S. A-JUFOUT and K. KHANDAKJI: DYNAMIC SIMUATION DYNAMIC SIMUATION OF STATING AND CHOPPE SPEED CONTO OF WOUND-OTO INDUCTION MOTO SAEH A-JUFOUT, KAMA KHANDAKJI Department of Electrcal Engneerng, Faculty of Engneerng, Tafla Techncal Unersty, Tafla, Jordan E-mals: drjufout@yahoo.com, drhandaj@yahoo.com Abstract: Ths research artcle presents dynamc smulaton of startng and speed-control of the wound-rotor nducton motor d on mathematcal modellng. The behaour of ths motor has been represented by a system of dfferental equatons for flux lnages and angular elocty. The dfferental equatons for the flux lnages hae been expressed n the Cartesan system of coordnates, whch decreased the number of equatons by one thrd. Startng and dfferent speed-control modes of the motor hae been computed and analyzed. The deeloped model has been erfed by drect comparson wth expermental results obtaned n the laboratory. Keywords: Wound-otor Motor, Startng, Speed Control, Dynamc Smulaton, Cartesan Coordnates. INTODUCTION The aalablty of specal-purpose smulaton languages, masse computng capabltes at a decreasng cost per operaton and adances n smulaton methodologes hae made smulaton one of the most wdely used and accepted tools n operaton research and system analyss. Smulaton enables the study of the nternal nteracton of a complex system, or of a subsystem wthn a complex system. The nowledge ganed n desgnng a smulaton model may be of great alue toward suggestng mproement n the system under nestgaton and by changng smulaton nputs and obserng the resultng output; aluable nsght may be obtaned n whch arables are most mportant and how arables nteract. Snce 999, n the laboratory of electrcal machnes at Tafla Techncal Unersty, a sgnfcant amount of research was deoted to the three-phase nducton motor: drect startng (Al-Jufout, 999; Al-Jufout, ); open-crcut transton wye-delta startng (Al- Jufout, ); autotransformer reduced oltage startng (Al-Jufout, ); arable-frequency dre (Al-Jufout, ); reclosng (Al-Jufout, ); symmetrcal and asymmetrcal modes of operaton (Al-Jufout, ), but we felt that the wor was ncomplete untl the operaton of the wound-rotor nducton motor was smulated. Ths smulaton s the subject of the proposed research artcle. Although a wound-rotor motor costs more than a squrrel-cage one, t offers many adantages: the wye-connected wth a common leer prodes speed control, torque adjustment at loced rotor and current lmtng durng startng and acceleraton (Wld, ). ecently, many artcles about the wound-rotor nducton motor are publshed. In (Sen, 99) a comprehense reew of the state of the art n the feld of electrc motor dres and control strateges s presented. It s ponted out that dre technology has seen mpresse growth durng the last three decades. In (Aran, 5) two orthogonal axs models for smulaton of three-phase nducton motors hang asymmetrcal wndngs and nter-turn short crcuts on the stator are presented. The frst model assumes that each stator phase wndng has a dfferent number of turns. The second model assumes that each phase has two wndngs n seres, representng the unaffected porton and the shorted porton, respectely. In (Zhang et al, ) the method to mplement the dynamc smulaton for an nducton motor ector-control system s explaned. A unfed method for modellng and smulaton of electrcal dres usng state-space formulaton n MATAB/Smuln s presented n (Hoang, ), where the proposed method has been successfully mplemented n a smulaton pacage called "Power System Blocset" for use n MATAB/Smuln enronment and an applcaton example of a drect torque control of the nducton motor dre s presented. In (Cunha et al, 5) the model of the nducton machne ncludng rotor bar and end-rng faults, wth a mnmum of computatonal complexty s deeloped. And a technque s beng deeloped whch wll allow the detecton and dentfcaton of specfc faults wthn -phase nducton motors durng the startng transent as explaned n (Elder et al, 989). In (Khandaj and Zdrozs, 5), a mathematcal analyss of hostng electrc dre system ncorporatng three-phase reersble oltage- I.J. of SIMUATION Vol. 8 No ISSN 7-8x onlne, 7-8 prnt
