Two-Phase Asynchronous Motor - Simulation and Measurement
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1 Zeszyty problemowe Maszyny Elektryczne Nr 1/13 cz. II 5 Želmíra Ferková, Ján Kaňuch Techncal Unversty of Košce Two-Phase Asynchronous Motor - Smulaton and Measurement Abstract: The paper addresses modellng of a two-phase nducton motor. Based on geometrc dmensons, the model was created n the D and 3D ANSYS Maxwell program. Transent process at the motor start-up was calculated wthn the same program, too. Another model was made up based on the nducton motor mathematcal descrpton n the MATLAB/Smulnk program. Waveforms of the motor currents and torques are compared. Models created n MATLAB/Smulnk and ANSYS are compared wth measurements. For measurements was used a symmetrcal two phase power supply. 1. Introducton Three-phase nducton machnes are powered by three-phase symmetrcal voltage. Wndngs of the motors are arranged wthn the stator and mutually shfted by 1 electrcal degrees. These machnes operate wth crcular magnetc felds. Sngle-phase motors have two wndngs (phases) n ther stators, whch are mutually shfted by 9 electrcal degrees. One of the wndngs s man and the other one s auxlary. Both phases are powered by s sngle-phase network. Tme shft of the voltage n the auxlary wndng s usually due to a capactor connected n seres wth the auxlary wndng. Ths creates an ellptc magnetc feld. The motor torque conssts of a forward and a backward component. If both man and auxlary wndngs of a snglephase motor wll be dentcal and powered by two-phase voltage, crcular magnetc feld wll be developed wthn the machne. The paper compares ndvdual two-phase motor models, one developed wthn MATLAB/Smulnk and the other n the ANSYS Maxwell program. The ANSYS Maxwell model works on geometrc dmensons and takes nto consderaton non-lnearty of the used magnetc materal. The MATLAB/ Smulnk model works wth constant parameters that were attaned by measurements performed on a real motor.. Mathematcal model To smulate two-phase motor n MATLAB/ Smulnk program used was a model that takes nto account asymmetrcal wndngs [1]. Varyng number of turns n phases reflects parameter a. The system of fxed stator coordnates α-β s appled. In ths specfc case, asymmetry of the nvestgated motor parameters s due to the wndng producton. Number of turns n the man and auxlary phases s dentcal. Components of stator and rotor voltages of twophase nducton motor can by expressed as follows: d s us Rs s (1) d s us Rss () r r u Rr r ar r (3) d r ur Rrr ar r (4) where a - s the man per auxlary wndng turns rato. The components of stator and rotor flux lnkages are: s Ls s Lm r, s Lss Lmr L L, L L r m s r r r m s r r The components of stator and rotor currents are: Lψ L L L Lψ L L L ψ mα Lmα ψ mα Lmα,, Lψ Lmβψ L L L mβ L ψ L ψ mβ L L L mβ (5) (6) Electromagnetc torque produced by the machne s gven by the equaton (7). m p( L L ) (7) m s r m s r
2 6 Zeszyty problemowe Maszyny Elektryczne Nr 1/13 cz. II d m m J (8) z where: s, s, r, r are the stator and rotor flux lnkages, s, s, r, r are the stator and rotor currents, Ls, Lr, Lm are the stators, rotor, magnetzng nductances, R, R are the stator and rotor resstances, J s m r s the electrcal rotor angular speed, s the rotor moment of nerta, s the electromagnetc torque of motor. 3. Model of the motor n ANSYS/Maxwell The same motor was smulated n the ANSYS/ Maxwell program. When drectly connected to the voltage the start-up of the motor was calculated. The motor magnetc feld was calculated by the fnte elements method n D and 3D space. Fg. Magnetc feld of motor (Maxwell D) Fg. 1 Model of two-phase motor Taken nto account at calculatng were nonlnear propertes of the magnetc crcutry materal. In space llustrated used motor model s shown n Fg. 1. Waveforms of the magnetc feld calculated n Maxwell D are shown n Fg. for tme t=,15 s (Fg. and tme t=,5 s (Fg.. Dstrbuton of the B- vectors calculated n Maxwell 3D for tme t=,1 s s shown n Fg. 3. The motor s suppled by two-phase symmetrcal voltage. Calculated waveforms of currents for ndvdual phases, the nner torque and speed are demonstrated n Fg. 4 for D smulaton and n Fg. 5 for 3D smulaton. [A] Fg.3 B-vectors calculaded by Maxwell 3D Wndng Currents Curve Info Current(PhaseA) Current(PhaseB)
3 Zeszyty problemowe Maszyny Elektryczne Nr 1/13 cz. II 7.8 Torque Movng1.Torque 3 5 Speed 3D Curve Info Movng1.Speed Torque [NewtonMeter] speed [rpm] [A] Torque [mnewtonmeter] 3 1 XY Plot Movng1.Speed 1 3 c) Fg. 4 Calculated waveforms of two-phase motor- D soluton: ( -currents, -torque, c)-speed ) Current 3D Current(PhaseA) Current(PhaseB) Torque 3D Movng1.Torque Movng1.Speed [rpm] c) Fg. 5 Calculated waveforms of two-phase motor- 3D soluton: ( -currents, -torque, c)-speed ) There are small dfferences between the solutons n the transent state. They are caused manly by dfferent number of elements and by nfluence of the end wndngs. 3D soluton worked wth mesh elements (the calculaton took approxmately 15 hours) and D soluton worked wth 498 mesh elements (calculaton took several mnutes). 4. Computer smulaton and expermenttal results Based on equatons 1-8, model of the two-phase asynchronous motor n the MATLAB/Smulnk program was created. For calculatons used motor parameters (resstances, nductances, and the moment of nert had been attaned by measurements performed on a specfc motor. Suppled values are shown n table 1. Table 1: Parameters of the motor R = 3,9 R = 51 R = 31,1 R = 51,35 L mα = 1,187 H L = 1,77 H L mβ = 1,35 H L = 1,4 H L = 1,77 H J=,16 kg.m L = 1,4 H f= 5 Hz Start-up of the motor through drect connectng to the supply wthout loadng was smulated. The calculated waveform was compared wth results of measurement performed on a real two-phase motor. For the sake of precson, fed to the model nput was voltage as sensed readoff durng measurements (Fg. 6). From the pcture t s obvous that the supply voltage was not perfectly snusodal and that the supply was relatvely soft. Calculated angular speed waveform s shown n Fg. 9, and calculated motor torque waveform n Fg. 1.
4 8 Zeszyty problemowe Maszyny Elektryczne Nr 1/13 cz. II Waveforms of currents attaned by modellng were comparable wth the measurement results. Fg. 7 llustrates the calculated waveform of the frst phase current, and also measured current waveform. Shown n Fg. 8 are both calculated and measured waveforms of the second phase current. The waveforms demonstrate relatvely hgh degree of congruence. speed [rpm] tme [ms] Fg. 9 The rotaton speed of the two-phase nducton motor.8 Fg. 6 The supply voltage of the two-phase nducton motor (the frst and second phase) Fg. 7 Comparson of the current n frst phase n smulaton and measurement of the twophase nducton motor Fg. 8 Comparson of the current n second phase n smulaton and measurement of the two-phase nducton motor torque [Nm] tme[ms] Fg. 1 The electromagnetc torque of the twophase nducton motor at no-load start Fgures 11 and 1 compare calculated waveforms of the torque and currents obtaned from MATLAB/Smulnk and ANSYS Maxwell D. At the nput of both models there was smultaneously two-phase symmetrcal 115 V, 5 Hz sne voltage. Start-up by drect connectng and wthout loadng was smulated n both cases. In Fgs. 11 and 11 there are compared the waveforms of currents of ndvdual phases. The torque waveforms are compared n Fg. 1. Good agreement of current waveforms can be seen n the steady state. The program ANSYS Maxwell takes nto account the magnetc crcut non-lnear propertes, whch led to dfferences between the current waveforms n the transent process. Oscllatons n the torque waveforms are due to not entrely perfect symmetry of wndngs. Taken nto account n the Maxwell waveform s non-lnearty of the motor parameters, as well as the mpact of wndng slots.
