Design and Control of High-Speed Solid-Rotor Synchronous Reluctance Drive with Three-Phase LC Filter

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1 Design an Contol of High-Spee Soli-Roto Synchonous Reluctance Dive with Thee-Phase LC Filte Jae-Do Pak The Pennsylvania State Univesity 11 Electical Engineeing East Univesity Pak, PA Claue Khalizaeh Pentayne Powe Copoation 75 Lassen St. Chatswoth, CA Heath Hofmann The Pennsylvania State Univesity 11 Electical Engineeing East Univesity Pak, PA Abstact Synchonous eluctance machines with soli oto constuction have avantages in cetain high-spee applications such as flywheel enegy stoage systems. Howeve, the soli oto allows the flow of ey cuents, esulting in heat geneation. A thee-phase LC filte can euce oto losses ue to the switching hamonics geneate by a 3-phase invete. This pape investigates the esign an contol of a high-spee synchonous eluctance ive with a thee-phase LC filte. A two-phase ynamic moel of the ive which incopoates the LC filte ynamics is pesente. This moel is use to peict oto losses ue to switching hamonics using phaso analysis. A feefowabase cuent egulato is utilize, which is moifie to inclue the effects of the LC filte. Simulation an expeimental esults valiate the popose appoach. NOMENCLATURE [L ] Two-phase oto inuctance matix [L s ] Two-phase stato inuctance matix [M] Two-phase mutual inuctance matix [R ] Two-phase oto[ esistance ] matix 1 I Ientity matix [ 1 ] 1 J Rotation matix 1 ω e Electical oto angula velocity θ e Electical oto position i s Stato cuent comman vecto in oto efeence fame v s Stato voltage comman vecto in oto efeence fame Roto flux linkage vecto in oto efeence fame s Stato flux linkage vecto in oto efeence fame i i Inucto cuent vecto in oto efeence fame i Roto cuent vecto in oto efeence fame i s Stato cuent vecto in oto efeence fame v l Inucto voltage vecto in oto efeence fame v c Capacito voltage vecto in oto efeence fame v i Invete output voltage vecto in oto efeence fame v s Stato voltage vecto in oto efeence fame i cx Thee-phase filte capacito cuent, x=a,b,c Thee-phase invete output cuent, x=a,b,c i ix i sx L ls P R s V bus v cx v ix Thee-phase machine stato cuent, x=a,b,c Stato leakage inuctance Pole numbe of the machine Stato phase esistance DC bus voltage Thee-phase filte capacito voltage, x=a,b,c Thee-phase invete output voltage, x=a,b,c I. INTRODUCTION Synchonous eluctance machines have avantages in cetain high-spee applications, such as flywheel enegy stoage systems. The oto of a synchonous eluctance machine esign can possess excellent stuctual integity if the oto saliency is ceate by altenating layes of magnetic an non-magnetic metals connecte by a high-stength boning pocess, such as bazing [1]. Howeve, une these conitions it is ifficult to laminate the oto, an so ey cuents can be geneate ue to time-vaying magnetic fiels in the oto. Although the oto of a synchonous eluctance machine woul ieally have zeo oto losses in steay-state because the spatial flux wave otates in synchonism with the oto, in eality the oto can be subjecte to high-fequency flux oscillations ue to vaious hamonics, such as PWM switching, stato teeth, an wining hamonics. Roto losses ue to wining an tooth hamonics ae ictate by the esign of the synchonous eluctance machine, as iscusse in [1]. These types of losses can be chaacteize only with the use of sophisticate machine moels, such as those geneate by finite element analysis. Roto losses ue to time hamonics in the voltage an cuent wavefoms can, howeve, to a cetain extent be chaacteize with the smooth-aigap moels use in the vecto contol of AC electic machines. One concen with these ey cuents is thei effect on the oveall electical ynamics of the machine. Howeve, the oto losses in synchonous eluctance machines have been omitte in the equivalent cicuit base moel in many eseaches [5], [6], [7], o hamonic components ae not consiee [8]. In pevious wok [], the authos pesente a technique to contol the stato cuents of the synchonous eluctance machine IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.

