RCHIVES OF ELECRICL ENGINEERING VOL. 64 pp. 89-05 05 DOI 0.55/aee-05-0009 Modellng and performance analyss of dual-channel swtched reluctance motor PIOR OGUSZ MRIUSZ KORKOSZ JN PROKOP Rzeszow Unversty of echnology Faculty of Electrcal and Computer Engneerng ul. Wncentego Pola 5-959 Rzeszów Poland e-mal: pbogu/mkosz/prokop@prz.edu.pl Receved: 8.0.04 revsed:..04 bstract: he paper s a presentaton of an analyss concernng performance of a /8 dual-channel swtched reluctance motor DCSRM. Formulas consttutng a base for a non-lnear mathematcal model of DCSRM are presented. Smulaton and laboratory tests were carred out for the motor operatng n the dual-channel and sngle-channel mode. he results of the feld theory-based calculatons are presented n the form of fluxes n ndvdual phases expressed as functons of currents and a rotor poston angle. he results of the computer smulatons are shown as the statc characterstcs of fluxes and the torque as well as voltage current and torque waveforms. he results of the laboratory tests are also presented. Key words: dual channel swtched reluctance motor DCSRM mathematcal model SRM. Introducton he so-called crtcal drves e.g. fuel pump drves n arcraft or electrc motorcar propulson systems are nowadays expected to be hghly resstant to falures of both the electrc motor and the motor supplyng crcut. soluton potentally capable to meet requrements mposed on crtcal drves conssts n selecton of the dual-channel swtched reluctance motor DCSRM [-5]. DCSRMs can be used n the so-called dual-channel operaton mode where correspondng phases of both channels are suppled at the same tme or n the sngle-channel operaton mode [-]. In a falure condton consstng n damage of a phase wndng n one of the channels or a malfuncton of the crcut supplyng the channel the motor s capable to operate n the sngle-channel mode allowng thus to mantan the drve operaton contnuty. he purpose of the present paper s to present an analyss of performance of a DCSRM carred out on the grounds of smulaton and laboratory tests performed on a three-phase dualchannel DCSRM. Fgure shows the cross-secton of a /8 DCSRM wth one phase of channel u and channel u marked as an example. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
90 P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. Fg.. schematc vew of crosssecton of a /8 three-phase DCSRM Fgure presents a schematc dagram of the crcut supplyng a three-phase DCSRM wth converter crcuts supplyng channel and channel wndngs. he examned motor can be operated n the so-called dual-channel mode where the correspondng phases of both channels and are pulse-lke suppled at the same tme or n the sngle-channel operaton mode where the pulsed supply s provded only to phases of one of the channels or. Fg.. schematc dagram of the crcut supplyng a /8 three-phase DCSRM For the examned DCSRM a mathematcal crcut model has been developed takng nto account non-lnearty of the magnetc crcut and mutual lnkages both between wndngs of a gven channel or and between phases of two dfferent channels and. he paper presents results of smulatons that were further verfed by means of laboratory measurements. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 9. mathematcal model of DCSRM o model a three-phase DCSRM the so-called flux-based feld-crcut model wth ndrect lnkage has been used. In such a model the functonal dependence of relevant fluxes on the rotor poston and phase currents were determned by means of D feld methods and then the set of the obtaned relatonshps was used n the crcut model. he machne model dscussed here takes nto account the non-lnearty of the magnetsaton characterstcs and all lnkages exstng between phases of both channels. For the purpose of the present model t s assumed that the fluxes of the ndvdual phases for both channels and can be expressed as the sums of the fluxes dependng on the rotor poston angle and only one phase current n a gven channel accordng to the defnton [6 9] where: 4 Defnng voltage vectors u u and current vectors as well as resstance matrces R R for channels and respectvely n the form [ ] u u u u [ ] u u u u [ ] [ ] 5 dag R R R R dag R R R R 6 and makng use of defntons and the current-voltage equaton and the formula for the electromagnetc torque e wthn the framework of the crcut model of DCSRM can be wrtten n the form [6 9] rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. 