Allen-Bradley. 135 Dundas St. Cambridge, Ontario N I R 5x1. Abstract. The recent increase in the application of Medium. Voltage Variable Frequency Drives to ...
MEDIUM VOLTAGE MOTOR HARMONIC HEATING, TORQUES AND VOLTAGE STRESS WHEN APPLIED ON VFDs Copyright Material IEEE Paper No. PCIC-96-16
Frank A. DeWinter Senior Member IEEE Allen-Bradley 135 Dundas St. Cambridge, Ontario N I R 5x1
Dr. Bin Wu Member IEEE Ryerson Polytechnic University 350 Victoria St. Toronto, Ontario M5B 2K3
the large number of both motor and drive vendors, as well as the custom nature of many of the designs for motors and drives some generalities will need to be made.
Abstract The recent increase in the application of Medium Voltage Variable Frequency Drives to AC motors has raised concerns regarding the effects the drives have on the motors. Most of the published data available is for low voltage motors and drives, which are not necessarily accurate for the medium voltage applications. We will address the harmonic heating, torques and voltage stress that are induced on the motors when they are applied on various types of drives. Results from both modelling and field measured data will be used to provide general guidelines.
Introduction There have been several well written papers and a few books over the past years which address the topics of motor voltage stress, harmonic heating and harmonic torques, but they have been from the point of view of low voltage motors up to 600 volts. They were also primarily concerned with Pulse Width Modulated (PWM) Voltage Source Inverters (VSI), 6 step output Current Source Inverters (CSI) or 6 step output Variable Voltage Inverters (WI). This paper will address the medium voltage applications of 2300 volts through 7200 volts. In these voltage ranges, the motors have different design criteria and margins than normally expected on low voltage motors. The drives available at this voltage level are often different than at low voltage. This paper does not try to recommend a type of drive to be used, but will categorize their different effects on motors primarily by their power structure. It is felt that each type of drive has its own individual strengths and weaknesses in performance, price, simplicity or motor effects. The effects of different drive configurations on motors will be addressed both qualitatively and quantitatively. Due to
Induction Motors On medium voltage motors there are several key design variations that are made to meet specific performance criteria, which affect the actual performance on various drives. The majol'ity of the induction motors at medium voltage have been originally designed for fixed speed operation. In fact about half of these drives are applied to existing medium voltage induction motors. A significant variation in individual motors is in the rotor bar design and in the leakage inductance, as outlined in references 3 & 14, which significantly affect the harmonic heating and torques and voltage stress on certain drive designs. The design of the stator insulation varies greatly in the amount and distribution of the strand, turn and ground wall insulation between motor manufacturers. The strand and interturn insulation is more important on drives with high DV/DT, while turn and ground wall insulation is more critical on drives with a neutral to ground voltage. Figure 1 is the simplified single phase equivalent motor model which will be used in explaining the effects of these stresses.
R2
(q)
Fig 1 Single Phase Motor Model
96-CH35988-6/96/0000-0131 $05.00 0 1996 IEEE
ISBN: 0-7803-3587-2
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Where: VI is the voltage applied to the motor XI is the stator leakage reactance II is the current drawn by the motor RI is the stator resistance Rc is the effective resistance for the core or iron loss XM is the magnetizing inductance E, is the motor back EMF X2 is the rotor leakage inductance l2is the effective rotor current R2 is the effective rotor resistance for copper losses R2(jSs ) is effective rotor resistance for calculating shaft power s is the motor slip From basic motor theory we can see that the key areas of concern for harmonic heating of the motors can be modelled as the sum of the additional stator copper losses, rotor copper losses and iron losses for a given harmonic current I,,. In fact the additional iron losses will be low because Rc and XM are very large compared to the rotor impedance, forcing most of the harmonic current through the rotor. The harmonic torque is proportional to the effective harmonic rotor current times the effective rotor resistance divided by slip. The problem with modelling both the harmonic torque and losses is adequately determining the effective rotor leakage inductance and rotor resistance for a particular harmonic frequency, taking into account the actual rotor bar design. To properly determine these characteristics with this model it would be necessary to create parallel paths of effective rotor resistance and reactance for a double cage rotor and multiple paths for more complex shapes.
