Variable-frequency drive
A variable-frequency drive (VFD) is a system for controlling the rotational speed of an alternating current (AC) electric motor by controlling the frequency of the electrical power supplied to the motor.[1][2][3] A variable frequency drive is a specific type of adjustable-speed drive. Variable-frequency drives are also known as adjustable-frequency drives (AFD), variable-speed drives (VSD), AC drives, microdrives or inverter drives.
Variable-frequency drives are used in a wide number of applications to control pumps, fans, hoists, conveyors, and other machinery.
Benefits
Energy savings
AC motor-driven applications that do not require full speed can save energy by controlling the motor with a variable speed drive. Energy cost saving with variable torque can be significant, often paying for the cost of VFD within a matter of months. In variable torque applications such as fans and blowers, the torque required varies roughly with the square of the speed, and the horsepower required varies roughly with the cube of the speed, resulting in a large reduction of horsepower for even a small reduction in speed. The motor will consume only 25% as much power at 63% speed than it will at 100% speed. This is referred to as the Affinity Laws, which define the relationships between speed, flow, torque, and horsepower.[4]
In the United States, an estimated 60-65% of electrical energy is used to supply motors, 75% of which are variable torque fan, pump and compressor loads. [5] Eighteen percent of the energy used in the 40 million motors in the U.S. could be saved by efficient energy improvement technologies such as VFDs[6] Only about 3% of all AC motors are provided with AC drives[7]
An energy consumption breakdown of the global population of AC motor installations is as shown in the following table:
| Small | General Purpose - Medium-Size | Large | |
|---|---|---|---|
| Power | 10W to 750W | 750W to 375kW | 375kW to 100MW |
| Phase, voltage | 1-ph., <240V | 3-ph., 200V to 1kV | 3-ph., 1kV to 20kV |
| % total motor energy | 9% | 68% | 23% |
| Total stock | 2 billion | 230 million | 0.6 million |
Starting torque control
Across-the-line single-speed starters start motors abruptly, subjecting the motor to a high starting torque and to current surges that are up to 8 times the full-load current. Variable speed drives instead gradually ramp the motor up to operating speed to lessen mechanical and electrical stress, reducing maintenance and repair costs, and extending the life of the motor and the driven equipment.
Reduced-voltage starting methods also accelerate a motor gradually, but VF drives can be programmed to ramp up the motor much more gradually and smoothly, and can operate the motor at less than full speed to decrease wear and tear. Variable speed drives can also run a motor in specialized patterns to further minimize mechanical and electrical stress. For example, an S-curve pattern can be applied to a conveyor application for smoother decel/accel control, which reduces the backlash that can occur when a conveyor is accelerating or decelerating.
The following table compares AC and DC drive technologies.[9]
| Criteria | Brushed DC Drives | Brushless DC Drives | AC Drives |
|---|---|---|---|
| Drive complexity | Low | High | High |
| Motor complexity | High | Low | Low |
| Inherent fault protection | No (needs fuses) | No | Yes |
| Lifetime maintenance | Required (Motor brushes) | Low (Bearings) | Low (Bearings) |
| Control performance | Low | High (Closed loop control) | High (Closed loop control) |
VFD types
Variable frequency drives can be classified according to the overall basic method of operation:
- Variable-voltage inverter (VVI) or 'six-step' drives
- Voltage-source inverter (VSI) drives
- Current-source inverter (CSI) drives
- Cycloconverter or matrix drives
- Load commutated inverter (LCI) drives.
In a VVI drive, the DC output of the SCR-bridge converter is smoothed via capacitor bus and series-reactor connection to supply via Darlington Pair or IGBT inverter quasi-sinusoidal, six-step voltage input to the motor. In a VSI drive, the DC output of the diode-bridge converter stores energy in the capacitor bus to supply stiff voltage input to the inverter. In a CSI drive, the DC output of the SCR-bridge converter stores energy in series-reactor connection to supply stiff current input to the inverter.
A cycloconverter or matrix drive has no AC-to-DC converter and instead briefly connects each output terminal to the appropriate input phase, making up the desired variable-frequency output waveforms by selective commutation from the fixed-frequency input waveforms.
In a LCI drive, the DC output of the SCR-bridge converter stores energy via DC link inductor circuit to supply stiff quasi-sinusoidal six-step current input to a second SCR-bridge's inverter and an over-excited synchronous machine.
