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An induction motor, 3 phase induction motor or asynchronous motor is an AC electric motor in which the electric current in the rotor needed to produce torque is obtained by electromagnetic induction from the magnetic field of the stator winding.^{[1]} An induction motor can therefore be made without electrical connections to the rotor.^{[a]} An induction motor's rotor can be either wound type or squirrelcage type.
Threephase squirrelcage induction motors are widely used in industrial drives because they are rugged, reliable and economical. Singlephase induction motors are used extensively for smaller loads, such as household appliances like fans. Although traditionally used in fixedspeed service, induction motors are increasingly being used with variablefrequency drives (VFDs) in variablespeed service. VFDs offer especially important energy savings opportunities for existing and prospective induction motors in variabletorque centrifugal fan, pump and compressor load applications. Squirrel cage induction motors are very widely used in both fixedspeed and variablefrequency drive (VFD) applications.
In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations. By manually turning switches on and off, Walter Baily demonstrated this in 1879, effectively the first primitive induction motor.^{[2]}^{[3]}^{[4]}^{[5]}</ref>^{[6]}^{[6]}^{[7]}^{[8]}
The first commutatorfree two phase AC induction motor was invented by Hungarian engineer Ottó Bláthy, he used the two phase motor to propel his invention, the Electricity meter ^{[9]}^{[10]}
The first AC commutatorfree threephase induction motors were independently invented by Galileo Ferraris and Nikola Tesla, a working motor model having been demonstrated by the former in 1885 and by the latter in 1887. Tesla applied for US patents in October and November 1887 and was granted some of these patents in May 1888. In April 1888, the Royal Academy of Science of Turin published Ferraris's research on his AC polyphase motor detailing the foundations of motor operation.^{[5]}^{[11]} In May 1888 Tesla presented the technical paper A New System for Alternating Current Motors and Transformers to the American Institute of Electrical Engineers (AIEE)^{[12]}^{[13]}^{[14]}^{[15]} ^{[16]} describing three fourstatorpole motor types: one with a fourpole rotor forming a nonselfstarting reluctance motor, another with a wound rotor forming a selfstarting induction motor, and the third a true synchronous motor with separately excited DC supply to rotor winding.
George Westinghouse, who was developing an alternating current power system at that time, licensed Tesla’s patents in 1888 and purchased a US patent option on Ferraris' induction motor concept.^{[17]} Tesla was also employed for one year as a consultant. Westinghouse employee C. F. Scott was assigned to assist Tesla and later took over development of the induction motor at Westinghouse.^{[12]}^{[18]}^{[19]}^{[20]} Steadfast in his promotion of threephase development, Mikhail DolivoDobrovolsky invented the cagerotor induction motor in 1889 and the threelimb transformer in 1890.^{[21]}^{[22]} Furthermore, he claimed that Tesla's motor was not practical because of twophase pulsations, which prompted him to persist in his threephase work.^{[23]} Although Westinghouse achieved its first practical induction motor in 1892 and developed a line of polyphase 60 hertz induction motors in 1893, these early Westinghouse motors were twophase motors with wound rotors until B. G. Lamme developed a rotating bar winding rotor.^{[12]}
The General Electric Company (GE) began developing threephase induction motors in 1891.^{[12]} By 1896, General Electric and Westinghouse signed a crosslicensing agreement for the barwindingrotor design, later called the squirrelcage rotor.^{[12]} Arthur E. Kennelly was the first to bring out the full significance of complex numbers (using j to represent the square root of minus one) to designate the 90º rotation operator in analysis of AC problems.^{[24]} GE's Charles Proteus Steinmetz greatly developed application of AC complex quantities including an analysis model now commonly known as the induction motor Steinmetz equivalent circuit.^{[12]}^{[25]}^{[26]}^{[27]}
Induction motor improvements flowing from these inventions and innovations were such that a 100horsepower induction motor currently has the same mounting dimensions as a 7.5horsepower motor in 1897.^{[12]}
In both induction and synchronous motors, the AC power supplied to the motor's stator creates a magnetic field that rotates in synchronism with the AC oscillations. Whereas a synchronous motor's rotor turns at the same rate as the stator field, an induction motor's rotor rotates at a somewhat slower speed than the stator field. The induction motor stator's magnetic field is therefore changing or rotating relative to the rotor. This induces an opposing current in the induction motor's rotor, in effect the motor's secondary winding, when the latter is shortcircuited or closed through an external impedance.^{[28]} The rotating magnetic flux induces currents in the windings of the rotor;^{[29]} in a manner similar to currents induced in a transformer's secondary winding(s).
The induced currents in the rotor windings in turn create magnetic fields in the rotor that react against the stator field. Due to Lenz's Law, the direction of the magnetic field created will be such as to oppose the change in current through the rotor windings. The cause of induced current in the rotor windings is the rotating stator magnetic field, so to oppose the change in rotorwinding currents the rotor will start to rotate in the direction of the rotating stator magnetic field. The rotor accelerates until the magnitude of induced rotor current and torque balances the applied mechanical load on the rotation of the rotor. Since rotation at synchronous speed would result in no induced rotor current, an induction motor always operates slightly slower than synchronous speed. The difference, or "slip," between actual and synchronous speed varies from about 0.5 to 5.0% for standard Design B torque curve induction motors.^{[30]} The induction motor's essential character is that it is created solely by induction instead of being separately excited as in synchronous or DC machines or being selfmagnetized as in permanent magnet motors.^{[28]}
For rotor currents to be induced, the speed of the physical rotor must be lower than that of the stator's rotating magnetic field ($n_{s}$); otherwise the magnetic field would not be moving relative to the rotor conductors and no currents would be induced. As the speed of the rotor drops below synchronous speed, the rotation rate of the magnetic field in the rotor increases, inducing more current in the windings and creating more torque. The ratio between the rotation rate of the magnetic field induced in the rotor and the rotation rate of the stator's rotating field is called "slip". Under load, the speed drops and the slip increases enough to create sufficient torque to turn the load. For this reason, induction motors are sometimes referred to as "asynchronous motors".^{[31]}
An induction motor can be used as an induction generator, or it can be unrolled to form a linear induction motor which can directly generate linear motion.
An AC motor's synchronous speed, $n_{s}$, is the rotation rate of the stator's magnetic field,
where $f$ is the motor supply's frequency, where $p$ is the number of magnetic poles and where $n_{s}$ and $f$ have identical units. For $f$ in unit Hertz and $n_{s}$ in RPM, the formula becomes
For example, for a fourpole threephase motor, $p$ = 4 and $n_{s}={120f \over {4}}$ = 1,500 and 1,800 , RPM synchronous speed, respectively, for 50 Hz and 60 Hz supply systems.
The two figures at right and left above each illustrate a 2pole 3phase machine consisting of three polepairs with each pole set 60º apart.
Slip, $s$, is defined as the difference between synchronous speed and operating speed, at the same frequency, expressed in rpm, or in percentage or ratio of synchronous speed. Thus
where $n_{s}$ is stator electrical speed, $n_{r}$ is rotor mechanical speed.^{[34]}^{[35]} Slip, which varies from zero at synchronous speed and 1 when the rotor is at rest, determines the motor's torque. Since the shortcircuited rotor windings have small resistance, even a small slip induces a large current in the rotor and produces significant torque.^{[36]} At full rated load, slip varies from more than 5% for small or special purpose motors to less than 1% for large motors.^{[37]} These speed variations can cause loadsharing problems when differently sized motors are mechanically connected.^{[37]} Various methods are available to reduce slip, VFDs often offering the best solution.^{[37]}
The typical speedtorque relationship of a standard NEMA Design B polyphase induction motor is as shown in the curve at right. Suitable for most low performance loads such as centrifugal pumps and fans, Design B motors are constrained by the following typical torque ranges:^{[30]}^{[b]}