2 I bus v ia L v sa i ix R l L f i sx V bus Invete v ib C v sb Syn. Reluctance Machine v ix v l R c v sx v ic v cx C f v sc Fig. 1. High-spee synchonous eluctance ive with thee-phase LC filte Fig.. Single-phase moel of thee-phase LC filte in stationay efeence fame which takes into account the electical ynamics associate with the conucting oto. Anothe concen with these ey cuents is the esulting heat geneation in the oto [1]. A flywheel which is suppote by magnetic beaings an spinning in vacuum has only blackboy aiation to emove the heat fom the oto, a elatively poo heat tansfe mechanism. As a esult, heat geneate by the oto ey cuents must be minimize. These ey cuents can be geneate by switching hamonics geneate by the 3-phase invete, wining hamonics ue to the nonsinusoial wining constuction, an slot hamonics ue to the use of a slotte stato. A thee-phase LC filte, as shown in Fig. 1, can be use to euce switching hamonics, an hence oto conuction losses, in the synchonous eluctance machine. Howeve, ue to the elatively low atio between the funamental an switching fequencies in high-spee applications, the esign of such an LC filte, an the contol of the esulting system, can be challenging. This pape iscusses esign an contol issues associate with the inclusion of a thee-phase LC filte in a high-spee soli-oto synchonous eluctance ive. The petinent issues that affect the selection of the LC filte paametes ae iscusse. A technique to estimate the oto losses in the synchonous eluctance machine is pesente. A moifie feefowa contol algoithm which takes the effects of the LC filte into account is utilize. Simulations an expeiments have been pefome on an 1kW, 53kpm synchonous eluctance ive, an the esults ae pesente. II. MODEL OF FILTER-MACHINE SYSTEM IN ROTOR REFERENCE FRAME A. Synchonous Reluctance Machine Moel The two-phase moel of the soli-oto synchonous eluctance machine is the same as that pesente in []. The soli oto is moelle in the oto efeence fame by iect an quaatue winings, simila to the case of squiel-cage inuction machines. The ynamic expessions fo the machine in the oto efeence fame ae theefoe given as follows. t s = v s R s i s Jω e s, (1) t = [R ] i, () whee x = [ x x q ] [ Y, [Y ]= Y q ], (3) the supescipt epesents the oto efeence fame, an the an q subscipts epesent iect an quaatue values, espectively. The stato an oto fluxes in the machine can be epesente as s =[L s ] i s [M] i, (4) =[L ] i [M] i s. (5) We note again that zeo oto cuent is typically assume in synchonous eluctance machines, as ieally thee is no cuent in the oto, which otates synchonously with the funamental component of the stato wining excitation. Howeve, in eality oto cuents ae geneate by the vaious time hamonics the oto expeiences. Placing an LC filte at the invete output is one metho to mitigate oto losses ue to invete switching hamonics. The effect of the LC filte on the synchonous eluctance machine will be investigate in the following section. B. Thee-Phase LC Filte in Roto Refeence Fame A single-phase iagam of a thee-phase LC filte is shown in Fig.. As the 3-phase capacitance in the actual filte is eltaconnecte, the equivalent single-phase capacitance is given as C f =3C. By applying Kichhoff s cuent an voltage laws, the cicuit equations fo the iagam can be witten as follows. t i ix = 1 (v ix v sx R l i ix ), (6) L f t v cx = 1 i cx, (7) C f i cx = i ix i sx, (8) v cx = v sx R c i cx, (9) whee the subscipt x enotes phase (i.e, a, b, o c ), an the supescipt s enotes the stationay efeence fame. The pesence of the LC filte theefoe as aitional ynamics associate with the inucto cuent an capacito voltage. The synchonous eluctance machine, howeve, is most easily moelle in the oto efeence fame ue to the saliency of the oto stuctue. The above ynamics, which ae epesente in the stationay efeence fame, shoul theefoe IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.

