i v D-axi Q-axi... Equivalent of an iealize -phae ynchronou machine. r t Ψ r t Ψ w Lw v L v v v w-axi v-axi In Fig., in aition to the well-known - q- an -axe, there exit other zero equence hown by w, u an v. D- q- an -axe component correpon to (+), (-) an () equence in ymmetrical component frame. W, u an v component correpon to other equence in ymmetrical component frame when the number of phae i more than 3. ote that w-axi only exit when the number of phae i even. Depening on the number of phae, aitional u- an v- zero equence may exit. U an v component alway appear in pair. Exitence of thi i a great avantage in moeling ymmetrical multi-phae machine with arbitrary number of phae a the ifferential equation of the zero equence can be olve inepenently. D- an q- axe are alo ientical to the one for 3-phae machine. Meaurement of machine parameter i alo poible through well-known tet [3]. Aitional tet i neee for the meaurement of zero equence propoe here. Such proceure an poible experimental valiation are ubject of future paper. III. IMPLEMEAIO OF HE MULI-PHASE SYCHROOUS MACHIE MODEL IO HE EVIROME OF HE REAL-IME DIGIAL SIMULAOR he RDS imulator i a combination of computer harware an oftware eigne pecifically for the olution

4 of power ytem electromagnetic tranient in real time. Each unit of RDS i calle a rack. Every rack conit of proceor eicate to the olution of the power ytem network, power ytem evice, an control component [4]. Each imulation time-tep i ivie into computation interval an communication interval. Similar to other electromagnetic tranient program uch a EMP an EMDC, Dommel algorithm [6] i ue for icretization of the ytem ifferential equation. Subequently, the noal olution i ue for calculation of noe voltage. Differential equation of power ytem component are icretize to a orton of conuctance an current ource which are pae to the network olution uring a communication interval ( ) every time-tep [4]. hi i how the network olution i olve for the normal time-tep moule ue for general power ytem tuie. Small ime-step Moule: One of the imulation tool in the RDS imulator i calle the mall time-tep moule. hi moule which wa introuce in 5 i uitable for moeling containing converter with high frequency witching uch a PWM [9]. hi moule contain a library of it own incluing power electronic component, electric machine, tranformer, tranmiion line, non-linear element, control component, etc. he mall time-tep network olution a well a component in the are execute with a time-tep of (.4µ ~.5µ). Due to the mall ize of the imulation time-tep an the relative convenience of moeling electric machine in rotor q frame of reference, the interface-bae approach [7], [8] i ue to moel the multi-phae ynchronou machine. In thi approach, a machine i coniere a an external ubnetwork to the main ytem; it receive the terminal voltage at every time-tep, compute wining current an inject them back to the network olution. Special projection an integration technique are ue to make the moel mathematically precie. orque an Mechanical Swing Equation: Per-unit electromagnetic torque i calculate uing (4). A expecte, zero equence o not contribute to electromagnetic torque. If the mechanical wing equation are olve inie the moel, then the following equation a hown in (4) can be ue to calculate the rotor pee. Alternatively, the mechanical wing equation can be calculate uing a multi-ma moel a thi option i available in other machine moel in the library [4]. = Ψ i Ψ i ( ) e q q = H ω+ D ω m e t Feature an Capabilitie of the Moel: With the above ecription, the multi-phae ynchronou machine moel i implemente in the environment of the RDS imulator. hi ection ecribe the capabilitie of thi moel. he baic icon for thi component appear a hown in Fig. 3. he number of phae for the machine can be electe (4) by the uer from a menu. Bae on the electe number of phae, tator terminal an neutral will be available for external connection. Aitionally, an option i available to acce both en of each tator wining a hown in Fig. 3. hi option allow uer to connect both en of tator wining to power electronic converter a eire in particular configuration []. Fig. 3. he icon for multi-phae ynchronou machine moel. he moeling technique can be applie