Torque Control of CSI Fed Induction Motor Drives

Transcription

1 1 Torque Control of CSI Fed Inducton Motor Drves Aleksandar Nkolc Electrcal Engneerng Insttute Nkola Tesla Belgrade Serba 1. Introducton An electrc drve s an ndustral system whch performs the converson of electrcal energy to mechancal energy (n motorng or vce versa (n generator brakng for runnng varous processes such as: producton plants transportaton of people or goods home applances pumps ar compressors computer dsc drves robots musc or mage players etc. About 5% of electrcal energy produced s used n electrc drves today. Electrc drves may run at constant speed or at varable speed. Nowadays most mportant are varable speed drves especally n Europe where accordng to the Ecodesgn for Energy-Usng Products Drectve (25/2/EC (the "EuP Drectve" and ts regulaton regardng electrc motors (Regulaton 64/29/EC on 1 January motors wth a rated output of kW must meet hgher energy effcency standards or meet the 211 levels and be equpped wth a varable speed drve. The frst motor used n varable speed applcatons was DC motor drve snce t s easly controllable due to the fact that commutator and stator wndngs are mechancally decoupled. The cage rotor nducton motor became of partcular nterest as t s robust relable and mantenance free. It has lower cost weght and nerta compared to commutator DC motor of the same power ratng. Furthermore nducton motors can work n drty and explosve envronments. However the relatve smplcty of the nducton motor mechancal desgn s contrasted by a complex dynamc structure (multvarable nonlnear mportant quanttes not observable. In the last two decades of the 2 th century the technologcal mprovements n power semconductor and mcroprocessor technology have made possble rapd applcaton of advanced control technques for nducton motor drve systems. Nowadays torque control of nducton motor s possble and has many advantages over DC motor control ncludng the same system response and even faster response n case of the latest control algorthms. Two most spread ndustral control schemes employs vector or feld-orented control (FOC and drect torque control (DTC. Current source nverters (CSI are stll vable converter topology n hgh voltage hgh power electrcal drves. Further advances n power electroncs and usage of new components lke SGCT (Symmetrc Gate Commutated Thyrstor gves the new possbltes for ths type of converter n medum voltage applcatons. Power regeneraton durng brakng what s a one of man bult-n feature of CSI drves s also mert for hgh power drves. Despte the

2 4 Torque Control above advantages the confguraton based on a thyrstor front-end rectfer presents a poor and varable overall nput power factor (PF snce the current s not snusodal but trapezodal waveform. Also the mplementaton of CSI drve systems wth on-lne control capabltes s more complex than for voltage source nverters (VSI due to the CSI gatng requrements. Regardng mentoned dsadvantages CSI drves are of nterest for research n the feld of torque control algorthms such as vector control (or FOC and drect torque control (DTC. Ths chapter wll present basc FOC and DTC algorthms for CSI drves and show all features and dsadvantages of those control schemes (sluggsh response phase error large torque rpples need for adaptve control etc.. Usng recent analyss tools lke powerful computer smulaton software and experments on developed laboratory prototype two new FOC and DTC solutons wll be presented n the chapter. The proposed FOC enables CSI drve to overcome mentoned nconvenences wth better dynamc performances. Ths enhancement reles on fast changes of the motor current wthout phase error smlar to the control of current regulated voltage source PWM nverter. The realzed CSI drve has more precse control accomplshed by the mplemented correcton of the reference current. Ths correcton reduces the problem of the ncorrect motor current components produced by the non-snusodal CSI current waveform. On the other sde proposed DTC algorthm s completely new n the lterature and the only such a control scheme ntended for CSI nducton motor drves. Presented DTC s based on the constant swtchng frequency absence of coordnate transformaton and speed sensor on the motor shaft. Furthermore snce flux estmator s based only on DC lnk measurements there s not necessty for any sensor on the motor sde whch s one of man drve advantages. In ths case by combnaton of vector control and basc DTC a robust algorthm s developed that has a faster torque response and t s smpler for mplementaton. 2. Characterstcs of current source nverters The most prevalng ndustral drve confguraton n low voltage range s based on IGBT transstors as power swtches and voltage-source nverter (VSI topology. On the other sde the nducton motor drves wth thyrstor type current-source nverter (CSI also known as auto sequentally commutated nverter Fg. 1 possess some advantages over voltage-source nverter drve but t has a larger torque rpples snce the current wave-form s not snusodal. Furthermore due to the nature of the CSI operaton the dynamc performance that exsts n VSI PWM drves could not be acheved. But CSI permts easy power regeneraton to the supply network under the breakng condtons what s favorable n large-power nducton motor drves. At low voltage range (up to 1kV ths type of nverter s very rare and abandoned but ths confguraton s stll usable at hgh power hgh voltage range up to 1kV and several MW. In tracton applcatons bpolar thyrstor structure s replaced wth gate turn-off thyrstor (GTO. Nowadays current source nverters are very popular n medum-voltage applcatons where symmetrc gate-commutated thyrstor (SGCT s utlzed as a new swtchng devce wth advantages n PWM-CSI drves (Wu 26. New developments n the feld of mcroprocessor control and applcaton n electrcal drves gves possblty for employment of very complex and powerful control algorthms. Torque control of CSI fed nducton motor drves becomes also vable and promsng soluton snce some of CSI control dsadvantages could be overcome usng mproved mathematcal models and calculatons.