3 i R l v v i c L f v l Jω L i Jω C e e f i v f c Fig. 3. Thee-phase LC filte epesente in two-phase oto efeence fame TABLE I MACHINE, FILTER, AND INVERTER PARAMETERS Numbe of Poles P 4 Stato Resistance R s 17 mω Diect Stato Inuctance L s 54.4 µh Quaatue Stato Inuctance L sq 15.6 µh Diect Mutual Inuctance M 44.8 µh Quaatue Mutual Inuctance M q 6. µh Diect Roto Inuctance L 45.6 µh Quaatue Roto Inuctance L q 7.7 µh Diect Roto Resistance R 11.4 mω Quaatue Roto Resistance R q 15.4 mω Fille Capacito C f 75 µf Filte Inuctance L f 5.5 µh Capacito ESR R c µω Inucto Resistance R l 5 µω Invete DC Bus Voltage V bus 54V R c C f i s v s be tansfome to the oto efeence fame in oe to be analyze with the synchonous eluctance machine ynamics in Eqs. (1)-(5). By applying 3- phase convesions an oto efeence fame tansfomations, the following oto efeence fame epesentation of the thee-phase LC filte can be obtaine. t i s = 1 ( ) v i v s R l i i Jω e i L s, f (1) t v c = 1 i c Jω e v C c, f (11) i c = i i i s, (1) v c = v s R c i c (13) The esulting moel of the LC filte can now be incopoate with the synchonous eluctance machine moel in the pevious section an the combine filte-machine ynamics can be witten in matix fom, as shown in Eq. (14). The machine an filte paametes an vaiables use in the analysis pesente in this pape ae povie in Table I. III. LC FILTER DESIGN A. Resonant Fequency The pefomance of the LC filte is lagely etemine by the esonant fequency it intouces into the system. Since these filtes typically have little amping ue to loss mechanisms, the esonance fequency shoul be place so that it is not excite. The esonance fequency of the filte has to be sufficiently below the lowest PWM switching hamonic fequency to ensue goo filteing. Howeve, the esonant fequency shoul also be sufficiently above the funamental fequency to avoi avese effects. Futhemoe, the pesence of the LC filte can slow the tansient esponse of the system to a cetain egee. This consieation also equies that the esonant fequency of the filte be sufficiently high. B. Filte Paametes Once the esonance fequency of the LC filte is etemine, thee ae a theoetically infinite numbe of combinations of inuctance an capacitance fo the LC filte. Although each physically possible combination has the same fequency chaacteistics, they will have a iffeent effect on the oveall system pefomance. Incease filte inuctance will achieve moe sinusoial invete cuent wavefoms, but also esults in a lage voltage op acoss the filte inucto, theeby eucing the voltage that can be applie to the machine an hence eucing the powe ating of the ive. Highe capacitance fo a given esonance fequency achieves smalle inucto voltage op, an will also impove the powe facto of the invete loa ue to the compensation of eactive powe by the filte capacito. Howeve, a lage capacitance coul be poblematic ue to the lage invete cuents equie to chage an ischage the capacitos. Futhemoe, the ion in the oto of the synchonous eluctance machine can have a (small) emanent magnetization, an hence the machine behaves slightly like a pemanent magnet machine. In cetain flywheel applications, such as uninteuptible powe supplies, the system spens most of its time spinning at top spee with the invete isable. The pesence of the capacitos in the LC filte in such a situation pesent a path fo ciculating cuents to flow ue to the voltage pouce by this emanent magnetization, theeby ceating a spinning loss in the system. Futhemoe, cae must be taken that a esonant fequency geneate by the capacito an the machine inuctances is not excite, which equies placing this esonant fequency well above the funamental opeating ange as well. IV. ESTIMATION OF ROTOR LOSSES A. Roto Losses in Synchonous Reluctance Machines Invete output voltages ae geneate by pulse-withmoulation techniques an hence they contain hamonic voltage components, as shown in Fig. 4. The funamental fequency (1.8kHz) an switching fequency (18kHz) fothe simulation wee chosen so that the switching fequency is an integal multiple of the funamental electical fequency, thus simplifying the computation of the hamonic spectum. It can IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.