Most packaged AC drives are VSI-PWM type using pulse width modulation. Control the motor's frequency is in one of several operating modes including open-loop Volts-per-Hertz control, field-oriented control (FOC), closed-loop speed control with slip compensation, or direct torque control (DTC), PWM not however being needed or typically used with DTC.
Variable frequency drives are also categorized by the torque and power characteristics of the load:
- Variable torque, such as in fan, pump and blower applications
- Constant torque, such as in conveyor and displacement pump applications
- Constant power, such as in machine tool and traction applications.
It is lastly useful to relate VFDs in terms of the following two classifications[10][11][12][13][14][15]:
- In terms of various AC machines as shown in Table 1 below
- In terms of various low and medium voltage topologies shown in Table 2 below.
VFD type tables
 |
Table 1: Machines
| |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Table 2: Topologies
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||
Legend for Tables 1&2
| ^ | Inverter switching device (with std. diode rectifier) |
| ^^ | Inverter and rectifier switching device |
| AFE | Active front end |
| BLDM | PM trapezoid machine (Brushless DC electric motor) |
| CME | Common mode elimination |
| CHB | Cascaded H-bridge |
| CSI | Current source inverter |
| CSR | Current source rectifier |
| GCT | Gate controlled thyristor |
| GTO | Gate turn-off thyristor |
| IGBT | Insulated gate bipolar transistor |
| LCI | Load commutated inverter |
| LV | Low voltage |
| MV | Medium voltage |
| NPC | Neutral point clamped |
| PAM | Pulse-amplitude modulation |
| PM | Permanent magnet |
| PMSM | Permanent magnet synchronous generator |
| PWM | Pulse-width modulation |
| SCR | Silicon controlled rectifier |
| SGCT | Symmetrical gate controlled thyristor |
| SRM | Switched reluctance motor |
| SyRM | Synchronous reluctance machine |
| VRM | Variable reluctance machine |
| VSI | Voltage source inverter |
| VVI | Variable voltage inverter |
| WFSM | Wound field synchronous machine |
| WRIM | Wound rotor induction motor |
System description
A variable frequency drive system generally consists of an AC motor, a controller and an operator interface.[16][17]
Motor
The motor used in a VFD system is usually a three-phase induction motor. Some types of single-phase motors can be used, but three-phase motors are usually preferred. Various types of synchronous motors offer advantages in some situations, but induction motors are suitable for most purposes and are generally the most economical choice. Motors that are designed for fixed-speed operation are often used. Certain enhancements to the standard motor designs offer higher reliability and better VFD performance, such as MG-31 rated motors.[18]
Controller
Variable frequency drive controllers are solid state electronic power conversion devices. The usual design first converts AC input power to DC intermediate power using a rectifier or converter bridge. The rectifier is usually a three-phase, full-wave diode bridge. The DC intermediate power is then converted to quasi-sinusoidal AC power using an inverter switching circuit. The inverter circuit is probably the most important section of the VFD, changing DC energy into three channels of AC energy that can be used by an AC motor. These units provide improved power factor, less harmonic distortion, and low sensitivity to the incoming phase sequencing than older phase controlled converter VFD's. Since incoming power is converted to DC, many units will accept single-phase as well as three-phase input power (acting as a phase converter as well as a speed controller); however the unit must be derated when using single phase input as only part of the rectifier bridge is carrying the connected load.[19]
As new types of semiconductor switches have been introduced, these have promptly been applied to inverter circuits at all voltage and current ratings for which suitable devices are available. Introduced in the 1980s, the insulated-gate bipolar transistor (IGBT) became the device used in most VFD inverter circuits in the first decade of the 21st century.[20][21][22]
AC motor characteristics require the applied voltage to be proportionally adjusted whenever the frequency is changed in order to deliver the rated torque. For example, if a motor is designed to operate at 460 volts at 60 Hz, the applied voltage must be reduced to 230 volts when the frequency is reduced to 30 Hz. Thus the ratio of volts per hertz must be regulated to a constant value (460/60 = 7.67 V/Hz in this case). For optimum performance, some further voltage adjustment may be necessary especially at low speeds, but constant volts per hertz is the general rule. This ratio can be changed in order to change the torque delivered by the motor.[23]
In addition to this simple volts per hertz control more advanced control methods such as vector control and direct torque control (DTC) exist. These methods adjust the motor voltage in such a way that the magnetic flux and mechanical torque of the motor can be precisely controlled.