to any number of phae, an in fact the moel i tete for up to phae. However, for practical reaon, the number of phae will be limite to 6 for the mall time-tep verion of the moel. Similar to other machine moel in the library, mechanical wing equation can be olve either inie the moel or outie uing a multi-ma moel. Fiel excitation voltage can be receive in normal unit from the excitation ytem [4]. Magnetic aturation i alo incorporate into thi moel [8]. he machine accept - an q-axi ata both in the form of reactance an time contant. Another menu receive machine zero equence reactance an reitance in pu. ABLE I how the approximate execution time (on a PB5 proceor [4]) for the machine with ifferent number of phae. ABLE I EXECUIO IME VS UMBER OF PHASES umber of Phae Execution ime (µ) IV. VALIDAIO OF HE MODEL AD IME-DOMAI SIMULAIO RESULS hi ection provie valiation for the multi-phae ynchronou machine moel preente in thi paper. he focu of thi ection i to provie valiation for the capability of the propoe moel in accurately olving the ifferential equation of a ymmetrical multi-phae ynchronou machine tate in () an (). o valiate the performance of the propoe moel in tranient conition, a mall off-line tan-alone electromagnetic tranient program incluing a tan-alone multi-phae ynchronou machine moel i evelope. In orer to provie a valiation to the analyi which i provie

5 in Section II an the - q- an aitional zero equence provie in Fig., the ifferential equation of the multi-phae ynchronou machine are irectly olve in phae omain. he ata for the ynchronou machine uner the tet i hown in Appenix I. Although multi-phae ynchronou machine rating are generally in the range of maximum few MVA, the ata for the machine preente in thi paper belong to a larger MVA alient-pole ynchronou machine. he reaon for thi election i that tranient an ub-tranient time contant of larger machine are more itinct. he higher MVA rating provie a better platform for thorough valiation of the moel uner tranient conition epecially hort fault. o check the valiity of the moel for a conventional 3- phae ynchronou machine, a ingle phae fault i imulate in both the real time moel an the tan-alone program. o check the valiity of the moel for a ynchronou machine with higher orer phae, a 5-phae ynchronou machine i moele. ranient behavior of the moel i tuie uner both ymmetrical 5-phae an aymmetrical ingle phae fault. A. Aymmetrical Fault on a 3-Phae Synchronou Machine In thi ection, the propoe multi-phae ynchronou machine moel i configure to be a conventional 3-phae ynchronou machine moel. During the real-time imulation, while the rotor pee i et to ynchronou, the machine i operating in open- an it fiel voltage i ajute uch that the terminal voltage of pu i achieve ( normal fiel voltage). After reaching teay tate conition, a oli phae-neutral hort- i applie to the terminal A of the machine. he fault i applie at the time that phae A voltage croe zero. Variation of the fiel current an the tator phae A current of the machine for the firt 3.5 econ of the hort i hown in Figure 4a an 4b repectively. In each figure there are three curve, one correponing to the real-time moel labele a Propoe Moel, one correponing to the PSCAD tanar ynchronou machine moel labele a Stanar an the other correponing to the off-line phae omain olution labele a Off-Line Solution. A hown in Fig 4, the three curve are initinguihable, etablihing the fact that the propoe moel i to the off-line phae omain machine moel. Conequently the integrity of tranformation ue in thi paper i valiate. ote that applying a ingle-phae fault excite the zero equence in aition to the - an q-axe. B. Aymmetrical Fault on a 5-Phae Synchronou Machine In thi ection, the above experiment in Section IV-A i repeate when the number of machine phae i 5. he propoe multi-phae ynchronou machine moel i configure to be a ymmetrical 5-phae ynchronou machine moel. During the imulation, the machine i operating in open- an it fiel voltage i ajute uch that the terminal voltage of pu i achieve ( normal fiel voltage). Similarly, in teay-tate, a oli phae-neutral hort- i applie to terminal A of the machine at the zero-croing of the phae A voltage. Other phae were left open. Variation of the fiel current an