4 ( ) I Jωe I t [M] Rs I (Jω e I t )[L s] [R ][L ] t [M] t I R l I L f (Jω e I t ) C f (Jω e I t ) I R cc f (Jω e I t ) I R cc f (Jω e I t ) = v s i i s i i v i (14) 15 Phase A Invete Voltage 1 Two Phase Invete Voltages in Roto Refeence Fame V ia 5 V i Hamonic # v ia (t) (V) 1 1 V iq Time (sec) x Hamonic # Fig. 4. Top: Simulate magnitue of complex Fouie seies coefficients of epesentative phase A invete voltage with espect to DC neutal. Bottom: Time wavefom of phase A invete voltage econstucte fom above hamonics. be seen that, ue to the close poximity of the funamental fequency an the switching fequency, non-negligible hamonics exist at faily low hamonic fequencies. The hamonics pesente hee ae in the stationay efeence fame. In oe to incopoate these time hamonics into the moel, a metho of tansfoming these hamonics into the oto efeence fame is necessay. Such an appoach is outline below. B. Tansfomation of Stationay Time Hamonics into Roto Refeence Fame In oe to etemine how time hamonics in the stationay efeence fame ae tansfee into the oto efeence fame, we consie the case of a two-phase vecto x s in the stationay efeence fame. x s (t) = n= e jnωt Xs [n], (15) whee the supescipt s coespons to the stationay efeence fame, Xs [n] ae the (complex) Fouie coefficients of x s, an ω is a funamental fequency of which all fequencies of inteest ae integal multiples. The esulting funamental Fig. 5. Simulate magnitue of complex Fouie seies coefficients of two-phase invete voltages in oto efeence fame. peio is theefoe given by: T = π ω (16) We note that the hamonics of two-phase vaiables can be etemine simply by pefoming a 3- phase convesion on the hamonics of the thee-phase vaiables. This two-phase vecto is tansfome into the oto efeence fame as follows: x (t) =e Jθe x s (t), (17) whee θ e is the (electical) oto position. Assuming that the oto is spinning at a constant electical spee ω e,the efeence fame tansfomation can be epesente as, x (t) =e J(ωetθ) x s (t) (18) The vecto in the oto efeence fame is theefoe given by: x (t)= e J(ωetθ) e jnωt Xs [n] = n= n= e [jnωti (ωetθ)j] Xs [n] (19) Assuming that the oto electical spee is an integal multiple of ω (i.e., ω e = mω ), the hamonics in the oto efeence fame ae given by: IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.

5 X [n ]= 1 T e jn ω t x (t)t T = 1 { } T e [j(n n )I mj]ω t t e Jθ Xs [n] T n= () If we assume the exponent of the natual matix exponential in the integal is nonsingula, the integal is evaluate as: T e [j(n n )I mj]ω t t = (1) Hence the only nonzeo hamonics of the voltage in the oto efeence fame occu when the matix component of the exponent is singula. The eteminant of this matix is given by: et (j(n n )I mj) = (n n ) m () The eteminant is theefoe zeo, an hence the matix is singula, in the cases n = n m an n = n m. Wenow examine these two specific cases. 1) Case 1: n = n m: T ) Case : n = n m: T e [j(n n )I mj]ω t t = T (I jj) (3) e [j(n n )I mj]ω t t = T (I jj) (4) Hence, a given hamonic n of the voltage in the stationay fame elates to hamonics in the oto efeence fame as follows: X [n m]= 1 (I jj) e Jθ Xs [n], X [n m]= 1 (I jj) e Jθ Xs [n] (5) Theefoe a fequency ω s in the stationay efeence fame will geneate excitation in the oto efeence fame at fequencies ω s ω e an ω s ω e : X (ω s ω e )= 1 (I jj) e Jθ Xs (ω s ), X (ω s ω e )= 1 (I jj) e Jθ Xs (ω s ) (6) We note that moe than one fequency in the stationay efeence fame can be associate with a specific fequency in the oto efeence fame, an hence the contibutions of the two stationay fequencies must be combine. Fig. 5 pesents the esulting two-phase, oto efeence fame hamonics of the invete voltage spectum of Fig. 4. The lowe hamonic content of these two-phase voltages as compae to the singlephase content of Fig. 4 can be ascibe to the emoval of common-moe