Although space vector pulse-width modulation (PWM) is becoming increasingly popular[24], sinusoidal PWM (SPWM) is the most straightforward method used to vary drives' motor voltage (or current) and frequency. With SPWM control (see Fig. 1), quasi-sinusoidal, variable-pulse-width output is constructed from intersections of a saw-toothed carrier frequency signal with a modulating variable sinusoidal voltage (or current) and frequency signal.[25][20][26]
Operation of the motors above rated name plate speed (base speed) is possible, but is limited to conditions that do not require more power than the nameplate rating of the motor. This is sometimes called "field weakening" and, for AC motors, means operating at less than rated volts/hertz and above rated name plate speed. Permanent magnet synchronous motors have quite limited field weakening speed range due to the constant magnet flux linkage. Wound rotor synchronous motors and induction motors have much wider speed range. For example, a 100 hp, 460 V, 60 Hz, 1775 RPM (4 pole) induction motor supplied with 460 V, 75 Hz (6.134 V/Hz), would be limited to 60/75 = 80% torque at 125% speed (2218.75 RPM) = 100% power.[27] At higher speeds the induction motor torque has to be limited further due to the lowering of the breakaway torque of the motor. Thus rated power can be typically produced only up to 130...150% of the rated name plate speed. Wound rotor synchronous motors can be run at even higher speeds. In rolling mill drives often 200...300% of the base speed is used. Naturally the mechanical strength of the rotor and the lifetime of the bearings also limit the maximum speed of the motor. Consulting the motor manufacturer is recommended if more than 150% speed is required by the application.
An embedded microprocessor governs the overall operation of the VFD controller. The main microprocessor programming is in firmware that is inaccessible to the VFD user. However, some degree of configuration programming and parameter adjustment is usually provided so that the user can customize the VFD controller to suit specific motor and driven equipment requirements.[20]
Operator interface
The operator interface provides a means for an operator to start and stop the motor and adjust the operating speed. Additional operator control functions might include reversing, and switching between manual speed adjustment and automatic control from an external process control signal. The operator interface often includes an alphanumeric display and/or indication lights and meters to provide information about the operation of the drive. An operator interface keypad and display unit is often provided on the front of the VFD controller as shown in the photograph above. The keypad display can often be cable-connected and mounted a short distance from the VFD controller. Most are also provided with input and output (I/O) terminals for connecting pushbuttons, switches and other operator interface devices or control signals. A serial communications port is also often available to allow the VFD to be configured, adjusted, monitored and controlled using a computer.[20][28][29]
Operation
When a VFD starts a motor, it initially applies a low frequency and voltage to the motor. The starting frequency is typically 2 Hz or less. Thus starting at such a low frequency avoids the high inrush current that occurs when a motor is started by simply applying the utility (mains) voltage by turning on a switch. After the start of the VFD, the applied frequency and voltage are increased at a controlled rate or ramped up to accelerate the load without drawing excessive current. This starting method typically allows a motor to develop 150% of its rated torque while the VFD is drawing less than 50% of its rated current from the mains in the low speed range. A VFD can be adjusted to produce a steady 150% starting torque from standstill right up to full speed.[30] Note, however, that cooling of the motor is usually not good in the low speed range. Thus running at low speeds even with rated torque for long periods is not possible due to overheating of the motor. If continuous operation with high torque is required in low speeds an external fan is usually needed. The manufacturer of the motor and/or the VFD should specify the cooling requirements for this mode of operation.
In principle, the current on the motor side is in direct proportion to the torque that is generated and the voltage on the motor is in direct proportion of the actual speed, while on the network side, the voltage is constant, thus the current on line side is in direct proportion of the power drawn by the motor, that is U.I or C.N where C is torque and N the speed of the motor (we shall consider losses as well, neglected in this explanation).
- n stands for network (grid) and m for motor
- C stands for torque [Nm], U for voltage [V], I for current [A], and N for speed [rad/s]
We neglect losses for the moment:
- Un.In = Um.Im (same power drawn from network and from motor)
- Um.Im = Cm.Nm (motor mechanical power = motor electrical power)
- Given Un is a constant (network voltage) we conclude: In = Cm.Nm/Un That is "line current (network) is in direct proportion of motor power".
