Modeling and Simulation of Voltage Source Inverter with Voltage Drop and Its Application for Direct Torque Control of Induction Motors

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1 Modeling nd Simultion of Voltge Source Inverter with Voltge Drop nd Its Appliction for Direct Torque Control of Induction Motors H. L. Bui,*, Shoudo Hung, D. C. Phm College of Electricl nd Informtion Engineering, Hunn University, Chin. College of Electricl Engineering, Hnoi University of Industry, Vietnm. Deprtment of Electricl Engineering, Industril University of Ho Chi Minh City, Vietnm. * Corresponding uthor. Tel.: ; emil: blhien@yhoo.com Mnuscript submitted October, 06; ccepted October 8, 06. doi: /ijcee Abstrct: Power electronics nd electricl mchines nowdys offer n extremely wide rnge of industril pplictions. Their modeling nd simultion re lso gret interest to engineers. In some simultion pplictions, nonliner of the power electronic devices is neglected due to its simplicity. Therefore, the performnce of the control system obtined is not the sme s experimentl results. In this pper, model of two-level three-phse voltge source inverter hving its voltge drops is proposed. Then ppliction to direct torque control of three-phse induction motors with the proposed model hs studied. Finlly, the simultion results re provided to verify the effectiveness of the proposed work. Key words: Direct torque control, modeling nd simultion, three-phse induction motor, inverter, voltge drop.. Introduction Power electronics nd electricl mchines hs been mjor chnge in industril pplictions in recent yers []-[6], including electric, hybrid, nd plug-in vehicles (EVs) in the utomotive industry [7], photovoltic (PV) [8] nd wind energy conversion systems (WECS) in the renewble energy industry, [9] or high voltge direct current (HVDC) nd flexible c trnsmission systems (FACTS) [0]. Specilly, two-level three-phse voltge source inverter (VSI) is considered s mture technology nd becoming n industril stndrd for the demnd for energy sving. Accordingly, ppliction to VSI fed three-phse induction motors (IM) cn be considered vlid solution for energy sving becuse these motors re simple nd rugged electricl mchine with dpttion to severl lod situtions, nd low cost cquisition nd mintennce. Direct torque control (DTC) is one of the dvnced control schemes for c drives [4], []. It is chrcterized by simple control lgorithm, esy digitl implementtion nd robust opertion. In recent yers, direct torque control (DTC) strtegies of induction motor (IM) drives hve been widely implemented in industril vrible speed pplictions which it is one of the dvnced control schemes for c drives. Introduced in the middle of the 980s, it is chrcterized by simple control lgorithm, esy digitl implementtion nd robust opertion. Since then, severl investigtions crried out in order to improve the performnce of the originl DTC strtegy. The mjor focused fetures re the uncontrolled switching 94

2 frequency of the inverter nd the high torque ripple resulting from the use of flux nd torque hysteresis controllers [4]. S S vb S S S5 b S6 S vb b c S4 S5 S4 S6 S c () An idel voltge source inverter. (b) A rel voltge source inverter with IGBTs/Diodes. Fig.. Voltge source inverter. In some simultion pplictions, minly the voltge drops of the power electronic devices (e.g. IGBTs, Diodes etc.) re neglected due to its simplicity []. Therefore, the performnce of the control system obtined is not the sme s the experimentl results []. In order to overcome this, the model of non-idel two-level three-phse VSI (rel VSI) is proposed in the pper. Then ppliction to direct torque control of three-phse induction motors with the proposed model re studied. The pper is structured so tht model of n ide inverter is reviewed in Section. Section proposes rel inverter. A generl description of the induction motor model is showed in Section 4. The direct torque control is discussed in Section 5, the simultion results re showed in Section 6, nd conclusions re drwn in Section 7.. Model of n Ide Inverter Fig. () shows n idel two-level three-phse voltge source inverter (VSI) with six idelized switches, S to S6 nd dc constnt voltge source connecting three-phse lod. This inverter hving the power devices is considered s idel switches which there re no snubbers nd gte drive circuits. Ech phse leg of the VSI is represented by switch tht hs three input terminls s follow: vs v 0 vs 0 () vbs vb 0 vs 0 () vcs vc 0 vs 0 () where vs, vbs, nd vcs re the phse-to-neutrl voltges. vs vbs vcs v 0 vb 0 vc 0 vs 0 (4) Assuming tht the system is blnced opertion vs vbs vcs 0 v 0 vb 0 vc 0 v v v vs 0 b 0 c 0 vs 0 95 (5) (6) (7)