S. A-JUFOUT and K. KHANDAKJI: DYNAMIC SIMUATION controlled wound-rotor nducton motor s llustrated. In (Sh et al, 999; Seer and Ayaz, ; agonotte et al, 999; Boglett and Carpaneto, ; O'Sullan, ; Ayasun and Nwanpa, 5), dfferent models of the nducton motor are deeloped, but each of the aboementoned artcles soles one certan problem and mostly for steady-state conons. Although the speed control by the controller s relately an old technology, t s stll found n ndustry, thus, the objecte of ths paper s to deelop a comprehense mathematcal model for smulatng both the transent and steady-state operatng conons of the wound-rotor nducton motor, such as: unloaded and loaded startng wth current-, speed- or tme-controlled startng, shortcrcut at the termnals of the motor, sudden load change (fxed or arable load), speed control and any other symmetrcal operatng conons.. DYNAMIC MODE OF THE WOUND- OTO MOTO The three-phase, wound-rotor nducton motor can be mathematcally modeled by representng t as a system of dfferental equatons for flux lnages and angular elocty. The state equatons can be expressed n Cartesan coordnate system (, ) as follows: d d S S ( ) () S S µ d S ( ) () σ Ext µ ( ) () d Ext ) σ where S S d ( () = ( ) (5) J τ e τ m,,, - The flux lnages of the stator and the rotor crcuts n and coordnates respectely;,, - The resstances of the stator, rotor S Ext crcuts and the external startng respectely;, - The leaage nductances of the stator σ S σ and the rotor crcuts respectely;, S - The appled oltages n and coordnates respectely;, µ - The flux lnages of the magnetzaton branch n and coordnates respectely; - The angular elocty of the motor; J - The combned rotor and mechancal load nerta; τ, e τ - The electromagnetc and the mechancal m torque respectely. The electromagnetc torque and the flux lnages of the magnetzaton branch can be calculated as follows: τ e [ ] S = () S S = (7) µ S = (8) Where the contrbutng coeffcents can be calculated as follows: S = = σ µ µ σ σ where - The nductance of the magnetzaton branch. µ The stator currents can be calculated as follows: S S µ (9) () = () = () The acte and reacte powers can be determned by the followng formulas, by whch the power factor wth whch the motor operates can also be calculated: I.J. of SIMUATION Vol. 8 No ISSN 7-8x onlne, 7-8 prnt
S. A-JUFOUT and K. KHANDAKJI: DYNAMIC SIMUATION P Q S S = () S () S The starter and speed controller wth the use of contactors or a common leer can be smply modeled by logc conon operators or commands. Nowadays, the crcut shown n fgure s more wdely used. AC ne regulaton, smoothness and the ablty to be used n closed-loop control system for torque and speed control, where the equalent resstance of the external resstance s nersely proportonal to the duty cycle of the chopper. The duty cycle can be calculated as follows: D T T on cycle T on T on T = = (5) where T, on T - The duraton durng whch the thyrstor off s on and off respectely. off The maxmum alue of the external, n per unt, can be calculated as follows: To Control System To Control System Fgure : Chopper speed control of the wound-rotor nducton motor In adon to speed control, torque adjustment at loced rotor and current lmtng durng startng and acceleraton, ths crcut prodes better speed X = Ext. max S () where the reactance of the stator equals ts leaage nductance n per unt. Fgure shows the closed-loop control system for torque- and speed control of the wound-rotor motor, where the PID speed and rotor-current controllers allow speed and torque control n transent and steady-state conons. The rotor-current controller mantans constant dynamc (acceleratng or deceleratng) torque n transents, thus mnmzng the duraton of the transents. Here the speed controller mantans constant motor speed wth aratons of the load. Power Supply Setpont speed 5 7 Fgure : Closed-loop control system for torque and speed control of the wound-rotor motor: ) speed-controller, ) rotor-current controller, ) chopper, ) wound-rotor, 5) mechancal part of the motor, ) current sensor, 7) speed sensor Comparng the aboe descrbed model wth the exstng ones, the followng adantages can be obtaned: It s comprehense for smulaton of many symmetrcal operatng conons. It conssts only of fe dfferental equatons. The coeffcents n the dfferental I.J. of SIMUATION Vol. 8 No ISSN 7-8x onlne, 7-8 prnt
