MEBS 6000 010 Utilitie ervice Induction Motor peed control Not long ago, induction machine were ued in application for which adjutable peed i not ruired. Before the power electronic era, and the pule width modulation in particular, peed control of induction machine wa limited to highly inefficient method with a narrow range of peed. With the advance in olid tate device and variable fruency power convertor, different approache to induction motor drive ytem have emerged and developed that reult in more ophiticated operation. Induction machine can now be ued in high performance application where precie movement i ruired. The peed control of an induction motor ruire more elaborate technique than the peed control of dc machine. The peed torque characteritic of an induction motor i given by Pg 3V R' Td ω R' ω R1 + where + X ω i the ynchronou peed in rad/, R i the tator reitance, 1 ' R i the rotor reitance referred to the tator, X i the combined inductive reactance of the motor, referred to the tator, i the lip, and V i the terminal voltage input to each tator winding. In HK for LV intallation, it i 0V and 380V for tar and delta connected motor repectively. By examining thi uation, it can be een that the lip,, or the peed, ω, can be controlled if at leat one of the following variable or parameter i altered: - armature or rotor reitance, - armature or rotor inductance, - magnitude of terminal voltage, - fruency of terminal voltage. We will look at peed control by changing voltage and fruency in detail. K.F. Chan (Mr.) Page 1 of 3 July 010
MEBS 6000 010 Utilitie ervice Controlling peed uing rotor reitance If we aume teady tate operation, and the mall lip approximation, the developed torque uation can be reduced to T d 3V ω R' If the voltage, fruency, and torque are kept contant, the increae in R ' reult in an increae in the lip, in other word, a decreae in peed. The following figure how the motor characteritic for the cae when a reitance R add i added to the rotor circuit. The increae in rotor reitance doe not change the ynchronou peed or the magnitude of the maximum torque, it only kew the characteritic o the maximum torque occur at a lower peed. Adding a reitance to the rotor circuit doe not caue the motor peed to change by any appreciable value at light loading condition. The difference in peed between point 1 and in the above figure i rather mall. Although at heavy loading condition, T, the motor peed may change by a wider range from point 3 to point 4 the peed range i till narrow. Therefore, controlling the motor peed by changing the rotor (or tator) reitance i not conidered a realitic option. In addition, thi method increae the motor loe ubtantially. K.F. Chan (Mr.) Page of 3 July 010
MEBS 6000 010 Utilitie ervice Controlling peed uing inductance Adding inductance to the motor winding i an unrealitic option for the following reaon: 1) The phyical ize of the inductance ruired to make a izable change in peed i likely to be larger than the motor itelf. ) Unlike variable reitance, variable inductance ruire expenive and elaborate deign. 3) The inertion of inductance reduce the tarting torque. 4) The inertion of inductance conume reactive power that further lower the already low power factor of induction motor. K.F. Chan (Mr.) Page 3 of 3 July 010
MEBS 6000 010 Utilitie ervice Controlling peed by adjuting the tator voltage Several technique can be ued to change the tator voltage of the motor. Among them are fixed pule modulation (FPM) or the phae control by SCR hown here below: A een in the torque uation, the motor torque i proportional to the quare of it tator voltage. For the ame lip and fruency, a mall change in motor voltage reult in a relatively large change in torque. A 10% reduction in voltage caue a 19% reduction in developed torque a well a the tarting and maximum torque. The following figure how characteritic of the motor under voltage control. It how curve for different value of the tator voltage. Note that the lip at the maximum torque remain unchanged ince it i not a function of the voltage: max R 1 R' + X For normal operation in the linear region, the above figure how that the motor peed can be modetly changed when the voltage i altered. However, a wide range of peed K.F. Chan (Mr.) Page 4 of 3 July 010
