UNINTERRUPTIBLE power supply (UPS) systems have

Transcription

1 3038 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008 Contol of High-Speed Solid-Roto Synchonous Reluctance Moto/Geneato fo Flywheel-Based Uninteuptible Powe Supplies Jae-Do Pak, Membe, IEEE, Claude Kalev, Membe, IEEE, and Heath F. Hofmann, Membe, IEEE Abstact A hybid contolle, consisting of a model-based feedfowad contolle and a popotional integal feedback compensato, fo a solid-oto synchonous eluctance moto/geneato in a high-speed flywheel-based uninteuptible powe supply application is poposed in this pape. The feedfowad contolle takes most of the contol output of the cuent egulato based on the machine model, and the PI contolles compensate the possible inaccuacies of the model to impove the pefomance and obustness of the complete contol system. The machine cuent tacking eo caused by paamete inaccuacy in the model-based contolle is mathematically analyzed and utilized to dynamically compensate the estimated flux linkage to eliminate the steady-state eo in cuent egulation. Stability analysis is also pesented, and it can be seen that the egulation pefomance and obustness of the system ae impoved by the poposed hybid contolle. Simulation and expeimental esults consisting of a flywheel enegy stoage system validates the pefomance of the contolle. Index Tems Flywheel, model-based contol, synchonous eluctance moto, uninteuptible powe supply (UPS). NOMENCLATURE i s Cuent eo vecto in oto efeence fame. λ a Flux linkage estimation eo vecto in oto efeence fame. v s Voltage command eo vecto in oto efeence fame. Ld 0 Roto inductance matix. 0 q L s Stato inductance matix. M Mutual inductance matix. R Roto esistance matix. 0 1 J Rotation matix. 1 0 ω e Electical oto angula velocity. A Full-ode system matix of the synchonous eluctance machine. λ Roto flux linkage vecto in oto efeence fame. λ s Stato flux linkage vecto in oto efeence fame. ĩ s Stato cuent command vecto in oto efeence fame. ṽ s Stato voltage command vecto in oto efeence fame. Stato cuent vecto in oto efeence fame. i s Manuscipt eceived Febuay 28, 2007; evised Januay 7, Fist published Febuay 22, 2008; last published July 30, 2008 (pojected). J. Pak and C. Kalev ae with Pentadyne Powe Copoation, Chatswoth, CA USA ( jaedo.pak@pentadyne.com). H. F. Hofmann is with The Pennsylvania State Univesity, Univesity Pak, PA USA. Digital Object Identifie /TIE v s x K i K p L ls R s Stato voltage vecto in oto efeence fame. Machine state vecto. Integal gain in feedback compensato. Popotional gain in feedback compensato. Stato leakage inductance. Stato esistance. I. INTRODUCTION UNINTERRUPTIBLE powe supply (UPS) systems have been widely utilized to impove the electic powe quality fo citical loads. Fo anomalies such as inteuptions o sags, a UPS suppots the load using its stoed enegy. The enegy stoage device fo UPS systems has histoically been the lead-acid battey. Howeve, ecently, thee has been geat inteest in finding altenatives fo lead-acid batteies due to thei opeating/ maintenance cost and envionmental impact. Advances in powe electonics, magnetic beaings, and high-stength cabon fibes have esulted in flywheel enegy stoage systems that can be used as a substitute o supplement fo lead-acid batteies in UPS systems 1 5. High-powe flywheels can povide backup powe to handle the majoity of powe disuptions that last fo 5 seconds o less 1 and still have time to cove longe outages until a backup system can cove the full load. Flywheels can also be used in conjunction with batteies. This can educe the numbe of shot chage/dischage cycles of the batteies, which geatly extends thei lifetime. It also impoves the battey eliability and peseves the battey capacity fo longe distubances. Synchonous eluctance machines have advantages as a moto/geneato in flywheel enegy stoage systems due to the zeo spinning losses when no toque is being geneated by the machine, as opposed to pemanent magnet machines with a stato ion. Futhemoe, the oto of a synchonous eluctance machine design can possess