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2 1 Torque Control of CSI Fed Inducton Motor Drve Alekandar Nkolc Electrcal Engneerng Inttute Nkola Tela Belgrade Serba 1. Introducton An electrc drve an ndutral ytem whch perform the converon of electrcal energy to mechancal energy (n motorng or vce vera (n generator brakng for runnng varou procee uch a: producton plant tranportaton of people or good home applance pump ar compreor computer dc drve robot muc or mage player etc. About 5% of electrcal energy produced ued n electrc drve today. Electrc drve may run at contant peed or at varable peed. Nowaday mot mportant are varable peed drve epecally n Europe where accordng to the Ecodegn for Energy-Ung Product Drectve (25/2/EC (the "EuP Drectve" and t regulaton regardng electrc motor (Regulaton 64/29/EC on 1 January motor wth a rated output of kW mut meet hgher energy effcency tandard or meet the 211 level and be equpped wth a varable peed drve. The frt motor ued n varable peed applcaton wa DC motor drve nce t ealy controllable due to the fact that commutator and tator wndng are mechancally decoupled. The cage rotor nducton motor became of partcular nteret a t robut relable and mantenance free. It ha lower cot weght and nerta compared to commutator DC motor of the ame power ratng. Furthermore nducton motor can work n drty and explove envronment. However the relatve mplcty of the nducton motor mechancal degn contrated by a complex dynamc tructure (multvarable nonlnear mportant quantte not obervable. In the lat two decade of the 2 th century the technologcal mprovement n power emconductor and mcroproceor technology have made poble rapd applcaton of advanced control technque for nducton motor drve ytem. Nowaday torque control of nducton motor poble and ha many advantage over DC motor control ncludng the ame ytem repone and even fater repone n cae of the latet control algorthm. Two mot pread ndutral control cheme employ vector or feld-orented control (FOC and drect torque control (DTC. Current ource nverter (CSI are tll vable converter topology n hgh voltage hgh power electrcal drve. Further advance n power electronc and uage of new component lke SGCT (Symmetrc Gate Commutated Thyrtor gve the new poblte for th type of converter n medum voltage applcaton. Power regeneraton durng brakng what a one of man bult-n feature of CSI drve alo mert for hgh power drve. Depte the

3 4 Torque Control above advantage the confguraton baed on a thyrtor front-end rectfer preent a poor and varable overall nput power factor (PF nce the current not nuodal but trapezodal waveform. Alo the mplementaton of CSI drve ytem wth on-lne control capablte more complex than for voltage ource nverter (VSI due to the CSI gatng requrement. Regardng mentoned dadvantage CSI drve are of nteret for reearch n the feld of torque control algorthm uch a vector control (or FOC and drect torque control (DTC. Th chapter wll preent bac FOC and DTC algorthm for CSI drve and how all feature and dadvantage of thoe control cheme (luggh repone phae error large torque rpple need for adaptve control etc.. Ung recent analy tool lke powerful computer mulaton oftware and experment on developed laboratory prototype two new FOC and DTC oluton wll be preented n the chapter. The propoed FOC enable CSI drve to overcome mentoned nconvenence wth better dynamc performance. Th enhancement rele on fat change of the motor current wthout phae error mlar to the control of current regulated voltage ource PWM nverter. The realzed CSI drve ha more prece control accomplhed by the mplemented correcton of the reference current. Th correcton reduce the problem of the ncorrect motor current component produced by the non-nuodal CSI current waveform. On the other de propoed DTC algorthm completely new n the lterature and the only uch a control cheme ntended for CSI nducton motor drve. Preented DTC baed on the contant wtchng frequency abence of coordnate tranformaton and peed enor on the motor haft. Furthermore nce flux etmator baed only on DC lnk meaurement there not necety for any enor on the motor de whch one of man drve advantage. In th cae by combnaton of vector control and bac DTC a robut algorthm developed that ha a fater torque repone and t mpler for mplementaton. 2. Charactertc of current ource nverter The mot prevalng ndutral drve confguraton n low voltage range baed on IGBT trantor a power wtche and voltage-ource nverter (VSI topology. On the other de the nducton motor drve wth thyrtor type current-ource nverter (CSI alo known a auto equentally commutated nverter Fg. 1 poe ome advantage over voltage-ource nverter drve but t ha a larger torque rpple nce the current wave-form not nuodal. Furthermore due to the nature of the CSI operaton the dynamc performance that ext n VSI PWM drve could not be acheved. But CSI permt eay power regeneraton to the upply network under the breakng condton what favorable n large-power nducton motor drve. At low voltage range (up to 1kV th type of nverter very rare and abandoned but th confguraton tll uable at hgh power hgh voltage range up to 1kV and everal MW. In tracton applcaton bpolar thyrtor tructure replaced wth gate turn-off thyrtor (GTO. Nowaday current ource nverter are very popular n medum-voltage applcaton where ymmetrc gate-commutated thyrtor (SGCT utlzed a a new wtchng devce wth advantage n PWM-CSI drve (Wu 26. New development n the feld of mcroproceor control and applcaton n electrcal drve gve poblty for employment of very complex and powerful control algorthm. Torque control of CSI fed nducton motor drve become alo vable and promng oluton nce ome of CSI control dadvantage could be overcome ung mproved mathematcal model and calculaton.