3 Torque Control of CSI Fed Inducton Motor Drves 5 Ld T1' T' T5' T1 T T5 C1 C C5 8V 5Hz D1 D D5 L1 L2 L D4 D2 C6 D6 T4 T2 T6 C4 C2 W V U M ~ AC MOTOR T4' T2' T6' Fg. 1. Basc CSI topology usng thyrstors as power swtches Two most mportant torque control schemes are presented namely FOC and DTC. Both control schemes wll be shown wth all varatons known from lterature ncludng those proposed by prevous research work of author. All presented torque control algorthms basc and proposed by author are analyzed and verfed by smulatons and experments.. Vector control In the past DC motors were used extensvely n areas where varable-speed operaton was requred snce ther flux and torque could be controlled easly by the feld and armature current. However DC motors have certan dsadvantages whch are due to the exstence of the commutator and brushes. On the other sde nducton motors have less sze for the same power level has no brushes and commutator so they are almost mantenance free but stll has dsadvantages. The control structure of an nducton motor s complcated snce the stator feld s revolvng. Further complcatons arse due to the fact that the rotor currents or rotor flux of a squrrel-cage nducton motor cannot be drectly montored. The mechansm of torque producton n an AC and DC machne s smlar. Unfortunately that smlarty was not emphaszed before 1971 when the frst paper on feld-orented control (FOC for nducton motors was presented (Blaschke Snce that tme the technque was completely developed and today s mature from the ndustral pont of vew. Today feld orented controlled drves are an ndustral realty and are avalable on the market by several producers and wth dfferent solutons and performance..1 Basc vector control of CSI drves Many strateges have been proposed for controllng the moton of CSI fed nducton motor drves (Bose 1986; Novotny & Lpo 1988; Wu et al. 1988; Deng & Lpo 199; Vas 199. The vector control has emerged as one of the most effectve technques n desgnng hghperformance CSI fed nducton motor drves. Compared to the PWM VSI drves CSI has advantage n the reversble drves but t has a larger torque rpples snce the current waveform s not snusodal. Furthermore due to the nature of the CSI operaton the dynamc performance that exsts n PWM drves are not acheved wth the exstng vector control algorthms. The well-known ("basc" structure of a CSI fed nducton motor drve wth ndrect vector control s shown n Fg. 2 (Bose 1986; Vas 199.

4 6 Torque Control supply sd sq α PI controller resolver slp calculator - dc s lead crcut ω s Δ CSI rng counter rf 1/s ω e Fg. 2. Indrect vector control of a CSI fed nducton machne Ths method makes use of the fact that satsfyng the slp relaton s a necessary and suffcent condton to produce feld orentaton.e. f the slp relaton s satsfed (denoted as slp calculator n Fg. 2 current d component wll be algned wth the rotor flux. Current commands are converted to ampltude and phase commands usng resolver (rectangular to polar coordnate transformaton. The current ampltude command s drectly employed as the reference for the current PI controller ntended for controllng the nput converter (three phase full wave brdge rectfer. The phase command s passed through a lead crcut such that phase changes are added nto the nverter frequency channel snce these nstantaneous phase changes are not contaned n the slp frequency command sgnal comng from the slp calculator..2 Proposed vector control of CSI drves In the vector controlled CSI drves found n (Bose 1986; Wu et al. 1988; Deng & Lpo 199; Vas 199; Novotny & Lpo 1996 and shown n prevous chapter the problems of the speed response are reported. Ths s nfluenced by the nstantaneous phase error and as a result these confguratons have slower torque response compared to the current regulated PWM drves. In addton to the phase error the commutaton delay and the non-snusodal supply that s nhered n CSI operaton must be generally compensated for to acheve acceptable vector control. To overcome these dsadvantages the phase error elmnaton and the reference current correcton should be performed. In ths chapter the vector control algorthm that elmnates the two drawbacks s shown (Nkolc & Jeftenc 26. The suggested algorthm produces the performance of the CSI drve that exsts n the PWM vector controlled drves. That enables ths smple and robust confguraton to be used n applcatons where reversble operaton s a mert. The necessty for the phase error elmnaton can be explaned wth the help of the followng phasor dagram: sd Δ sq1 Ψ r s1 s e sq2 s2 ω r M Fg.. Phasor dagram wth shown phase error

5 Torque Control of CSI Fed Inducton Motor Drves 7 When the torque command s stepped from sq1 to sq2 (wth a constant sd the current vector should nstantaneously change from s1 to s2. The slp frequency should also change mmedately. The resolver does gve the correct ampltude and the new slp frequency wll be obtaned by the slp calculator. However although the phase change Δ s added by a lead crcut as shown n Fg. 2 snce the nstant phase changes are not contaned n the slp frequency command sgnal comng from the slp calculator (Bose 1986; Deng & Lpo 199; Novotny & Lpo 1996 the stator current command wll correspond to the vector s n Fg. and there wll be a phase error n the vector control system. Ths would result n an nstantaneous loss of the feld-orentaton that produces a very sluggsh response of both flux and torque. Ths problem could be overcome by the proposed algorthm whch unfes features of both PWM and CSI converter. The resolver s stll used to calculate the rectfer reference current but for the nverter thyrstors control a method used n the current controlled PWM nverter s mplemented. Instead of a lead crcut (shown n Fg. 2 the new algorthm ncludes a synchronous to stator transformaton (T -1 to transfer the d-q commands to the three-phase system. Ths s essental for achevng a fast torque response snce the torque value s determned by the fundamental harmonc of the stator current. For correct frng of the thyrstors n the nverter the swtchng tmes should be properly determned to ensure that the phase angle of the motor current matches the phase angle of the reference currents n a-b-c system. The reference snusodal currents obtaned as a result of transformaton T -1 are dvded by the value obtaned on the resolver output to produce currents of unty ampltudes. Introducton of these currents nto the comparator wth trgger level equal to.5 gves the proper thyrstor conducton tme of 12 degrees. Ths s llustrated n Fg. 4 where a s unty snusodal current a s scaled CSI output current and a1 s fundamental stator current a1 a Currents [p.u.] a phase angle [degrees] Fg. 4. Waveforms of the reference current and fundamental stator current The algorthm possesses the addtonal advantage regardng the practcal realzaton. In dgtal control system the lead crcut dvdes the dfference of the two succeedng samples wth the samplng tme. Snce the samplng tme s small ths operaton produces the computatonal error. The phasor dagram from Fg. wth removed phase error s presented n Fg. 5. Wthout the phase error (Δ = the step of the torque command produces the new stator current command ( s = s2. Due to non-snusodal currents of the CSI the average values of the motor d-q currents sd_av and sq_av and the resultng stator current vector s greater than the correspondng references shown n Fg. 5. To mprove proposed algorthm and avod mproper resultant d-q motor currents the rectfer reference current correcton s performed.