excellent stuctual integity if the oto saliency is ceated by altenating layes of magnetic and nonmagnetic metals connected by a high-stength bonding pocess, such as bazing. Howeve, when such a oto is utilized fo the machine, the conventional synchonous eluctance machine models become inaccuate, paticulaly fo the case of steep toque changes, because the flux dynamics of the oto due to eddy cuent flow ae not taken into consideation 6. Feedfowad cuent egulatos fo electic machines ae one solution fo high-speed applications, as typical feedback egulatos can be poblematic in field-oiented contol due to the speed dependence of the machine dynamics. A sufficiently /$ IEEE Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

2 PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs 3039 accuate model of the machine can make a model-based feedfowad contolle a easonable appoach, as the stability issue becomes avoidable due to the inheently stable machine dynamics. It has been shown that the conventional model of the synchonous eluctance machine, which does not conside the oto flux dynamics, can ceate a cuent oveshoot duing tansients when used in a cuent egulato, as the pedicted back electomotive foce (EMF) is much highe than the actual back EMF of the machine. This makes it poblematic to utilize the conventional model to design a model-based contolle fo a machine with a conducting oto. This issue has been esolved in the authos pevious wok 6. Although the model utilized in the feedfowad contolle descibes the machine well, the feedfowad contolle elies heavily upon accuate knowledge of the paametes fo good pefomance. Howeve, pactically, it is had to measue all paametes exactly. Some of them may be difficult to measue, and initially measued paametes can easily vay with opeating conditions such as tempeatue and the nonlinea magnetic popeties of the ion in the machine. A feedfowad-contolled system geneates inaccuate output if the paametes ae not coect and does not take into account unmodeled dynamics o distubances. As a esult, the efficiency will be non-optimal, because the actual opeating point of the machine will be off fom the commanded one if the paametes ae inaccuate. Futhemoe, the invete may tip at high powe levels if the eoneous opeating point equies a highe than necessay cuent to geneate the desied toque. This can cause poblems fo some citical opeating conditions unless the cuent eo is eliminated popely. A hybid contolle which incopoates a feedback PI compensato into a model-based feedfowad contolle to impove the pefomance and obustness of cuent egulation fo a highspeed solid-oto synchonous eluctance machine is poposed in this pape. The machine cuent tacking eo caused by the paamete mismatch is mathematically analyzed and is utilized to dynamically compensate the estimated flux-linkage to eliminate the steady state eo in cuent egulation. Stability analysis is also pefomed, and it will be shown that the egulation pefomance and obustness of the system ae impoved. The poposed contolle yields an impoved tansient esponse fo a fast-changing toque command with the model, as well as good tacking pefomance fom the PI egulato. This is paticulaly desiable fo applications such as flywheel-based o flywheel battey hybid enegy stoage systems, because fast esponse is an impotant pefomance facto of UPS systems, and impoved tacking pefomance yields bette efficiency. The poposed contolle has been expeimentally validated with a solid-oto synchonous eluctance moto/geneato based flywheel enegy stoage system. II. MODEL-BASED FEEDFORWARD CONTROLLER 6 A. Continuous-Time Model The feedfowad contolle which is utilized in this pape is based on the machine model pesented in 6. The equivalent cicuit model is shown in Fig. 1. Unlike the equivalent-cicuitbased models in pevious studies 7 9, this model takes the Fig. 1. Equivalent cicuit model of synchonous eluctance machine in synchonous efeence fame. dynamics of the oto flux-linkage into account and, theefoe, bette epesents the flux behavio in the machine. This