S. A-JUFOUT and K. KHANDAKJI: DYNAMIC SIMUATION equatons do not depend on the angular elocty; consequently there s no need to recalculate them at eery step of soluton. It can be used for both transent and steadystate analyss. Its parameters can smply be dentfed n per unt by usng the engneerng methods. egardless of these adantages the mentoned aboe numercal model can be used only for symmetrcal modes analyss, due to the use of Cartesan coordnate system.. EXPEIMENTA SETUP The tested motor s a standard three-phase woundrotor nducton motor for whch the ratngs are lsted n table. The motor s connected to a general power supply for laboratory conons. The load s quadratc and has a torque characterstc nearly proportonal to the square of the motor speed. Voltage, current and speed were measured and recorded usng a dgtal osclloscope. Two tests were performed: Drect startng wth startng shortcrcuted. oaded startng wth speed-controlled startng. Table : ated alues of the tested wound-rotor nducton motor Value ated Voltage, V ated Current, A ated Power, W ated Speed, rpm 8 Power Factor.75 Frequency, Hz 5 The parameters of the equalent crcut were determned expermentally and are lsted n table. Table : s of the equalent crcut of the tested motor Value, Ω esstance of the stator.9 eaage reactance of the stator.9 esstance of the rotor.8 eaage reactance of the rotor.5 eactance of the magnetzaton branch 5.5 Comparng the results measured n the laboratory for the aboe mentoned experments wth the modellng results aldates the deeloped model, where the error s wthn the range of (-5)%.. ESUTS AND DISCUSSION The aboe mentoned dfferental equatons can be soled by fourth-order unge-kutta method (chard and Douglas, ). The appled oltages are gen and the equalent crcut parameters (resstances and nductances) can be defned n per unt by engneerng methods (Ftzgerald et al, 99). Smulaton n ths paper s performed n per unt alues. Table dsplays the formulas used to determne the alues used n the aboedescrbed model. Table : Per unt system and alues used for the tested motor Value for Base Formula the Tested Motor Voltage, V Current, A Power, VA Impedance, Ω Angular Velocty, rad/sec. V I = V rated rated 9.59 = I. S = V V I 5.5 Z =.9 I = syn. Speed, rpm n = n syn. Z Inductance, H =. Torque, N.m Moment of Inerta, N.m.sec. Tme, sec. S P τ =. S P J t =. = / Table shows the parameters of the equalent crcut of the tested motor calculated n per unt. Table : s of the equalent crcut of the tested motor Value, p.u. esstance of the stator. eaage nductance of the stator. esstance of the rotor. eaage nductance of the rotor.78 Magnetzaton branch nductance.8 The mechancal load can be ether a constant or as a functon of the angular elocty (fan or pump load). In ths research the loadng coeffcent s gen by the followng formula: I.J. of SIMUATION Vol. 8 No ISSN 7-8x onlne, 7-8 prnt
S. A-JUFOUT and K. KHANDAKJI: DYNAMIC SIMUATION =..7 (7) To demonstrate the effect of the startng, the motor, frstly, s started wth short-crcuted startng. Fgure shows the phase tme-doman startng current, where the nrush current s 8.5 p.u. and the ampltude of the startng current s about 7.5 p.u. The startng duraton s.98 sec. 5-5 -....8....8 Fgure : The stator phase current of the woundrotor motor at start-up wth short-crcuted startng Fgure shows the electromagnetc torque of the motor at start-up wth short-crcuted startng, where the nrush torque s.9 p.u. and the startng torque s about.9 p.u. Fgure and fgure also show the steady-state conons, where the current s.85 p.u. and the electromagnetc torque s.78 p.u. 7.5 5.5 -.5-5....8....8 Fgure : The electromagnetc torque of the woundrotor