3 vbs vb 0 vc 0 v 0 (8) vcs vc 0 v 0 vb 0 (9) Equtions (7)-(9) re model of n idel VSI. / vo / / -/ vn S g / vbo / vbn S vco / / vcn S5 Fig.. MATLAB/Simulink model for n idel VSI []. Fig. shows MATLAB/Simulink model for n idel VSI, including six idelized switches.. Model of Rel Inverter The power electronic devices (e.g. IGBTs, Diodes etc.) re nonliner. It is well-known tht the voltges drop of the power electronic devices cuses distorted motor voltge nd incresing motor current hrmonic distortion, nd reduction of the fundmentl voltge/current component. This model includes the voltge drops in the IGBT switching devices nd the freewheeling diodes which is shown in Fig. (b). It is known tht the instntneous voltge drops of one converter leg presented by switching device or freewheeling diode cn be represented by n on-stte forwrd voltge drop connected in series with n on-stte resistnce. Thus, this voltge drop of one inverter leg cn been clculted by Eqution (0) [] vdrop v f Roni (0) where vf is the on-stte forwrd voltge drop nd Ron is the on-stte resistnce. In ddition, the inverter voltge drop on one inverter leg depends on both its instntneous switching stte nd its relevnt phse current direction. There re four cses considered s follows: Cse : if the current flows to lod ( > 0) nd the (S=) s shown in Fig. () then the terminl voltge vo is defined by cn been clculted s vo vi v fi Roni () where vi is the voltge drop of the IGBT; vfi nd Roni re the forwrd drop of IGBT, on-stte resistnce of IGBT, respectively. Cse : if ( < 0) nd the (S=) s shown in Fig. (b) then the terminl voltge vo is defined by vo vd v fd Rond () where vd is the voltge drop of the Diode; vfd nd Rond re the forwrd drop of Diode, on-stte resistnce of Diode, respectively. Cse : if the current flows to lod ( < 0) nd the (S= 0) s shown in Fig. (c) then the terminl voltge vo is defined by 96

4 vo vi v fi Roni () Cse 4: if the current flows to lod ( > 0) nd the (S= 0) s shown in Fig. (d) then the terminl voltge vo is defined by vo vd v fd Rond (4) Equtions (7)-(9) nd Equtions ()-(4) verify mthemticl model of VSC hving its voltge drop. S v V fi S vi Roni v S4 0 (b) S= nd < 0 S 0 S 0 V fi S4 v S4 0 () S= nd > 0 V fd S vd Rond vi V fd v S4 Roni vd v Rond (c) S=0 nd < 0 (d) S=0 nd >0 Fig.. Anlysis of ech phse leg for proposed VSI. -bs (u[])*roni -vfi Cse +u[]+bs(u[])*rond vfd Cse Diode -u[]-bs(u[])*rond S v 0 Cse 4 Vf+bs (u[])*roni Cse () MATLAB/Simulink model on one rel VSI leg. ibcs i_ v _0 S inverter _leg _ i_b g v _b0 Sb inverter _leg _b i_c v _c0 Sc inverter _leg _c (b) MATLAB/Simulink model on three rel VSI legs Fig. 4. Anlysis MATLAB/Simulink model of proposed VSI. 97

5 Bse on Equtions (7)-(9) nd Equtions ()-(4), MATLAB/Simulink model on one rel VSI leg is developed s shown in Fig. 4(). Also, Fig. 4(b) shows MATLAB/Simulink model of VSI hving its voltge drops. 4. Mthemticl Model of Three-Phse Induction Motors 4.. Voltge Equtions The voltge equtions with respect to mchine vribles my be expressed s v s Rs i s v r Rr ir dλs j λs dλr j ( r )λr (5) (6) where v s nd vr re the sttor nd rotor voltge vectors, respectively; is nd ir re the sttor nd rotor current vectors, respectively; λs nd λr re the sttor nd rotor flux linkge vectors, respectively; Rs nd Rr re the sttor nd rotor winding resistnce, respectively. 4.. Flux-Linkge Equtions The flux-linkge equtions my be expressed s where λs Ls i s Lm ir (7) λr Lr ir Lm i s (8) Ls Lls Lm represents the sttor self-inductnce; Lr Llr Lm represents the rotor self-inductnce; Lls nd Llr re the sttor nd rotor lekge inductnces, respectively; nd Lm is the mgnetizing inductnce. Note tht ll the rotor prmeters nd vribles, such s Rr, Llr, ir, ir nd, in the bove questions re referred to the sttor side. 4.. Electromgnetic Torque Eqution The electromgnetic torque eqution, given Te P Lm s r sin T Ls Lr (9) where P is the number of pole pirs Motion Eqution The motion eqution, given d r P Te TL J (0) where J is the totl moment of inerti of the rotor nd lod, P is the number of pole pirs, TL is the lod torque 5. Direct Torque Control DTC is n dvnced control method originlly developed for induction mchine drives, which is good solution for medium nd high power electricl drive pplictions. This method hs dvntge in terms of 98