allows a significant impovement on tansient esponse, paticulaly fo the solid-oto synchonous eluctance machine whose oto cuents, geneated by the flux-linkage dynamics, ae not negligible 6. The machine is modeled in the oto efeence fame by diect and quadatue windings and is simila to the case of squiel-cage induction machines, yet includes a magnetic saliency of the oto. The dynamic expessions fo the machine in the oto efeence fame ae given as follows: d λ a = dt di s dt = whee R λ a + ( ) 2 R i ML s (1) L s M 2 1 { ( ) 2 v s R s + R i ML s ω e J (L s M 2 ) i s+ λ a + λ M a = R λ a } (2) λ. (3) B. Feedfowad Contolle Implementation It is staightfowad to build a sufficiently accuate machine dynamics model fo a flywheel system, due to its slowly vaying speed. Hence, a easonably accuate command voltage fo the given cuent commands can be detemined fom the model. The voltages fo a cuent ĩ s and esulting flux linkage ˆλ a ae given as ṽ s = R s ĩ s + ω e J L s M 2 ĩ s + ω e J ˆλ a + d (L s M 2 ) ĩ dt s + λ a. (4) It has been found that sufficient pefomance can be achieved by neglecting dynamic tems and appoximating the stato voltage as follows: } ṽ s = R sĩ s + ω e J {L lsĩ s + ˆλ a. (5) Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

3 3040 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008 Note that measued stato leakage inductance L ls is utilized in the contolle instead of L s (M 2 / ). This is because both the diect and quadatue values of L s (M 2 / ) ae appoximately equal to the stato leakage inductance L ls and, hence, can be estimated, as well as the stato esistance R s, though teminal measuements of the stato with the oto emoved. The flux-linkage vecto ˆλ a can be estimated by numeically integating (1) using command cuents ˆλ a = t R ˆλ a + R ( ML ) 2 ĩ sdt. (6) The invese of the oto time constants R / and the oto excitation esistance R (M/ ) 2 can be obtained expeimentally, as discussed in 6. When incoectly estimated, flux-linkage values ˆλ a ae utilized to calculate command voltage as in (5), an eoneous command voltage ṽ s is geneated ṽ s = v s + v s (12) = R sĩ s + ω e J (L s M 2 ) ĩ s + ˆλ a. (13) This voltage eo will esult in a stato cuent eo. The elationship between flux-linkage estimation and the cuent can be detemined fom the command values in (13) and the actual values fom the command in (5), and the steady-state eo of the machine cuent caused by mismatched paametes can be epesented as follows: i s = ( R s I + ω e J L s M 2 ) 1 ω ej λ a. (14) III. PI FEEDBACK COMPENSATOR A. Eo Caused by Paamete Mismatch Among the thee sets of diect and quadatue paametes and the scala paamete equied fo the model used in the contolle, it has been assumed that L s (M 2 / ), which can be appoximated by the stato leakage inductance L ls, and R s have exact values in this pape. Howeve, the othe paametes containing and M and R will vay due to nonlinea magnetics and oto tempeatue, espectively. Equation (6) is used to estimate the flux-linkage. If an eo exists in the time constant and/o excitation esistance, the estimated flux-linkage will have the following additive eo tem: ˆλ a = ˆλ a0 + ˆλ a (7) t R ) = + 1 (ˆλ a0 L + λ a ( ) 2 + R + 2 ĩ ML sdt (8) whee ˆλ a0 epesents the ight amount of the flux linkage fo the given cuent command. Then, the eo in the flux-linkage estimation can be sepaated as ˆλ a = t Diffeentiating yields 1 ˆλ R a0 + 1 L λ a + 2 ĩ sdt. (9) d dt λ a = 1 ˆλ a0 R + 1 L λ a + 2 ĩ s. (10) Assuming steady-state opeation, the eo tems of the fluxlinkage estimation become dc offsets. Howeve, it is difficult to tell which paamete is incoect fom the output, because the eos ae a combination of paametes, cuent, and flux-linkage 1 λ R ( a = ˆλ a0 L 2 ) ĩ s. (11) B. Feedback-Compensato Implementation In steady-state, the eo of the cuent is popotional to that of the estimated flux-linkage, which comes in tun fom paamete eos, as shown in (14). Hence, a flux-linkage compensato using a PI egulato is given as follows: ( λ a = K p + K ) i i s R s ωe 1 J i s (15) s whee the tem R