motor at start-up wth short-crcuted startng The same tested motor wth the same loadng conons s started wth speed-controlled startng. Ths s assumed to hae four dscrete alues. The reducton of resstance s accomplshed by speed-controlled contactors or common leer. Fgure 5 shows the phase tme-doman startng current from whch t s obous that the startng prodes current lmtng durng startng and acceleraton, where the nrush current s 5.5 p.u. and the startng current s about.7 p.u. whle the startng duraton s decreased to. sec. as shown n fgure. Fgure 7 shows the electromagnetc torque of the motor at start-up wth speed-controlled startng that prodes hgher startng torque, where the nrush torque s 7. p.u. and the startng torque s about.5 p.u. Fgure 5, fgure and fgure 7 show that the steady-state conons are the same as before. - -.....5..7.8.9.. Fgure 5: The stator phase current of the woundrotor motor at start-up wth speed-controlled startng..8......5..7.8.9.. Fgure : The angular elocty of the wound-rotor motor at start-up wth speed-controlled startng 8 -.....5..7.8.9.. Fgure 7: The electromagnetc torque of the woundrotor motor at start-up wth speed-controlled startng The spes seen n the electromagnetc torque of fgure 7 are caused by the swtchng of the startng as shown n fgure 8 and may be undesrable for the dren mechansm. To obtan a smoother startng, the s to be controlled by the chopper shown n fgure. I.J. of SIMUATION Vol. 8 No 5 ISSN 7-8x onlne, 7-8 prnt
S. A-JUFOUT and K. KHANDAKJI: DYNAMIC SIMUATION Fgure 9 and fgure show the phase tme-doman startng current and electromagnetc torque at startup wth chopper speed-controlled startng. The startng process s smoother n comparson wth the one obsered n fgure 5 and fgure 7 respectely....8........5..7.8.9. Fgure 8: The alue of speed-controlled startng connected to the wound-rotor 8 - - - -8.....5..7.8.9.. Fgure 9: The stator phase current of the woundrotor motor at start-up wth chopper speedcontrolled startng 8 -.....5..7.8.9.. Fgure : The electromagnetc torque of the woundrotor motor at start-up wth chopper speedcontrolled startng 5. CONCUSION A mathematcal model for the dynamc smulaton of startng and speed control of the wound-rotor nducton motor has been deeloped and expermentally erfed. Ths model conssts of a system of dfferental equatons for flux lnages and angular elocty. The number of these dfferental equatons s decreased by one thrd by usng the Cartesan coordnate system. The model allows for the obseraton of the followng arables: Stator and rotor currents; Acte and reacte powers; Power factor wth whch the motor operates; Torque and angular elocty; Angular rotor poston (one more dfferental equaton should be added to the model). It allows for the dynamc smulaton of the followng operatng conons: oaded and unloaded startng wth current-, speed- or tme-controlled startng ; Impulse- speed control; Sudden load change (fxed or arable load); Short-crcut at the motor termnals; oced rotor. In adon, the model can be used for the smulaton of both transent and steady-state operatng conons, whle the use of the Cartesan coordnate system restrcts ts use only for symmetrcal modes of operaton. EFEENCES Al-Jufout S.A. 999, "Modellng of Transents and Steady-State Operaton of the Inducton Motor," In Proc. th European Smulaton Symposum. Socety for Computer Smulaton Internatonal, pp. 7-7, Germany. Al-Jufout S.A., "Analyss of the Squrrel-Cage Inducton Motor Startng Process on the Bass of Computatonal Modellng," Smulaton Seres, Socety for Computer Smulaton Internatonal, ol., no., pp. 5-8, USA. Al-Jufout S.A., "Dynamc Behaor Analyss of Open-Crcut Transton Wye-Delta Starter," Pastan Journal of Appled Scences, Asan Networ for Scentfc Informaton, ol., no. 8-9, pp. 579-58, Pastan. Al-Jufout S.A., "Modellng of the Autotransformer-Type educed-voltage Starter," In Proc. th Internatonal Conference on Qualty, elablty and Mantenance, Professonal Engneerng Publshng mted, Unersty of Oxford, pp. 7-, UK. Al-Jufout S.A., "Computatonal Modellng for Sold-State Varable-Frequency Inducton Motor Dre," In Proc. th European Smulaton Multconference, Socety for Computer Smulaton Internatonal, pp. 9-, Belgum. I.J. of SIMUATION Vol. 8 No ISSN 7-8x onlne, 7-8 prnt