4 Torque Control of CSI Fed Inducton Motor Drve 5 Ld T1' T' T5' T1 T T5 C1 C C5 8V 5Hz D1 D D5 L1 L2 L W V U D4 D2 C6 D6 M ~ T4 T2 T6 C4 C2 AC MOTOR T4' T2' T6' Fg. 1. Bac CSI topology ung thyrtor a power wtche Two mot mportant torque control cheme are preented namely FOC and DTC. Both control cheme wll be hown wth all varaton known from lterature ncludng thoe propoed by prevou reearch work of author. All preented torque control algorthm bac and propoed by author are analyzed and verfed by mulaton and experment.. Vector control In the pat DC motor were ued extenvely n area where varable-peed operaton wa requred nce ther flux and torque could be controlled ealy by the feld and armature current. However DC motor have certan dadvantage whch are due to the extence of the commutator and bruhe. On the other de nducton motor have le ze for the ame power level ha no bruhe and commutator o they are almot mantenance free but tll ha dadvantage. The control tructure of an nducton motor complcated nce the tator feld revolvng. Further complcaton are due to the fact that the rotor current or rotor flux of a qurrel-cage nducton motor cannot be drectly montored. The mechanm of torque producton n an AC and DC machne mlar. Unfortunately that mlarty wa not emphazed before 1971 when the frt paper on feld-orented control (FOC for nducton motor wa preented (Blachke Snce that tme the technque wa completely developed and today mature from the ndutral pont of vew. Today feld orented controlled drve are an ndutral realty and are avalable on the market by everal producer and wth dfferent oluton and performance..1 Bac vector control of CSI drve Many tratege have been propoed for controllng the moton of CSI fed nducton motor drve (Boe 1986; Novotny & Lpo 1988; Wu et al. 1988; Deng & Lpo 199; Va 199. The vector control ha emerged a one of the mot effectve technque n degnng hghperformance CSI fed nducton motor drve. Compared to the PWM VSI drve CSI ha advantage n the reverble drve but t ha a larger torque rpple nce the current waveform not nuodal. Furthermore due to the nature of the CSI operaton the dynamc performance that ext n PWM drve are not acheved wth the extng vector control algorthm. The well-known ("bac" tructure of a CSI fed nducton motor drve wth ndrect vector control hown n Fg. 2 (Boe 1986; Va 199.

5 6 Torque Control upply d q α PI controller reolver lp calculator - dc lead crcut ω CSI Δ rng counter Fg. 2. Indrect vector control of a CSI fed nducton machne Th method make ue of the fact that atfyng the lp relaton a neceary and uffcent condton to produce feld orentaton.e. f the lp relaton atfed (denoted a lp calculator n Fg. 2 current d component wll be algned wth the rotor flux. Current command are converted to ampltude and phae command ung reolver (rectangular to polar coordnate tranformaton. The current ampltude command drectly employed a the reference for the current PI controller ntended for controllng the nput converter (three phae full wave brdge rectfer. The phae command paed through a lead crcut uch that phae change are added nto the nverter frequency channel nce thee ntantaneou phae change are not contaned n the lp frequency command gnal comng from the lp calculator..2 Propoed vector control of CSI drve In the vector controlled CSI drve found n (Boe 1986; Wu et al. 1988; Deng & Lpo 199; Va 199; Novotny & Lpo 1996 and hown n prevou chapter the problem of the peed repone are reported. Th nfluenced by the ntantaneou phae error and a a reult thee confguraton have lower torque repone compared to the current regulated PWM drve. In addton to the phae error the commutaton delay and the non-nuodal upply that nhered n CSI operaton mut be generally compenated for to acheve acceptable vector control. To overcome thee dadvantage the phae error elmnaton and the reference current correcton hould be performed. In th chapter the vector control algorthm that elmnate the two drawback hown (Nkolc & Jeftenc 26. The uggeted algorthm produce the performance of the CSI drve that ext n the PWM vector controlled drve. That enable th mple and robut confguraton to be ued n applcaton where reverble operaton a mert. The necety for the phae error elmnaton can be explaned wth the help of the followng phaor dagram: d Δ q1 1/ Ψ r 1 e rf ω e q2 2 ω r M Fg.. Phaor dagram wth hown phae error

6 Torque Control of CSI Fed Inducton Motor Drve 7 When the torque command tepped from q1 to q2 (wth a contant d the current vector hould ntantaneouly change from 1 to 2. The lp frequency hould alo change mmedately. The reolver doe gve the correct ampltude and the new lp frequency wll be obtaned by the lp calculator. However although the phae change Δ added by a lead crcut a hown n Fg. 2 nce the ntant phae change are not contaned n the lp frequency command gnal comng from the lp calculator (Boe 1986; Deng & Lpo 199; Novotny & Lpo 1996 the tator current command wll correpond to the vector n Fg. and there wll be a phae error n the vector control ytem. Th would reult n an ntantaneou lo of the feld-orentaton that produce a very luggh repone of both flux and torque. Th problem could be overcome by the propoed algorthm whch unfe feature of both PWM and CSI converter. The reolver tll ued to calculate the rectfer reference current but for the nverter thyrtor control a method ued n the current controlled PWM nverter mplemented. Intead of a lead crcut (hown n Fg. 2 the new algorthm nclude a ynchronou to tator tranformaton (T -1 to tranfer the d-q command to the three-phae ytem. Th eental for achevng a fat torque repone nce the torque value determned by the fundamental harmonc of the tator current. For correct frng of the thyrtor n the nverter the wtchng tme hould be properly determned to enure that the phae angle of the motor current matche the phae angle of the reference current n a-b-c ytem. The reference nuodal current obtaned a a reult of tranformaton T -1 are dvded by the value obtaned on the reolver output to produce current of unty ampltude. Introducton of thee current nto the comparator wth trgger level equal to.5 gve the proper thyrtor conducton tme of 12 degree. Th llutrated n Fg. 4 where a unty nuodal current a caled CSI output current and a1 fundamental tator current a1 a Current [p.u.] a phae angle [degree] Fg. 4. Waveform of the reference current and fundamental tator current The algorthm poee the addtonal advantage regardng the practcal realzaton. In dgtal control ytem the lead crcut dvde the dfference of the two ucceedng ample wth the amplng tme. Snce the amplng tme mall th operaton produce the computatonal error. The phaor dagram from Fg. wth removed phae error preented n Fg. 5. Wthout the phae error (Δ = the tep of the torque command produce the new tator current command ( = 2. Due to non-nuodal current of the CSI the average value of the motor d-q current d_av and q_av and the reultng tator current vector greater than the correpondng reference hown n Fg. 5. To mprove propoed algorthm and avod mproper reultant d-q motor current the rectfer reference current correcton performed.