components in the 3- phase convesion pocess. I I q I I q Two Phase Roto Cuents in Roto Refeence Fame (Unfiltee) Hamonic # Two Phase Roto Cuents in Roto Refeence Fame (Filtee) Hamonic # Fig. 6. Simulate two-phase oto cuents in oto efeence fame, 13kW geneating, 54kpm, minimum-flux-linkage opeating point. Top: Without LC filte. Bottom: With LC filte. Once the stationay hamonic components ae tansfome into the oto efeence fame, a phaso analysis is conucte by substituting t x with jω x, whee ω coespons to a paticula hamonic fequency as seen in the oto efeence fame. Applying this theoy to the filte-machine system in Eq. (14), the esulting set of equations ae theefoe given in Eq. (7), an hamonic fequency components in the oto efeence fame can be etemine. The esulting oto cuent hamonics in the oto efeence fame fo a 13kW geneating, 54kpm (i.e., 1.8kHz funamental electical fequency), minimum-flux-linkage opeating point, both without an with the thee-phase LC filte, ae shown in Fig. 6. The switching fequency in this simulation is once again 18kHz. It can be seen that, with the exception of the 3 hamonic, the hamonics ae ecease by the LC filte, significantly so at the highe hamonics. The eason fo the slight incease in IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.

6 I (Jω e Ijω )[M] R s I (Jω e Ijω )[L s ] [R ]jω [L ] jω [M] I R l I L f (Jω e Ijω ) C f (Jω e Ijω ) I R c C f (Jω e Ijω ) I R c C f (Jω e Ijω ) V s Ī Ī s Ī i = V i (7) the 3 hamonic is its poximity to the esonant fequency ceate by the LC filte. R s L ls C. Roto Loss Calculation Fom the phaso analysis of the peceing section, the coppe losses in the oto can be calculate as follows by summing the losses ue to each oto efeence fame hamonic cuents: i spk K 1 K i s i sq M R L M q R q Lq R L - 1 s 1 s - R L q q ω e λ s λ sq v s v sq P = n 3 [R ] Ī [n] (8) R s L ls Fom the peceing simulations, a oto loss of 83W is estimate without the LC filte. Intouction of the LC filte euces the oto losses to 59W, o by oughly a facto of 5. It shoul be note, howeve, that these losses ae ough estimates, as they o not take into account effects such as the tempeatue an fequency epenence of the oto esistance. Futhemoe, it is woth epeating that oto losses ue to othe effects, such as wining an tooth hamonics, ae not epesente in this analysis. Howeve, these loss estimates can seve as a guie in the esign of the LC filte. V. CONTROL OF THE FILTER-MACHINE SYSTEM A. Open Loop Contolle The aitional ynamics of the LC filte can complicate a feeback contol scheme, paticulaly when the funamental fequency of opeation is close to the esonance fequency of the convete. A feefowa contolle oes not have these limitations, povie the natual ynamics of the system ae benign. Howeve, the pesence of the LC filte equies moification of the feefowa contolle pesente in [] to compensate the voltage op an phase shift associate with the filte. A moel-base feefowa contolle [] was utilize to etemine the appopiate comman voltages applie to a synchonous eluctance machine with an electically conucting oto. It is a easonable choice fo systems which have slowly vaying spee, such as flywheel systems. Fom the moel pesente in [], appopiate feefowa voltage commans fo a esie cuent i s ae given by v s = R s i s ω e J {L ls i s } λ a, (9) [ ] ( ) ] λ R a λ a [R i t L ML s (3) Fig. 7. Feefowa cuent contol algoithm in oto efeence fame i s ω e θ e Fee Fowa Contolle 3T s v s Jω C e f Deatime Compensato i c i v i Jω L e f Invese Pak Tansfom abc* v c Fig. 8. Moification of feefowa contolle of Fig. 9 to inclue LC filte, eatime compensation, an stationay feeback egulato to emove DC components fom invete output This open-loop contolle theefoe takes into account the inuce oto cuents in synchonous eluctance machine with a soli oto configuation. The block iagam of the contolle