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  IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 6, DECEMBER 2004 1329 Direct Torque and Frequency Control of Double-Inverter-Fed Slip-RingInduction Motor Drive Gautam Poddar and V. T. Ranganathan  , Senior Member, IEEE   Abstract— A novel sensorless scheme for direct torque and fre-quencycontrolofadouble-inverter-fedslip-ringinductionmotorispresented. Theanalysis ofa double-inverter-fedinductionmotor isgiven to derive the proposed controller. Various frequency profilesare analyzed for a direct frequency controller. A novel frequencyprofile is suggested to make the sensorless drive operation reliableand machine parameter independent at any rotor speed. Simula-tion and experimental results are presented from a 50-hp drive,demonstratingthatthedrivecandeliverfulltorquefrom0to2-p.u.speed in either direction. Thus, double the rated power can be ex-tracted from the motor without overloading it.  Index Terms— Double inverter, sensorless control, slip-ringmotor. N OMENCLATURE , Stator and rotor self inductances, respectively.Mutual inductance., Stator and rotor leakage factors.Total leakage factor., Stator and rotor resistances, respectively.Stator current vector in stationary reference frame.Rotor current vector in rotor reference frame.Stator voltage vector in stationary reference frame.Rotor voltage vector in rotor reference frame.Stator supply frequency with respect to stationaryframe.Rotor supply frequency with respect to rotor frame.Rotor speed in electrical radians per second.I. I NTRODUCTION A grid-connected slip-ring induction motor with currentinjection on the rotor side can be operated in supersyn-chronous mode to produce up to two times the rated nominalpower. The current injection can be achieved using either acycloconverter [1] or back-to-back voltage-source inverters [2]. The grid-connected machine, however, is not capable of speedreversal without change of connections. Manuscript received November 19, 2002; revised January 2, 2004. Abstractpublished on the Internet September 10, 2004. This work was supported by theMinistry of Information Technology, Government of India.G.PoddariswiththePowerElectronicsGroup,ElectronicsResearchandDe-velopment Centre of India, Trivandrum 695 033, India (e-mail: gautam@erdc-itvm.org).V. T. Ranganathan is with the Electrical Engineering Department, Indian In-stitute of Science, Bangalore 560 012, India (e-mail: vtran@ee.iisc.ernet.in).Digital Object Identifier 10.1109/TIE.2004.837897 A more versatile configuration is one where both the statorand the rotor of a slip-ring machine are fed from variable-fre-quency inverters. The resulting drive can operate in all fourquadrants of the torque–speed plane [3]. The vector controlscheme proposed by Kawabata  et al.  uses two separate torquecurrent controllers for the stator and the rotor inverters. Itis shown in the present work that the torque components of currents on the two sides are proportional to each other (5).Therefore, controlling them simultaneously but independentlycan lead to instability problems. Practically, during transientoperation, the condition given in (5) cannot be met by usingseparate proportional–integral (PI) current controllers. Further-more, the scheme requires operation of the inverters at verylow fundamental frequency at some speeds of operation. It isalso sensitive to machine parameters and exhibits excessiveovershoot in the torque component of current during reversal.In [7], the authors of this paper demonstrated the sensorlessvector control operation of this double-inverter-fed slip-ringdrive with torque current control only from the stator side. Asimple scalar control on the rotor side is proposed there.No abnormal rise in machine currents is noticed during alltransient operations. However, this sensorless vector controlscheme is dependent on the estimation of machine leakageparameters.In this paper, a new scheme for direct torque and frequencycontrol of the double-inverter-fed slip-ring induction motor isproposed. The scheme takes into account the proportionalitybetween the torque current components on the two sides andthereby avoids instability problems in current control. By usingnovel frequency versus speed profiles for the two inverters,it is ensured that the fundamental frequency of operation oneither side is always above a certain minimum value. This inturn means that simple sensorless schemes can be used forestimating