7 8 Torque Control d Δ = q1 1 = q2 2 q_av d_av Ψ r Fg. 5. Phaor dagram wthout phae error In the vector controlled nducton motor drve fed by a CSI a problem of ncorrect copyng of the d-q reference to the motor ext. A tated earler the reaon non-nuodal current waveform produced by a CSI. The deal CSI current a qua-quare waveform (hown n Fg. 4. The Fourer analy of th waveform gve the expreon: a = Id n( ωt n(5ωt n(7ωt 5 7 The prevou relaton how that the fundamental component of AC output current ha the ampltude 1 percent greater than the value of DC lnk current. For correct reproducton of the d-q reference and atfactory vector control t not uffcent to adjut only the phae of the fundamental motor current and the phae angle of the generated command. The fnetunng of the motor current n d-q frame requred. To avod upplementary hardware and oftware a procedure that rele only on the value calculated off-lne propoed. The correpondng relaton between the mean value of the motor current n d-q frame and the commanded d-q current calculated. For propoed correcton t not uffcent to ue the dfference between current of 1% from (1 becaue the correcton depend on the phae angle of the d-q component and the nverter commutaton proce. At lower peed the commutaton proce could be neglected nce t much horter than the motor current cycle. Takng all th n conderaton the rectfer reference current corrected concernng the reference ampltude the phae angle and the commutaton duraton. The rectfer reference current formed n that manner now ntroduced to the current controller to obtan utable motor d-q current and acheve dered vector control. The calculaton tart from the fundamental reference current from the reolver: (1 2 ( d ( q and the phae angle (alo obtaned from the reolver: 2 = (2 ( d / = arctan ( Snce the nverter commutaton proce not neglected the waveform of the nverter output current repreented by a trapezodal approxmaton analyzed n (Cavaln et al wth adequate precon. Trapezodal waveform very near to the real current cone waveform due to the hort commutaton perod a explaned n (Boe Th approxmaton aume that durng the commutaton perod the nverter current re wth q

8 Torque Control of CSI Fed Inducton Motor Drve 9 a contant rate of change. For rated rectfer current I d the current rate of change durng the commutaton equal to I d /t c where t c correpondng commutaton tme calculated from the value of the commutaton crcut component. The adequate commutaton angle could be obtaned a a product of the nverter frequency ω e and partcular commutaton tme. Th tme nterval determned from the current rate of change I d /t c and the reference value of the DC lnk current therefore the commutaton angle : d c e I t = ω (4 Snce the nverter current perodcal the trapezodal waveform n all three phae could be repreented on a horter angle nterval wth the followng equaton: < < < < < = ( d d d d a I I I I (5 2 ( ( = a b (6 4 ( ( = a c (7 where range from to the commutaton angle and the phae angle obtaned from (. The ntantaneou value of d-q current are olved by a three phae to d-q frame tranformaton T: = = = ( ( ( / 4 co( / 2 co( co( / 4 n( / 2 n( n( 2 ( ( ( 2 ( ( c b a c b a q d T (8 The average value of the current n d and q ax obtaned from (8 on the range from to be: = _ d ( 1 av ( d d (9

9 1 Torque Control 1 q _ av ( = q ( d (1 The ampltude of the motor current vector n polar coordnate could be determned ung the average value obtaned from (9 and (1: 2 d 2 _ av q _ av ( = ( ( (11 The dfference between reference ampltude calculated from (2 and the reultng tator ampltude obtaned from (11 hown n Fg. 4. To avod th dfference the correpondng correcton factor f cor ntroduced a a rato of the reference (2 and the actual motor current (11: f cor ( = (12 ( For mulaton and practcal realzaton purpoe the correcton factor f cor computed from (2 (12 and placed n a look-up table wth the followng retrcton: d contant q changed only to t rated value wth lmted to 1 p.u. for gven reference all poble value of and are calculated ung ( and (4 repectvely. The rectfer reference current that provde the correct value of motor current d-q component now: = f ( (1 ref The nterdependence between correcton factor f cor commutaton angle and phae angle preented n Fg. 6 a a -D graph. cor Correcton factor f cor [p.u.].7.4 Commutaton angle [rad] Phae angle [rad] 2.5. Fg. 6. Correcton factor commutaton angle and phae angle nterdependence

10 Torque Control of CSI Fed Inducton Motor Drve 11 The calculated reult of the current correcton n d-ax and q-ax are preented n Fg. 7a and Fg. 7b repectvely. The corrected current are gven along wth reference and motor average d-q current (value wthout correcton. The flux command held contant (.7 p.u. whle torque command changed from.7 p.u. to.7 p.u. Motor current n d-ax [p.u.] d corrected = d [p.u.] d not corrected [p.u.] Torque command q [p.u.] a Motor current n q-ax [A] Torque command q [A] b q corrected = q [p.u.] q not corrected [p.u.] Fg. 7. Calculated motor current corrected n d-ax and q-ax (ab repectvely From the prevou analy the new reolver wth current correcton formed a hown n Fg. 8. Th tructure ued both n the mulaton and the experment. The new reolver conted of the block Cartean to polar (the coordnate tranformaton and the block Correcton that degnate the nterdependence gven n Fg. 6. A tated before th nterdependence placed n a -D look-up table ung (2-(12. d q Cartean to polar x tc/id Correcton f cor Reolver wth correcton x lp calculator ω ω e ω r ref Fg. 8. New reolver wth current correcton To analyze dynamc performance of the propoed CSI drve the torque repone of the "bac" tructure hown n Fg. 2 compared to the repone of the new vector control algorthm. Th done by mulaton of thee two confguraton' mathematcal model n Matlab/Smulnk. The frt model repreent the drve wth bac arrangement and the econd the drve wth new control algorthm. The mulaton of both model done wth everal ntal condton. Magnetzng (d-ax current for rated flux ha been determned from the motor parameter and t value (.7p.u. contant durng mulaton. The rated q-ax current ha been determned from the magnetzng current and the rated full-load current ung (2. At frt mulaton of both model are tarted wth d-ax command et to.7p.u no-load and all ntal condton equal to zero. When the rotor flux n d-ax approache to the teady tate the machne excted. Th value of d-ax flux now ntal