6 ese of implementtion nd less computtion time. The DTC is chrcterized by the bsence of PI regultors, coordinte trnsformtions, current regultors, nd PWM signls genertors. However, the DTC presents some disdvntges tht cn be summrized in the following points such s difficulty to control torque nd flux t very low speed, vrible switching frequency behvior, high noise level t low speed, lck of direct current control. The principle nd implementtion of DTC re follows s 5.. Principle of Direct Torque Control The electromgnetic torque is given by the following eqution Te P Lm s r sin T Ls Lr () The dynmic of the sttor flux vector is governed by the sttor voltge eqution expressed in the sttionry reference frme, s follows dλs v s Rs is () Neglecting the voltge drop Rsis cross the sttor resistnce dλs vs () The torque comprtor s Te *, for Te Te T T dte 0, for e Te* Te e T * e, for Te Te (4) The flux comprtor s *, for s s d s 0, for * s s (5) 5.. Sttor Flux nd Torque Clcultion The sttor voltge component estimtion eqution to estimte the sttor flux s follows v s Rs i s d s (6) The sttor flux component estimtion eqution to estimte the sttor flux s follows s v s Rs i s (7) The sttor voltge component estimtion eqution to estimte the sttor flux s follows v s Rs i s d s (8) The sttor flux component estimtion eqution to estimte the sttor flux s follows 99

7 s v s Rs i s (9) The electromgnetic torque estimtion eqution is given by the following eqution Te p si s si s *s + - PI Te* Speed Te controller Flux error s *r (0) + S - Flux controller Switching tble Torque error + S - Flux sector Torque controller Motor Flux nd torque signls estimtor IM Fig. 5. DTC scheme for n induction motor drive. Tble. Motor Prmeters Prmeter Rted sttor line-line voltge Rted speed Number of pole pirs Rted sttor frequency Rted torque Sttor winding resistnce Rotor winding resistnce Sttor lekge inductnce Rotor lekge inductnce Mgnetizing inductnce Moment of inerti Symbol Vn nr P f Tn Rs Rr Lls Lr Lm J Vlue Unit V rpm Hz N.m H H H kg.m Tble. Prmeters of Proposed Inverter Prmeter Forwrd drop of IGBT On-stte resistnce of IGBT Forwrd drop of Diode On-stte resistnce of Diode Symbol vfi Roni vfd Roni Vlue Unit V V The mgnitude of sttor flux linkge vector is given by s s s () The ngulr position of sttor flux linkge vector is given by s rctn s s () 5.. Control System The block digrm of the DTC control system for the IM is shown in Fig. 5. This block includes the DTC controller, VSI, nd IM. 00

8 () vs () vs (b) vbs (b) vbs (c) vcs (c) vcs (d) Three-phse currents (d) Three-phse currents (e) Flux Te (N.m) (e) Flux (f) Electromgnetic torque Fig. 7. Performnce nlysis of idel VSI. (f) Electromgnetic torque Fig. 6. Performnce nlysis of proposed VSI. 6. Simulted Studies In order to fully study the effect of the forwrd voltges drop of the power electronic devices in the power converter on the performnce of control system, comprtive simultion studies were crried out by using MATLAB/Simulink. The simultion method uses Runge-Kutt lgorithm with step size of 0.00ms. First, the MATLAB/Simulink model of IM is built bsed on its mthemticl model which is shown in the section 4. 0

