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}} Larger single phase motors are split-phase motors and have a second stator winding fed with out-of-phase 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 capacitor-start 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 capacitor-run 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. An AC motor's synchronous speed, f s {\displaystyle f_{s}} , is the rotation rate of the stator's magnetic field, 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.

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] [46] [51] [52] [53] [54] Steinmetz equivalent circuit 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)%. 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 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] 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

The first AC commutator-free polyphase 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 four-stator-pole motor types: one having a four-pole rotor forming a non-self-starting reluctance motor, another with a wound rotor forming a self-starting induction motor, and the third a true synchronous motor with a separately excited DC supply to the rotor winding. 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] 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 ]Self-starting polyphase induction motors produce torque even at standstill. Available squirrel-cage induction motor starting methods include direct-on-line starting, reduced-voltage reactor or auto-transformer starting, star-delta starting or, increasingly, new solid-state soft assemblies and, of course, variable frequency drives (VFDs). [39] 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: 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).

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] In two-pole single-phase motors, the torque goes to zero at 100% slip (zero speed), so these require alterations to the stator such as shaded-poles 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 single-phase motor can cause the rotor to turn in either direction, so the starting circuit determines the operating direction. 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 ]

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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. 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] 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] 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: Although polyphase motors are inherently self-starting, their starting and pull-up torque design limits must be high enough to overcome actual load conditions.

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.The power factor of induction motors varies with load, typically from about 0.85 or 0.90 at full load to as low as about 0.20 at no-load, [39] due to stator and rotor leakage and magnetizing reactances. [45] 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. [46] 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.