the machine flux. The resulting control thus has verylittle dependence on machine parameters. However, a directtorque control (DTC) type of bang-bang control scheme doesnot ensure the constant inverter switching frequency unlike thesensorlessvectorcontrol schemepresentedin[7].Theproposeddirect control scheme for torque and frequency enables fastdynamic control over the speed range of 2 p.u., includingzero speed. Results from simulation as well as an experimental50-hp drive are presented to demonstrate the performance of the scheme.Since the full torque can be obtained up to twice rated speed,the power output can be up to twice the rating of the machine.The drive is, therefore, an attractive alternative in high-power 0278-0046/04$20.00 © 2004 IEEE  1330 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 6, DECEMBER 2004 TABLE IC OMPARISON OF  H IGH -P OWER  D RIVES  U SING  V ARIOUS  M OTORS FOR A T YPICAL  1-MW R ATING Fig. 1. Double-inverter-fed slip-ring induction motor drive. applications to other schemes with complex topologies such asthree-levelinvertersandcycloconverters.Acomparisonofhigh-power drives using various motors is given in Table I for a typ-ical1-MWratingtoestablishtheadvantageofthisdriveintermsof power ratings. The drives considered here are meant for vari-able-speed operation down to zero speed, with speed reversal.In applications where the speed range is limited and centeredaround the synchronous speed, the grid-connected slip-ring in-duction machine with rotor-side control [2] is the economicalsolution.II. F UNDAMENTALS OF  B ASIC  C ONFIGURATION The con fi guration of a double-inverter-fed induction motordrive is shown in Fig. 1. A three-phase insulated gate bipolartransistor (IGBT) inverter feeds power to the slip-ring induc-tion motor through its stator terminals. Another three-phase in-verter feeds power to the same motor through its rotor termi-nals. Both the inverters have a common dc bus. This dc bus isinterfaced with the three-phase grid through a converter as ina conventional drive. If the regenerative braking is desired forhigh-powerdrives,thenafront-endconvertermaybechosenbe-tweendcbusandthegridtodelivertheregenerativepowertothe Fig. 2. Stator  fl ux and rotor  fl ux of the motor with respect to the rotor and thestator. grid. Otherwise, a simple diode recti fi er can be the cost-effec-tive alternative to the sophisticated front-end converter. Unlikethe grid-connected slip-ring motor drive with rotor-side controlscheme [2], the front-end converter is not essential here. Now,themachineanalysisisgiventoidentifythecontrolmethodsuit-able for this con fi guration.  A. Machine Torque and Torque Current  At any instant of time, the stator  fl ux vector, rotor  fl ux vector,and the rotor position are shown in Fig. 2 with respect to thestatoraxis.Theequationofthestator fl uxinthestatorcoordinatesystem is(1)The air-gap  fl ux in the stator coordinate is(2)and the rotor  fl ux equation in the rotor coordinates is(3)The developed electromagnetic torque of the machine is(4)Therefore,thetorqueisproportionaltothevectorproductoftwocurrents ( ). Now, both these currents are resolved alongthe air-gap  fl ux ( ) axis as shown in Fig. 3. The followingresults are obtained:(5)(6)From the above equations, it is clear that the quadrature-axisstator current generates the machine torque. The rotorquadrature-axis current is developed automatically as there fl ection of . Hence, the machine torque is required to becontrolled only from one side, for example, the stator side.From (1), (3), and (4), the electromagnetic torque can berewritten as(7)The above equation shows that the electromagnetic torque isalso the cross product of the stator and rotor  fl uxes, i.e., the  PODDAR AND RANGANATHAN: DOUBLE-INVERTER-FED SLIP-RING INDUCTION MOTOR DRIVE 1331 Fig. 3. Phasor diagram of machine  fl uxes and currents with air-gap  fl uxorientation. product of , , and the sine of angle between two  fl uxes(Fig. 2). Therefore, the controlled variations of the angle con-trolthemachinetorquedirectlyandthetorquecurrentindirectly.  