MEBS 6000 010 Utilitie ervice control cannot be accomplihed by thi technique alone. Neverthele, it i an excellent method for reducing tarting current and increaing efficiency during light loading condition. The loe are reduced, particularly core loe, which are proportional to the quare of the voltage. Keep in mind that the terminal voltage cannot exceed the rated value to prevent the damage of the winding inulation. Thi technique i thu only uitable for peed reduction below the rated peed. K.F. Chan (Mr.) Page 5 of 3 July 010
MEBS 6000 010 Utilitie ervice Example 1 A 3 phae, 6-pole, 380 Volt, 50Hz tar connected induction motor ha a rotor reitance referred to the tator of 0.5 Ω. The induction motor i driving a travellator ruiring contant load torque of 10 Nm. Ignore the rotational loe, calculate the motor peed at full load. Alo calculate the motor peed if the voltage i reduced by 0%. Aume that the upply fruency i kept contant. Anwer ' Pd 3V R Td ω ' R ω R1 + where V i input voltage + X Near full peed, i mall, o we may aume that R R >> ' 1 << X ' 3V R o Td ' R ω T d 3V ω R ' 380 3 3 10 1000 π 0.5 60 0.0435 peed at full voltage i K.F. Chan (Mr.) Page 6 of 3 July 010
MEBS 6000 010 Utilitie ervice n n ( 1 ) 1000(1 0.0435) 956 RPM T d new T d 1 Vnew V new o 1 (0.0435) 0. 068 0.8 new New peed at 80% voltage 100(1-0.068) 93 RPM K.F. Chan (Mr.) Page 7 of 3 July 010
MEBS 6000 010 Utilitie ervice Controlling peed by adjuting the upply fruency In teady tate, the induction motor operate in the mall lip region where the peed of the motor i alway cloe to the ynchronou peed of the rotating flux: n 60 f p where f i the upply fruency, p i the number of pole of the motor. Since the ynchronou peed i directly proportional to the fruency of the tator voltage, any change in fruency reult in an uivalent change in motor peed. The following figure how torque-peed characteritic of an induction motor under different upply fruency. The effect of fruency on motor current i determined by the following formula: I' V R' R1 + + X Under the ame peed, or ame, a fruency i reduced, X i alo reduced, thu I ' i increaed. The overall effect i depicted in the following diagram: K.F. Chan (Mr.) Page 8 of 3 July 010
MEBS 6000 010 Utilitie ervice Fruency manipulation appear to be an effective method for peed control that ruire a imple dc/ac convertor with variable witching interval imilar to the one a hown below: However, there are evere limitation to thi method: very low fruencie may caue motor damage due to exceive current, and large fruencie may tall the motor. K.F. Chan (Mr.) Page 9 of 3 July 010
MEBS 6000 010 Utilitie ervice Effect of exceively high fruency The decreae in upply fruency reult in the following 5 change: 1) A decreae in the no-load peed (ynchronou peed). ) An increae in the maximum torque. The maximum torque i given by 3V Tmax ω + + R1 R1 X It how that the maximum torque i inverely proportional to both the ynchronou peed ω and the uivalent reactance of the winding X. Each of thee quantitie increae by increaing the fruency. Hence the maximum torque increae when the fruency of the upply voltage decreae. 3) An increae in the tarting torque. The tarting torque of an induction motor, T t 3V ω R' X It can be een that tarting torque increae when the ynchronou peed and uivalent reactance decreae, a upply fruency decreae. 4) A decreae in peed at the maximum torque. Due to decreae in fruency, the lip at maximum torque max R' increae when the uivalent reactance R1 + X decreae. The ynchronou peed alo decreae on fruency reduction, o the combined effect i reduction in peed at the maximum torque. 5) An increae in the tarting current. The tarting current can be computed by etting 1 in the motor current formula: I' V, or R' R1 + + X I' t ( R + R' ) + X 1 V When the fruency decreae, the uivalent reactance decreae and the tarting current increae. On the other hand, at high fruencie, the reitance of the motor winding may alo increae due to the kin effect thu further K.F. Chan (Mr.) Page 10 of 3 July 010
MEBS 6000 010 Utilitie ervice increaing the tarting current. Now let u examine the cae when the increae in fruency i exceive. The above diagram how characteritic for different value of tator fruency. Aume that the load torque i contant, the motor operate initially at fruency f 1. The teady tate operation i repreented by point 1. Now aume that the fruency of the tator voltage increae to a higher value, f, where the new maximum torque of the motor i le than the load torque. In thi cae, no teady tate operating point can be achieved, and the motor eventually tall or even operate under braking. One olution to thi problem i to increae the upply voltage when the fruency i increaed. K.F. Chan (Mr.) Page 11 of 3 July 010