Over a motor's normal load range, the torque's slope is approximately linear or proportional to slip because the value of rotor resistance divided by slip, $R_{r}^{'}/s$, dominates torque in linear manner.^{[38]} As load increases above rated load, stator and rotor leakage reactance factors gradually become more significant in relation to $R_{r}^{'}/s$ such that torque gradually curves towards breakdown torque. As the load torque increases beyond breakdown torque the motor stalls.
There are three basic types of competing small induction motors: singlephase, splitphase and shadedpole types and small polyphase motors.
In twopole singlephase motors, the torque goes to zero at 100% slip (zero speed), so these require alterations to the stator such as shadedpoles to provide starting torque. A single phase induction motor requires separate starting circuitry to provide a rotating field to the motor. The normal running windings within such a singlephase motor can cause the rotor to turn in either direction, so the starting circuit determines the operating direction.
In certain smaller singlephase motors, starting is done by means of a shaded pole with a copper wire turn around part of the pole. The current induced in this turn lags behind the supply current, creating a delayed magnetic field around the shaded part of the pole face. This imparts sufficient rotational field energy to start the motor. These motors are typically used in applications such as desk fans and record players, as the required starting torque is low, and the low efficiency is tolerable relative to the reduced cost of the motor and starting method compared to other AC motor designs.
Larger single phase motors are splitphase motors and have a second stator winding fed with outofphase current; such currents may be created by feeding the winding through a capacitor or having it receive different values of inductance and resistance from the main winding. In capacitorstart designs, the second winding is disconnected once the motor is up to speed, usually either by a centrifugal switch acting on weights on the motor shaft or a thermistor which heats up and increases its resistance, reducing the current through the second winding to an insignificant level. The capacitorrun designs keep the second winding on when running, improving torque. A resistance start design uses a starter inserted in series with the startup winding, creating reactance.
Selfstarting polyphase induction motors produce torque even at standstill. Available squirrel cage induction motor starting methods include directonline starting, reducedvoltage reactor or autotransformer starting, stardelta starting or, increasingly, new solidstate soft assemblies and, of course, VFDs.^{[39]}
Polyphase motors have rotor bars shaped to give different speedtorque characteristics. The current distribution within the rotor bars varies depending on the frequency of the induced current. At standstill, the rotor current is the same frequency as the stator current, and tends to travel at the outermost parts of the cage rotor bars (by skin effect). The different bar shapes can give usefully different speedtorque characteristics as well as some control over the inrush current at startup.
Although polyphase motors are inherently selfstarting, their starting and pullup torque design limits must be high enough to overcome actual load conditions.
In wound rotor motors, rotor circuit connection through slip rings to external resistances allows change of speedtorque characteristics for acceleration control and speed control purposes.
Before the development of semiconductor power electronics, it was difficult to vary the frequency, and cage induction motors were mainly used in fixed speed applications. Applications such as electric overhead cranes used DC drives or wound rotor motors (WRIM) with slip rings for rotor circuit connection to variable external resistance allowing considerable range of speed control. However, resistor losses associated with low speed operation of WRIMs is a major cost disadvantage, especially for constant loads.^{[40]} Large slip ring motor drives, termed slip energy recovery systems, some still in use, recover energy from the rotor circuit, rectify it, and return it to the power system using a VFD.
In many industrial variablespeed applications, DC and WRIM drives are being displaced by VFDfed cage induction motors. The most common efficient way to control asynchronous motor speed of many loads is with VFDs. Barriers to adoption of VFDs due to cost and reliability considerations have been reduced considerably over the past three decades such that it is estimated that drive technology is adopted in as many as 3040% of all newly installed motors.^{[41]}
The stator of an induction motor consists of poles carrying supply current to induce a magnetic field that penetrates the rotor. To optimize the distribution of the magnetic field, windings are distributed in slots around the stator, with the magnetic field having the same number of north and south poles. Induction motors are most commonly run on singlephase or threephase power, but twophase motors exist; in theory, induction motors can have any number of phases. Many singlephase motors having two windings can be viewed as twophase motors, since a capacitor is used to generate a second power phase 90° from the singlephase supply and feeds it to the second motor winding. Singlephase motors require some mechanism to produce a rotating field on startup. Cage induction motor rotor's conductor bars are typically skewed to avoid magnetic locking.
Standardized NEMA & IEC motor frame sizes throughout the industry result in interchangeable dimensions for shaft, foot mounting, general aspects as well as certain motor flange aspect. Since an open, drip proof (ODP) motor design allows a free air exchange from outside to the inner stator windings, this style of motor tends to be slightly more efficient because the windings are cooler. A lower speed requires a larger frame.^{[42]}
The method of changing the direction of rotation of an induction motor depends on whether it is a threephase or singlephase machine. In the case of threephase, reversal is straightforwardly implemented by swapping connection of any two phase conductors.
In a singlephase splitphase motor, reversal is achieved by changing the connection between the primary winding and the start circuit. Some singlephase splitphase motors that are designed for specific applications may have the connection between the primary winding and the start circuit connected internally so that the rotation cannot be changed. Also, singlephase shadedpole motors have a fixed rotation, and the direction cannot be changed except by disassembly of the motor and reversing the stator to face opposite relative to the original rotor direction.
The power factor of induction motors varies with load, typically from around 0.85 or 0.90 at full load to as low as about 0.20 at noload,^{[39]} due to stator and rotor leakage and magnetizing reactances.^{[43]} Power factor can be improved by connecting capacitors either on an individual motor basis or, by preference, on a common bus covering several motors. For economic and other considerations, power systems are rarely power factor corrected to unity power factor.^{[44]} Power capacitor application with harmonic currents requires power system analysis to avoid harmonic resonance between capacitors and transformer and circuit reactances.^{[45]} Common bus power factor correction is recommended to minimize resonant risk and to simplify power system analysis.^{[45]}
(See also Energy savings) Full load motor efficiency varies from about 85% to 97%, related motor losses being broken down roughly as follows:^{[46]}
Various regulatory authorities in many countries have introduced and implemented legislation to encourage the manufacture and use of higher efficiency electric motors. There is existing and forthcoming legislation regarding the future mandatory use of premiumefficiency inductiontype motors in defined equipment. For more information, see: Premium efficiency.
Many useful motor relationships between time, current, voltage, speed, power factor, and torque can be obtained from analysis of the Steinmetz equivalent circuit (also termed Tequivalent circuit or IEEE recommended equivalent circuit), a mathematical model used to describe how an induction motor's electrical input is transformed into useful mechanical energy output. The equivalent circuit is a singlephase representation of a multiphase induction motor that is valid in steadystate balancedload conditions.
The Steinmetz equivalent circuit is expressed simply in terms of the following components:
Paraphrasing from Alger in Knowlton, an induction motor is simply an electrical transformer the magnetic circuit of which is separated by an air gap between the stator winding and the moving rotor winding.^{[28]} The equivalent circuit can accordingly be shown either with equivalent circuit components of respective windings separated by an ideal transformer or with rotor components referred to the stator side as shown in the following circuit and associated equation and parameter definition tables.^{[39]}^{[44]}^{[47]}^{[48]}^{[49]}^{[50]}
Circuit Parameter Definitions  