11 12 Torque Control for the ubequent mulaton. For the econd mulaton the pule gven a a torque command wth the ampltude of.2p.u. and duraton of.5. Wth no-load the motor wll be accelerated from zero peed to the new teady-tate peed (.2p.u. whch the ntal condton for the next mulaton. Fnally the quare wave torque command appled to both model wth equal potve and negatve ampltude (±.2p.u and the oberved dynamc torque repone extracted from the lope of the peed (Lorenz The quare wave duty cycle (.9 conderably greater than the rotor tme contant (T r =.1 hence the rotor flux could be condered contant when the torque command changed. Fg. 9 how torque peed and rotor flux repone of both model. It could be notced that the torque repone of the bac tructure lghtly lower (Fg. 9a whle the propoed algorthm gve almot ntantaneou torque repone (Fg. 9b. Th tatement could be verfed clearly from the peed repone analy. In both cae the torque command the ame. In the new model th quare wave torque command produce peed varaton from.2p.u. to.6p.u. wth dentcal lope of the peed. But n the bac model at the end of the frt cycle the peed could not reach.6p.u. for the ame torque command due to the fact Motor torque and peed [p.u.] tme [] a.8 Rotor flux [p.u.] Ψ rd Ψ rq tme [] c Motor torque and peed [p.u.] tme [] b Rotor flux [p.u.] tme [] Fg. 9. Torque peed and rotor flux of the bac tructure (a (c and of the propoed algorthm (b (d Ψ rd Ψ rq d

12 Torque Control of CSI Fed Inducton Motor Drve 1 that torque repone lower. Alo n the next cycle (negatve torque command the peed doe not return to.2p.u. for the ame reaon. From dfferent lope of the peed n thee two model t could be concluded that propoed algorthm produce qucker torque repone. The rotor q-ax flux dturbance n tranent regme that ext n the bac model (Fg. 9c greatly reduced by the propoed algorthm n the new model (Fg. 9d. It could be een that ome dturbance alo ext n the cae of d-ax flux but they are almot dappeared n the new model. To llutrate the gnfcance and facltate the undertandng of theoretcal reult obtaned n the prevou ecton a prototype of the drve contructed. The prototype ha a tandard thyrtor type frequency converter dgtally controled va Intel 16-bt 8C196KC2 mcrocontroller. Inducton motor ued n laboratory 4kW 8V 5Hz machne. The peed control of the drve and a prototype photo are hown n Fg. 1. Smplcty of th block dagram confrm that the realzed control algorthm eaer for a practcal actualzaton. The propoed crcut for the phae error elmnaton at frt teted on the mulaton model. The mulaton performed n uch a manner that C code for a mcrocontroller could be drectly wrtten from the model. The value that are read from look-up table n a real ytem (cone functon quare root are alo preented n the model a table to properly emulate calculaton n the mcrocontroller. Fg. 11a how waveform of the unty nuodal reference ( a and b whle Fg. 11b ndcate nverter thyrtor wtchng tme wth changed wtchng equence when the phae changed (.18 marked wth an arrow. On thee dagram t could be oberved that thyrtor T 1 and T 2 are wtched to ON tate when unty reference a and b reach.5 p.u. repectvely. Fg. 11cd repreent the ntant phae varaton of the current n a and b phae after the reference current altered. The correpondng current wthout command change are dplayed wth a thn lne for a clear obervaton of the ntant when the phae changed. ω ref ω r _ Speed controller q Mcrocontroller d Reolver (Fg. 7 ref _ I d q d Slp calculator ω e ω ω r Current controller arcco U c ~ 2= 1/ abc Frng crcut wthout phae error α I d 6 ω r e 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

13 14 Torque Control 1. a b b a 6 4 Current [p.u.] Current a [A] tme [] a tme [] c 6 T1 4 T2 T T4 T5 T tme [] b Current b [A] tme []..4 d Fg. 11. Reult of the phae error elmnaton (ab - mulaton cd - expermental The effect of the reference current correcton are gven by the pecfc experment. To etmate d and q component the motor current n a and b phae and the angle e between a-ax and d-ax are meaured. Th angle obtaned n the control algorthm (Fg. 1 a a reult of a dgtal ntegraton: ( n = ( n 1 ω T (14 e e where n a ample T the ample tme and ω e exctaton frequency. The ntegrator reet every tme when e reache or 6 degree. The eaet way for acqurng the value of th angle to change the tate of the one mcrocontroller' dgtal output at the ntant when the ntegrator reet. On the tme range between two ucceedng pule the angle changed lnearly from to 6 degree (for one rotatng drecton. Snce only th tme range needed for determne the current n d and q ax the reet gnal from the dgtal output proceed to the external ynchronzaton nput of the ocllocope. In that way the motor phae current are meaured only on the partcular tme (angle range. The correpondng current n d-q axe are calculated from (8 ung for e a and b expermentally determned value. The expermental reult are gven n Fg. 12 wth dabled peed controller. e

14 Torque Control of CSI Fed Inducton Motor Drve 15 Motor current n d-ax [A] corrected d [A] not corrected d [A] 1..5 d [A] Torque command q [A] a Motor current n q-ax [A] q [A] Torque command q [A] b q corrected [A] q not corrected [A] Fg. 12. Expermental reult of the motor current correcton n d-ax and q-ax (ab repectvely The flux reference wa mantaned contant at 2.96A (.7p.u. and torque command wa changed from 1.5A (.5p.u. to.a (.78 p.u.. The nverter output frequency retaned the ame durng experment ( 2Hz by varyng the DC motor armature current. From Fg. 12 t could be een that for the propoed algorthm average value of d-q component n the p.u. ytem are almot equal to correpondng reference. On the other de n the ytem wthout correcton there a dfference up to 15% whch confrmed the reult obtaned from calculaton hown n Fg. 7. Th dfference produce teady tate error what make uch a ytem unacceptable for vector control n hgh performance applcaton. On the Fg. 1 the motor peed and rotatng drecton change are hown wth enabled peed controller. The reference peed wapped from -2mn -1 to 2mn Motor peed [mn -1 ] Fg. 1. The motor peed reveral In Fg. 14 the nfluence of the load change to the peed controller preented. A a load DC machne (6kW 2VDC controlled by a drect change of the armature current va - phae rectfer ued. At frt the nducton motor work unloaded n a motor regon (M wth the reference peed of 2mn -1 that produce the torque command current q1 = A. After that the DC machne tarted wth t torque n the ame drecton wth rotatng drecton of the nducton motor. That tart the breakng of the nducton motor and t goe to the generator regon (G. In th operatng regon the power from DC lnk tme []