MEBS 6000 010 Utilitie ervice Example A 380V, pole, 50Hz, tar connected indication motor ha an inductive reactance of 4 Ω and a tator reitance of 0. Ω. The rotor reitance referred to the tator i 0.3Ω. The motor i driving an ecalator having a contant torque load of 40 Nm at a peed of 900 RPM. Aume that thi torque include the motor rotational loe. a) Calculate the maximum fruency of the upply voltage that would not reult in talling the motor. b) Calculator the motor current at 50Hz. c) Calculate the motor current at the maximum fruency computed in (a) above. d) Calculate the power delivered to the load at 50Hz. e) Calculate the power delivered to the load at the fruency computed in (a) above. Aume that the upply voltage i kept contant. Anwer a) T max ω ( R + 3V 1 1 X R + ) Near full peed, a R 1 i 0. Ω, while X i 4Ω, we may aume that R 1 << X, o T max V ω 3 X f Let the new fruency be f. The motor inductive reactance at f i X. 50 The maximum torque at f i T max 3V f f ω 50 50 X Now, in order not to tall the motor, T max mut be at leat 40 Nm, o 3V 40 f 3000 f π 4 50 60 50 K.F. Chan (Mr.) Page 1 of 3 July 010
wherev M.Sc.(Eng) in building ervice MEBS 6000 010 Utilitie ervice 380 3 Hz f 59. 9 3000 900 b) 0. 033 3000 I ' V R R + ' + X 0. + 380 3 0.3 0.033 + 4 1.9A c) Now S max R 1 R ' X + 59.9 At the new fruency, X (4) 4. 79 50 S 0. 0.3 max + 4.79 0.066 Current at new fruency i 380 ' I 3 31. 71A 0.3 0. + + 4.79 0.066 K.F. Chan (Mr.) Page 13 of 3 July 010
MEBS 6000 010 Utilitie ervice 900 d) Pd Tdω 40 π 1. 1 kw 60 e) New peed at the new fruency i (1-0.066)(59.9)(60) 3370 RPM 3370 Pd Tdω 40 π 14. 1 kw 60 K.F. Chan (Mr.) Page 14 of 3 July 010
MEBS 6000 010 Utilitie ervice Effect of exceively low fruency Reducing the upply fruency reduce the peed of an induction motor. However, fruency reduction may reult in an increae in motor current I' V R' R1 + + X At very low fruencie, the uivalent reactance of the motor X i very low. Since X i the limiting parameter for motor current at tarting, it large reduction could lead to an exceive current beyond the rating of the machine. K.F. Chan (Mr.) Page 15 of 3 July 010
MEBS 6000 010 Utilitie ervice Example 3 A 480V, pole, 60Hz, tar connected indication motor ha an inductive reactance of 4 Ω and a tator reitance of 0. Ω. The rotor reitance referred to the tator i 0.3Ω. The motor i driving an ecalator having a contant torque load of 40 Nm at a peed of 3500 RPM. Aume that thi torque include the motor rotational loe. Calculate the motor peed and tarting current if the fruency i decreaed to 50Hz. The upply voltage i kept contant. Anwer At 60Hz, the tarting current i I ' ' ( R + R ) + 1 V X where V i input voltage to the winding, i.e., phae voltage in thi cae 480 3 (0.5) + 4 68.75Amp At 50Hz, X 50 4 3. 33Ω 60 480 ' I 3 t 8. Amp 0.5 + 3.33 Thi i about 0% increae in tarting current but at 16% drop in peed. Now, at 50Hz, the ynchronou peed i 3000 RPM, i.e. 314.16 rad/. At mall lip, K.F. Chan (Mr.) Page 16 of 3 July 010
T d 3V ω R ' M.Sc.(Eng) in building ervice MEBS 6000 010 Utilitie ervice where V i the phae to neutral voltage for tar connection. Thu 480 40 314.16(0.3) 0.0164 Thu new peed at 50Hz i 3000(1-0.0164) 951 RPM. Thi i about 16% drop in peed. K.F. Chan (Mr.) Page 17 of 3 July 010
Voltage/fruency control M.Sc.(Eng) in building ervice MEBS 6000 010 Utilitie ervice Now increae in upply fruency increae the motor peed and reduce the maximum torque of the motor. Increae in voltage reult in an increae in the maximum torque of the motor. If we combine thee two feature, we can achieve a control deign by which the peed increae and the torque i kept the ame. Thi i known a voltage/fruency control, v/f. The above diagram how 3 characteritic; one i ued a our reference at voltage V 1 and fruency f 1. For the arbitrary fan type load in the figure, the reference operating point i 1. If we increae the fruency of the upply to f while keeping the voltage V 1 unchanged, the peed of the motor increae and the maximum torque decreae. The load torque in thi cae i higher than the maximum torque provided by the motor. Thu, no teady tate operating point can be achieved and the motor eventually tall. Now let u keep the upply fruency to the new value of f, but alo increae the magnitude of the voltage to V. The motor characteritic in thi cae tretch and the maximum torque increae. The motor operate at point and a new teady tate pointy i achieved. Change in voltage and fruency i a powerful method for peed control. Note that both fruency and voltage can change imultaneouly by the pule width modulation technique. K.F. Chan (Mr.) Page 18 of 3 July 010