s ω 1 e J i s is included in an attempt to decouple the diect and quadatue dynamics. With the addition of this feedback compensato, the contol pefomance can be impoved by compensating the deviation of model paametes fom the actual machine. The model-based contolle geneates most of the contol output and has aleady esolved the oveshoot issue of the solid-oto synchonous eluctance machine 6. Hence, the feedback can have educed gain so that it can be less sensitive to noise o andom eos and have less of an impact on the stability of the system. In ode to educe the numbe of states in the system, the integal pat of the PI egulato can be integated into the flux estimato (6) as follows: ˆλ a = t R ˆλ a + R ( ML ) 2 ĩ s + K i i sdt. (16) The block diagam of the feedback compensato with the model-based feedfowad contolle is shown in Fig. 2. IV. STABILITY ANALYSIS A. Feedfowad Contol The state vaiables of the machine ae defined as x = λ ad λ aq i sd i sq T. (17) Moeove, the machine dynamics equations of (1) and (2) can be epesented in matix fom in (18) (20), shown at the bottom of the next page. Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

4 PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs 3041 Fig. 2. Block diagam of the feedback compensated model-based contol system. Fig. 3. State-space diagam of the feedfowad contol system. Fom the contolle equations epesented in (5) and (6), the following matix notation has been used: R  = (21) ( ) 2 ˆB = R (22) ML Ĉ = ω e J (23) ˆD = R s I + ω e J L s M 2. (24) Thus, the complete system dynamics ae given by ẋ A 04 2 B 04 2 = ˆλ a  xˆλ + a ˆB ṽ s ĩ s. (25) The state-space diagam is shown in Fig. 3. Because the voltage command vecto ṽ s is synthesized based on the estimated flux-linkage vecto ˆλ a and the cuent command vecto ĩ s ṽ s = Ĉˆλ a + ˆD ĩ s. (26) Equation (25) can be futhe simplified as follows: ẋ A B Ĉ B ˆḒ = ˆλ a  xˆλ + ĩ a B s. (27) Fig. 4. Eigenvalues of the feedfowad-contolled system when the speed of the machine is inceased fom 0 to /min. Aows denote inceasing oto speed. The eigenvalues of (27) ae shown in Fig. 4. The system is stable, but it can be seen that the eigenvalues move towad the oigin and incease in the imaginay diection as the oto speed is inceased. A = B = 0 C =0 I R R ( M ) 2 1 { } L s M 2 R ω e J L s M 2 1 T { 1 ( ) 2 } L s M 2 M R s + R ω e J L s M 2 (18) (19) (20) Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

5 3042 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008 Fig. 5. State-space diagam of the feedback compensated system. Flux compensation. B. Feedback Compensation Actual measued cuent values ae extacted fom the machine state vecto x by matix C; theefoe, the cuent eo vecto can be given as i s = ĩ s Cx. (28) Taking the PI-compensato output and decoupling tem into consideation, the system dynamics ae given by whee x = Ax + Bṽ s =(A BĈFC)x + BĈˆλ a + B( ˆD + ĈF) ĩ s (29) ṽ s = Ĉˆλ a + ĈF i s + ˆD ĩ s (30) F = K p I R s ωe 1 J. (31) The state-space diagam is shown in Fig. 5. With the integato pat of the contolle incopoated with the flux estimato, as shown in (16), the complete contol system with the PI compensato can be epesented in matix fom, as shown as follows: ẋ A B ĈFC BĈ = ˆλ a K i C Â x ˆλ a + B( ˆD + ĈF) ĩ ˆB + K i I s. (32) Fig. 6 shows the eigenvalues of the compensated system with K p = L ls and K i = L ls. It can be seen that the highly speeddependent eigenvalues of the system have significantly faste decay ates than the feedfowad system. V. C OMPARISON WITH VOLTAGE-COMPENSATION SCHEME The estimated flux-linkage, including the PI-compensation tem, will eventually be utilized to detemine the voltage command though the model in the feedfowad contolle. By changing the placement of PI egulato and decoupling tems, it is possible to implement a voltage-compensated cuent egulato. This configuation becomes a conventional feedback cu- Fig. 6. Eigenvalues of the feedfowad-contolled system with compensato when the speed of the machine is inceased fom 0 to /min. Case of K p = L ls and K i = L ls. Aows denote inceasing oto speed. ent egulato and additive feedfowad compensation, which is shown in Fig. 7. The output of the PI feedback compensato, which is stato voltage command, will be given as ṽ PI (K = p + K ) i i s + ω e J s L s M 2 i s (33) whee the tem ω e JL s (M 2 / ) i s is included in an attempt to decouple the diect and quadatue dynamics. As well as this PI egulato output, the feedfowad compensation voltage calculated fom the model is added to the command } ṽ s = ṽ PI + R sĩ s + ω e J {L lsĩ s + ˆλ a. (34) The state-space diagam is shown in Fig. 8. Taking the PI-egulato output and decoupling tem into consideation, the system dynamics will be given as x = Ax + Bṽ s =(A BFC)x + BĈˆλ a + Bp + B( ˆD + F) ĩ s (35) Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

6 PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs 3043 Fig. 7. Block diagam of conventional cuent-feedback contolle with feedfowad compensation. Fig. 8. State-space diagam of the feedback-compensated system. Voltage compensation. whee ṽ s = Ĉˆλ a + p + F i s + ˆD ĩ s (36) F = ω e J L s M 2 + K p I. (37) The dynamics of the compensato can be deived as follows: p = K i i s = K i Cx + K i ĩ s. (38) Theefoe, the complete contol system with the PI compensato can be epesented in matix fom as x A BFC BĈ B x ˆλ a = Â ˆλ a p K i C p + B( ˆD + F) ˆB ĩ s. (39) K i I Note that the flux-compensation scheme, as opposed to the voltage-compensation scheme, has two less integatos. Figs. 9 and 10 show the eigenvalues of the flux-compensated and voltage-compensated system at /min with vaying gains. K p and K i have been vaied fom zeo to L ls and to R s fo flux and voltage compensato, espectively. The poles with zeo gain of Figs. 9 and 10 ae diffeent because of the decoupling tems. It can be seen that the oscillating mode in the flux-compensation scheme has a lowe oscillation fequency and faste decay. Fig. 9. Eigenvalues of the feedfowad-contolled system with flux compensato when the PI gains ae inceased fom 0 to L ls at /min. Aows denote inceasing gain. VI. EXPERIMENTAL RESULTS To validate the theoy, expeiments using the poposed fluxcompensated cuent egulato ae pefomed on a 120 kw 4-pole solid-oto synchonous eluctance machine. The oto consists of altenating layes of a feomagnetic and nonmagnetic mateial. The machine paametes ae shown in Table I. This machine is a pat of a flywheel enegy stoage system manufactued by Pentadyne Powe Copoation that is capable Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

7 3044 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008 Fig. 11. Expeimental setup of flywheel enegy-stoage system. Fig. 10. Eigenvalues of the feedfowad-contolled system with voltage compensato when the PI gains ae inceased fom 0 to R s at /min. Aows denote inceasing gain. TABLE I MACHINE/CONTROLLER PARAMETERS Fig. 12. Expeimentally measued flux linkages in synchonous efeence fame. Offsets due to the emanent magnetization can be seen. (a) λ sd.(b)λ sq. of poviding 120 kw of dc electical powe fo up to 20 s ove a speed ange of /min. The machine is diven by a thee-phase invete, and the poposed contol algoithm, which has been shown in Fig. 2, is implemented in a DSP-based contolle. Analog/digital convetes sample machine cuents synchonously with the cente-based pulsewidth-modulated geneato, which opeates at a switching fequency of 18 khz. Analog low-pass filtes with 128 khz bandwidth ae applied to educe the effects of noise and ipple. The sampling/calculation delay and input/output filteing should be caefully consideed fo discete-time contolle implementation, because these can esult in an infeio pefomance o poo stability magin, paticulaly due to the low switching-to-fundamental fequency atio. Delays should be compensated popely, as discussed in 6, fo the feedfowad contolle. The poposed cuent egulato is then used as an inne egulato in a bus voltage contol algoithm, simila to that pesented in 10. The bus voltage egulato geneates the toque command fo the machine so that the dc powe to the load can be