15 16 Torque Control return to the upply network. The reference torque command current change t value and gn ( q2 = 1.72A. When DC machne wtched off the nducton motor goe to the motor regon (M and the reference torque command current now q = -1.48A. -15 Motor peed [mn -1 ] M G M q1 q2 q tme [] Fg. 14. The load change at motor peed of 2mn Drect torque control The drect torque control (DTC one of the actvely reearched control cheme of nducton machne whch baed on the decoupled control of flux and torque. DTC provde a very quck and prece torque repone wthout the complex feld-orentaton block and the nner current regulaton loop (Takahah & Noguch 1986; Depenbrok DTC the latet AC motor control method (Ttnen et al developed wth the goal of combnng the mplementaton of the V/f-baed nducton motor drve wth the performance of thoe baed on vector control. It not ntended to vary ampltude and frequency of voltage upply or to emulate a DC motor but to explot the flux and torque producng capablte of an nducton motor when fed by an nverter (Buja et al Drect torque control concept In t early tage of development drect torque control developed manly for voltage ource nverter (Takahah & Noguch 1986; Ttnen et al. 1995; Buja Voltage pace vector that hould be appled to the motor choen accordng to the output of hytere controller that ue dfference between flux and torque reference and ther etmate. Dependng on the way of electng voltage vector the flux trajectory could be a crcle (Takahah & Noguch 1986 or a hexagon (Depenbrok 1988 and that trategy known a Drect Self Control (DSC motly ued n hgh-power drve where wtchng frequency need to be reduced. Controller baed on drect torque control do not requre a complex coordnate tranform. The decouplng of the nonlnear AC motor tructure obtaned by the ue of on/off control whch can be related to the on/off operaton of the nverter power wtche. Smlarly to drect vector control the flux and the torque are ether meaured or motly etmated and ued a feedback gnal for the controller. However a oppoed to vector control the tate of the power wtche are determned drectly by the etmated and the reference torque and flux gnal. Th acheved by mean of a wtchng table the nput of whch are the

16 Torque Control of CSI Fed Inducton Motor Drve 17 torque error the tator flux error and the tator flux angle quantzed nto x ecton of 6. The output of the wtchng table are the ettng for the wtchng devce of the nverter. The error gnal of the tator flux quantzed nto two level by mean of a hytere comparator. The error gnal of the torque quantzed nto three level by mean of a three tage hytere comparator (Fg. 15. ψ n - peed controller - T e - δ ψ optmal wtchng electon table S A S B S C motor model a b c me ω me ψ a ψ b T e ψ et T et polar coordnate tranform. Fg. 15. Bac concept of drect torque control The equaton for the developed torque may be expreed n term of rotor and tator flux: T e = M L L M r ψ ψ n( δ 2 ψ where δ Ψ the angle between the tator and the rotor flux lnkage pace phaor. For contant tator and rotor flux the angle δ Ψ may be ued to control the torque of the motor. For a tator fxed reference frame (ω e = and R = t may be obtaned that: 1 ψ = T t u n The tator voltage pace phaor may aume only x dfferent non zero tate and two zero tate a hown n Fg. 16. The change of the tator flux vector per wtchng ntant therefore determned by equaton (16 and Fg. 16. The zero vector V and V 7 halt the rotaton of the tator flux vector and lghtly decreae t magntude. The rotor flux vector however contnue to rotate wth almot ynchronou frequency and thu the angle δ Ψ change and the torque change accordngly a per (15. The complex tator flux plane may be dvded nto x ecton and a utable et of wtchng vector dentfed a hown n Table 1 where dψ and dt e are tator flux and torque error repectvely whle S 1 6 are ector of 6 where tator flux rede. Further reearche n the feld of DTC are motly baed on reducng torque rpple and mprovement of etmaton proce. Th yeld to development of ophtcated control algorthm contant wtchng cheme baed on pace-vector modulaton (Caade et al. 2 hytere controller wth adaptve bandwdth PI or fuzzy controller ntead of hytere comparator jut to name a few. r dt (15 (16

17 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 vector of three phae 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 wtchng vector n VSI DTC drve 4.2 Standard DTC of CSI drve Although the tradtonal DTC developed for VSI for ynchronou motor drve the CSI propoed (Va 1998; Boldea 2. Th type of converter can be alo appled to DTC nducton motor drve (Va 1998 and n the chapter uch an arrangement preented. The nducton motor drve wth thyrtor type CSI (alo known a auto equentally commutated nverter poe ome advantage over voltage-ource nverter drve. CSI permt eay power regeneraton to the upply network under the breakng condton what favorable n large-power nducton motor drve. In tracton applcaton bpolar thyrtor tructure replaced wth gate turn-off thyrtor (GTO. Nowaday current ource nverter are popular n medum-voltage applcaton (Wu 26 where ymmetrc gatecommutated thyrtor (SGCT utlzed a a new wtchng devce (Zargar et al. 21 wth advantage n PWM-CSI drve. DTC of a CSI-fed nducton motor nvolve the drect control of the rotor flux lnkage and the electromagnetc torque by applyng the optmum current wtchng vector. Furthermore t poble to control drectly the modulu of the rotor flux lnkage pace vector through the rectfer voltage and the electromagnetc torque by the upply frequency of CSI. Bac CSI DTC trategy (Va 1998 hown n Fg. 17.

18 Torque Control of CSI Fed Inducton Motor Drve 19 ~ Ψ r - Rotor flux controller Controlled rectfer T e - Torque comparator Optmal wtchng vector CSI L F Ψ r et Ψ r poton T e et Ψ r & T e Etmator IM Fg. 17. DTC of CSI drve baed on hytere control The tator flux value needed for DTC control loop not convenent to meaure drectly. Intead of that the motor flux etmaton performed. In the voltage-baed etmaton method the motor flux can be obtaned by ntegratng t back electromotve force (EMF. The EMF calculated from the motor voltage and current (17 and the only motor parameter requred the tator wndng retance. In practce th mple ntegraton replaced by more ophtcated cloed-loop etmator ung flterng technque adaptve ntegraton or even oberver and Extended Kalman flter (Holtz 2. ( R dt t u ψ = ψ (17 For DTC of CSI fed nducton motor drve the approprate optmal nverter currentwtchng vector (Fg. 18 are produced by ung an optmal current-wtchng table mlarly to the table gven for VSI drve (Table 2. The man dfference that n CSI ext only one hytere comparator for torque and only one zero wtchng current vector. b 2 5/6-5/6 /2 /6 -/6 1 a 4 -/2 6 5 c Fg. 18. Current vector n CSI