surface of the rotor bar. The value of the reactance will vary approximately with frequency, although in a complex rotor bar the effective leakage inductance will be not be fully proportional to frequency. Therefore the relative magnitudes at the 5th harmonic will be as follows; * R2 will be approximately twice that of RI * RI will be about 160th of X1 * Ll will be slightly higher than L2 * X2 will be approximately equal to X I because slip frequency is now 6 times fundamental * XMwill be several hundred times the magnitude of R2 * Rc will still be a few thousand times of R2 From this we can see that most of the harmonic current which enters the stator will tend to travel through the rotor path. For a given harmonic the primary relationship between the amount of harmonic voltage and harmonic current is set by the leakage inductance of the machine. The calculated harmonic current or voltage produced by a drive is often based on classical analysis, which predicts that with a six step drive there will be a maximum of 20% fifth harmonic and 14% seventh harmonic etc. These values are also often used in calculating the reduced harmonics produced with a PWM algorithm. Due to the DC ripple, particularly at lower speeds and loads, these theoretical values are low. In reference 15 the comparison of different models is given. There are some basic conclusions we can gain from the above models: 1) For a given motor design the harmonic heating due to a particular harmonic is the individual harmonic current squared times the sum of the stator resistance plus effective rotor resistance at that frequency.
The following are the typical relative sizes for a medium voltage 4 pole motor, at the fundamental frequency; * R1 is approximately equal to R2, which is approximately 1/1Oth of XI * L1 will be approximately equal to L2 * X2 will be much less than XI because slip frequency is low and less than RI or R2 * XMwill be a few hundred times the magnitude of R2 * Rc will be a few thousand times R2
2) Again for a given motor design the harmonic torque due to a particular harmonic is proportional to the square of the harmonic current times the effective rotor resistance at that frequency.
When we start to look at the relative magnitudes for the harmonic impedances, the significant change is that the effective slip for the rotor characteristics will change from around a half a hertz to about 360 hertz for the 5th harmonic. The value of the stator resistance will remain unchanged, and the rotor resistance will increase as the harmonic current is forced to the - 132
3) The amount of harmonic heating and torque
can be predicted for a particular motor by either measuring or accurately modelling the harmonic current independent of the drive type, whether it is CSI or VSI based.
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4) By varying the leakage inductance and the effective rotor resistance it is possible to greatly alter the harmonic torques and heating, for most drive designs. Drive Topologies All electronic variable frequency drives manufactured today produce at least some harmonic current and voltage which will be impressed on the motor, along with additional voltage stress in at least some part of the electrical system because they utilize non-linear devices. The magnitude and frequency does vary according to the drive design. Through the use of more complex hardware and/or control designs it is possible to reduce the effect of the harmonics producing motor heating and torques, but this normally adds to the cost of equipment. The one advantage of most drives is that because they rectify to DC and then invert back to AC, there will be very little voltage or current unbalance compared to fixed frequency operation on the power utility bus. Motors that have been designed for operation on fixed frequency will have margin allowed for in the thermal design for operation on voltage unbalance from the power system.
There are a number of different types of drives being applied to medium voltage motors on the market today. The first category is low voltage drives with transformers on the output of the drive to step the low voltage up to medium voltage, and although normally these are Voltage Source Inverter-Pulse Width Modulated (VSI-PWM), they can also be Current Source Inverter (CSI). The second category is drives operating at medium voltage for induction motors and these can be CSI, CSI with output filter capacitors (CSI-CAP), Pulse Width Modulated CSI with output filter capacitors (CSI-PWM) or finally Pulse Width Modulated VSI (VSl-PWM). The third category of medium voltage drives are those designed specifically for synchronous motors called Load Commutated Inverters (LCI). All of the current source type of drives which operate at medium voltage such as the CSI, CSI-CAP, CSI-PWM and LCI will normally use individual SCR thyristors or GTO thyristors in series for each leg to attain the higher voltage ratings. It is more difficult to series GTOs on the VSI-PWM drive so it uses a unique Neutral Point Clamped inverter and is normally limited to 3300 volts. An overview of each type of drive power structure is covered below, along with a few distinguishing characteristics, to assist in later discussions on the motor effects.