contolled. It is not necessay to egulate the machine speed in this configuation. The block diagam of the expeimental system is shown in Fig. 11. The machine model utilized in the poposed contolle accommodates the oto flux dynamics to avoid the huge oveshoot in fast toque tansient 6; hence, the model-based pat geneates most of the contol output, and the feedback compensato only geneates a elatively small coective component to the command voltages. The feedback gains can be eadily tuned expeimentally to obtain the desied pefomance. Fist, the popotional gain that compensates about 80% of the eo without integal gain was detemined. Subsequently, the integal gain was inceased to find the value that eliminates the steadystate eo popely. The contolle was able to avoid too much oveshoot while quickly eliminating the offsets fom paamete inaccuacies. The poposed model-based feedfowad contolle assumes linea magnetic behavio, meaning that the flux-linkages of the machine ae linealy elated to the cuents. In pactice, howeve, this elationship is nonlinea. While satuation of the machine ion is one possible nonlinea effect, in the system unde study, this effect is not significant in the opeating ange of the machine due to the elatively lage ai gap. Anothe nonlinea magnetic popety which has moe of an effect on the system unde study is the emanent magnetization of the ion in the oto of the machine, which is shown in Fig. 12. Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

8 PARK et al.: CONTROL OF SYNCHRONOUS RELUCTANCE MOTOR/GENERATOR FOR FLYWHEEL-BASED UPSs 3045 Fig. 13. Expeiment: 150 A step commands in synchonous efeence fame at /min. Model-based contolle. Offsets due to the emanent magnetization can be seen. Uppe: diect-axis. Lowe: quadatue-axis. (a) Command cuent ĩ s. (b) Actual cuent i s. Fig. 15. Expeiment: 150 A step commands in synchonous efeence fame at /min. Model-based contolle with flux-based PI compensato. The offsets ae emoved by the PI compensatos. Uppe: diect-axis. Lowe: quadatue-axis. (a) Command cuent ĩ s. (b) Actual cuent i s. Fig. 14. Expeiment: A amp commands in synchonous efeence fame at /min. Model-based contolle. Eos due to the emanent magnetization can be seen. Uppe: diect-axis. Lowe: quadatue-axis. (a) Command cuent ĩ s. (b) Actual cuent i s. Fig. 16. Expeiment: A cuent commands in synchonous efeence fame at /min. Model-based contolle with flux-based PI compensato. The eos ae emoved by the PI compensatos. Uppe: diect-axis. Lowe: quadatue-axis. (a) Command cuent ĩ s. (b) Actual cuent i s. This ceates eos in the cuent tacking that ae paticulaly impotant at elatively low powe levels. Although these eos can be emoved by incopoating the nonlineaity into the machine model, this phenomenon is left unmodeled so that it can be utilized to validate the pefomance of the feedback compensato. As expected, when using only the model-based contolle, the system shows offsets/eos in cuent tacking when a step cuent command of 150 A and a amp command fom 0 to 300 A wee applied to the system. The esults ae shown in Figs. 13 and 14. This is most likely because the emanent magnetization is not consideed in the model. Howeve, the eo can be effectively emoved by the poposed hybid contolle, as shown in Figs. 15 and 16, because the PI contolle compensates the unmodeled nonlineaity. VII. CONCLUSION In this pape, a hybid contolle consisting of a model-based feedfowad contolle and a PI feedback compensato fo a solid-oto synchonous eluctance moto/geneato has been poposed. The poposed contol scheme has been applied to a moto/geneato in a high-speed flywheel-based UPS system. It has been shown that the poposed hybid contolle with PI feedback compensato, in addition to the model-based contolle consideing flux dynamics in the solid-oto scheme, easily compensates eos in the flux-linkage estimato caused by inaccuate paametes o unmodeled dynamics, as well as impoves the egulation pefomance fo the cuent commands and the stability of the system. Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.