9 The prmeters of the motor re given in Tble. In the simultion, the sttor flux linkge reference is set to Wb. Also, the Electromgnetic torque reference is set to.65 N.m. The DC bus voltge of inverter is set to 00 V. Tble shows prmeters of proposed inverter. The proposed inverter is compred to the idel inverter in terms of its bility to DTC of IM by evluting: () The phse A output voltge wveform; (b) The phse B output voltge wveform; (c) The phse C output voltge wveform; (d) The phse A, phse B, nd phse C output voltge wveforms; (e) Mgnitude of sttor flux linkge vector; (f) Electromgnetic torque. Fig. 6 shows set of simultion wveforms for ppliction DTC of IM with proposed inverter. Fig. 6() illustrtes the proposed inverter output voltge wveform in phse A. Fig 6(b) illustrtes the proposed inverter output voltge wveform in phse B. Fig. 6(c) illustrtes the proposed inverter output voltge wveform in phse C. It is obvious from Fig. 6(), Fig. 6(b), nd Fig. 6(c) tht reduction the voltge components. Similrly, Fig. 7 shows set of simultion wveforms for the idel inverter study. Fig. 7() illustrtes the proposed inverter output voltge wveform in phse A. Fig. 7(b) illustrtes the proposed inverter output voltge wveform in phse B. Fig. 7(c) illustrtes the proposed inverter output voltge wveform in phse C. It is obvious from Fig. 7 tht no reduction of the voltge components. As cn be seen in Figs. 6(f) nd 7(f) tht higher electromgnetic torque ripple under the proposed inverter when compred to the idel inverter cse. These simultion results confirm tht the mthemticl model of the VSI hving its voltge drops is correct. 7. Conclusion In this pper, model of two-level three-phse voltge source inverter hving its voltge drops is proposed. Then pplicting to direct torque control of three-phse induction motors with the proposed model hs studied. The proposl cn be esily expnded to other pplictions. References [] Vs, P., Sensorless Vector nd Direct Torque Control. Oxford: Oxford University Press. [] Kzmierkowski, M., Krishnn, R., nd Blbjerg, F. (00). Control in Power Electronics: Selected Problems. New York: Acdemic. [] Bose, B. K. (006). Power Electronics nd Motor Drives: Advnces nd Trends. Acdemic Press. [4] Wu, B. (006). High-Power Converters nd AC Drives. Wiley-IEEE Press. [5] Rshid, M. H. (006). Power electronics hndbook, nd ed. New York: Acdemic. [6] Bose, B. K. (009). Power Electronics nd Motor Drives Recent Progress nd Perspective. IEEE Trnsctions on Industril Electronics, 56(), [7] Nm, K. H. (00). AC motor control nd electricl vehicle pplictions. CRC Press. [8] Teodorescu R., Liserre M., & Rodrıguez P. (0). Grid converters for photovoltic nd wind power systems. IEEE Press. [9] Hui, J. C. Y., Bkhshi A., nd Jin P. K. (06, July). An energy mngement scheme with power limit cpbility nd n dptive mximum power point trcking for smll stndlone PMSG wind energy systems. IEEE Trnsctions on Power Electronics, (7). [0] Wei, S., Vittl, V. (006). LP-bsed OPF for corrective FACTS control to relieve overlods nd voltge 0

10 violtions, IEEE Trnsctions on Power Systems. (4), [] Buj, G. S. nd Kzmierkowski, M. P. (004). Direct torque control of PWM inverter-fed AC motors A survey. IEEE Trnsctions on Industril Electronics, 5(4), [] Kho, D. Hong., Zhu, Z. Q., nd Mrtin, P. F. (0). Influence nd compenstion of inverter voltge drop in direct torque-controlled four-switch three-phse PM brushless AC drives, IEEE Trnsctions on Power Electronics, 6(8), H. L. Bui received the B.Eng nd M.S degrees in electricl engineering respectively from Hnoi University of Technology, Hnoi, Vietnm in 00 nd 005. He is lecturer in Deprtment of Electricl Engineering, Hnoi University of Industril, Vietnm. Now he is Ph.D student of the College of Electricl nd Informtion Engineering of Hunn University, Chin. His key reserch interests include power electronic converter for motor, wind power system, nd solr power system. Shoudo Hung ws born in Chin in 96. He received B.S. degree in Electric Mchine nd Ph.D. degree in Electricl Engineering from Hunn University, Chin, in 98 nd 000, respectively. From 98 to 99, he worked t the Hunn Motor fctory s technicl Director. Since 995, he hs been with the College of Electricl nd Informtion Engineering, Hunn University. From 008 to 009, he ws Visiting Scholr t the Energy College, Alborg University, Denmrk. He is currently Vice President of the College of Electricl nd Informtion Engineering, Hunn University, Chin. He is lso n Executive Director of the Trnsctions of Chin Electrotechnicl Society, Director of the Hunn Assocition nd Automtion, Director of the Energy Assocition of Chin, nd Committee Member of the lrge Motor Electrotechnicl Society of Chin. His current reserch interests include power electronics nd mchine technology, control of power converters, wind power genertion, nd power qulity. D. C. Phm received the B.Eng nd M.Eng degrees from Ho Chi Minh City University of Technology, Ho Chi Minh, Vietnm, in 00 nd 007, respectively, nd the Ph.D. degree from Hunn University, Chin in 0. He is lecturer in Deprtment of Electricl Engineering, Industril University of Ho Chi Minh City. His key reserch interests include power electronics, electricl mchines, nd dvnced control techniques for electricl drives. 0