MEBS 6000 010 Utilitie ervice (Adopted from CARROW R.S. Electrician' technical reference. Variable-fruency drive) PWM technique i the mot common type of induction motor peed control ued in building ervice application nowaday. There are everal variation where the v/f ratio i alo adjuted to provide a pecial operating performance. The mot common method, though, i the fixed v/f ratio. K.F. Chan (Mr.) Page 19 of 3 July 010
MEBS 6000 010 Utilitie ervice The above diagram how the characteritic of an induction motor operating under contant v/f control. Now T max 3V ω R1 + R1 + X If we aume that the uivalent inductive reactance X, at fruencie near the rated value, i much larger than the armature reitance, the uation can be approximated a T max 3V ω X 3V 4π f p ( πfl ) K.F. Chan (Mr.) Page 0 of 3 July 010
It can be thu be een that M.Sc.(Eng) in building ervice MEBS 6000 010 Utilitie ervice T max V f It i now clear that when the v/f ratio i kept contant, the maximum torque i unchanged. However, it mut be kept in mind that thi approximation may not be valid at very low fruencie when X i not much larger than the R 1. Another feature of the contant v/f control i that the magnitude of the tarting current i almot contant. At 1 I' t ( R + R' ) + X 1 V Aume that ( ) X >> R + R' (thi aumption i valid for fruencie cloe to 1 the rated fruency), the tarting current can thu be approximated a V 1 V I' t X πl f Thi uation again how that when v/f i kept contant, the tarting current remain unchanged; thi i another advantage of v/f control. Almot all PWM fruency inverter ued for induction motor peed control in building ervice application employ thi fixed v/f control. When the change in voltage i ued to control the induction machine, whether it i a voltage control or v/f control, one mut be careful not to increae the voltage magnitude beyond the rating of the motor. Exceive voltage can caue intant damage to the inulation of the motor winding, leading to hort and internal fault. Uually, the voltage hould be kept below 110% of the rated value. Mot motor ued for building ervice application in HK are uitable for 380V/50Hz or 480V/60Hz power upply. Therefore, it i poible to increae the motor output by increaing the fruency up to 60Hz. However, it i dangerou to increae the upply voltage beyond 110% of the rated voltage of 480V, unle the motor i pecially deigned. K.F. Chan (Mr.) Page 1 of 3 July 010
MEBS 6000 010 Utilitie ervice PWM fruency inverter drive PWM fruency inverter can be contant voltage ource (VSI) or current ource (CSI). Almot all modern day fruency inverter drive are VSI. Voltage ource inverter allow a variable fruency upply to be obtained from a dc upply. One example of olid tate VSI fruency inverter control chematic i hown herebelow: [Adopted from HERMAN, Stephen L. Indutrial Motor Control] The tepped wave inverter illutrated above ue SCR in the ac/dc converion ection, i.e. the power upply ection, and junction tranitor in the dc/ac inverion. SCR control the output voltage by chopping the incoming waveform. Thi can caue harmonic on the line. When bipolar junction tranitor, which are current controlled device, are employed a witche, they are generally driven into aturation by upplying them with an exceive amount of bae-emitter current. Saturating the tranitor caue the collector-emitter voltage to drop to between 0.04 and 0.03V. Thi mall voltage drop allow the tranitor to control large amount of current without being detroyed. When a junction tranitor i driven into aturation, however, it cannot recover or turn off a quickly a normal. Thi limit the fruency repone of the tranitor. Therefore, new deign of VSD employ MOSFET or IGBT (for larger rating). K.F. Chan (Mr.) Page of 3 July 010