19 2 Torque Control S 1 dt e / S 2 / 2/ S 2/ S / S 5-2/ -/ S 6 -/ Table 2. Optmal wtchng vector n CSI DTC drve 4. Propoed DTC of CSI drve In DTC cheme the preence of hytere controller for flux and torque determne varable-wtchng-frequency operaton for the nverter. Furthermore ung DTC cheme a fat torque repone over a wde peed range can be acheved only ung dfferent wtchng table at low and hgh peed. The problem of varable wtchng frequency can be overcome by dfferent method (Va 1998; Caade et al. 2. In (Caade et al. 2 a oluton baed on a tator flux vector control (SFVC cheme ha been propoed. Th cheme may be condered a a development of the bac DTC cheme wth the am of mprovng the drve performance. The nput command are the torque and the rotor flux wherea the control varable are the tator flux component. The prncple of operaton baed on drvng the tator flux vector toward the correpondng reference vector defned by the nput command. Th acton carred out by the pace-vector modulaton (SVM technque whch apple a utable voltage vector to the machne n order to compenate the tator flux vector error. In th way t poble to operate the nducton motor drve wth a contant wtchng frequency. In propoed DTC CSI drve hown n Fg. 19 the nput are rotor flux and torque a n VSI preented n (Caade et al. 2 but now a a control varable the tator flux angle α ued (Nkolc & Jeftenc 28. Supply L DC U DC CSI PI current controller Reolver _ref α - I DC q α q calculator I DC Rotor flux poton e Rotor flux and torque etmator Modfed optmal wtchng table α M ~ PI rotor flux controller d - Ψ r Ψ r T e - PI torque controller T e Ψ r T e_ref Fg. 19. Propoed contant-wtchng DTC trategy n CSI fed nducton motor drve

20 Torque Control of CSI Fed Inducton Motor Drve 21 Although th confguraton could remnd on feld-orented control the man dfference abence of coordnate tranformaton nce t not neceary to ue coordnate tranformaton to acheve correct frng angle a n vector control of the ame drve (Nkolc & Jeftenc 26. Identcal reult would be obtaned when phae angle between d-q current reference and rotor flux vector angle e = arctan(ψ rβ /Ψ rα are ummed and reultng angle α than ued to determne ector of 6 degree where rede rotor flux vector. In that way phae angle act a a torque control command. When reference torque changed q momentary changed. Phae angle move tator current vector n drecton determned by the gn of torque reference and t value accelerate or decelerate flux vector movement accordng to the value of the reference torque (Fg. 2. β 2 Ψ r _ref1 2 (α 1 1 (α 6 (α 2 α α 2 _ref2 α Fg. 2. Selectng proper current vector n propoed DTC algorthm 5 Th modfcaton mple omewhere dfferent wtchng table for actvatng nverter wtche from that hown n Table 2. Now α (angle between referent α-ax and reference current vector determne whch current vector hould be choen: 2 for torque ncreae 6 for torque decreae or 1 for keepng torque at the current value. Current vector Angle range (degree 1 α > and α 6 2 α > 6 and α 12 α > 12 and α 18 4 α > 18 or α α > -12 and α -6 6 α > -6 and α Table. Optmal wtchng table n propoed DTC It neceary to emphaze the mportance of zero pace vector. In VSI there are two zero voltage vector: V denote cae when all three wtche from the one half of nverter are wtched ON whle V 7 repreent tate when wtche are OFF. Contrary n CSI (ung analogy to the VSI zero current vector repreent cae when all thyrtor are OFF. That could lead to both torque and motor peed decreae. Due to the nature of commutaton n CSI t convenent to keep the elected current vector at ntant when zero current vector choen.

21 22 Torque Control The voltage and the current of CSI fed nducton motor neceary for tator flux calculaton can be recontructed from the DC lnk quantte knowng the tate of the conductng nverter wtche. In one duty cycle of the output current CSI ha x commutaton. In that cae x nterval of 6 degree can be defned n whch the current and the voltage change t value. In every nterval the current from DC lnk flow through two nverter leg and two motor phae wndng. The motor lne voltage equal to the DC voltage on the nverter nput reduced for the voltage drop on the actve emconductor.e. eral connecton of the thyrtor and dode n each nverter leg (Fg. 1. Th voltage drop forward voltage and for dode t about.7v-.8v and for thyrtor t about 1V-1.5V. In th algorthm the average value of the overall forward voltage ued (2V but for the practcal realzaton t choen from the emconductor dataheet or determned expermentally. It can be generally concluded that the voltage drop on the correpondng thyrtor-dode par could have the followng value n dependence of the conductng thyrtor T x where x = 1 6: - V TDx = V F when T x conductng - V TDx =.5 U DC when conduct thyrtor from the ame half-brdge where T x - V TDx = U DC V F when conduct thyrtor from the ame nverter leg where T x. Thee reult are ued for the voltage calculaton n all conductng nterval and they are ummarzed n Table 4. Pror to the flux etmaton the current and voltage gven n the Table 4 hould be converted to α-β tatonary frame. The retance of the tator wndng needed for tator flux calculaton can be ealy determned from the mple experment when the motor n the tandtll. When only thyrtor T 1 and T 6 conduct the DC current wll flow through motor phae a and b. Snce the motor n the tandtll the only voltage drop on the tator retance R : U ab = 2 R (18 when the wndng are Y-connected. Generally for the motor voltage value calculated from Table 4 and any type of the motor wndng connecton the tator retance : R Uab = k a U = k DC a 2 V where k = 1 for Delta connecton and k =2 for Y connecton. Relaton (19 can be ealy mplemented n the control oftware f the thyrtor T 1 and T 6 are wtched ON pror the motor tart and the tator retance determned from the meaured DC lnk current and voltage and the knowng voltage drop on the thyrtor-dode par ung Table 4. I DC F (19 Actve Thyrtor 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 meaurement