Units  
$f_{s}$  stator synchronous frequency  Hz 
$n_{r}$  rotor speed in revolutions per minute  rpm 
$n_{s}$  synchronous speed in revolutions per minute  rpm 
$I_{s}$  stator or primary current  A 
$I_{r}^{'}$  rotor or secondary current referred to stator side  A 
$I_{m}$  magnetizing current  A 
$j={\sqrt {1}}$  imaginary number, or 90° rotation, operator  
$K_{TE}$  $=X_{m}/(X_{s}+X_{m})$ Thévenin reactance factor  
$m$  number of motor phases  
$p$  number of motor poles  
$P_{em}$  electromechanical power  W or hp 
$P_{gap}$  air gap power  W 
$P_{r}$  rotor copper losses  W 
$P_{o}$  input power  W 
$P_{h}$  core loss  W 
$P_{f}$  friction and windage loss  W 
$P_{rl}$  running light watts input  W 
$P_{sl}$  strayload loss  W 
$R_{s},X_{s}$  stator or primary resistance and leakage reactance  Ω 
$R_{r}^{'},X_{r}^{'}$  rotor or secondary resistance & leakage reactance referred to the stator side  Ω 
$R_{o},X_{o}$  resistance & leakage reactance at motor input  Ω 
$R_{TE},X_{TE}$  Thévenin equivalent resistance & leakage reactance combining $R_{s},X_{s}$ and $X_{m}$  Ω 
$s$  slip  
$T_{em}$  electromagnetic torque  Nm or ft.lb. 
$T_{max}$  breakdown torque  Nm or ft.lb. 
$V_{s}$  impressed stator phase voltage  V 
$X_{m}$  magnetizing reactance  Ω 
$X$  $X_{s}+X_{r}^{'}$  Ω 
$Z_{s}$  stator or primary impedance  Ω 
$Z_{r}^{'}$  rotor or secondary impedance referred to the primary  Ω 
$Z_{o}$  impedance at motor stator or primary input  Ω 
$Z$  combined rotor or secondary and magnetizing impedance  Ω 
$Z_{TE}$  Thévenin equivalent circuit impedance, $R_{TE}+X_{TE}$  Ω 
$\omega _{r}$  rotor speed  rad/s 
$\omega _{s}$  synchronous speed  rad/s 
$Y$  $=GjB={\frac {1}{Z}}={\frac {1}{R+jX}}={\frac {R}{Z^{2}}}{\frac {jX}{Z^{2}}}$  mho 
$\left\vert Z\right\vert$  ${\sqrt {R^{2}+X^{2}}}$  Ω 
The following ruleofthumb approximations apply to the circuit:^{[50]}^{[51]}^{[52]}
Basic Electrical Equations  