9 3046 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 8, AUGUST 2008 REFERENCES 1 Flywheel Enegy Stoage, U.S. Depatment of Enegy, Rep. DOE/ EE-0286, Sep B. Robets and J. McDowall, Commecial successes in powe stoage, IEEE Powe Enegy Mag., vol. 3, no. 2, pp , Ma./Ap J. M. Gueeo, L. G. de Vicuna, and J. Uceda, Uninteuptible powe supply systems povide potection, IEEE Ind. Electon. Mag., vol. 1, no. 1, pp , Sping R. G. Lawence, K. L. Caven, and G. D. Nichols, Flywheel UPS, IEEE Ind. Appl. Mag., vol. 9, no. 3, pp , May/Jun R. Hebne, J. Beno, and A. Walls, Flywheel batteies come aound again, IEEE Spect., vol. 39, no. 4, pp , Ap J. Pak, H. Hofmann, and C. Khalizadeh, Feedfowad contol of high-speed solid-oto synchonous eluctance machines with oto dynamics model, in Conf. Rec. 39th IEEE IAS Annu. Meeting, Oct. 2004, pp A. Vagati, M. Pastoelli, and G. Fanceschini, High-pefomance contol of synchonous eluctance motos, IEEE Tans. Ind. Appl.,vol.33,no.4, pp , Jul./Aug L. Xu, X. Xu, T. A. 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Pess, Jae-Do Pak (S 04 M 07) eceived the B.S. and M.S. degees in electical engineeing fom Hanyang Univesity, Seoul, Koea, in 1992 and 1994, espectively, and the Ph.D. degee fom The Pennsylvania State Univesity, Univesity Pak, in Fom 1994 to 2001, he was a Reseach Enginee with LG Industial Systems, Anyang, Koea. Since 2004, he has been with Pentadyne Powe Copoation, Chatswoth, CA, whee he is cuently a Contols Softwae Enginee. His cuent inteests include flywheel enegy stoage systems, powe convetes, and ac machine dives. Claude Kalev (M 93) eceived the degee in electonic engineeing fom Califonia Polytechnic State Univesity, San Luis Obispo. Since June 2002, he has been the Vice Pesident of the Electical Engineeing Depatment, Pentadyne Powe Copoation, Chatswoth, CA, which he cofounded when the company was incopoated in His inteests include high-speed otating machiney, magnetic-beaing-system development, high-vacuum systems, and molecula dag pump design. M. Kalev is a membe of Tau Beta Pi and the Golden Key Hono Society. Heath F. Hofmann (M 89) eceived the B.S. degee in electical engineeing fom the Univesity of Texas at Austin in 1992 and the M.S. and Ph.D. degees in electical engineeing and compute science fom the Univesity of Califonia, Bekeley, in 1997 and 1998, espectively. He is cuently an Associate Pofesso with Pennsylvania State Univesity, Univesity Pak. His eseach aea is in powe electonics, specializing in the design and contol of electomechanical systems. His specific inteests include enegy havesting (i.e., the geneation of electicity fom one s envionment), flywheel enegystoage systems, and electic dives fo electic and hybid electic vehicles. D. Hofmann was the ecipient of a Pize Pape Awad (Fist Pize) by the Electic Machines Committee at an IEEE Industy Applications Society Annual Meeting in Authoized licensed use limited to: UNIV OF COLORADO DENVER. Downloaded on Septembe 24, 2009 at 18:07 fom IEEE Xploe. Restictions apply.