6 8 Torque Control sd Δ = sq1 s1 s = sq2 s2 sq_av s sd_av Ψ r Fg. 5. Phasor dagram wthout phase error In the vector controlled nducton motor drve fed by a CSI a problem of ncorrect copyng of the d-q references to the motor exst. As stated earler the reason s non-snusodal current waveform produced by a CSI. The deal CSI current s a quas-square waveform (shown n Fg. 4. The Fourer analyss of ths waveform gves the expresson: a = Id sn( ωt sn(5ωt sn(7ωt 5 7 The prevous relaton shows that the fundamental component of AC output current has the ampltude 1 percent greater than the value of DC lnk current. For correct reproducton of the d-q references and satsfactory vector control t s not suffcent to adjust only the phase of the fundamental motor current and the phase angle of the generated commands. The fnetunng of the motor currents n d-q frame s requred. To avod supplementary hardware and software a procedure that reles only on the values calculated off-lne s proposed. The correspondng relaton between the mean values of the motor currents n d-q frame and the commanded d-q currents s calculated. For proposed correcton t s not suffcent to use the dfference between currents of 1% from (1 because the correcton depends on the phase angle of the d-q components and the nverter commutaton process. At lower speed the commutaton process could be neglected snce t s much shorter than the motor current cycle. Takng all ths n consderaton the rectfer reference current s corrected concernng the reference ampltude the phase angle and the commutaton duraton. The rectfer reference current formed n that manner s now ntroduced to the current controller to obtan sutable motor d-q currents and acheve desred vector control. The calculaton starts from the fundamental reference current from the resolver: s 2 ( sd ( sq and the phase angle (also obtaned from the resolver: 2 = (2 ( sd / = arctan ( Snce the nverter commutaton process s not neglected the waveform of the nverter output current s represented by a trapezodal approxmaton analyzed n (Cavaln et al wth adequate precson. Trapezodal waveform s very near to the real current cosne waveform due to the short commutaton perod as explaned n (Bose Ths approxmaton assumes that durng the commutaton perod the nverter current rses wth sq (1

7 Torque Control of CSI Fed Inducton Motor Drves 9 a constant rate of change. For rated rectfer current I d the current rate of change durng the commutaton s equal to I d /t c where t c s correspondng commutaton tme calculated from the values of the commutaton crcut components. The adequate commutaton angle could be obtaned as a product of the nverter frequency ω e and partcular commutaton tme. Ths tme nterval s determned from the current rate of change I d /t c and the reference value of the DC lnk current s therefore the commutaton angle s: s d c e I t = ω (4 Snce the nverter current s perodcal the trapezodal waveform n all three phases could be represented on a shorter angle nterval wth the followng equatons: < < < < < = ( d d d d a I I I I (5 2 ( ( = a b (6 4 ( ( = a c (7 where ranges from to s the commutaton angle and s the phase angle obtaned from (. The nstantaneous values of d-q currents are solved by a three phase to d-q frame transformaton T: = = = ( ( ( / 4 cos( / 2 cos( cos( / 4 sn( / 2 sn( sn( 2 ( ( ( 2 ( ( c b a c b a sq sd T (8 The average values of the currents n d and q axs obtaned from (8 on the range from to be: = _ d ( 1 av ( sd sd (9

8 1 Torque Control 1 sq _ av ( = sq ( d (1 The ampltude of the motor current vector n polar coordnates could be determned usng the average values obtaned from (9 and (1: 2 sd 2 _ av sq _ av ( = ( ( (11 s The dfference between reference ampltude calculated from (2 and the resultng stator ampltude obtaned from (11 s shown n Fg. 4. To avod ths dfference the correspondng correcton factor f cor s ntroduced as a rato of the reference (2 and the actual motor current (11: s f cor ( = (12 ( For smulaton and practcal realzaton purposes the correcton factor f cor s computed from (2 (12 and placed n a look-up table wth the followng restrctons: sd s constant sq s changed only to ts rated value wth s lmted to 1 p.u. for gven references all possble values of and are calculated usng ( and (4 respectvely. The rectfer reference current that provdes the correct values of motor current d-q components s now: s s = f ( (1 ref The nterdependence between correcton factor f cor commutaton angle and phase angle s presented n Fg. 6 as a -D graph. cor 1. Correcton factor f cor [p.u.] Commutaton angle [rad] Phase angle [rad] 2.5. Fg. 6. Correcton factor commutaton angle and phase angle nterdependence

9 Torque Control of CSI Fed Inducton Motor Drves 11 The calculated results of the current correcton n d-axs and q-axs are presented n Fg. 7a and Fg. 7b respectvely. The corrected currents are gven along wth references and motor average d-q currents (values wthout correcton. The flux command s held constant (.7 p.u. whle torque command s changed from.7 p.u. to.7 p.u. Motor currents n d-axs [p.u.] sd corrected = sd [p.u.] sd not corrected [p.u.] Torque command sq [p.u.] a Motor currents n q-axs [A] Torque command sq [A] b sq corrected = sq [p.u.] sq not corrected [p.u.] Fg. 7. Calculated motor current corrected n d-axs and q-axs (ab respectvely From the prevous analyss the new resolver wth current correcton s formed as shown n Fg. 8. Ths structure s used both n the smulatons and the experments. The new resolver s conssted of the block Cartesan to polar (the coordnate transformaton and the block Correcton that desgnates the nterdependence gven n Fg. 6. As stated before ths nterdependence s placed n a -D look-up table usng (2-(12. sd sq s Cartesan to polar slp calculator ω s x ω e tc/id ω r Correcton f cor s Resolver wth correcton x ref Fg. 8. New resolver wth current correcton To analyze dynamc performances of the proposed CSI drve the torque response of the "basc" structure shown n Fg. 2 s compared to the response of the new vector control algorthm. Ths s done by smulatons of these two confguratons' mathematcal models n Matlab/Smulnk. The frst model represents the drve wth basc arrangement and the second s the drve wth new control algorthm. The smulaton of both models s done wth several ntal condtons. Magnetzng (d-axs current for rated flux has been determned from the motor parameters and ts value (.7p.u. s constant durng smulatons. The rated q-axs current has been determned from the magnetzng current and the rated full-load current usng (2. At frst smulatons of both models are started wth d-axs command set to.7p.u no-load and all ntal condtons equal to zero. When the rotor flux n d-axs approaches to the steady state the machne s excted. Ths value of d-axs flux s now ntal