With a VFD, the stopping sequence is just the opposite as the starting sequence. The frequency and voltage applied to the motor are ramped down at a controlled rate. When the frequency approaches zero, the motor is shut off. A small amount of braking torque is available to help decelerate the load a little faster than it would stop if the motor were simply switched off and allowed to coast. Additional braking torque can be obtained by adding a braking circuit (resistor controlled by a transistor) to dissipate the braking energy. With 4-quadrants rectifiers (active-front-end), the VFD is able to brake the load by applying a reverse torque and reverting the energy to the network.
Power line harmonics
While harmonics in PWM wave can easily be filtered by carrier frequency related filter inductance to supply near-sinusoidal currents to the motor load[31], the diode rectifier of the VFD takes non-linear half-phase current pulses out of the AC grid, creating harmonic current distortion, and hence voltage distortion, of the power line input. When the VFD loads are relatively small in comparison to the large, 'stiff' power system available from the utility, the effects of VFD harmonic distortion of the AC grid can often be within acceptable limits. Furthermore, in low voltage networks, harmonics caused by single phase equipment such as computers and TVs are partially cancelled by three-phase diode bridge harmonics because their 5th and 7th harmonics are in counterphase[32].
However, when the total VFD load in one location is large enough, the load can have a negative impact on the AC power waveform available to other utility customers in the same grid.
When the utility's voltage becomes distorted due to harmonics, losses in other loads such as normal fixed-speed AC motors are increased. This may in the worst case lead to overheating and shorter operating life. Also substation transformers and compensation capacitors are affected negatively. In particular, capacitors can cause resonance conditions that can unacceptably magnify harmonic levels.
In order to limit the voltage distortion, owners of VFD load may be required to install filtering equipment to reduce harmonic distortion below acceptable limits. Alternatively, the utility may adopt a solution by installing filtering equipment of its own at substations affected by the large amount of VFD equipment being used. In high power installations harmonic distortion can be reduced by supplying multi-pulse rectifier-bridge VFDs from transformers with multiple phase-shifted windings.[33]
Furthermore, it is possible, instead of the diode rectifier, to use a transistor circuit similar to that which controls the motor. Such rectifiers are referred to by various designations including active infeed converter (AIC), active rectifier, IGBT Supply Unit (ISU), Active Front End (AFE) or four-quadrant operation. With PWM control of the transistors and filter inductors in the lines, the AC current can be made nearly sinusoidal. Even better attenuation of the harmonics can be obtained by using an LCL (inductor-capacitor-inductor) filter instead of single three-phase filter inductor (reference required).
An additional advantage of the active infeed converter over the diode bridge is its ability to feed back the energy from the DC side to the AC grid. Thus no braking resistor is needed and the efficiency of the drive is improved if the drive is frequently required to brake the motor.
Application considerations
Long lead effects
The output voltage of a PWM VFD consists of a train of pulses switched at what is called the carrier frequency. Because of the rapid rise time of these pulses, transmission line effects of the cable between the drive and motor must be considered. Since the transmission-line impedance of the cable and motor are different, pulses tend to reflect back from the motor terminals into the cable. The resulting voltages can produce overvoltages equal to 2 times the DC bus voltage or up to 3.1 times the rated line voltage for long cable runs, putting high stress on the cable and motor windings and eventual insulation failure. Note that standards for three-phase motors rated 230 V or less adequately protect against such long lead overvoltages. On 460 or 575 V systems and inverters with 3rd generation 0.1 microsecond rise time IGBTs, the maximum recommended cable distance between VFD and motor is about 50 m or 150 feet. Solutions to overvoltages caused by long lead lengths include minimizing cable distance, lowering carrier frequency, installing dv/dt filters (that decrease the steepness of the pulses), using inverter duty rated motors (that are rated 600 V to withstand pulse trains with rise time less than or equal to 0.1 microsecond, of 1,600 V peak magnitude), and installation of sinewave low pass filters. Regarding lowering of carrier frequency, note that audible noise is noticeably increased for carrier frequencies less than about 6 kHz and is most noticeable at about 3 kHz. Note also that selection of optimum PWM carrier frequency for AC drives involves balancing noise, heat, motor insulation stress, common mode voltage induced motor bearing current damage, smooth motor operation, and other factors.