the tator phae A current of the machine for the firt 3.5 econ of the hort i hown in Figure 5a an 5b repectively. A can be een again, the reult are matching. A expecte, tator current have lower magnitue compare to the 3-phae machine with the ame MVA rating hown in Fig. 4. ote that applying a ingle-phae fault on a five phae machine excite multiple zero equence in aition to the conventional zero equence known for 3-phae machine. Reearcher have evelope approximate analytical olution for the ingle phae hort current in a 3-phae machine []. Developing an analytical olution for aymmetrical fault on multi-phae ynchronou machine remain a ubject of further reearch. C. A Symmetrical 5-Phae Fault on a 5-Phae Synchronou Machine he experiment i repeate with a ymmetrical 5-phae hort on a 5-phae ynchronou machine. he imulation reult for the fiel current an the tator phae A current are hown in Figure 6a an 6b repectively. A can be een again, the reult are ientical to the off-line phae omain olution. ote that in the cae of a ymmetrical 5-phae fault on a five phae machine, only - an q-axe are excite an the reult will be imilar to the one for a 3-phae machine in per-unit quantitie. Current (orm) Current (ka) Propoe Moel Off_Line Solution Stanar 4 (a) Fig. 4. Single phae fault on a 3-phae ynchronou machine. (a) Fiel wining current. (b) Stator phae A current. Reult overlap. (b)

6 Current (orm) Current (ka) 4 3 Propoe Moel Off_Line Solution (a) Fig. 5. Single phae fault on a 5-phae ynchronou machine. (a) Fiel wining current. (b) Stator phae A current. Reult overlap. Fig. 6. Current (orm) Current (ka) Propoe Moel Off_Line Solution (b) (a) (b) phae fault on a 5-phae ynchronou machine. (a) Fiel wining current. (b) Stator phae A current. Reult overlap. V. COCLUSIOS AD CORIBUIOS Analyi of ymmetrical multi-phae ynchronou machine i preente through extenion of the two reaction theory to ymmetrical multi-phae machine. A etaile tranient multi-phae ynchronou machine moel wa evelope for real-time igital imulation. he metho i applicable to off-line electromagnetic tranient program a well. he moel preente in thi paper wa valiate uing tan-alone off-line imulation. Example for application of thi moel in imulating new cheme of win farm an propulion ytem for naval application i planne to be preente in future publication. In aition to the multi-phae machine moel, multi-phae control component for tranforming phae quantitie (ab n) to general tationary two-phae quantitie (αβ) an general rotating two reaction component (q) are evelope an ae to RSCAD library. hi et of moel not only ha inutrial application in the above technical fiel, but alo provie a tool to tuy an analyze multi-phae ytem. VI. APPEDIX I ABLE II PARAMEERS OF HE SYCHROOUS MACHIE [] Per-Unit Bae Value Line-neutral rate voltage Rate MVA 7.97 kv MVA Rate Frequency 6 Hz D- an Q-axe Parameter Per-Unit value Stator Leakage Reactance.3 D-axi Unaturate Magnetizing Reactance.66 Fiel Wining Leakage Reactance.68 D-axi Damper Leakage Reactance.546 Q-axi Magnetizing Reactance.58 Q-axi Damper Leakage Reactance.393 Stator Reitance. Fiel Reitance.47 D-axi Damper Reitance.47 Q-axi Damper Reitance.45 Zero Sequence Parameter Per-Unit value Zero Sequence Reactance.3 Zero Sequence Reitance. U Zero Sequence Reactance.3 U Zero Sequence Reitance. V Zero Sequence Reactance.3 V Zero Sequence Reitance. VII. APPEDIX II hi appenix preent the ummary of tranformation matrice ue in thi paper. ote that tranformation matrice lite in thi appenix are in the non-orthogonal form. Here, the imenion of matrice i the number of phae. ranformation matrice from phae quantitie (ab n) to ymmetrical component an the general two-phae quantitie (αβ) are hown below. In thee equation: ( f ) = ( f f f ab n a b n) ( f ) = ( f f f ) f = f f = f + ( f ) = ( f f f f f f α u w v β) α β ik,, where: = number of phae ranformation matrix from the phae quantitie (ab n) to (5)