Low Voltage Drives with Step Up Transformers Transformer MVAV
Rectlf,er
DC Link L
Medium
Capacitor
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inverter
Transformer LV/MV
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Voltage Supply
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-
Medium Voltage
p J -
Figure 2 Low Voltage, Voltage Source PWM Notes 1) The actual drive could be a low voltage VSI-PWM (LV VSI-PWM) or a low voltage 6 step CSI (LV CSl). 2) These drives will typically be 200 to 1700 horsepower (HP), with the LV VSI-PWM normally requiring parallel inverters above 750 HP to meet the current requirements and are often connected in a 12 pulse configuration to the output transformer.
3) Although a VSI-PWM drive with GTOs is shown, the use of IGBTs in this size range is becoming common,
and therefore it. is necessary to carefully analyze the voltage stress in these cases due to the high dv/dt during switching. 4) The effects of the VSI-PWM or LV CSI drives listed in figures 3 and 5 also apply to the low voltage drives.
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$ Rectifier
DC Llnk
Inverter
Medium
Medium Voltage
SUiaPlY
Figure 3 Medium Voltage, Voltage Source PWM Notes 1) This drive is characterised by a diode rectifier, a 3) The drive imposes a harmonic voltage on the motor, large DC link capacitor, similar to LV VSI-PWM drives, and therefore the amount of harmonic current but the inverter will normally use GTOs arranged in a absorbed by the motor is inversely proportional to neutral point clamped (NPC) or three level output frequency and motor leakage inductance. arrangement with twice the number of devices of the 4) The typical PWM pattern will reduce in the number LV VSI-PWM. of pulses per half cycle as the fundamental frequency 2) Due to the difficulty of putting inverter devices in approaches 50 to 60 hertz, and will become a 6 step series on the VSI-PWM drive it uses the NPC inverter output voltage at 60 hertz. The PWM patterns used in the upper speed ranges, prior to becoming 6 step will to reach a normal maximum voltage of 3300 volts. reduce a few lower order harmonics, but will increase higher order voltage harmonics.
Medium Voltaae CSI with PWM and Motor Filter Capacitors (CSI-PWM)
Medium
Voltage Supply
11 -
i
Voltage
[qy ~
Figure 4 Medium Voltage PWM Current Source
Notes 1) Characterized by an SCR rectifier, a large DC link inductor, a GTO inverter, and a medium sized output filter capacitor (approximately 0.4 to 0.7 KVAR per HP). 2) There are wide variations in the actual PWM patterns used, which result in the variations on motor filter sizing. At low speeds some designs use minimal or no PWM wave shaping, but all eliminate or reduce the harmonics which would excite the output filter capacitor/ motor leakage reactance resonance.
3) No additional commutation circuitry is required on the inverter due to the use of GTOs. 4) Similar to the capacitor assisted current source, the higher frequency harmonics are absorbed by the capacitor, and therefore if a motor has a higher leakage inductance than normal it will absorb less harmonic currents, although it is not a big factor with this type of drive. 5) When the PWM pattern is used throughout the speed range, the current harmonics impressed on the motor are low, typically less than 5% and the harmonic
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torque pulsations produced are typically less than 1YO, throughout the speed range. Medium Voltaae CSI with a 6 step output (CSl) Transformer
Rectifier
DC Link
Inverter
Medium
Medium Voltage
Supply
u. u
U
Figure 5 Medium Voltage 6 Step Current Source Inverter
Notes 1) Characterized by an SCR rectifier, a large DC link inductor, an SCR inverter and a commutating network on the inverter SCRs usually made up of individual diodes and capacitors.
2) The current to the motor is approximately square wave and therefore the harmonic torque and heating are independent of the leakage inductance. 3) The magnitude of the voltage stress is a function of the leakage inductance, and therefore it is common to have a motor with lower leakage inductance than seen on standard motors.
