where f {\displaystyle f} is the frequency of the power supply, p {\displaystyle p} is the number of magnetic poles, and f s {\displaystyle f_{s}} is the synchronous speed of the machine. For f {\displaystyle f} in hertz and n s {\displaystyle n_{s}} synchronous speed in RPM, the formula becomes: The first commutator-free single-phase AC induction motor was invented by Hungarian engineer Ottó Bláthy; he used the single-phase motor to propel his invention, the electricity meter. [9] [10] Polyphase motors have rotor bars shaped to give different speed-torque 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 speed-torque characteristics as well as some control over the inrush current at startup. O u t p u t M e c h a n i c a l P o w e r ÷ I n p u t E l e c t r i c a l P o w e r {\displaystyle \eta =OutputMechanicalPower\div InputElectricalPower}

The typical speed-torque 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]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. The generating mode for induction motors is complicated by the need to excite the rotor, which begins with only residual magnetization. In some cases, that residual magnetization is enough to self-excite the motor under load. Therefore, it is necessary to either snap the motor and connect it momentarily to a live grid or to add capacitors charged initially by residual magnetism and providing the required reactive power during operation. Similar is the operation of the induction motor in parallel with a synchronous motor serving as a power factor compensator. A feature in the generator mode in parallel to the grid is that the rotor speed is higher than in the driving mode. Then active energy is being given to the grid. [2] Another disadvantage of the induction motor generator is that it consumes a significant magnetizing current I 0 = (20–35)%. 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 {\displaystyle R_{r}'/s} , dominates torque in a 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 {\displaystyle 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 small induction motors: split-phase single-phase, shaded-pole single-phase, and polyphase. The General Electric Company (GE) began developing three-phase induction motors in 1891. [12] By 1896, General Electric and Westinghouse signed a cross-licensing agreement for the bar-winding-rotor design, later called the squirrel-cage 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 improved the application of AC complex quantities and developed an analytical model called the induction motor Steinmetz equivalent circuit. [12] [25] [26] [27] For example, for a four-pole, three-phase motor, p {\displaystyle p} = 4 and n s = 120 f 4 {\displaystyle n_{s}={120f \over 4}} = 1,500RPM (for f {\displaystyle f} = 50Hz) and 1,800RPM (for f {\displaystyle f} = 60Hz) synchronous speed. History [ edit ] A model of Nikola Tesla's first induction motor at the Tesla Museum in Belgrade, Serbia Squirrel-cage rotor construction, showing only the center three laminations

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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. An AC motor's synchronous speed, f s {\displaystyle f_{s}} , is the rotation rate of the stator's magnetic field, Breakdown torque T max {\displaystyle T_{\text{max}}} happens when s ≈ R r ′ / X {\displaystyle s\approx R_{\text{r}}'/X} and I s ≈ 0.7 L R C {\displaystyle I_{\text{s}}\approx 0.7\;LRC} such that T max ≈ K V s 2 / 2 X {\displaystyle T_{\text{max}}\approx KV_{\text{s}}

An induction motor or asynchronous motor is an AC electric motor in which the electric current in the rotor that produces torque is obtained by electromagnetic induction from the magnetic field of the stator winding. [1] An induction motor therefore needs no electrical connections to the rotor. [a] An induction motor's rotor can be either wound type or squirrel-cage type. In a single-phase split-phase motor, reversal is achieved by reversing the connections of the starting winding. Some motors bring out the start winding connections to allow selection of rotation direction at installation. If the start winding is permanently connected within the motor, it is impractical to reverse the sense of rotation. Single-phase shaded-pole motors have a fixed rotation unless a second set of shading windings is provided. 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] [6] [7] [8] In wound rotor motors, rotor circuit connection through slip rings to external resistances allows change of speed-torque characteristics for acceleration control and speed control purposes.The two figures at right and left above each illustrate a 2-pole 3-phase machine consisting of three pole-pairs with each pole set 60° apart. The number of magnetic poles, p {\displaystyle p} , is equal to the number of coil groups per phase. To determine the number of coil groups per phase in a 3-phase motor, count the number of coils, divide by the number of phases, which is 3. The coils may span several slots in the stator core, making it tedious to count them. For a 3-phase motor, if you count a total of 12 coil groups, it has 4 magnetic poles. For a 12-pole 3-phase machine, there will be 36 coils. The number of magnetic poles in the rotor is equal to the number of magnetic poles in the stator. Regulatory authorities in many countries have implemented legislation to encourage the manufacture and use of higher efficiency electric motors. Some legislation mandates the future use of premium-efficiency induction motors in certain equipment. For more information, see: Premium efficiency. Steinmetz equivalent circuit [ edit ] 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. At a given power rating, lower speed requires a larger frame. [44] Rotation reversal [ edit ]

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 T-equivalent 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 single-phase representation of a multiphase induction motor that is valid in steady-state balanced-load conditions. Slip, s {\displaystyle 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 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 {\displaystyle 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] Induction motor improvements flowing from these inventions and innovations were such that a modern 100- horsepower induction motor has the same mounting dimensions as a 7.5-horsepower motor in 1897. [12] Principle [ edit ] 3-phase motor [ edit ] A three-phase power supply provides a rotating magnetic field in an induction motor. Inherent slip – unequal rotation frequency of stator field and the rotor 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 rotor, in effect the motor's secondary winding. [28] The rotating magnetic flux induces currents in the rotor windings, [29] in a manner similar to currents induced in a transformer's secondary winding(s).

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Speed control [ edit ] Resistance [ edit ] Typical speed-torque curves for different motor input frequencies as for example used with variable-frequency drives For an electric motor, the efficiency, represented by the Greek letter Eta, [49] is defined as the quotient of the mechanical output power and the electric input power, [50] calculated using this formula: n s = 2 f p ⋅ ( 60 s e c o n d s m i n u t e ) = 120 f p ⋅ ( s e c o n d s m i n u t e ) {\displaystyle n_{s}={2f \over p}\cdot \left({\frac {60\ \mathrm {seconds} }{\mathrm {minute} }}\right)={120f \over {p}}\cdot \left({\frac {\mathrm {seconds} }{\mathrm {minute} }}\right)} . [32] [33] See also: Fleming's left-hand rule for motors Standard torque [ edit ] Speed-torque curves for four induction motor types: A) Single-phase, B) Polyphase cage, C) Polyphase cage deep bar, D) Polyphase double cage Typical speed-torque curve for NEMA Design B Motor Transient solution for an AC induction motor from a complete stop to its operating point under a varying load