is shown in Fig. 7. The peak cuent comman i spk in the iagam comes fom an oute bus voltage egulato feeback loop, an the paamete K etemines the opeating point of the synchonous eluctance machine (e.g., minimum cuent, minimum flux-linkage, o maximum powe facto). B. Compensation fo LC Filte When using an LC filte, the feefowa appoach pesente above must be moifie to incopoate the aitional voltages an cuents associate with the LC filte. This is accomplishe as follows: ṽ i = ṽ l ṽ s (31) = Jω e L f ĩ i ṽ s (3) ( = Jω e [L f ] Jω e C f ṽ s ) ĩ s ṽ s (33) A block iagam of the oveall contol system stuctue, incluing compensation fo the LC filte, is shown in Fig. IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.

7 3 Two Phase Commans in Roto Refeence Fame (Uncompensate) 3 Two Phase Commans in Roto Refeence Fame(Compensate) Voltage (V) 1 Voltage (V) x x Voltage (V) 1 Voltage (V) x x Cuent (A) 5 Cuent (A) Time (sec) x Time (sec) x 1 3 Fig. 9. Simulation: Roto efeence fame two-phase voltage an cuent without LC filte compensation. 13kW geneating, 54kpm, minimum-flux-linkage opeating point. Dashe line: Comman, Soli line: Actual. Top: Stato voltage, iect-axis. Mile: Stato voltage, quaatue-axis. Bottom: Uppe:Stato cuent, iect-axis. Lowe: Stato cuent, quaatue-axis. Fig. 1. Simulation: Roto efeence fame two-phase voltage an cuent with LC filte compensation. 13kW geneating, 54kpm, minimum-flux-linkage opeating point. Dashe line: Comman, Soli line: Actual. Top: Stato voltage, iect-axis. Mile: Stato voltage, quaatue-axis. Bottom: Uppe:Stato cuent, iect-axis. Lowe: Stato cuent, quaatue-axis. 8. Also shown in the iagam is ea-time compensation an a oto position peicto base upon oto spee, which ae iscusse in etail in []. Simulations ae pefome to veify the compensation of the LC filte, an the esults ae shown in Figs The uncompensate an compensate two-phase, oto-efeencefame stato voltages an stato cuents, as well as thei esie values, ae shown. The stato cuent comman is ientical fo both cases. It can be seen that the compensato moifies the amplitue an phase of the voltage comman fom the feefowa contolle to emove the stato cuent eo. C. Expeimental Valiation Expeimental esults wee geneate on a 53kpm, 1kW synchonous eluctance ive which is pat of a flywheel enegy stoage system manufactue by Pentayne Powe Copoation, capable of poviing 1kW of DC electical powe fo up to secons []. The system block iagam an a pictue of the machine oto/flywheel im ae shown in Figs. 11-1, espectively. Although the oto cuent cannot be iectly measue, the effect of the LC filte on inuce oto cuents was veifie by measuing the oto tempeatue. By aing the LC filte, the measue tempeatue ise of the oto when the flywheel was chage fom 5kpm to 53kpm was euce by appoximately a facto of 8. This impovement is highe than that peicte by the moel. This coul be attibute to the fact that the effective oto esistance is highe than the simulate value at highe fequencies ue to skin an poximity effects. Hence the highe hamonic fequencies, which ae well-filtee by the LC filte, will geneate highe oto losses than peicte without the LC filte. The invete an stato phase cuents associate with a 1kW DC step loa on the flywheel system ae shown in Fig. 13. It can be seen that the cuent ipple fom the switching hamonics is effectively emove fom the stato cuent wavefom. The stato cuent wavefom matches quite well with the simulate esult. It shoul also be note that the filtee stato cuent will also euce heating in the stato as well, an theefoe the aition of the LC filte impoves the oveall themal pefomance of the system. VI. CONCLUSION In this pape, esign an contol issues associate with the inclusion of a thee-phase LC filte in a high-spee solioto synchonous eluctance machine ive ae iscusse. IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.