9 R 0 0 R u u dt d 7 * e W c 8 where * c W s the total magnetc feld co-energy n the ar gap. Equaton 8 whch s an expresson for the electromagnetc torque e n a three phase DCSRM under assumptons and 4 can be wrtten n the form [6 9] 0 0 0 0 0 kk k k k kk k k k kk e k k d d d d d 9 or n short. mutual mutual phase mutual phase e 0 Indvdual components of the r.h.s. of Equaton 0 representng formula for the resultant torque e correspond to torque components orgnatng from phase currents phase phase and mutual lnkages mutual mutual wthn channels and and the torque related wth flux lnkages between channels. mutual In the case of sngle-channel operaton mode the expresson for the torque can be reduced to the frst two components of the r.h.s. of Equaton 0. For the purpose of development of a DCSRM smulaton model flux vectors and n Equatons and 4 can be separated accordng to the defnton: mutual phase. mutual phase where the ndvdual components represent respectvely the phase fluxes subscrpt phase and the mutual lnkage fluxes between the phases subscrpt mutual wth respect to the gven channels and accordng to the relatonshps rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 9 phase mutual phase mutual. 4 Fgure shows a block dagram representng schematcally structure of the smulaton model based on voltage-current equatons 7 n a dual-channel DCSRM wth mutual lnkages both between phases of ndvdual channels or and between phases of dfferent channels taken nto account. Fg.. schematc dagram of the smulaton model based on voltage-current equatons of a DCSRM Functonal dependences of the fluxes on the rotor poston and current n gven phase represented by Equatons and 4 as well as n the formula for the electromagnetc torque gven by Equaton 9 are most often calculated wth the use of the feld approach. hey are descrbed wth the use of varous technques e.g. analytcally by means of seres of the varable wth coeffcents dependng on the current or numercally n the form of look-up tables or artfcal neural networks NN. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
94 P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. ased on Equatons 7 and 9 a smulaton model n Matlab/Smulnk system [6] has been developed. Functonal dependences of ndvdual fluxes on the rotor poston and currents n relevant phases occurrng n Equaton 7 and n Equaton 9 representng a formula for the torque were determned by means of D feld calculatons. hey are descrbed n a tabular form wth the use of -D Look-Up able blocks from Smulnk s lbrary. Smulaton studes carred out for a model DCSRM wth /8 confguraton nvolved calculatons of the so-called statc characterstcs and as far as tme-dependency s concerned analyses of voltage current and the torque waveforms. Operaton of the motor was examned n both sngleand dual-channel operaton mode for constant rotor speed.. nalyss of DCSRM statc characterstcs.. Magnetc feld dstrbuton n a three-phase DCSRM Smulaton studes on the magnetc feld dstrbuton patterns by means of the Fnte Element Method were carred out n D for a /8 three-phase dual channel DCSRM [7]. Magnetc feld dstrbuton analyss was carred out for dfferent rotor postons startng from the so-called unalgned poston.e. the rotor poston angle assumed conventonally as 0 up to the so-called algned poston correspondng to angle π/8. Calculatons were carred out for the motor operatng n the dual-channel mode for both dfferent and equal values of currents n channels and from the range 0 0 under sngle-channel operaton mode. Dual-channel operaton mode Fgure 4 shows example dstrbuton patterns of magnetc flux lnes for the dual-channel operaton mode under assumpton that only the frst phases of both channels and wth phase currents beng fxed and equal to each other 0 for three rotor poston angles.e. 0 π/8 and π/8 producng flux dstrbuton patterns shown on Fgures 4a 4b and 4c respectvely. a b c Fg. 4. Magnetc feld dstrbutons patterns for 0 and: a 0; b π/8; c π/8 rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 95 Magnetc fluxes n the examned DCSRM follow the so-called short or long flux paths whch has an essental effect on resultant propertes of the machne and on the produced electromagnetc moment n partcular. Sngle-channel operaton mode Examples of the flux dstrbuton patterns under sngle-channel operaton mode for rotor poston angles 0 π/8 and π/8 under the assumpton that only the frst phase of channel s suppled wth current 0 are presented n Fgure 5. a b c Fg. 5. Magnetc feld dstrbutons patterns for 0 c π/8 0 and: a 0; b π/8; From analyss of the magnetc feld dstrbuton patterns one may draw a concluson that wth DCSRM operaton n the dual-channel mode and under the assumpton of equalty of currents n correspondng phases of channels and the resultant fluxes n the conductng poles of a gven channel s phases depend only on currents of these phases as the fluxes nduced by currents of the remanng phases vrtually cancel each other out. ased on feld theory calculatons for ndvdual phases of both channels and the socalled statc characterstcs of the motor were determned.e. phase self- and mutual fluxes and the resultant electromagnetc torque as functons of the current and the rotor poston... Statc characterstcs of the three-phase DCSRM ased on feld theory calculatons for ndvdual phases of both channels and phase self- and mutual fluxes and the torque were determned as functons of the current and the rotor poston angle. Dual-channel operaton mode Fgures 6 and 7 present example calculaton results for flux characterstcs and Fgure 8 shows a plot of motor torque e for dual-channel operaton mode under the assumpton that currents n both phases of channels and have the same ntensty. Sngle-channel operaton mode In Fgures 9 and 0 calculaton results for selected flux characterstcs are presented whle Fgure shows a plot of motor torque e all under sngle-channel operaton mode. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
96 P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. Fg. 6. he current-angle characterstcs of flux under dual-channel operaton mode Fg. 7. he current-angle characterstcs of flux under dual-channel operaton mode Fg. 8. orque e as a functon of current and angle under dual-channel operaton mode rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 97 Fg. 9. he current-angle characterstcs of flux under sngle-channel operaton mode Fg. 0. he current-angle characterstcs of flux under sngle-channel operaton mode Fg.. orque e as a functon of current and angle under sngle-channel operaton mode rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
98 P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. It can be seen from comparng Fgures 8 and that the resultant motor statc torque n dual-channel operaton mode for the same phase current values n both channels s more than twce as large as ths n the sngle-channel operaton mode. 4. nalyss of DCSRM voltage current and torque waveforms Smulatons of voltage current and torque waveforms were carred out for the machne supples n dual-channel and sngle-channel mode. y way of an example under dual-channel operaton mode Fgure shows smulatons results n the form of voltages and currents n ndvdual phases of channel as functons of the rotor poston whereas Fgure s a plot of the supply current as a functon of the same varable. he resultant motor electromagnetc torque as a functon of the rotor poston for the dual-channel operaton s presented n Fgure 4. Fg.. Phase voltages a and currents b of channel as functons of the rotor poston under dual-channel operaton For the sngle-channel operaton mode channel phase voltages and currents as functons of the rotor poston are shown n Fgure 5. Smlarly Fgure 6 presents waveforms of voltages nduced n three phases of channel for the sngle-channel operaton mode.e. wth channel beng suppled. Further Fgure 7 shows a plot of the supply current as a functon rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 99 Fg.. he supply current as a functon of the rotor poston under dual-channel operaton Fg. 4. he torque as a functon of the rotor poston under dual-channel operaton Fg. 5. Voltages a and currents b as functons of the rotor poston under sngle-channel operaton mode rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
00 P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. Fg. 6. Voltages nduced n channel phases as functons of the rotor poston angle under sngle-channel operaton mode Fg. 7. he supply current as a functon of the rotor poston under sngle-channel operaton mode Fg. 8. Channel torque as a functon of the rotor poston under sngle-channel operaton mode of rotor angle whle Fgure 8 presents the torque produced by the motor s channel as a functon of the same parameter under sngle-channel operaton mode. he average torque value eav of Fgure 8 s almost three tmes lower than that obtaned n the case of the dual-channel operaton mode Fg. 4. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 0 5. Results of laboratory tests wth a DCSRM model Laboratory tests were carred out wth a model of DCSRM desgned by the present authors. n overvew of the machne s shown n Fgure 9a whereas a vew of the stator and the rotor wth the bearng dsk s presented n Fgure 9b. a b Fg. 9. he DCSRM model: a stator; b rotor he torque-current-angle characterstcs measured for dfferent current values are shown n Fgures 0 and under dual- and sngle-channel operaton mode respectvely. Fgure presents plots of the motor torque average value eav as a functon of current I under snglechannel and dual-channel operaton mode. Fg. 0. Statc torque-angle characterstcs for dfferent current values under dual-channel operaton mode It follows from the statc characterstcs presented n Fgures 0 and that the torque produced n the dual-channel operaton mode s more than twce as large as the one observed under the sngle-channel operaton mode whch s a feature consstent wth the results of the smulaton calculatons. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