7 ymmetrical component i hown in (6): S = ik α(i )(k ) where : (6) α = e jδ ranformation matrix from the phae quantitie to the general two-phae quantitie (αβ) i hown in (7): co (i )(k )δ J = ik co (π)(k ) in ( + i )(k )δ i = i< + i= + i> + (7) ranformation matrix from the general two-phae quantitie to general two reaction component (q) i hown in (8). ote that in the convention ue in thi paper, -axi lea q-axi. f co(θ ) in(θr ) fα r = fq in(θr ) co(θr ) fβ (8) VIII. ACKOWLEDGME he author i grateful to the valuable recommenation provie by Profeor Hami oliyat from exa A&M Univerity. he author incerely appreciate the high value technical upport from the colleague at RDS echnologie Inc. IX. REFERECES [] oliyat, H. A, Analyi an Simulation of Five-Phae Synchronou Reluctance Machine Incluing hir Harmonic of Airgap MMF, IEEE ran. On Inutry Application, vol. 34, no., pp , March/April 998. [] L. Para, On avantage of multi-phae machine, Inutrial Electronic Society, 5. IECO 5. (IECO 5), Raleigh, ov 5. [3] E. Levi, "Multiphae Electric Machine for Variable-Spee Application," IEEE ran. on Inutrial Electronic, Vol. 55 (5), May 8, pp [4] E.A. Klinghirn, High Phae Orer Inuction Motor - Part IDecription an heoretical Conieration, IEEE ran. On Power Apparatu an Sytem, vol. PAS-, no., pp , Jan [5] R. H. Park, "wo reaction theory of ynchronou machine, Part," AIEE ranaction, vol. 48, pp , 99. [6] R. H. Park, "wo reaction theory of ynchronou machine, Part," AIEE ranaction, vol. 5, p 35, 933. [7] R. F. Schiferl, C. M. Ong, Six Phae Synchronou Machine with AC an DC Stator Connection, Part I: Equivalent Circuit Repreentation an Steay-State Analyi, IEEE ran. On Power Apparatu an Sytem, vol. PAS-, no.8, pp , Aug [8] M.R. Aghaebrahimi, an R.W. Menzie, A tranient moel for the ual woun ynchronou machine, International Power Sytem ranient Canaian Conference on Electrical an Computer Engineering (CCECE 997), St John, May, 997. [9] A. B. Dehkori, P. eti, A.M Gole, an.l. Maguire, Development an Valiation of a Comprehenive Synchronou Machine Moel for a Real-ime Environment, IEEE ran. On Energy Converion, vol. 5, no., pp , Mar. [] A.B. Dehkori, A.M Gole, an.l. Maguire, Permanent magnet ynchronou machine moel for real-time imulation, International Power Sytem ranient Conference (IPS 5), Montreal, June, 5. [] Y. H. Ku, "ranient Analyi of AC Machinery," AIEE ranaction, vol. 48, p. 77, 99. [] Charle L. Fortecue, Metho of Symmetrical Co-Orinate Applie to the Solution of Polyphae etwork," AIEE ranaction, vol. 37, part II, pp. 7 4, 98. [3] P. Va, Parameter Etimation, Conition Monitoring, Diagnoi of Electrical Machine, Oxfor Science. Publication, 993. [4] RDS Uer Manual, RDS echnologie Inc., Winnipeg, Canaa, 6. [5] ational aiwan Univerity, Collecte Scientific Paper of Profeor Yu Hiu Ku, 97. [6] H. W. Dommel, Digital computer olution of electromagnetic tranient in ingle an multiphae network",ieee ran. Power Apparatu an Sytem, vol.pas-88, o.4, pp , Apr [7] A.M. Gole, R.W. Menzie, D.A. Woofor an H. uranli, Improve interfacing of electrical machine moel in electromagnetic tranient program," IEEE ran. Power Apparatu an Sytem, vol. PAS-3, no. 9, pp , Sept [8].L. Maguire, An Efficient Saturation Algorithm for Real ime Synchronou Machine Moel uing Flux Linkage a State Variable, Electrimac, Montreal, Canaa, June. IEEE ran. Power Apparatu an Sytem, vol. PAS-3, no. 9, pp , Sept [9]. Maguire an J. Giebrecht, Small timetep (< μ) VSC Moel for the Real ime Digital Simulator, International Conference on Power Sytem ranient (IPS 5) in Montreal, Canaa, June 93, 5, paper o. IPS5-68 [] C. Concoria, Synchronou machine theory an performance, ew York, John Wiley &Son, Inc., 95, p. 8. [] IEEE Committee Report, Firt benchmark moel for computer imulation of ubynchronou reonance, IEEE ran. on Power Apparatu an Sytem, vol. PAS-96, o.5, pp , Sept./Oct Ali B. Dehkori (S 97, M ) receive the B.Sc. an M.Sc. egree in electrical engineering from Sharif Univerity of echnology, ehran, Iran an Ph.D. egree from the Univerity of Manitoba in 999, an repectively. He worke a a reearch engineer for Sharif Univerity of echnology in power quality project in. Hi reearch interet are on the moeling of power ytem an power electronic component an in particular electric machine for Electromagnetic ranient Program an Real ime Digital Simulation, the area that he ha been working on for over 4 year. Dr. Dehkori i a recipient of Denni Woofor Prize, for the mot outtaning grauate thei ealing with power ytem moeling an imulation. He i currently employe by RDS echnologie Inc., Winnipeg, Canaa.