10 12 Torque Control for the subsequent smulatons. For the second smulaton the pulse s gven as a torque command wth the ampltude of.2p.u. and duraton of.5s. Wth no-load the motor wll be accelerated from zero speed to the new steady-state speed (.2p.u. whch s the ntal condton for the next smulaton. Fnally the square wave torque command s appled to both models wth equal postve and negatve ampltudes (±.2p.u and the observed dynamc torque response s extracted from the slope of the speed (Lorenz The square wave duty cycle (.9s s consderably greater than the rotor tme constant (T r =.1s hence the rotor flux could be consdered constant when the torque command s changed. Fg. 9 shows torque speed and rotor flux responses of both models. It could be notced that the torque response of the basc structure s slghtly slower (Fg. 9a whle the proposed algorthm gves almost nstantaneous torque response (Fg. 9b. Ths statement could be verfed clearly from the speed response analyss. In both cases the torque command s the same. In the new model ths square wave torque command produces speed varatons from.2p.u. to.6p.u. wth dentcal slope of the speed. But n the basc model at the end of the frst cycle the speed could not reach.6p.u. for the same torque command due to the fact Motor torque and speed [p.u.] a.8 Rotor flux [p.u.] Ψ rd Ψ rq c Motor torque and speed [p.u.] b Rotor flux [p.u.] Fg. 9. Torque speed and rotor flux of the basc structure (a (c and of the proposed algorthm (b (d Ψ rd Ψ rq d

11 Torque Control of CSI Fed Inducton Motor Drves 1 that torque response s slower. Also n the next cycle (negatve torque command the speed does not return to.2p.u. for the same reason. From dfferent slopes of the speed n these two models t could be concluded that proposed algorthm produces qucker torque response. The rotor q-axs flux dsturbance n transent regme that exsts n the basc model (Fg. 9c s greatly reduced by the proposed algorthm n the new model (Fg. 9d. It could be seen that some dsturbances also exst n the case of d-axs flux but they are almost dsappeared n the new model. To llustrate the sgnfcance and facltate the understandng of theoretcal results obtaned n the prevous secton a prototype of the drve s constructed. The prototype has a standard thyrstor type frequency converter dgtally controled va Intel s 16-bt 8C196KC2 mcrocontroller. Inducton motor used n laboratory s 4kW 8V 5Hz machne. The speed control of the drve and a prototype photo are shown n Fg. 1. Smplcty of ths block dagram confrms that the realzed control algorthm s easer for a practcal actualzaton. The proposed crcut for the phase error elmnaton s at frst tested on the smulaton model. The smulaton s performed n such a manner that C code for a mcrocontroller could be drectly wrtten from the model. The values that are read from look-up tables n a real system (cosne functon square root are also presented n the model as tables to properly emulate calculaton n the mcrocontroller. Fg. 11a shows waveforms of the unty snusodal references ( a and b whle Fg. 11b ndcates nverter thyrstors swtchng tmes wth changed swtchng sequence when the phase s changed (.18s marked wth an arrow. On these dagrams t could be observed that thyrstors T 1 and T 2 are swtched to ON state when unty references a and b reach.5 p.u. respectvely. Fg. 11cd represents the nstant phase varaton of the currents n a and b phases after the reference current s altered. The correspondng currents wthout command changes are dsplayed wth a thn lne for a clear observaton of the nstant when the phase s changed. ω ref ref ω r _ Resolver (Fg. 7 _ I d Current controller arccos U c Speed controller s s Slp calculator ω e ~ 2= 1/s sq sq Mcrocontroller sd sd abc ω s Frng crcut wthout phase error α I d 6 ω r e ω r M ~ E Rectfer L DC CSI Fg. 1. CSI fed nducton motor drve wth mproved vector control algorthm: control block dagram (left laboratory prototype (rght

12 14 Torque Control 1. a b b a 6 4 Current [p.u.] a [A] Current a c 6 T1 4 T2 T T4 T5 T6 b [A] Current b d Fg. 11. Results of the phase error elmnaton (ab - smulaton cd - expermental The effects of the reference current correcton are gven by the specfc experment. To estmate d and q components the motor currents n a and b phases and the angle e between a-axs and d-axs are measured. Ths angle s obtaned n the control algorthm (Fg. 1 as a result of a dgtal ntegraton: e n = e( n 1 ωe Ts ( (14 where n s a sample T s s the sample tme and ω e s exctaton frequency. The ntegrator s reset every tme when e reaches or 6 degrees. The easest way for acqurng the value of ths angle s to change the state of the one mcrocontroller's dgtal output at the nstants when the ntegrator s reset. On the tme range between two succeedng pulses the angle s changed lnearly from to 6 degrees (for one rotatng drecton. Snce only ths tme range s needed for determne the currents n d and q axs the reset sgnal from the dgtal output s processed to the external synchronzaton nput of the osclloscope. In that way the motor phase currents are measured only on the partcular tme (angle range. The correspondng currents n d-q axes are calculated from (8 usng for e a and b expermentally determned values. The expermental results are gven n Fg. 12 wth dsabled speed controller.

13 Torque Control of CSI Fed Inducton Motor Drves 15 Motor currents n d-axs [A] corrected sd [A] not corrected sd [A] 1. sd [A] Torque command sq [A] a Motor currents n q-axs [A] sq [A] Torque command sq [A] b sq corrected [A] sq not corrected [A] Fg. 12. Expermental results of the motor current correcton n d-axs and q-axs (ab respectvely The flux reference was mantaned constant at 2.96A (.7p.u. and torque command was changed from 1.5A (.5p.u. to.a (.78 p.u.. The nverter output frequency s retaned the same durng experment ( 2Hz by varyng the DC motor armature current. From Fg. 12 t could be seen that for the proposed algorthm average values of d-q components n the p.u. system are almost equal to correspondng references. On the other sde n the system wthout correcton there s a dfference up to 15% whch confrmed the results obtaned from calculatons shown n Fg. 7. Ths dfference produces steady state error what makes such a system unacceptable for vector control n hgh performance applcatons. On the Fg. 1 the motor speed and rotatng drecton changes are shown wth enabled speed controller. The reference speed s swapped from -2mn -1 to 2mn Motor speed [mn -1 ] Fg. 1. The motor speed reversal In Fg. 14 the nfluence of the load changes to the speed controller s presented. As a load DC machne (6kW 2VDC controlled by a drect change of the armature current va - phase rectfer s used. At frst the nducton motor works unloaded n a motor regon (M wth the reference speed of 2mn -1 that produces the torque command current sq1 = A. After that the DC machne s started wth ts torque n the same drecton wth rotatng drecton of the nducton motor. That starts the breakng of the nducton motor and t goes to the generator regon (G. In ths operatng regon the power from DC lnk

14 16 Torque Control returns to the supply network. The reference torque command current changes ts value and sgn ( sq2 = 1.72A. When DC machne s swtched off the nducton motor goes to the motor regon (M and the reference torque command current s now sq = -1.48A. -15 Motor speed [mn -1 ] M G M sq1 sq2 sq Fg. 14. The load changes at motor speed of 2mn Drect torque control The drect torque control (DTC s one of the actvely researched control schemes of nducton machnes whch s based on the decoupled control of flux and torque. DTC provdes a very quck and precse torque response wthout the complex feld-orentaton block and the nner current regulaton loop (Takahash & Noguch 1986; Depenbrok DTC s the latest AC motor control method (Ttnen et al developed wth the goal of combnng the mplementaton of the V/f-based nducton motor drves wth the performance of those based on vector control. It s not ntended to vary ampltude and frequency of voltage supply or to emulate a DC motor but to explot the flux and torque producng capabltes of an nducton motor when fed by an nverter (Buja et al Drect torque control concepts In ts early stage of development drect torque control s developed manly for voltage source nverters (Takahash & Noguch 1986; Ttnen et al. 1995; Buja Voltage space vector that should be appled to the motor s chosen accordng to the output of hysteress controllers that uses dfference between flux and torque references and ther estmates. Dependng on the way of selectng voltage vector the flux trajectory could be a crcle (Takahash & Noguch 1986 or a hexagon (Depenbrok 1988 and that strategy known as Drect Self Control (DSC s mostly used n hgh-power drves where swtchng frequency s need to be reduced. Controllers based on drect torque control do not requre a complex coordnate transform. The decouplng of the nonlnear AC motor structure s obtaned by the use of on/off control whch can be related to the on/off operaton of the nverter power swtches. Smlarly to drect vector control the flux and the torque are ether measured or mostly estmated and used as feedback sgnals for the controller. However as opposed to vector control the states of the power swtches are determned drectly by the estmated and the reference torque and flux sgnals. Ths s acheved by means of a swtchng table the nputs of whch are the

15 Torque Control of CSI Fed Inducton Motor Drves 17 torque error the stator flux error and the stator flux angle quantzed nto sx sectons of 6. The outputs of the swtchng table are the settngs for the swtchng devces of the nverter. The error sgnal of the stator flux s quantzed nto two levels by means of a hysteress comparator. The error sgnal of the torque s quantzed nto three levels by means of a three stage hysteress comparator (Fg. 15. ψ n - speed controller - T e - δ ψ optmal swtchng selecton table S A S B S C motor model sa s b s c me ω me ψ s a ψ s b T e ψ est T est polar coordnate transform. Fg. 15. Basc concept of drect torque control The equaton for the developed torque may be expressed n terms of rotor and stator flux: T e = ψ ψ sn( δ M 2 s r ψ Ls Lr M where δ Ψ s the angle between the stator and the rotor flux lnkage space phasors. For constant stator and rotor flux the angle δ Ψ may be used to control the torque of the motor. For a stator fxed reference frame (ω e = and R s = t may be obtaned that: 1 t ψ s = us dt Tn The stator voltage space phasor may assume only sx dfferent non zero states and two zero states as shown n Fg. 16. The change of the stator flux vector per swtchng nstant s therefore determned by equaton (16 and Fg. 16. The zero vectors V and V 7 halt the rotaton of the stator flux vector and slghtly decrease ts magntude. The rotor flux vector however contnues to rotate wth almost synchronous frequency and thus the angle δ Ψ changes and the torque changes accordngly as per (15. The complex stator flux plane may be dvded nto sx sectons and a sutable set of swtchng vectors dentfed as shown n Table 1 where dψ and dt e are stator flux and torque errors respectvely whle S 1 6 are sectors of 6 where stator flux resdes. Further researches n the feld of DTC are mostly based on reducng torque rpples and mprovement of estmaton process. Ths yelds to development of sophstcated control algorthms constant swtchng schemes based on space-vector modulaton (Casade et al. 2 hysteress controllers wth adaptve bandwdth PI or fuzzy controllers nstead of hysteress comparators just to name a few. (15 (16

16 18 Torque Control q V (1 V 2 (11 V 4 (11 V ( V 7 (111 V 1 (1 d V 5 (1 V 6 (11 Fg. 16. Voltage vectors of three phase VSI nverter dψ dt e -/6 S 1 /6 1 S 2 /6 /2 S /2 2/ S 4 2/ -2/ S 5-2/ -/2 S 6 -/2 -/6 1 V 2 V V 4 V 5 V 6 V 1 V V 7 V V 7 V V 7-1 V 6 V 1 V 2 V V 4 V 5 1 V V 4 V 5 V 6 V 1 V 2 V 7 V V 7 V V 7 V -1 V 5 V 6 V 1 V 2 V V 4 Table 1. Optmal swtchng vectors n VSI DTC drve 4.2 Standard DTC of CSI drves Although the tradtonal DTC s developed for VSI for synchronous motor drves the CSI s proposed (Vas 1998; Boldea 2. Ths type of converter can be also appled to DTC nducton motor drve (Vas 1998 and n the chapter such an arrangement s presented. The nducton motor drves wth thyrstor type CSI (also known as auto sequentally commutated nverter possess some advantages over voltage-source nverter drve. CSI permts easy power regeneraton to the supply network under the breakng condtons what s favorable n large-power nducton motor drves. In tracton applcatons bpolar thyrstor structure s replaced wth gate turn-off thyrstor (GTO. Nowadays current source nverters are popular n medum-voltage applcatons (Wu 26 where symmetrc gatecommutated thyrstor (SGCT s utlzed as a new swtchng devce (Zargar et al. 21 wth advantages n PWM-CSI drves. DTC of a CSI-fed nducton motor nvolves the drect control of the rotor flux lnkage and the electromagnetc torque by applyng the optmum current swtchng vectors. Furthermore t s possble to control drectly the modulus of the rotor flux lnkage space vector through the rectfer voltage and the electromagnetc torque by the supply frequency of CSI. Basc CSI DTC strategy (Vas 1998 s shown n Fg. 17.

17 Torque Control of CSI Fed Inducton Motor Drves 19 ~ Ψr - Rotor flux controller Controlled rectfer Te - Torque comparator Optmal swtchng vectors CSI LF Ψr est Ψr poston Te est Ψr & Te Estmator IM Fg. 17. DTC of CSI drve based on hysteress control The stator flux value needed for DTC control loop s not convenent to measure drectly. Instead of that the motor flux estmaton s performed. In the voltage-based estmaton method the motor flux can be obtaned by ntegratng ts back electromotve force (EMF. The EMF s calculated from the motor voltage and current (17 and the only motor parameter requred s the stator wndng resstance. In practce ths smple ntegraton s replaced by more sophstcated closed-loop estmators usng flterng technques adaptve ntegraton or even observers and Extended Kalman flters (Holtz 2. s s s ( R dt t s s = us s s s (17 ψ ψ For DTC of CSI fed nducton motor drve the approprate optmal nverter currentswtchng vectors (Fg. 18 are produced by usng an optmal current-swtchng table smlarly to the table gven for VSI drve (Table 2. The man dfference s that n CSI exst only one hysteress comparator for torque and only one zero swtchng current vector. b 2 5/6-5/6 /2 /6 -/6 1 a 4 -/2 6 5 c Fg. 18. Current vectors n CSI

18 2 Torque Control S 1 dt e / S 2 / 2/ S 2/ S / S 5-2/ -/ S 6 -/ Table 2. Optmal swtchng vectors n CSI DTC drve 4. Proposed DTC of CSI drves In DTC schemes the presence of hysteress controllers for flux and torque determnes varable-swtchng-frequency operaton for the nverter. Furthermore usng DTC schemes a fast torque response over a wde speed range can be acheved only usng dfferent swtchng tables at low and hgh speed. The problem of varable swtchng frequency can be overcome by dfferent methods (Vas 1998; Casade et al. 2. In (Casade et al. 2 a soluton based on a stator flux vector control (SFVC scheme has been proposed. Ths scheme may be consdered as a development of the basc DTC scheme wth the am of mprovng the drve performance. The nput commands are the torque and the rotor flux whereas the control varables are the stator flux components. The prncple of operaton s based on drvng the stator flux vector toward the correspondng reference vector defned by the nput commands. Ths acton s carred out by the space-vector modulaton (SVM technque whch apples a sutable voltage vector to the machne n order to compensate the stator flux vector error. In ths way t s possble to operate the nducton motor drve wth a constant swtchng frequency. In proposed DTC CSI drve shown n Fg. 19 the nputs are rotor flux and torque as n VSI presented n (Casade et al. 2 but now as a control varable the stator flux angle α s s used (Nkolc & Jeftenc 28. Supply L DC U DC CSI PI current controller Resolver s_ref α - I DC sq s α s sq calculator I DC Rotor flux poston e Rotor flux and torque estmator Modfed optmal swtchng table α s M ~ PI rotor flux controller sd - Ψ r Ψ r T e - PI torque controller T e Ψ r T e_ref Fg. 19. Proposed constant-swtchng DTC strategy n CSI fed nducton motor drve

19 Torque Control of CSI Fed Inducton Motor Drves 21 Although ths confguraton could remnd on feld-orented control the man dfference s absence of coordnate transformaton snce t s not necessary to use coordnate transformaton to acheve correct frng angle as n vector control of the same drve (Nkolc & Jeftenc 26. Identcal result would be obtaned when phase angle s between d-q current references and rotor flux vector angle e = arctan(ψ rβ /Ψ rα are summed and resultng angle α s s than used to determne sector of 6 degrees where resdes rotor flux vector. In that way phase angle s acts as a torque control command. When reference torque s changed sq s momentary changed. Phase angle s moves stator current vector s n drecton determned by the sgn of torque reference and ts value accelerate or decelerate flux vector movement accordng to the value of the reference torque (Fg. 2. β 2 Ψ r s_ref1 2 (α s1 1 (α s 6 (α s2 α s α s2 s_ref2 α Fg. 2. Selectng proper current vector n proposed DTC algorthm 5 Ths modfcaton mples somewhere dfferent swtchng table for actvatng nverter swtches from that shown n Table 2. Now α s (angle between referent α-axs and reference current vector s determnes whch current vector should be chosen: 2 for torque ncrease 6 for torque decrease or 1 for keepng torque at the current value. Current vector Angle range (degrees 1 α s > and α s 6 2 α s > 6 and α s 12 α s > 12 and α s 18 4 α s > 18 or α s α s > -12 and α s -6 6 α s > -6 and α s Table. Optmal swtchng table n proposed DTC It s necessary to emphasze the mportance of zero space vectors. In VSI there are two zero voltage vectors: V denotes case when all three swtches from the one half of nverter are swtched ON whle V 7 represent state when swtches are OFF. Contrary n CSI (usng analogy to the VSI zero current vector represent case when all thyrstors are OFF. That could lead to both torque and motor speed decrease. Due to the nature of commutaton n CSI t s convenent to keep the selected current vector at nstants when zero current vector s chosen.

20 22 Torque Control The voltage and the current of CSI fed nducton motor necessary for stator flux calculaton can be reconstructed from the DC lnk quanttes knowng the states of the conductng nverter swtches. In one duty cycle of the output current CSI has sx commutatons. In that case sx ntervals of 6 degrees can be defned n whch the current and the voltage changes ts values. In every nterval the current from DC lnk flows through two nverter legs and two motor phase wndngs. The motor lne voltage s equal to the DC voltage on the nverter nput reduced for the voltage drop on the actve semconductors.e. seral connecton of the thyrstor and dode n each nverter leg (Fg. 1. Ths voltage drop s forward voltage and for dodes t s about.7v-.8v and for thyrstors t s about 1V-1.5V. In ths algorthm the average value of the overall forward voltage s used (2V but for the practcal realzaton t s chosen from the semconductors datasheets or determned expermentally. It can be generally concluded that the voltage drop on the correspondng thyrstor-dode par could have the followng values n dependence of the conductng thyrstor T x where x = 1 6: - V TDx = V F when T x s conductng - V TDx =.5 U DC when conducts thyrstor from the same half-brdge where T x s - V TDx = U DC V F when conducts thyrstor from the same nverter leg where T x s. These results are used for the voltage calculaton n all conductng ntervals and they are summarzed n Table 4. Pror to the flux estmaton the currents and voltages gven n the Table 4 should be converted to α-β statonary frame. The resstance of the stator wndngs needed for stator flux calculaton can be easly determned from the smple experment when the motor s n the standstll. When only thyrstors T 1 and T 6 conducts the DC current wll flow through motor phases a and b. Snce the motor s n the standstll the only voltage drop s on the stator resstance R s : U ab = 2 (18 Rs a when the wndngs are Y-connected. Generally for the motor voltage value calculated from Table 4 and any type of the motor wndng connecton the stator resstance s: Uab Rs = k s a U = DC k I s 2 V where k s = 1 for Delta connecton and k s =2 for Y connecton. Relaton (19 can be easly mplemented n the control software f the thyrstors T 1 and T 6 are swtched ON pror the motor start and the stator resstance s determned from the measured DC lnk current and voltage and the knowng voltage drop on the thyrstor-dode par usng Table 4. DC F (19 Actve Thyrstors a b U ab U bc 1 T1T6 I DC U DC 2 V F.5 U DC V F 2 T1T2 I DC I DC.5 U DC V F.5 U DC V F TT2 I DC.5 U DC V F U DC 2 V F 4 TT4 I DC U DC 2 V F.5 U DC V F 5 T5T4 I DC I DC.5 U DC V F.5 U DC V F 6 T5T6 I DC.5 U DC V F U DC 2 V F Table 4. Motor current and voltage determned only by DC lnk measurements

21 Torque Control of CSI Fed Inducton Motor Drves 2 The man feedback sgnals n DTC algorthm are the estmated flux and torque. They are obtaned as outputs of the estmator operatng n stator reference frame. Ths estmator at frst performs electro-motve force (EMF ntegraton (17 to determne the stator flux vector and than calculates the flux ampltude and fnd the sector of 6 degrees n α-β plane where flux vector resdes accordng to the partton shown n Fg. 2. After the stator current and voltage are determned by prevously explaned reconstructon of stator voltages and currents pure ntegrator n (17 yelds flux vector whch components are subsequently lmted n ampltude to the magntude values of the stator flux references. The trajectory of flux vector s not crcular n the presence of DC offset. Snce ts undsturbed radus equals Ψ s the offset components tend to drve the entre trajectory toward one of the ±Ψ s boundares. A contrbuton to the EMF offset vector can be estmated from the dsplacement of the flux trajectory (Holtz 2 as: ( Ψ Ψ 1 EMF off αβ = αβ max αβ (2 mn Δ t where the maxmum and mnmum values n (2 are those of the respectve components Ψ sα and Ψ sβ and Δt s the tme dfference that defnes a fundamental perod. The sgnal EMF off s fed back to the nput of the ntegrator so as to cancel the offset component n EMF. The nput of the ntegrator then tends toward zero n a quas-steady state whch makes the estmated offset voltage vector equal the exstng offset Ψ s n (17. The trajectory of Ψ s s now exactly crcular whch ensures a precse trackng of the EMF offset vector. Snce offset drft s manly a thermal effect that changes the DC offset very slowly the response tme of the offset estmator s not at all crtcal. It s mportant to note that the dynamcs of stator flux estmaton do not depend on the response of the offset estmator (Holtz 2. The estmated rotor flux s calculated from the stator flux estmate usng motor parameters and reconstructed stator current: 2 Lr Ls Lr Lm Ψˆ rαβ = Ψˆ sαβ sαβ Lm Lm and ts poston n α-β reference frame s determned by: Ψrβ e = arctan (22 Ψrα Fnally from the estmated stator flux and reconstructed current vector the motor torque s: (21 T = p 2 e ( Ψ Ψ sβ sα sα sβ (2 where the stator flux and current vectors are gven n statonary α-β frame and p denotes the number of poles. The smulaton model s developed n Matlab/SIMULINK usng SmPowerSystems block lbrary that allows a very real representaton of the power secton (rectfer DC lnk nverter and nducton motor. All electrcal parameters (nductance of DC lnk motor parameters are the same as n real laboratory prototype also used for testng prevosly explaned FOC algorthm. Rated flux s.8wb and rated torque s 14Nm. Rectfer reference current s lmted to 12A and reference torque s lmted to 15% of rated torque (2Nm.

22 24 Torque Control Comparson between the basc and proposed DTC of CSI nducton motor drve are shown n Fg. 21 usng the same mathematcal model of CSI drve as used for FOC algorthm. Proposed DTC shows much better torque response from motor standstll. 2 2 Torque [Nm] 1-1 Torque [Nm] Fg. 21. Torque response for basc (left and proposed (rght DTC algorthm Dynamcal performances of DTC algorthm are analyzed at frst wth rated flux and zero torque reference than drve s accelerated up to 1rpm. The speed s controlled n closedloop va dgtal PI controller (proportonal gan: K P = 5 ntegral gan: K I =.5 torque lmt = 2Nm controller samplng tme: Ts = 4ms. The speed reference s set usng succeedng scheme: 1rpm at t =.25s than 1rpm at t =.6s. As could be seen from Fg. 22 a fast torque response s acheved wth correct torque reference trackng and slow rotor flux rpple around the reference value (<1.5%. For expermental purposes the same laboratory prototype of CSI drve s used as explaned before. The CSI feeds a 4kW nducton motor and as a mechancal load the 6kW DC machne wth controlled armature current s used (Nkolc & Jeftenc 28. The presented algorthm s not dependent on the motor power or the type of swtchng devces and t could be appled to any current source converter topology. The low-power nducton motor and standard type thyrstors are used just for the smplcty of the laboratory tests. The torque response s analyzed both wth drect torque demand and under the closed-loop speed control. Speed controller s mplemented wth soft start on ts nput and sample tme of 2ms. Torque lmt on the controller output s ±5Nm and s determned n such a way that under the maxmum torque value slp s equal to maxmal slp for current control: 1 smax = = 45 ω T (24 e where ω e s synchronous frequency (14rad/s and T r s rotor tme constant (78.7ms. Snce rotor flux s not measured but determned by estmaton ts value s checked wth that obtaned from smulaton. The comparson between smulated and estmated rotor flux whth zero speed (torque reference and rated flux reference are gven n Fg. 2 (a. Good performance of the flux estmator necessary for proper drect torque control could be observed from Fg. 2 (b where flux trajectory s shown startng from zero to ts rated value. Almost crcular flux trajectory wth equal ampltudes n both α and β axes assures correct offset compensaton. r