Motor input equivalent impedance
Stator current
Rotor current referred to the stator side in terms of stator current

Power Equations  

From Steinmetz equivalent circuit, we have
That is, air gap power is equal to electromechanical power output plus rotor copper losses
Expressing electromechanical power output in terms of rotor speed
Expressing $T_{em}$ in ft.lb.:

Torque Equations  

In order to be able to express $T_{em}$ directly in terms of $s$, IEEE recommends that $R_{s},X_{s}$ and $X_{m}$ be converted to the Thévenin equivalent circuit where
Since $R_{s}^{2}\gg {(X_{s}+X_{m})^{2}}$ and $X_{s}\ll {X_{m}}$, and letting $K_{TE}={\frac {X_{m}}{X_{s}+X_{m}}}$
For low values of slip:
For high values of slip
For maximum or breakdown torque, which is independent of rotor resistance
Corresponding slip at maximum or breakdown torque is
In footpound units

Linear induction motors, which work on same general principles as rotary induction motors (frequently threephase), are designed to produce straight line motion. Uses include magnetic levitation, linear propulsion, linear actuators, and liquid metal pumping.^{[55]}
This article uses material from the Wikipedia article "Induction motor", which is released under the Creative Commons AttributionShareAlike License 3.0. There is a list of all authors in Wikipedia
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