22 Torque Control of CSI Fed Inducton Motor Drve 2 The man feedback gnal n DTC algorthm are the etmated flux and torque. They are obtaned a output of the etmator operatng n tator reference frame. Th etmator at frt perform electro-motve force (EMF ntegraton (17 to determne the tator flux vector and than calculate the flux ampltude and fnd the ector of 6 degree n α-β plane where flux vector rede accordng to the partton hown n Fg. 2. After the tator current and voltage are determned by prevouly explaned recontructon of tator voltage and current pure ntegrator n (17 yeld flux vector whch component are ubequently lmted n ampltude to the magntude value of the tator flux reference. The trajectory of flux vector not crcular n the preence of DC offet. Snce t undturbed radu equal Ψ the offet component tend to drve the entre trajectory toward one of the ±Ψ boundare. A contrbuton to the EMF offet vector can be etmated from the dplacement of the flux trajectory (Holtz 2 a: ( Ψ Ψ 1 EMF off αβ = αβ max αβ (2 mn Δ t where the maxmum and mnmum value n (2 are thoe of the repectve component Ψ α and Ψ β and Δt the tme dfference that defne a fundamental perod. The gnal EMF off fed back to the nput of the ntegrator o a to cancel the offet component n EMF. The nput of the ntegrator then tend toward zero n a qua-teady tate whch make the etmated offet voltage vector equal the extng offet Ψ n (17. The trajectory of Ψ now exactly crcular whch enure a prece trackng of the EMF offet vector. Snce offet drft manly a thermal effect that change the DC offet very lowly the repone tme of the offet etmator not at all crtcal. It mportant to note that the dynamc of tator flux etmaton do not depend on the repone of the offet etmator (Holtz 2. The etmated rotor flux calculated from the tator flux etmate ung motor parameter and recontructed tator current: Ψˆ rαβ = L L r m Ψˆ αβ L Lr L L m 2 m αβ (21 and t poton n α-β reference frame determned by: Ψrβ e = arctan (22 Ψrα Fnally from the etmated tator flux and recontructed current vector the motor torque : T e = 2 p ( Ψ Ψ β α α β (2 where the tator flux and current vector are gven n tatonary α-β frame and p denote the number of pole. The mulaton model developed n Matlab/SIMULINK ung SmPowerSytem block lbrary that allow a very real repreentaton of the power ecton (rectfer DC lnk nverter and nducton motor. All electrcal parameter (nductance of DC lnk motor parameter are the ame a n real laboratory prototype alo ued for tetng prevoly explaned FOC algorthm. Rated flux.8wb and rated torque 14Nm. Rectfer reference current lmted to 12A and reference torque lmted to 15% of rated torque (2Nm.

23 24 Torque Control Comparon between the bac and propoed DTC of CSI nducton motor drve are hown n Fg. 21 ung the ame mathematcal model of CSI drve a ued for FOC algorthm. Propoed DTC how much better torque repone from motor tandtll. 2 2 Torque [Nm] 1-1 Torque [Nm] tme [] tme [] Fg. 21. Torque repone for bac (left and propoed (rght DTC algorthm Dynamcal performance of DTC algorthm are analyzed at frt wth rated flux and zero torque reference than drve accelerated up to 1rpm. The peed controlled n cloedloop va dgtal PI controller (proportonal gan: K P = 5 ntegral gan: K I =.5 torque lmt = 2Nm controller amplng tme: T = 4m. The peed reference et ung ucceedng cheme: 1rpm at t =.25 than 1rpm at t =.6. A could be een from Fg. 22 a fat torque repone acheved wth correct torque reference trackng and low rotor flux rpple around the reference value (<1.5%. For expermental purpoe the ame laboratory prototype of CSI drve ued a explaned before. The CSI feed a 4kW nducton motor and a a mechancal load the 6kW DC machne wth controlled armature current ued (Nkolc & Jeftenc 28. The preented algorthm not dependent on the motor power or the type of wtchng devce and t could be appled to any current ource converter topology. The low-power nducton motor and tandard type thyrtor are ued jut for the mplcty of the laboratory tet. The torque repone analyzed both wth drect torque demand and under the cloed-loop peed control. Speed controller mplemented wth oft tart on t nput and ample tme of 2m. Torque lmt on the controller output ±5Nm and determned n uch a way that under the maxmum torque value lp equal to maxmal lp for current control: 1 max = = 45 ω T (24 e where ω e ynchronou frequency (14rad/ and T r rotor tme contant (78.7m. Snce rotor flux not meaured but determned by etmaton t value checked wth that obtaned from mulaton. The comparon between mulated and etmated rotor flux whth zero peed (torque reference and rated flux reference are gven n Fg. 2 (a. Good performance of the flux etmator neceary for proper drect torque control could be oberved from Fg. 2 (b where flux trajectory hown tartng from zero to t rated value. Almot crcular flux trajectory wth equal ampltude n both α and β axe aure correct offet compenaton. r

24 Torque Control of CSI Fed Inducton Motor Drve 25 1 Rotor flux [Wb] Motor peed [rpm] Torque [Nm] tme [] Fg. 22. Smulaton reult for the propoed DTC method Ψ β [Wb] Ψ [Wb] Flux from mulated model Etmated tator flux tme [] (a Ψ α [Wb] (b Fg. 2. Rotor flux repone (a and t trajectory (b durng motor tart-up

25 26 Torque Control Motor peed and torque repone when the peed control loop cloed hown n Fg. 24. Repone tet are performed durng motor acceleratng from rpm to rpm than from rpm to 5rpm and back to rpm and rpm tme [] tme [] (a (b Fg. 24. Motor peed (a and torque (b repone under dfferent peed reference 5. Concluon In th chapter two man torque control algorthm ued n CSI fed nducton motor drve are preented namely FOC and DTC. The frt one prece vector control (FOC algorthm. The explaned nconvenence of the vector controlled nducton motor drve fed by a CSI could be overcome wth the new vector control algorthm. The man advantage of the uggeted algorthm compared to that known from the lterature better dynamc performance of the propoed CSI drve. Th enhancement rele on the fat change of the motor current wthout phae error mlar to the control of current regulated voltage ource PWM nverter. The realzed CSI drve ha more prece control accomplhed by the mplemented correcton of the reference current. Th correcton reduce the problem of the ncorrect motor d-q current value produced by the non-nuodal CSI current waveform. Next the two dfferent method of drect torque control n CSI fed nducton motor drve are preented. Contrary to the well-known hytere control derved from VSI drve new DTC algorthm baed on the contant wtchng frequency propoed. Mert of uch a oluton n comparon to the vector control of the ame drve abence of coordnate tranformaton and peed enor on the motor haft. Furthermore nce flux etmator baed only on DC lnk meaurement there not necety for any enor on the motor de whch one of man drve advantage. In th cae by combnaton of vector control and bac DTC a robut algorthm developed that ha a fater torque repone and t mpler for mplementaton. Moreover algorthm le entve to the parameter varaton than tandard FOC on the ame drve. Contrary to the lp calculaton ung rotor tme contant propoed algorthm ue tator retance for flux calculaton and t value could be checked every tme when motor topped ung explaned method for recontructon