Medium Voltaae CSI with Motor Filter Capacitors (CSI-CAP)
HTI
so
I
I
I
t
u
Figure 6 Medium Voltage Current Source Capacitor Assist
Notes 1) Characterized by an SCR rectifier, a large DC Link inductor, an SCR rectifier, a large output filter capacitor sized at approximately 1.O KVAR per HP which assists in inverter SCR commutation at high speeds and a low speed commutation circuit on the load side of the DC link. 2) This was one of the first types of medium voltage drive for induction motors. 3) The motor filter reactance is inversely proportional to frequency, so that lower order harmonic currents at lower motor speeds will be primarily be absorbed bythe motor, while at higher speeds most of the harmonic currents will be absorbed by the filter. The higher the
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motor leakage reactance, the less harmonic current that will be absorbed by the motor. 4) There are two major resonant frequencies between the output filter capacitor and the motor leakage and magnetizing inductances, which can be excited by the inverter harmonic currents. The leakage inductance resonance will be between 135 and 150 hertz, which can be excited by the 5th harmonic at95 to 30 hertz or the 7th harmonic at 19 to 21 hertz. This means that any sustained operation at these points can result in very high harmonic torques of 20 to 40 times rated fullload torque (ref. 8). 5) Some of the earlier designs of this type of drive utilized GTOs in the inverter along with a minimal harmonic reduction, but now most of the
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CSI drives using GTOs now incorporate a PWM
control and are covered Figure 4. Medium VoltaRe Load Commutated Inverter (LCI)
Voltage
Figure 7 Medium Voltage Load Commutated Inverter Notes 1) This type of drive is strictly for synchronous motors. 4) The six step output current will produce harmonic It is characterized by an SCR rectifier, a large DC link torques and heating independent of the operating Inductor, an SCR inverter and field control package. speed and motor inductance. From references 8 & 9 it 2) The LCI drive is almost identical to the six step CSI can be seen that typical 6th harmonic torques are 2 to drive except it has no commutation circuit on the 15% and there is additional heating of 20 to 30%. inverter devices. The synchronous motor is operated at 5) Typically these drives will be designed with 12 pulse a leading power factor to commutate off the inverter rectifiers and inverters to reduce the effects of the SCRs except at very low speeds where the rectifier harmonic currents. These are effectively two parallel drives phase shifted by 30 degrees and operating a 6 SCRs are used to turn off all current through the drive. 3) The motor used on an LCI drive is more similar in phase motor. rotor construction to a synchronous generator than to a 6)lt is extremely difficult to retrofit this type of drive to typical fixed speed synchronous motor. The motor is an existing synchronous motor, due to exciter normally designed for the specific drive and problems and that the damper windings in a standard synchronous motor would result in harmonic torques in application. excess of 25% of the fundamental and harmonic heating would require the motor to be derated by 20 to 25%.
Harmonic Torques The motor model in figure 1 is effective in helping to understand qualitatively the effects that harmonics can have in a motor with regard to producing torques and harmonic heating. To accurately predict the harmonic torques generated by harmonic currents, it is necessary to utilize more complex motor models such as a d-q model or a three-phase circuit model. This allows the careful calculation of the interaction of the torque and flux producing components. As more fully explained in reference 10, a 5th harmonic current (negative sequence) will rotate in the stator in a reverse rotation to the fundamental. Since the rotor is rotating in the same direction as the fundamental,
there will be a frequency difference of 6 times fundamental which results in a 6th harmonic torque. The 7th harmonic current (positive sequence) rotates around the stator in the same direction as the fundamental and rotor. It therefore also produces a 6th harmonic. As various characteristic harmonics are studied it will be seen that the 11th & 13th harmonic currents produce 12th harmonic torques, the 17th and 19th harmonic currents produce 18th harmonic torques etc. A motor that is driving a load that is either quite
sensitive to motor harmonic torques, or where there is a strong torsional resonance which is excited by a harmonic torque, requires special attention. To
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accurately model harmonic torques it is necessary to have the precise (within 0.5%) harmonic current or voltage magnitudes and angles produced by the drive. Many simple calculations of these currents or voltages do not account for the ripple in the DC link section of the drive. The DC ripple will increase the first characteristic harmonics as well as introduce inter harmonics. On a 3 phase system this can result in greatly underestimating the 5th harmonic Harmonic Heating The harmonic heating in a motor is composed of the additional stator copper losses, rotor copper losses and iron losses. It is easier to calculate these for individual harmonics and then add them. From figure 1, it can be seen that the stator copper losses can be calculated as x RI. Similarly the rotor losses can be calculated as : 1 x RZ. The value of R2 will vary with frequency and is primarily determined by the rotor bar shape, but can be generally modelled as twice the fundamental resistance for the 5th harmonic and higher. The iron losses can be calculated approximately as vI2 / R ~ In. practical cases, unless there is extreme harmonic voltage distortion, the iron loss increase due to harmonics is negligible, but the iron loss due to over fluxing the machine by running at higher than rated volts per hertz can be significant.