8 Bus Voltage Regulato s i s i Cuent s Regulato s v cm ω e A technique to estimate the oto losses in the synchonous eluctance machine ue to time hamonics associate with invete switching has been pesente an it shows that a simple thee-phase LC filte can euce the oto loss significantly. A feefowa contolle was moifie to compensate fo the pesence of the LC filte. Expeimental esults valiate the popose appoach. Loa Fig. 11. Fig. 1. v bus Extenal DC Bus Capacito Bank Invete LC Filte M/G Synchonous Reluctance Moto/Geneato, Flywheel Expeimental setup of flywheel enegy stoage system 4-pole synchonous eluctance oto an flywheel REFERENCES [1] H. Hofmann an S.R. Sanes. High spee synchonous eluctance machine with minimize oto losses, in IEEE Tansactions on Inusty Applications, 36():531.9, Ma.-Ap.. [] J.Pak, H.Hofmann, an C.Khalizaeh. Feefowa Contol of High- Spee Soli-Roto Synchonous Reluctance machines with Roto Dynamics Moel, in 39th IEEE IAS Annual Meeting Reco, Oct. 4. [3] H. Hofmann, R. Stoman, an M. Lanagan. Close-fom fequency moel of 3-phase invete ive fo DC istibution system analysis, in SAE Wol Congess, [4] J.Steinke. Use of the LC Filte to Achieve a Moto-fienly Pefomance of the PWM Voltage Souce Invete, in IEEE Tansactions of Enegy Convesion, 14(3):649.54, Sept [5] A. Vagati, M. Pastoelli, an G. Fanceschini. High-pefomance contol of synchonous eluctance motos, in IEEE Tansactions on Inusty Applications, Volume: 33, Issue: 4, July-Aug Pages: [6] L. Xu, X. Xu. T.A. Lipo, an D.W. Novotny. Vecto contol of a synchonous eluctance moto incluing satuation an ion loss, in IEEE Tansactions on Inusty Applications, Volume: 7, Issue: 5, Sept.-Oct Pages: [7] R.E. Betz et al. Contol of synchonous eluctance machines, in IEEE Tansactions on Inusty Applications, Volume: 9, Issue: 6, Nov.-Dec Pages: [8] L. Xu an J. Yao. A compensate vecto contol scheme of a synchonous eluctance moto incluing satuation an ion losses, in IEEE Tansactions on Inusty Applications, Volume: 8, Issue: 6, Nov.-Dec. 199 Pages: [9] S. Chen an G. Joos. Tansient pefomance of UPS system with synchonous-fame igital contolle, in Twenty-secon Intenational Telecommunications Enegy Confeence,. INTELEC Sept. Pages: [1] W. Santiago. Invete output filte effect on PWM moto ives of a flywheel enegy stoage system, in Secon Intenational Enegy Convesion Engineeing Confeence, Aug , 4. NASA/TM [11] Y. Soze, D. Toey, an S. Reva. New invete output filte topology fo PWM moto ives, in IEEE Tansactions on Powe Electonics, Volume: 15, Issue: 6, Nov. Pages: [1] J. Poakis an D. Manolakis. Digital signal pocessing, 3 E. Pentice- Hall, 1996 Fig. 13. Expeimental esult: 1kW DC loa step on flywheel enegy stoage system with LC filte. Top: Invete phase cuent. Bottom: Stato phase cuent IAS /5/$. 5 IEEE Authoize license use limite to: UNIV OF COLORADO DENVER. Downloae on Septembe 4, 9 at 18:9 fom IEEE Xploe. Restictions apply.