B. Machine Fluxes and Sharing of Magnetizing Current  The rotor  fl ux magnitude ( ) and the stator  fl ux magnitude( ) control the air-gap  fl ux magnitude ( ) as follows.Applying air-gap  fl ux orientation on machine  fl ux (1) – (3),(8)(9)(10)(11)(12)Solving (9) and (10), we get(13)(14)From (8), it is seen that the air-gap  fl ux magnitude ( ) isconstant as long as ( ) is constant. Equations (13) and(14) state that and depend on -axis stator  fl ux ( ) and-axis rotor  fl ux ( ) completely. At no load, -axis  fl uxes onboth sides ( ) become zero [see (11) and (12))]. There-fore, at that condition, the stator  fl ux magnitude equals the-axis fl ux andtherotor fl uxmagnitude equalsthe -axis fl ux . The proper values of and references can pro-duce de fi nite values of , , and the net magnetizing currentin the machine [see (8), (13), and (14)]. Thus, the selectionof and references can control the sharing of magnetizingcurrent between the stator winding and the rotor winding of themachine.However,withload,the -axis fl uxes( )onbothsidesof the machine become nonzero. Now, if the stator and the rotor fl uxes ( , ) are kept constant, then using (11) and (12),-axis  fl uxes can be written as(15)The above equations show that there are changes in values of -axis  fl uxes from no load to full load. This leads to changesin , , and [see (8), (13), and (14)]. However, for prac-tical machines, the leakage factors and are very small.Assuming rated constant  fl ux magnitudes for and , thevariations of -axis  fl ux magnitudes from no load to full loadwill be less than 5%. Hence, the choice of and can de-termine the magnetizing current and the sharing of magnetizingcurrent completely.III. P ROPOSED  C ONTROL  M ETHOD The block diagram of the proposed controller is shown inFig. 4.  A. Stator-Side Controller  As mentioned earlier, there is a torque controller to controlthe stator-side inverter. The algorithm is based on DTC [4] – [6].In this method, the electromagnetic torque ( ) of the machineis derived from the stator  fl ux ( ) and the stator currents ( )as follows.From (1) and (4), the machine torque can be rewritten as(16)Now, from (1), and in the  –  frame of stationarycoordinates are derived as follows:(17)The stator voltages and in the  –  frame are calculatedbased on the measurements of dc-bus voltage and the switchingstates of the inverter. To represent the switching state of the in-verter (Fig. 5), the switching function for phase 1is de fi nedas follows: when the upper switch of phase 1 is onand when the lower switch of phase 1 is on. Similarde fi nitions can be made for phases 2 and 3. Now, the voltageequations are(18)The stator line currents are expressed in the frame asfollows:(19)Now, the stator  fl ux angular velocity is obtained from the fol-lowing equation:(20)  1332 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 51, NO. 6, DECEMBER 2004 Fig. 4. Overall block diagram of the controller.Fig. 5. Typical voltage-source inverter. Therefore, the stator  fl ux position is derived as(21)There are eight voltage vectors ( ,) available for the voltage-source inverter.They are shown in Fig. 6 in the  –  stationary coordinatesystem. Among them, there are six nonzero voltage vectors( , ) and two zero voltagevectors ( , ). When one of six activevoltage vectors is chosen for the inverter, then the end of moves parallel to the voltage vector chosen. On the otherhand, the null vectors stop the  fl ux, whenever they are appliedto the inverter. By selecting appropriate voltage vector , theend of rotates at the frequency along the zigzag lineshown in Fig. 6. However, the average locus of is circular,as shown by the dotted line in Fig. 6. Fig. 6. Different inverter voltage vectors and the  fl ux path on    –    frame. Togetthecorrectvoltagevectorateachinstant, thefollowingmethod is adopted. The  –  plane is dividedinto six sectors. Ateveryinstant, isestimatedusing(21) togetthesectornumberthat contains the stator  fl ux at that moment. For example, inFig. 6 the stator  fl ux lies on the sector number II and rotatesin the anticlockwise direction. The rotor  fl ux trails the stator fl ux. If it is required to increase the torque, the stator  fl ux hasto be accelerated to increase the angle between the stator  fl uxand the rotor  fl ux as explained earlier [see (7)]. Therefore, thevoltage vector or can be selected. Now, if the stator  fl uxmagnitude has to be increased, then the voltage vector hasto be selected for the inverter. Otherwise, has to be selected.Similarly, to decrease the torque, or can be selected.The  fl ux magnitude error will decide the  fi nal voltage vectoruniquely among those two voltage vectors. For other sectors theunique voltage vector can also be selected at each instant on thebasis of torque error and the  fl ux error.
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