Motor bearing currents
PWM drives are inherently associated with high frequency common mode voltages and currents which may cause trouble with motor bearings. When these high frequency voltages find a path to earth through a bearing, sparking occurs between the bearing's ball and the bearing's race. Over time sparking causes erosion in the bearing race that can be seen as a fluting pattern. In large motors, the stray capacitance of the windings provides paths for high frequency currents that pass through the motor shaft ends leading to a ciculating type of bearing current. Poor grounding of motor stators can lead to shaft ground bearing currents. Small motors with poorly grounded driven equipment are susceptible to high frequency bearing currents. [38]
Prevention of high frequency bearing current damage uses three approaches: good cabling and grounding practices, interruption of bearing currents, and filtering or damping of common mode currents. Good cabling and grounding practices can include use of shielded, symmetrical-geometry power cable to supply the motor, installation of shaft grounding brushes, and conductive bearing grease. Bearing curents can be interrupted by installation of insulated bearings and specially designed electrostatic shielded induction motors. Filtering and damping high frequency bearing currents requires filters, lowering of carrier frequency, or using low voltage VFD with 3-level (instead of standard 2-level) inverter topology.
Since inverter-fed motor cables' high frequency current spikes can interfere with other cabling in facilities, such inverter-fed motor cables should not only be of shielded, symmetrical-geometry design but should also be routed at least 50 cm away from signal cables.
Available power ratings
VFDs are available with voltage and current ratings covering a wide range of single-phase and multi-phase AC motors. Low voltage (LV) drives are designed to operate at output voltages equal to or less than 690 V. While motor-application LV drives are available in ratings of up to the order of 5 or 6 MW,[39] economic considerations typically favor medium voltage (MV) drives with much lower power ratings. Different MV drive topologies (see Table 2) are configured in accordance with the voltage/current-combination ratings used in different drive controllers' switching devices[40] such that any given voltage rating is greater than or equal to one to the following standard nominal motor voltage ratings: generally either 2.3/4.16 kV (60 Hz) or 3.3/6.6 kV (50 Hz), with one thyristor manufacturer rated for up to 12 kV switching. In some applications a step up transformer is placed between a LV drive and a MV motor load. MV drives are typically rated for motor applications greater than between about 375 kW (500 hp) and 750 kW (1000 hp). MV drives have historically required considerably more application design effort than required for comparable LV drive applications.[41][42] The power rating of MV drives can reach 100 MW, a range of different drive topologies being involved for different rating, performance, power quality and reliability requirements.[12][15][13]
Dynamic braking
Using the motor as a generator to absorb energy from the system is called dynamic braking. Dynamic braking stops the system more quickly than coasting. Since dynamic braking requires that the rotor be moving, it becomes less effective at low speed and cannot be used to hold a load at a stopped position. During normal braking of an electric motor, the electrical energy produced by the motor is dissipated as heat inside of the rotor, which increases the likelihood of damage and eventual failure. Therefore, some systems transfer this energy to an outside bank of resistors. Cooling fans may be used to protect the resistors from damage. Modern systems have thermal monitoring, so if the temperature of the bank becomes excessive, it will be switched off.
Regenerative variable-frequency drives
Regenerative AC drives have the capacity to recover the braking energy of a load moving faster than the designated motor speed (an overhauling load) and return it to the power system.
Cycloconverters and current-source inverters inherently allow return of energy from the load to the line, while voltage-source inverters require an additional converter to return energy to the supply.[43]
Regeneration is only useful in variable-frequency drives where the value of the recovered energy is large compared to the extra cost of a regenerative system,[43] and if the system requires frequent braking and starting. An example would be conveyor belt drives for manufacturing, which stop every few minutes. While stopped, parts are assembled correctly; once that is done, the belt moves on. Another example is a crane, where the hoist motor stops and reverses frequently, and braking is required to slow the load during lowering. Regenerative variable-frequency drives are widely used where speed control of overhauling loads is required.[2][3][44]
See also
- Direct torque control
- Frequency changer
- Space vector modulation
- Variable speed air compressor
- Vector control (motor)
References
- ^ Campbell, Sylvester J. (1987). Solid-State AC Motor Controls. New York: Marcel Dekker, Inc. pp. 79–189. ISBN 0-8247-7728-X.
{{cite book}}: Cite has empty unknown parameter:|coauthors=(help) - ^ a b Jaeschke, Ralph L. (1978). Controlling Power Transmission Systems. Cleveland, OH: Penton/IPC. pp. 210–215.
{{cite book}}: Cite has empty unknown parameter:|coauthors=(help) Cite error: The named reference "Jaeschke" was defined multiple times with different content (see the help page). - ^ a b Siskind, Charles S. (1963). Electrical Control Systems in Industry. New York: McGraw-Hill, Inc. p. 224. ISBN 0070577463.
{{cite book}}: Cite has empty unknown parameter:|coauthors=(help) Cite error: The named reference "Siskind" was defined multiple times with different content (see the help page). - ^ http://www.emcsolutions.com/article_vfd_benefits.html
- ^ Bose, Bimal K. (June 2009). "The Past, Present, and Future of Power Electronics". Industrial Electronics Magazine, IEEE. 3 (2): 9. doi:10.1109/MIE.2009.932709.
- ^ Spear, Mike. "Adjustable Speed Drives: Drive Up Energy Efficiency". ChemicalProcessing.com. Retrieved 27 January 2012.
- ^ "Guide to Variable Speed Drives - Technical Guide No. 4" (PDF). Technical Guides (ABB). Retrieved 27 January 2012.
- ^ Waide, Paul (2011). "Energy-Efficiency Policy Opportunities for Electric Motor-Driven Systems" (PDF). Internation Energy Agency. Retrieved Jan. 27, 2012.
{{cite web}}: Check date values in:|accessdate=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^ http://www.optimacs.com/reports/Understanding%20the%20control%20system.pdf
- ^ "Variable Speed Pumping, A Guide to Successful Applications, Executive Summary" (PDF). USDOE - Europump - Hydraulic Institute. Retrieved 29 January 2012.
- ^ Bose, Bimal K. (2006). Power Electronics and Motor Drives : Advances and Trends. Amsterdam: Academic. p. 9. ISBN 978-0-12-088405-6.
- ^ a b Wu, Bin (2005). "High-Power Converters and AC Drives" (PDF). IEEE PES. Retrieved 3 February 2012.
- ^ a b "DuraBilt5i MV Topologies Comparisons & Features-Benefits" (PDF). TMEIC. Retrieved 3 February 2012.
- ^ Paes, Richard (2011). "An Overview of Medium Voltage AC Adjustable Speed Drives and IEEE Std. 1566 – Standard for Performance of Adjustable Speed AC Drives Rated 375 kW and Larger". Joint Power Engineering Society-Industrial Applications Society Technical Seminar. IEEE Southern Alberta Chapter: pp. 1-78.
{{cite journal}}:|access-date=requires|url=(help);|pages=has extra text (help); Check date values in:|accessdate=(help); Unknown parameter|month=ignored (help) - ^ a b Klug, Dieter-Rolf (2005). "High Power Medium Voltage Drives - Innovations, Portfolio, Trends". European Conference on Power Electronics and Applications. doi:10.1109/EPE.2005.219669.
{{cite conference}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help); Unknown parameter|booktitle=ignored (|book-title=suggested) (help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^ Jaeschke, pp. 210-211
- ^ NEMA Standards Publication (2001). Application Guide for AC Adjustable Speed Drive Systems. Rosslyn, VA USA: National Electrical Manufacturers Association (now The Association of Electrical Equipment and Medical Imaging Manufacturers). p. 3. Retrieved Mar. 27, 2008.
{{cite book}}: Check date values in:|accessdate=(help) - ^ NEMA, pp. 9-12
- ^ Campbell, pp. 79-83
- ^ a b c d Bartos, Frank J. (Sep. 1, 2004). "AC Drives Stay Vital for the 21st Century". Control Engineering. Reed Business Information. Retrieved Mar. 28, 2008.
{{cite journal}}: Check date values in:|accessdate=and|date=(help) [dead link] - ^ Eisenbrown, Robert E. (May 18, 2008). "AC Drives, Historical and Future Perspective of Innovation and Growth". Keynote Presentation for the 25th Anniversary of The Wisconsin Electric Machines and Power Electronics Consortium (WEMPEC). University of Wisconsin, Madison, WI, USA: WEMPEC. pp. 6–10. Retrieved Mar. 28, 2008.
{{cite conference}}: Check date values in:|accessdate=(help); Unknown parameter|booktitle=ignored (|book-title=suggested) (help) - ^ Jahn, Thomas M. (January 2001). "AC Adjustable-Speed Drives at the Millennium: How Did We Get Here?". IEEE Transactions on Power Electronics. 16 (1). IEEE: 17–25. doi:10.1109/63.903985.
{{cite journal}}: Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^ Bose, Bimal K. (1980). Adjustable Speed AC Drive Systems. New York: IEEE Press. p. 3. ISBN 0-87942-146-0.
{{cite book}}: Cite has empty unknown parameter:|coauthors=(help) - ^ Bose, Bimal K. (2011). "Energy Scenario and Impact on Power Electronics In the 21st Century" (PDF). Doha,Qatar. p. 12. Retrieved Feb.8, 2012.
{{cite web}}: Check date values in:|accessdate=(help); Unknown parameter|booktitle=ignored (help) - ^ Bose (2006), p. 183
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- ^ Cleaveland, Peter (Nov. 1, 2007). "AC Adjustable Speed Drives". Control Engineering. Reed Business Information. Retrieved Mar. 28, 2008.
{{cite journal}}: Check date values in:|accessdate=and|date=(help) [dead link][dead link] - ^ Campbell, pp. 107-129
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- ^ Janssen, Hansen (2000). "Harmonic Cancellation by Mixing Non-Linear Single-Phase and Three-Phase Loads". IEEE Trans. on Industry Applications. 36 (1).
{{cite journal}}:|access-date=requires|url=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help) - ^ "Guide to Harmonics with AC Drives - Technical Guide No. 6" (PDF). Technical Guides. ABB. May 17, 2002. Retrieved Jul. 29, 2009.
{{cite journal}}: Check date values in:|accessdate=(help) - ^ Skibinski, Gary (2004). "Line and Load Friendly Drive Solutions for Long Length Cable Applications in Electrical Submersible Pump Applications". Fifty-First Annual Conference Petroleum and Chemical Industry Technical Conference. IEEE: 269–278. doi:10.1109/PCICON.2004.1352810.
{{cite journal}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^ "Application Report Long Drive/Motor Leads" (PDF). Yaskawa Electric America, Inc. Retrieved 14 February 2012.
- ^ Malfait, A. (1994). "Audible Noise and Losses in Variable Speed Induction Motor Drives: Influence of the Squirrel Cage Design and the Switching Frequency". 29th Annual Meeting Proceedings of IEEE Industry Applications Society: 693–700.
{{cite journal}}:|access-date=requires|url=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help) - ^ "A-B Reliance GV3000 FAQs Who Cares About Carrier Frequency?" (PDF). Retrieved 15 February 2012.
- ^ "Bearing Currents in Modern AC Drive Systems - Technical Guide No. 5" (PDF). Technical Guides. ABB. 1999-12-01. Retrieved 2011-06-14.
- ^ "ACS800 Catalog - Single Drives 0.55 to 5600 kW". ABB. July 19, 2009. Retrieved Mar. 12, 2012.
{{cite journal}}: Check date values in:|accessdate=(help); Cite journal requires|journal=(help) - ^ Wu Slide 22
- ^ Bartos, Frank J. (Feb. 1, 2000). "Medium-Voltage AC Drives Shed Custom Image". Control Engineering. Reed Business Information. Retrieved Mar. 28, 2008.
{{cite journal}}: Check date values in:|accessdate=and|date=(help) [dead link] - ^ Lockley, Bill (2008). "Standard 1566 for (Un)Familiar Hands". IEEE Industry Applications Magazine. 14 (1): 21–28. doi:10.1109/MIA.2007.909800.
{{cite journal}}:|access-date=requires|url=(help); Check date values in:|accessdate=(help); Unknown parameter|coauthors=ignored (|author=suggested) (help); Unknown parameter|month=ignored (help) - ^ a b Dubey, Gopal K. (2001). Fundamentals of Electrical Drives (2 ed.). Pangbourne: Alpha Science Int. ISBN 1-84265-083-1.
- ^ Campbell, Sylvester J. (1987). Solid-State AC Motor Controls. New York: Marcel Dekker, Inc. pp. 70–190. ISBN 0-8247-7728-X.
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