Voltage Stress The additional voltage stress in the motor, imposed by a drive, can be due to the use of high speed semiconductors which can produce high voltage spikes or standing waves on VSI-PWM drives, or on CSI drives either ground wall stress due to shifts in the neutral to ground voltage, on CSI drives without output filtering, voltage spikes created by rapidly forcing a change in current to a motor and on CSI drives with large output filter capacitors an over voltage due to self excitation of the motor by the capacitors. The first type is due to the fast switching power semiconductor devices used on VSI-PWM drives. This can create interturn stress due to a high dv/dt, where the rise time of the voltage is less than 0.5 to 2.0 microseconds on large AC motors, depending on the insulation design [16 & 171. This fast a rise time would only occur with the use of devices such as IGBTs, rather than slower SCR or GTO thyristors. Most VSI drive vendors in this horsepower range use slower
GTOs and therefore they do not induce a voltage unbalance turn to turn on the first few turns of a winding. A related problem though for VSI-PWM drives is the possibility of creating a standing wave on longer motor cables due to the switching on the VSI-PWM drives which can theoretically result in a peak voltage which is twice the DC capacitor switched voltage. The length of cable where peak voltage will be reached is a product of the cable characteristic velocity (inversely proportional to the square root of the cable series inductance times it's parallel capacitance), with the rise time of the voltage. The actual magnitude of the voltage rise is a product of the theoretical twice the magnitude of the DC level switched times the attenuation factor, which is proportional to the total cable resistance divided by the characteristic impedance. The characteristic impedance is proportional to the square root of the cable inductance divided by the cable capacitance. On 480 volt systems [I71 it is possible to calculate the critical length of cable for IGBTs as 50 to 150 feet, and GTOs as 400 to 1000 feet. 5 kilovolt cable typically has a lower capacitance and marginally higher inductance than 1 kilovolt cable, therefore the critical cable length for 2.5 and 5 KV systems will be about 25% shorter and the attenuation will be about two-thirds of that of 480 volt systems. These dv/dt problems do not exist on CSI drives with capacitors on the output or with naturally commutated LCI drives, because the rise time of the voltage is in the order of milliseconds. The second type of voltage stress mentioned is the neutral to ground voltage, sometimes called common mode voltage, which is created in all variations of CSI and LCI drives. It is basically due to the asynchronous operation of the rectifier and inverter, which results in an instantaneous voltage across the DC link inductor of the rectified line voltage and rectified motor back EMF. Reference 4 covers the mathematical derivations of this voltage. This voltage will appear between neutral and ground on either the line or motor side of the drive, whichever is ungrounded, and both sides cannot be grounded at the same time. The primary effect is that if the drive uses only one DC link inductor in either the positive or negative leg the voltage line to ground can be as high as 2 1/2 times the line to neutral voltage. If the drive uses a DC link inductor in both the positive and negative legs then the voltage line to ground can be a maximum of twice the line to neutral voltage. The actual magnitude of this voltage is a
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function of the motor power factor, size of any output filter capacitors and commutation methods. In some CSI drive designs this voltage can be much lower. The solution to this voltage stress is to either design the motor ground wall insulation to handle it or to install an ungrounded transformer on the supply to the drive. The third type of stress is due to voltage spikes induced in the motor inductance by rapidly turning on or off current to the motor. This is characteristically seen on 6 step current source inverters, which do not utilize any out filter capacitors. The actual magnitude of the voltage spike is primarily a function of the motor leakage inductance and the magnitude of the stator current at the time of the switching. The solutions to reducing this problem can be to use motors with insulation rated for the higher phase to phase voltage spikes in combination with a leakage inductance which is much lower than on a typical across the line motor and voltage clamps on the drive inverter output. Alternately in CSI-CAP and CSI-PWM drives a large motor filter capacitor is utilized which eliminates this problem. The self excitation over voltage associated with CSI drives with large output filter capacitors is the same as that seen when over sized power factor correction capacitors are put on an induction motor. The potential voltage can be calculated in an identical method to that with power factor correction capacitors. This voltage would vary approximately from 120% for a small capacitor to 170% for a large capacitor. Self excitation will only occur if the drive remains connected to the motor while the motor is spinning at higher speeds and the drive is not controlling current. This typically happens under certain fault conditions, with drives that are configured as coast to stop or with over hauling loads. Self excitation is typically controlled in these cases by adding an output contactor.