MEBS 6000 010 Utilitie ervice [Adopted from HERMAN, Stephen L. Indutrial Motor Control] The above diagram how another type of VSI fruency inverter uing IGBT in the dc/ac inverter ection. IGBT have an inulated gate very imilar to ome type of FET. However, the gate i inulated and ha very high impedance, o the IGBT i a voltage not current controlled device. Thi type of fruency drive doe not ue SCR in the power upply, i.e. the ac/dc converter ection. Thi ha the advantage of greatly reducing the line harmonic aociated with SCR. The great diadvantage i that the fat witching rate of the tranitor can caue voltage pike in the range of up to 000V to be applied to the motor. At high witching fruency, capacitance between the cable connecting the fruency inverter and the motor become a concern. Line length from the inverter to the motor i thu of great concern with drive uing IGBT. Short line length are preferred. Generally, MOSFET i ued in low voltage and low power inverter, IGBT ued up to medium power level and GTO and inulated gate commutated thyritor are ued for high power level. K.F. Chan (Mr.) Page 3 of 3 July 010
MEBS 6000 010 Utilitie ervice Example 4 A 480V, pole, 60Hz, tar connected induction motor ha an inductive reactance of 4 Ω and a tator reitance of 0. Ω. The rotor reitance referred to the tator i 0.3Ω. The motor i driving a contant torque load of 40Nm at a peed of 3500 RPM. Aume that thi torque include the motor rotational loe. The motor i now upplied by contant voltage to fruency ratio control and the fruency i reduced to 50Hz. Calculate the new motor peed and the tarting current. Anwer For fixed v/f ratio, when the fruency i reduced to 50Hz, the voltage hould be 50 480 ( ) 400 Volt 60 At 400V, 50Hz, ω π (50) 314.16 rad / T d ω 3V ' R ' [( R1 + R ) + X ] 40 400 0.3 [ + 4 ] ( 314.16) ( 0. + 0.3) On implification, thi become 16.04 3.7 + 0.09 0 Note that for a quadratic uation: ax + bx + c 0 the olution can be written a: b ± b 4ac x a So 0.03 or 0.076 Motor peed i thu (1-0.076)3000 917RPM K.F. Chan (Mr.) Page 4 of 3 July 010
MEBS 6000 010 Utilitie ervice Alternatively we can aume (400) thu 40 314.16(0.3) 0.036 T d 3V where V i the input voltage. ω R ' The lip now i higher than by reducing the fruency alone (0.0164, Example 3). The tarting current at 480V, 60Hz i I ' t + V + ' ( R1 R ) X 480 3 ( 0. + 0.3) + 4 68.75A At 400V, 50Hz, X 50 (4) 60 3.33 So tarting current become 400 ' I 3 t 68. 5 Amp (0. + 0.3) + 3.33 Note that the tarting current i almot unchanged in thi cae while the tarting current will increae if fruency i reduced alone (8.Amp, Example 3). K.F. Chan (Mr.) Page 5 of 3 July 010
CSI (current ource inverter) M.Sc.(Eng) in building ervice MEBS 6000 010 Utilitie ervice The PWM fruency converter we have een i called voltage ource inverter (VSI) becaue the DC link i a contant voltage upply. There i another type of inverter called current ource inverter. A thyritor CSI i hown herebelow. Diode D1 to D6 and capacitor C 1 to C 6 provide commutation of thyritor T 1 to T 6, which are fired with a phae difference of 60 o in uence of their number. Thi inverter behave a a current ource due to the preence of large inductance L d in the dc link. (Adopted from DUBEY, G.K. Fundamental of Electrical Drive) The major advantage of CSI i it reliability. In the cae of VSI, a commutation failure will caue two device in the ame leg to conduct. Thi connect conducting device directly acro the ource cauing current through device uddenly rie to dangerou value. Thi problem would not hurt a CSI chiefly becaue that the inductor will limit the current. K.F. Chan (Mr.) Page 6 of 3 July 010
MEBS 6000 010 Utilitie ervice When a CSI i ued, the induction motor exhibit different characteritic a compared to the VSI. Mot noticeable i the low tarting torque. Thi i primarily due to the high rotor current I at tarting, which reduce the magnetizing current I m, becaue the current ource I 1 i contant: I + I1 I' I m The low magnetizing current at tarting reduce the flux of the motor; hence, it reduce the tarting torque. K.F. Chan (Mr.) Page 7 of 3 July 010
MEBS 6000 010 Utilitie ervice The other noticeable difference i that the peed of the motor in the normal operating region with CSI i tiffer (ha a flatter lope) than that of a VSI motor. Thi i becaue the core of the motor i aturated with flux in thi region. If the core aturate, mall change in the magnetizing current tend to have little or no effect on the flux. When load torque increae, the rotor current tend to increae, which reduce the magnetizing current (a I 1 i contant). When reduction of the magnetizing current doe not reduce the flux (in the aturation region), the peed of the motor remain almot unchanged. K.F. Chan (Mr.) Page 8 of 3 July 010