23 Torque Control of CSI Fed Inducton Motor Drves 25 1 Rotor flux [Wb] Motor speed [rpm] Torque [Nm] Fg. 22. Smulaton results for the proposed DTC method Ψ β [Wb] Ψ s [Wb] Flux from smulated model Estmated stator flux Ψ α [Wb] (a (b Fg. 2. Rotor flux response (a and ts trajectory (b durng motor start-up

24 26 Torque Control Motor speed and torque response when the speed control loop s closed s shown n Fg. 24. Response tests are performed durng motor acceleratng from rpm to rpm than from rpm to 5rpm and back to rpm and rpm (a (b Fg. 24. Motor speed (a and torque (b response under dfferent speed references 5. Conclusons In ths chapter two man torque control algorthms used n CSI fed nducton motor drves are presented namely FOC and DTC. The frst one s precse vector control (FOC algorthm. The explaned nconvenences of the vector controlled nducton motor drves fed by a CSI could be overcome wth the new vector control algorthm. The man advantage of the suggested algorthm compared to that known from the lterature s better dynamc performances of the proposed CSI drve. Ths enhancement reles on the fast changes of the motor current wthout phase error smlar to the control of current regulated voltage source PWM nverter. The realzed CSI drve has more precse control accomplshed by the mplemented correcton of the reference current. Ths correcton reduces the problem of the ncorrect motor d-q currents values produced by the non-snusodal CSI current waveform. Next the two dfferent methods of drect torque control n CSI fed nducton motor drve are presented. Contrary to the well-known hysteress control derved from VSI drve new DTC algorthm based on the constant swtchng frequency s proposed. Mert of such a soluton n comparson to the vector control of the same drve s absence of coordnate transformaton and speed sensor on the motor shaft. Furthermore snce flux estmator s based only on DC lnk measurements there s not necessty for any sensor on the motor sde whch s one of man drve advantages. In ths case by combnaton of vector control and basc DTC a robust algorthm s developed that has a faster torque response and t s smpler for mplementaton. Moreover algorthm s less senstve to the parameter varaton than standard FOC on the same drve. Contrary to the slp calculaton usng rotor tme constant proposed algorthm uses stator resstance for flux calculaton and ts value could be checked every tme when motor s stopped usng explaned method for reconstructon

25 Torque Control of CSI Fed Inducton Motor Drves 27 based only on DC lnk measurements. Other motor parameters (wndngs and mutual nductances are used only when flux reference s changed and ther values have no nfluence on the performance of the flux estmator due to the offset compensaton. The valdty of all presented torque control algorthms was proven by smulatons and expermental results on developed laboratory prototype of CSI drve. 6. References Blaschke F. (1971. A new method for the structural decouplng of A.C. nducton machnes Proceedngs of IFAC Symposum on Multvarable Techncal Control Systems pp ISBN Duesseldorf Germany October 1971 Amercan Elsever New York Bose BK. (1986. Power Electroncs and AC Drves Prentce-Hall ISBN New Jersey USA Novotny DW & Lpo TA. (1996. Vector Control and Dynamcs of AC Drves Oxford Unversty Press ISBN New York USA B Wu; SB Dewan & Sen PC. (1988. A Modfed Current-Source Inverter (MCSI for a Multple Inducton Motor Drve System. IEEE Transactons on Power Electroncs Vol. No. 1 January 1988 pp ISSN Lorenz RD. (1986. Tunng of Feld-Orented Inducton Motor Controllers for Hgh- Performance Applcatons IEEE Transactons on Industry Applcatons Vol. IA-22 No. 2 March 1986 pp ISSN Deng D & Lpo TA. (199. A Modfed Control Method for Fast Response Current Source Inverter Drves IEEE Transactons on Industry Applcatons Vol. IA-22 No. 4 July 1986 pp ISSN Vas P. (199. Vector Control of AC Machnes Clarendon Press ISBN-1: ISBN- 1: Oxford New York USA Cavalln A.; Loggn M. & Montanar GC. (1994. Comparson of Approxmate Methods for Estmate Harmonc Currents Injected by AC/DC Converters IEEE Transactons on Industal Electroncs Vol. 41 No. 2 Aprl 1994 pp ISSN Nkolc A. & Jeftenc B. (26. Precse Vector Control of CSI Fed Inducton Motor Drve European Transactons on Electrcal Power Vol.16 March 26 pp ISSN Zargar N. R.; Rzzo S. C.; Xao Y.; Iwamoto H.; Satoh K. & Donlon J. F. (21. A new current-source converter usng a symmetrc gate-commutated thyrstor (SGCT IEEE Transactons on Industry Applcatons Vol.7 21 pp ISSN Takahash I. & Noguch T. (1986. A New Quck-Response and Hgh-Effcency Control Strategy of an Inducton Motor IEEE Transactons on Industry Applcatons Vol. 22 No. 5 September/October 1986 pp ISSN Depenbrok M. (1988. Drect Self-Control (DSC of Inverter-Fed Inducton Machne IEEE Transactons on Power Electroncs Vol. PE- No. 4 October 1988 pp ISSN Ttnen P.; Pohjalanen P.& Lalu J. (1995. The next generaton motor control method: Drect Torque Control (DTC European Power Electroncs Journal Vol.5 March 1995 pp ISSN 99868