5 Zeszyty problemowe Maszyny Elektryczne Nr 1/13 cz. II 9 1 Matlab/Smulnk Maxwell D A [A] t [ms] 1 Matlab/Smulnk Maxwell D B [A] tme [ms] Fg. 11 Comparson of calculated waveforms of the current n programs MATLAB/Smulnk and ANSYS Maxwell D Fg. 13 Comparson of calculated waveforms of the current n programs ANSYS Maxwell D and ANSYS Maxwell 3D Torque [Nm] Matlab/Smulnk Maxwell D tme[ms] Fg. 1 Comparson of calculated of the torque waveforms n programs MATLAB/Smulnk and ANSYS Maxwell D Waveforms of currents and torque obtaned from ANSYS Maxwell D and 3D are compared n Fg. 13 and Fg. 14. Fg. 14 Comparson of calculated of the torque waveforms n programs ANSYS Maxwell D and ANSYS Maxwell 3D
6 3 Zeszyty problemowe Maszyny Elektryczne Nr 1/13 cz. II Concluson The paper presents three two-phase motor models. The frst model of the same motor was developed n MATLAB/Smulnk programs, the second one n ANSYS Maxwell D and the thrd model n ANSYS Maxwell 3D. We have compared results of waveforms from models. The results are not dentcal: the Smulnk model works wth constant parameters, whlst the ANSYS Maxwell D and 3D programmes calculate the magnetc feld usng the fnal elements method. The ANSYS Maxwell takes nto account nonlnearty of the magnetc materal, losses n the ron, as well as the nfluence of wndng slots. Whereas n queston s a D calculaton, nfluence of the end wndng s consdered only through addtonal nductance and resstance. Only the MATLAB/Smulnk model has been compared wth measurement results. The waveforms show approprate smlarty. The hgher current waveforms are caused manly by hgher harmoncs of the supply voltage. Acknowledgement We support research actvtes n Slovaka / Project s cofnanced from EU funds. Ths paper was developed wthn the Project "Centrum excelentnost ntegrovaného výskumu a využta progresívnych materálov a technológí v oblast automoblovej elektronky", ITMS 6155 (%). Ths work was supported by the Slovak Research and Development Agency under the contract No APVV (8%) Bblography [1] Kumsuwan, Y. - Srrattanawchakul, W. - Premrudeepreechacharn, S.: Analyss of two-phase nducton motor usng dynamc model based on MATLAB/Smulnk. Asan Journal on Energy and Envronment 1, 11(1), pp [] Ojo, O. - Omozus, O.: Parameter Estmaton of Sngle-Phase Inducton Machnes. IEEE Industry Applcatons Conference, vol. 4, September/October, pp [3] Popescu, M., E. - Demeter, D. - Mcu, V.: "Analyss of a voltage regulator for a two phase nducton motor drve." IEEE/IEMDC, May pp [4] Cracunas, G.: Feld orented control of a two phase nducton motor, Internatonal Symposum on System Theory, XI Edton, Craova, 3, pp [5] Hrabovcová V. - Rafajdus P.: Radal magnetc forces of sngle-phase permanenr splt-capactor motor. Journal of ELECTRICAL ENGINEERING, VOL. 57, NO. 4, 6, [6] Hrabovcová, V. - Rafajdus, P. - Franko, M.: Measurng and modelng of the electrcal machnes. Unversty of Žlna press, 4, Slovaka, (n Slovak). [7] Abdel-Rahm, N. - Shaltout, A.: Unsymmetrcal two-phase nducton motor drve wth slpfrequency control. IEEE Trans. Energy Converson, Vol. 4, No.3, September 9, pp [8] Krshnan, R.: Electrc Motor Drves: Modelng, Analyss and Control. Upper Saddle Rver, NJ: Prentce-Hall, 1, p. 35. [9] Kumsuwan, Y. - Watcharn, S. - Suttcha, P.: Analyss of a two-phase nducton motor usng dynamc model based on MATLAB/Smulnk. Asan Journal on Energy and Envronment, 11, no.4, pp Authors Ž. FERKOVÁ (doc. Ing. CSc.) graduated n electrcal engneerng from the Techncal Unversty Košce n 198 and receved her CSc. degree n At present she s actve as assocated professor of electrc machnes at the Department of Electrcal Engneerng and Mechatroncs, FEEaI TU Košce. Her professonal area covers desgn of electrcal machnes and ther performance. J. KAŇUCH (Ing. PhD.) graduated n electrcal engneerng from the Techncal Unversty Košce n 1986 and receved hs PhD. degree n 6. At present he works as assstant professor of electrcal engneerng and electrc machnes at the Department of Electrcal Engneerng and Mechatroncs, FEEaI TU Košce. Hs professonal area covers desgn of electrcal machnes, ther performance and vehcle electroncs. Revewer prof. dr hab. nż. Meczysław Ronkowsk
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