MEBS 6000 010 Utilitie ervice (Adopted from CARROW R.S. Electrician' technical reference. Variable-fruency drive) In ummary, the relative merit of VSI and CSI are: 1) CSI i more reliable becaue i. conduction of two device in the ame leg due to commutation failure doe not lead to harp rie of current through them and ii. it ha inherent protection againt a hort circuit acro motor terminal. ) Becaue of large inductance in the dc link and large inverter capacitor ruired for CSI circuit, CSI drive ha higher cot, weight and volume, lower peed range and lower dynamic repone. 3) The CSI drive i not uitable for multi motor drive. Hence, each motor i fed from it own inverter and rectifier. A ingle ac/dc converter power upply can be ued to feed a number of VSI dc/ac inverter motor ytem connected in parallel. Similarly a ingle VSI dc/ac inverter output ection can feed a number of motor connected in parallel. K.F. Chan (Mr.) Page 9 of 3 July 010
MEBS 6000 010 Utilitie ervice (Adopted from CARROW R.S. Electrician' technical reference. Variable-fruency drive) With advance in IGBT technology, and improvement in reliability of power electronic, VSI i gaining favour epecially in variable peed drive in building ervice application which uually involve maximum rating of a few hundred horepower only. Feature of fruency inverter drive Although the primary purpoe of a variable fruency drive i to provide peed control for an ac motor, mot drive provide function that other type of control do not. Many variable fruency drive can provide the low peed torque characteritic that i o deirable in dc motor. It i thi feature that permit ac quirrel cage motor to be able to replace dc motor for many application. Another feature i ramping. It i ued to accelerate and decelerate a motor over ome period of time and permit the motor to bring the load up to peed lowly a oppoed K.F. Chan (Mr.) Page 30 of 3 July 010
MEBS 6000 010 Utilitie ervice to imply connecting the motor directly to the line. Other feature are current limit, minimum and maximum hertz control. Inverter rated motor Due to the problem of exceive voltage pike caued by high witching fruency of olid tate drive, mot noticeably IGBT drive, ome manufacturer produce inverter rated motor. Thee motor are pecifically deigned to be operated by variable fruency drive. They differ from tandard motor in everal way: 1. Typical motor ue a fan connected to the haft to cool the motor. Some inverter rated motor contain a eparate blower for continuou cooling.. Inverter rated motor generally have inulating paper between the winding and the tator core. The high voltage pike produce high current that produce a trong magnetic field. The increaed magnetic field caue the motor winding to move, becaue magnetic field repel each other. Thi movement can eventually caue the inulation to wear off the wire and produce a grounded motor winding. [Adopted from Herman S.L. Indutrial Motor Control] 3. Inverter rated motor generally have phae paper added to the terminal lead. Phae paper i inulating paper added to the terminal lead that exit the motor. The high voltage pike affect the beginning lead of a coil much more than the wire inide the coil. The coil i an inductor that naturally oppoe a change of current. K.F. Chan (Mr.) Page 31 of 3 July 010
MEBS 6000 010 Utilitie ervice Mot of the inulation tre caued by high voltage pike occur at the beginning of a winding. 4. The magnet wire ued in the contruction of the motor winding ha a higher rated inulation than other motor. 5. The motor caing i larger in ize, due to the additional inulating paper. Alo larger caing help cool the motor. 6. For a given harmonic content in the voltage, the current harmonic are reduced when the motor ha higher leakage inductance thi alo reduce derating and torque pulation. Therefore, motor pecially deigned for inverter drive will have higher leakage inductance than their counterpart ued for inuoidal power upply. [Text and figure motly adopted from EL-SHARKAWI, Mohamed A., Fundamental of Electric Drive, Herman S.L. Indutrial Motor Control and DUBEY, G.K. Fundamental of Electrical Drive,] K.F. Chan (Mr.) Page 3 of 3 July 010