0 P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. Fg.. Statc torque-angle characterstcs for dfferent current values under sngle-channel operaton mode Fg.. orque average value as a functon of current under dual-channel and sngle-channel operaton mode Fg.. Channel phase voltage waveforms under dual-channel operaton mode rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 0 Fg. 4. Channel and phase current waveforms under dual-channel operaton mode Fg. 5. Channel phase voltage waveforms under sngle-channel operaton mode Fg. 6. Channel phase current waveforms under sngle-channel operaton mode rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
04 P. ogusz M. Korkosz J. Prokop rch. Elect. Eng. Fgures and 4 show plots of waveforms measured on the model and representng voltages and currents respectvely of the three motor phases under dual-channel operaton mode. Measured waveforms of the three phase voltages and the three phase currents are shown n Fgures 5 and 6 respectvely for channel under sngle-channel operaton mode whle Fgure 7 s a plot of waveforms representng voltages nduced on open termnals of ndvdual phases of channel. Fg. 7. Waveforms of voltages nduced n channel wth channel operatng under sngle-channel mode 6. Conclusons On the grounds of the research results presented above the followng conclusons can be drawn: $ he mathematcal model of dual-channel swtched reluctance motor proposed n ths paper takes nto account all lnkages occurrng between ndvdual phases of both channels and allows to develop a smulaton model capable to reproduce operaton of DCSRM under both dual-channel and sngle-channel mode. $ In dual-channel operaton mode the resultant motor torque s about.5 tmes larger than ths obtaned n the sngle-channel operaton mode and must not be calculated by means of smple addng the two torques produced by phase currents of both channels but the torque relatng to fluxes correspondng to lnkages between channels must also be taken nto account. $ oth statc characterstcs and tme-dependent waveforms measured on a laboratory model of DCSRM confrm fully the usefulness of the machne for operaton n both dual-channel and sngle-channel mode. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M
Vol. 64 05 Modellng and performance analyss of dual-channel swtched reluctance motor 05 Further research both smulatons and laboratory tests are requred to analyse DCSRM performance n the case of an asymmetry of supplyng and/or controllng both channels also n electrc falure condtons. References [] Radun.V. Ferrera C.. Rchter E. wo-channel Swtched Reluctance Starter/Generator Results. IEEE ransactons on Industry pplcatons 45: 06-04 998. [] Dng W. Lang D. Calculaton of Flux Lnkages of a /8 Dual-Channel SRM Includng Mutual Couplng and Saturaton: From Magnetc Crcut Model to FEM nalyss. Industry pplcatons Socety nnual Meetng IS 08. IEEE 008 pp. -8 008. [] Dng W. Lang D. Comparson of transent and steady-state performances analyss for a dualchannel swtched reluctance machne operaton under dfferent modes. Electrc Power pplcatons IE 48: 60-67 00. [4] Dng W Lang D Su H. Dynamc Modelng and Performance Predcton for Dual-Channel Swtched Reluctance Machne Consderng Mutual Couplng. IEEE ransactons on Magnetcs 469: 65-66 00. [5] Dng W. Comparatve Study on Dual-Channel Swtched Reluctance Generator Performances Under Sngle- and Dual-Channel Operaton Modes. IEEE ransactons on Energy Converson 7: 680-688 0. [6] Prokop J. Mathematcal models of multphase dual-channel swtched reluctance machnes. Przegląd Elektrotechnczny : 49-56 0 n Polsh. [7] ogusz P. Korkosz M. Prokop J. Statc characterstcs analyss of dual-channel swtched reluctance machne. Przegląd Elektrotechnczny 7a: 06-0 n Polsh. [8] ogusz P. Korkosz M. Prokop J. Mutual couplng analyss nfluence on dual-channel swtched reluctance motor propertes. Przegląd Elektrotechnczny 8: 09-6 0 n Polsh. [9] Prokop J. Mathematcal Modelng of Swtched Electrc Machnes. book n Polsh: Modelowane matematyczne maszyn elektrycznych przełączalnych Ofcyna Wydawncza Poltechnk Rzeszowske Rzeszów 0 Poland. [0] Dng W. Lu L. Lou J. Lu Y. Comparatve Studes on Mutually Coupled Dual-Channel Swtched Reluctance Machnes Wth Dfferent Wndng Connectons. IEEE ransactons on Magnetcs 49: 5574-5589 0. [] ML Documentaton MathWorks 0. rought to you by bloteka Glówna Zachodnopomorskego Unwersytetu echnologcznego w Szczecne uthentcated Download Date 6/6/5 9:5 M