S. A-JUFOUT and K. KHANDAKJI: DYNAMIC SIMUATION Al-Jufout S.A., "Analyss of the Inducton Motor eclosng Process," In Proc. nd Mddle East Symposum on Smulaton and Modellng, Socety for Computer Smulaton Internatonal, pp. 5-9, Jordan. Al-Jufout S.A., "Modellng of the Cage Inducton Motor for Symmetrcal and Asymmetrcal Modes of Operaton," Computers & Electrcal Engneerng Internatonal Journal, Pergamon- Elseer Scence td., ol. 9, no. 8, pp. 85-8, UK. Aran M., Kostc-Peroc D. and Unsworth P.J. 5, "Modellng and Smulaton of Inducton Motors wth Inter-Turn Faults for Dagnostcs," Electrc Power Systems esearch, ol. 75, no., pp. 57-. Ayasun S. and Nwanpa O. 5, "Inducton Motor Tests usng MATAB/Smuln and ther Integraton nto Undergraduate Electrc Machnery Courses," IEEE Transacton on Educaton, ol. 8, no., pp. 7-. Boglett A. and Carpaneto E., "An Accurate Inducton Motor Hgh Frequency Model for Electromagnetc Compatblty Analyss," Electrc Power Components and Systems, ol. 9, pp. 9-9. Cunha C.C., yra.o. and Flho B.C. 5, "Smulaton and Analyss of Inducton Machnes wth otor Asymmetres," IEEE Transactons on Industry Applcatons, ol., no., pp. 8-. Elder S., Watson J.F. and Thomson W.T. 989, "Fault Detecton n Inducton Motors as a esult of Transent Analyss," In Proc. th Internatonal Conference on Electrcal Machnes and Dres, pp. 8-8. Ftzgerald A.E., Kngsley C.Jr. and Umans S. D. 99, Electrc Machnery, McGraw Hll, UK. Hoang., "Modellng and Smulaton of Electrcal Dres Usng MATAB/Smuln and Power System Blocset," In Proc. 7 th Annual Conference of the IEEE Industral Electroncs Socety, ol., pp. -. Khandaj K.A. and Zdrozs K. 5, "Determnaton of Qualty s of Hostng Electrc Dre Systems wth -Phase Inducton Motors," In Proc. 5 th Internatonal Conference on Technology and Automaton, pp. 9-9. agonotte P.T., Mah H.A. and Poloujadoff M. 999, "Modellng and Identfcaton of s of Saturated Inducton Machne Operatng under Motor and Generator Conons," Electrc Power Components and Systems, ol. 7, pp. 7-. O'Sullan T.M., Schofeld N. and Bngham C.M., "Smulaton and Expermental Valdaton of Inducton Machne Dynamcs Drng Mult-Inertal oads," Internatonal Journal of Appled Electromagnetcs and Mechancs, ol. 9, pp. -. chard. and Douglas J., Numercal Analyss, Broos/Cole Publshng Company, 7 th ed. USA. Seer S. and Ayaz E., "A elablty Model for Inducton Motor Ball Bearng Degradaton," Electrc Power Components and Systems, ol., pp. 9-5. Sen, P.C. 99, "Electrc Motor Dres and Control- Past, Present, and Future," IEEE Transactons on Industral Electroncs. ol. 7, no., pp. 5-575. Sh K.., Chan T.F., Wong Y.K. and Ho S.. 999, "Modellng and Smulaton of the Three-Phase Inducton Motor usng Smuln," Internatonal Journal of Electrcal Engneerng Educaton, ol., pp. -7. Wld T., Electrcal Machnes, Dres and Power Systems. Prentce Hall, USA. Zhang C., Meng S., u J. and Zhao Z., "Dynamc Smulaton for Inducton Motor Vector- Control System," Journal of Unersty of Scence and Technology, ol., no., pp. -7. Bejng. AUTHOS BIOGAPHIES: Dr. Saleh Abdel-Hamd Al-Jufout receed hs Ph.D. n Electrcal Power Engneerng from Donets Natonal Techncal Unersty. In 997 he joned Al-Balqa' Appled Unersty then Tafla Techncal Unersty n 5. Currently, he s an assocate professor and Dean of Academc esearch and Graduate Studes. Hs research nterest ncludes mathematcal modellng of electrcal power systems, machnes and ther protecton. Dr. Kamal Abd Al-Majeed Khandaj receed hs Ph.D. n Electrc Dres and Automaton n 999 from o Natonal Polytechnc Unersty. In, he joned Al-Balqa' Appled Unersty then Tafla Techncal Unersty n 5. Currently, he s an assstant professor at Faculty of Engneerng. Hs research nterest ncludes enhancng the performance of electrc dres usng mcroprocessor control, nestgaton of abnormal modes of power semconductor dres and sual postonng. I.J. of SIMUATION Vol. 8 No 7 ISSN 7-8x onlne, 7-8 prnt