based on a hypothetical ideal motor. Generic data provided by a drive manufacturer as to the harmonic losses and torques are little value unless the specific motor parameters are known upon which this data is based, because motor inductance plays such a large role. Although at low voltage most drives now manufactured are some form of VSI-PWM; there is no similar consistency at medium voltage, therefore the purchaser must be more aware of individual strengths and weaknesses. Although there have been situations of high harmonic torques resulting in broken motor shafts and couplings or large voltage stress on medium voltage motors, these are primarily due to specific drive/motor designs rather than inherent on all drive designs. Generally the technology is available to reduce the amount of harmonic heating and torques produced by the motor from more sophisticated drives to less than the amount experienced as a result of normal voltage unbalance. References 1. D. Finney, Variable Frequency AC Motor Drive Systems, Peter Peregrinus Ltd., London, 1988. 2. A. Fitzgerald, C. Kingsley Jr., A. Kusko, Electric Machinery, McGraw-Hill Inc., New York, 1971. 3. R. Lawrence, Principles of Alternatina-Current Machinery, McGraw-Hill Book Co., New York, 1953. 4. R. Quirt, "Voltages to Ground in Load Commutated Inverters", IEEE Transactions on Industrial Applications, vol. IA-24, n0.3, pp. 526-530, May/June 1988.
5. J. Oliver, M. Samotyj, "Experience with Large Adjustable Speed Drives in Power Plants", IEE No.291 Conference Record on Power Electronics and Variable Frequency Drives, pp 225-228.
Conclusion It is difficult to accurately predict the exact harmonic
heating and torques in a motor due primarily due to the variations in rotor bar design. It is possible though to approximate these given the motor design parameters of the particular motor, including the locked rotor and rated currents, torques and power factors. This allows the calculation of the effective rotor resistance as a function of slip frequency. For an end user it is most meaningful to know these torques and additional heating as a function of a specific motor rather than
6. J. Steinke, "Control of a Neutral-Point-Clamped PWM Inverter for High Power AC Traction Drives", No.291 Conference Record on Power Electronics and Variable Frequency Drives, pp 214-217. 7. P. Espelage, J. Nowak, L. Walker, "Symmetrical GTO Current Source Inverter for Wide Speed Range Control of 2300 to 4160 Volt, 350 to 7000 HP, Induction Motors", IEEE 1988 IAS Conference Record, pp 302-307.
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8. S. LaGrone, M. Griggs, M. Bressani, “Application of
a 5500 RPM High Speed Induction Motor and Drive in a 7000 HP Natural Gas Compressor Installation”, 1992 PClC Conference Record, pp. 141-146. 9. W. Frey, “Retroffi Experience of an 8000 HP Pipeline Compressor Variable Speed Drive“, 1991 PClC Conference Record, pp 139-146.
10. P.G. Cummings, “Estimating Effect of System Harmonics on Losses and Temperature Rise of Squirrel-Cage Motors”, IEEE Transactions on Industrial Applications, vol. IA-22, no.6, pp 1121-1126, Nov/Dec 1986. 11. B.Wu,S. Dewan, G. Slemon, “PWM-CSI Inverter for Induction Motor Drives”, IEEE Transactions on Industrial Applications, vol. IA-28, no.1, pp 64-71, Jan/Feb 1992.
12. R. Daugherty, “Bus Transfer of AC Induction Motors, A Perspective”, 1989 PClC Conference Record, pp 219-227. 13. F. Dewinter, L. Benke, “Systems Engineering for Large Induction Motor Adjustable Frequency Drives”, 1991 PCIC Conference Record, pp 29-37. 14. J. Dymond, “Stall Time, Acceleration Time, Frequency of Starting: The Myths and the Facts”, 1991 PClC Conference Record, pp 19-27. 15. D. Rice, “A Detailed Analysis of Six-Pulse Converter Harmonic Currents”, 1992 PClC Conference Record, pp 153-163. 16. P. McLaren, M. Abdel-Rahman, “Modelling of Large AC Motor Coils for Steep-Fronted Surge Studies”, IEEE Transactions on lndusrial Applications, vol. IA-24, no.3,pp 422-426, May/June 1988. 17. A. Bonnett, “Analysis of the Impact of Pulse-Width Modulated Inverter Voltage Waveforms on A.C. Induction Motors”, 1994 IEEE Pulp and Papr Conference Record, pp 68-75.
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