26 Torque Control of CSI Fed Inducton Motor Drve 27 baed only on DC lnk meaurement. Other motor parameter (wndng and mutual nductance are ued only when flux reference changed and ther value have no nfluence on the performance of the flux etmator due to the offet compenaton. The valdty of all preented torque control algorthm wa proven by mulaton and expermental reult on developed laboratory prototype of CSI drve. 6. Reference Blachke F. (1971. A new method for the tructural decouplng of A.C. nducton machne Proceedng of IFAC Sympoum on Multvarable Techncal Control Sytem pp ISBN Dueeldorf Germany October 1971 Amercan Elever New York Boe BK. (1986. Power Electronc and AC Drve Prentce-Hall ISBN New Jerey USA Novotny DW & Lpo TA. (1996. Vector Control and Dynamc of AC Drve Oxford Unverty Pre ISBN New York USA B Wu; SB Dewan & Sen PC. (1988. A Modfed Current-Source Inverter (MCSI for a Multple Inducton Motor Drve Sytem. IEEE Tranacton on Power Electronc Vol. No. 1 January 1988 pp ISSN Lorenz RD. (1986. Tunng of Feld-Orented Inducton Motor Controller for Hgh- Performance Applcaton IEEE Tranacton on Indutry Applcaton Vol. IA-22 No. 2 March 1986 pp ISSN Deng D & Lpo TA. (199. A Modfed Control Method for Fat Repone Current Source Inverter Drve IEEE Tranacton on Indutry Applcaton Vol. IA-22 No. 4 July 1986 pp ISSN Va P. (199. Vector Control of AC Machne Clarendon Pre ISBN-1: ISBN- 1: Oxford New York USA Cavalln A.; Loggn M. & Montanar GC. (1994. Comparon of Approxmate Method for Etmate Harmonc Current Injected by AC/DC Converter IEEE Tranacton on Indutal Electronc Vol. 41 No. 2 Aprl 1994 pp ISSN Nkolc A. & Jeftenc B. (26. Prece Vector Control of CSI Fed Inducton Motor Drve European Tranacton 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-ource converter ung a ymmetrc gate-commutated thyrtor (SGCT IEEE Tranacton on Indutry Applcaton Vol.7 21 pp ISSN Takahah I. & Noguch T. (1986. A New Quck-Repone and Hgh-Effcency Control Strategy of an Inducton Motor IEEE Tranacton on Indutry Applcaton Vol. 22 No. 5 September/October 1986 pp ISSN Depenbrok M. (1988. Drect Self-Control (DSC of Inverter-Fed Inducton Machne IEEE Tranacton on Power Electronc 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 Electronc Journal Vol.5 March 1995 pp ISSN 99868

27 28 Torque Control Buja G.; Caade D. & Serra G. (1998. Drect Stator Flux and Torque Control of an Inducton Motor: Theoretcal Analy and Expermental Reult n Proceedng of the IEEE Internatonal Conference on Indutral Electronc IECON '98 pp. T5-T64 Vol. 1 ISBN Aachen Germany Augut/September 1998 IEEE New Jerey Va P. (1998. Senorle Vector and Drect Torque Control Oxford Unverty Pre ISBN New York USA Boldea I. (2. Drect Torque and Flux (DTFC of A.C. Drve: A Revew. Proceedng of the 9th Conference EPE-PEMC 2 pp ISBN Koce Slovaka September 2 EPE-PEMC Budapet Caade D.; Serra G.; Tan A.; Zarr L. & Profumo F. (2. Performance Analy of a Speed-Senorle Inducton Motor Drve Baed on a Contant-Swtchng-Frequency DTC Scheme IEEE Tranacton on Indutry Applcaton Vol.9 2 pp ISSN Wu B. (26. Hgh-power converter and AC drve John Wley & Son Inc. Hoboken ISBN ISBN New Jerey USA Nkolc A. & Jeftenc B. (28. Dfferent Method for Drect Torque Control of Inducton Motor Fed From Current Source Inverter WSEAS Tranacton on Crcut and Sytem Volume 7 Iue 7 January 28 pp ISSN Holtz J. (2. Drft- and Parameter-Compenated Flux Etmator for Pertent Zero- Stator-Frequency Operaton of Senorle-Controlled Inducton Motor IEEE Tranacton on Indutral Applcaton Vol.9 2 pp ISSN

28 Torque Control Edted by Prof. Moulay Tahar Lamchch ISBN Hard cover 292 page Publher InTech Publhed onlne 1 February 211 Publhed n prnt edton February 211 Th book the reult of npraton and contrbuton from many reearcher a collecton of 9 work whch are n majorty focaled around the Drect Torque Control and may be compred of three ecton: dfferent technque for the control of aynchronou motor and double feed or double tar nducton machne orented approach of recent development relatng to the control of the Permanent Magnet Synchronou Motor and pecal controller degn and torque control of wtched reluctance machne. How to reference In order to correctly reference th cholarly work feel free to copy and pate the followng: Alekandar Nkolc (211. Torque Control of CSI Fed Inducton Motor Drve Torque Control Prof. Moulay Tahar Lamchch (Ed. ISBN: InTech Avalable from: InTech Europe Unverty Campu STeP R Slavka Krautzeka 8/A 51 Rjeka Croata Phone: 85 ( Fax: 85 ( InTech Chna Unt 45 Offce Block Hotel Equatoral Shangha No.65 Yan An Road (Wet Shangha 24 Chna Phone: Fax: