Monday, 2 March 2015


Induction motor                                                                                                                                                                        An induction 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. An induction motor therefore does not requiremechanical commutation, separate-excitation or self-excitation for all or part of the energy transferred from stator to rotor, as inuniversal, DC and large synchronous motors. An induction motor's rotor can be either wound type or squirrel-cage type.

Three-phase squirrel-cage induction motors are widely used in industrial drives because they are rugged, reliable and economical. Single-phase induction motors are used extensively for smaller loads, such as household appliances like fans. Although traditionally used in fixed-speed service, induction motors are increasingly being used with variable-frequency drives (VFDs) in variable-speed service. VFDs offer especially important energy savings opportunities for existing and prospective induction motors in variable-torquecentrifugal fan, pump and compressor load applications. Squirrel cage induction motors are very widely used in both fixed-speed and VFD applications.                                                                                                                                                                                                                   

History[edit]


A model of Tesla's first induction motor, in Tesla Museum, Belgrade.
Early squirrel cage rotor
In 1824, the French physicist François Arago formulated the existence of rotating magnetic fields, termed Arago's rotations, which, by manually turning switches on and off, Walter Baily demonstrated in 1879 as in effect the first primitive induction motor.[1][2][3][4] Practical alternating current induction motors seem to have been 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 U.S. 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.[4][5] 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)[6][7][8][9][10] describing three four-stator-pole motor types: one with 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 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.[11] 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.[6][12][13][14] Steadfast in his promotion of three-phase development, Mikhail Dolivo-Dobrovolsky's invented the cage-rotor induction motor in 1889 and the three-limb transformer in 1890.[15][16] However, he claimed that Tesla's motor was not practical because of two-phase pulsations, which prompted him to persist in his three-phase work.[17] 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 two-phase motors with wound rotors until B. G. Lamme developed a rotating bar winding rotor.[6] The General Electric Company (GE) began developing three-phase induction motors in 1891.[6] By 1896, General Electric and Westinghouse signed a cross-licensing agreement for the bar-winding-rotor design, later called the squirrel-cage rotor.[6] Arthur E. Kennelly was the first to bring out full significance of the letter "i" (the square root of minus one) to designate the 90-degree rotation operator in complex number analysis of AC problems.[18] GE'sCharles Proteus Steinmetz greatly developed application of AC complex quantities including in terms now commonly known as the induction motor's Steinmetz equivalent circuit.[6][19][20][21] Induction motor improvements flowing from these inventions and innovations were such that a 100 horsepower induction motor currently has the same mounting dimensions as a 7.5 horsepower motor in 1897.[6]

Principles of operation[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 amagnetic field that rotates in time 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 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 short-circuited or closed through an external impedance.[22]The rotating magnetic flux induces currents in the windings of the rotor;[23] in a manner similar to currents induced in a transformer's secondary winding(s). The 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 rotor-winding 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 load. Since rotation at synchronous speed would result in no induced rotor current, an induction motor always operates 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.[24] The induction machine's essential character is that it is created solely by induction instead of being separately excited as in synchronous or DC machines or being self-magnetized as in permanent magnet motors.[22]
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.[25] An induction motor can be used as an induction generator, or it can be unrolled to form a linear induction motorwhich can directly generate linear motion.

Synchronous speed[edit]

An AC motor's synchronous speed, n_s, is the rotation rate of the stator's magnetic field, which is expressed in revolutions per minute as
n_s={120\times{f}\over{p}} (RPM),
where f is the motor supply's frequency in hertz and p is the number of magnetic poles.[26][27] That is, for a six-pole three-phase motor with three pole-pairs set 120° apart, pequals 6 and n_s equals 1,000 RPM and 1,200 RPM respectively for 50 Hz and 60 Hz supply systems.

Slip[edit]

Typical torque curve as a function of slip, represented as 'g' here.
Slip, s, is defined as the difference between synchronous speed and operating speed, at the same frequency, expressed in rpm or in percent or ratio of synchronous speed. Thus
s = \frac{n_s-n_r}{n_s}\,
where n_s is stator electrical speed, n_r is rotor mechanical speed.[9][28] Slip, which varies from zero at synchronous speed and 1 when the rotor is at rest, determines the motor's torque. Since the short-circuited rotor windings have small resistance, a small slip induces a large current in the rotor and produces large torque.[29] At full rated load, slip varies from more than 5% for small or special purpose motors to less than 1% for large motors.[30] These speed variations can cause load-sharing problems when differently sized motors are mechanically connected.[30] Various methods are available to reduce slip, VFDs often offering the best solution.[30]

Torque[edit]

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
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:[24][a]
  • Breakdown torque, 175-300 percent of rated torque
  • Locked-rotor torque, 75-275 percent of rated torque
  • Pull-up torque, 65-190 percent of rated torque.
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.[31] 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 torque increases beyond breakdown torque the motor stalls. Although polyphase motors are inherently self-starting, their starting and pull-up torque design limits must be high enough to overcome actual load conditions. 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.

Starting[edit]

See also: Motor controller
There are three basic types of competing small induction motors: single-phase split-phase and shaded-pole types, and small polyphase induction motors.
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.
In certain smaller single-phase 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 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.
Self-starting polyphase induction motors produce torque even at standstill. Available 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, VFDs.[32]
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.
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.

Speed control[edit]

Typical speed-torque curves for different motor input frequencies as for example used with variable-frequency drives.
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.[33] 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 variable-speed applications, DC and WRIM drives are being displaced by VFD-fed 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 30-40% of all newly installed motors.[34]

Construction[edit]

Typical winding pattern for a three-phase (U, V, W), four-pole motor. Note the interleaving of the pole windings and the resulting quadrupole field.
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, the 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 single-phase or three-phase power, but two-phase motors exist; in theory, induction motors can have any number of phases. Many single-phase motors having two windings can be viewed as two-phase motors, since a capacitor is used to generate a second power phase 90° from the single-phase supply and feeds it to the second motor winding. Single-phase motors require some mechanism to produce a rotating field on startup. Cage induction motor rotor's conductor bars are typically skewed to reduce noise.

Rotation reversal[edit]

The method of changing the direction of rotation of an induction motor depends on whether it is a three-phase or single-phase machine. In the case of three phase, reversal is carried out by swapping connection of any two phase conductors. In the case of a single-phase motor it is usually achieved by changing the connection of a starting capacitor from one section of a motor winding to the other. In this latter case both motor windings are similar (e.g. in washing machines).

Power factor[edit]

The power factor of induction motors varies with load, typically from around 0.85 or 0.90 at full load to as low as 0.35 at no-load,[32] due to stator and rotor leakage and magnetizing reactances.[35] 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.[36] Power capacitor application with harmonic currents requires power system analysis to avoid harmonic resonance between capacitors and transformer and circuit reactances.[37] Common bus power factor correction is recommended to minimize resonant risk and to simplify power system analysis.[37]

Efficiency[edit]

(See also Energy savings)
Full load motor efficiency varies from about 85 % to 97 %, related motor losses being broken down roughly as follows:[38]
  • Friction and windage, 5 % – 15 %
  • Iron or core losses, 15 % – 25 %
  • Stator losses, 25 % – 40 %
  • Rotor losses, 15 % – 25 %
  • Stray load losses, 10 % – 20 %.
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 premium-efficiency induction-type motors in defined equipment. For more information, see: Premium efficiency and Copper in energy efficient motors.

Saturday, 8 November 2014

Variation in Inductive Reactance and Capacitive Reactance with Frequency

Variation of Inductive Reactance Vs Frequency

Variation of Inductive Reactance Vs Frequency
Variation of Inductive Reactance Vs Frequency

We know that inductive reactance XL= 2πfL means inductive reactance is directly proportional to frequency ( XL&prop ƒ ). When the frequency is zero or in case of DC, inductive reactance is also zero, the circuit acts as a short circuit; but when frequency increases; inductive reactance also increases. At infinite frequency, inductive reactance becomes infinity and circuit behaves as open circuit. It means that, when frequency increases inductive reactance also increases and when frequency decreases, inductive reactance also decreases. So if we plot a graph between inductive reactance and frequency, it is a straight line linear curve passing through origin as shown in the figure above.

Variation of Capacitive Reactance Vs Frequency

Variation of Capacitive Reactance Vs Frequency
Variation of Capacitive Reactance Vs Frequency

It is clear from the formula of capacitive reactance XC = 1 / 2πfC that, frequency and capacitive reactance are inversely proportional to each other. In case of DC or when frequency is zero, capacitive reactance becomes infinity and circuit behaves as open circuit and when frequency increases and becomes infinite, capacitive reactance decreases and becomes zero at infinite frequency, at that point the circuit acts as short circuit, so the capacitive reactance increases with decease in frequency and if we plot a graph between capacitive reactance and frequency, it is an hyperbolic curve as shown in figure above.

Inductive Reactance and Capacitive Reactance Vs Frequency

Inductive Reactance and Capacitive Reactance Vs Frequency
Inductive Reactance and Capacitive Reactance Vs Frequency

From the above discussion, it can be concluded that the inductive reactance is directly proportional to frequency and capacitive reactance is inversely proportional to frequency, i.e at low frequency XL is low and XC is high but there must be a frequency, where the value of inductive reactance becomes equal to capacitive reactance. Now if we plot a single graph of inductive reactance vs frequency and capacitive reactance vs frequency, then there must occur a point where these two graphs cut each other. At that point of intersection, the inductive and capacitive reactance becomes equal and the frequency at which these two reactances become equal, is called resonant frequency, fr.
At resonant frequency, XL = XL

At resonance f = fr and on solving above equation we get,

Variation of Impedance Vs Frequency

Variation of Impedance Vs Frequency
Variation of Impedance Vs Frequency

At resonance in series RLC circuit, two reactances become equal and cancel each other. So in resonant series RLC circuit, the opposition to the flow ofcurrent is due toresistance only. At resonance, the total impedance of series RLC circuit is equal toresistance i.e Z = R, impedance has only real part but no imaginary part and this impedance at resonant frequency is called dynamic impedance and this dynamic impedance is always less than impedance of series RLC circuit. Before series resonance i.e before frequency, fr capacitive reactance dominates and after resonance, inductive reactance dominates and at resonance the circuit acts purely as resistive circuit causing a large amount of current to circulate through the circuit.

Resonant Current

Resonant Current
Resonant Current

In series RLC circuit, the total voltage is the phasor sum of voltage across resistorinductorand capacitor. At resonance in series RLC circuit, both inductive and capacitive reactance cancel each other and we know that in series circuit, the current flowing through all the elements is same, So the voltage across inductor and capacitor is equal in magnitude and opposite in direction and thereby they cancel each other. So, in a series resonant circuit,voltage across resistor is equal to supply voltage i.e V = Vr.
In series RLC circuit current, I = V / Z but at resonance current I = V / R , therefore the currentat resonant frequency is maximum as at resonance in impedance of circuit is resistance only and is minimum.
The above graph shows the plot between circuit current and frequency. At starting, when the frequency increases, the impedance Zc decreases and hence the circuit currentincreases. After some time frequency becomes equal to resonant frequency, at that point inductive reactance becomes equal to capacitive reactance and the impedance of circuit reduces and is equal to circuit resistance only. So at this point, the circuit current becomes maximum I = V / R. Now when the frequency is further increased, ZL increases and with increase in ZL, the circuit current reduces and then the current drops finally to zero as frequency becomes infinite.

Power Factor at Resonance

Power Factor at Resonance
Power Factor at Resonance

At resonance, the inductive reactance is equal to capacitive reactance and hence the voltageacross inductor and capacitor cancel each other. The total impedance of circuit is resistanceonly. So, the circuit behaves like a pure resistive circuit and we know that in pure resistive circuit, voltage and the circuit current are in same phase i.e Vr , V and I are in same phase direction. Therefore, the phase angle between voltage and current is zero and the power factor is unity.

Application of Series RLC Resonant Circuit

Since resonance in series RLC circuit occurs at particular frequency, so it is used for filtering and tuning purpose as it does not allow unwanted oscillations that would otherwise cause signal distortion, noise and damage to circuit to pass through it.
Summary
For a series RLC circuit at certain frequency called resonant frequency, the following points must be remembered. So at resonance:
  1. Inductive reactance XL is equal to capacitive reactance XC.
  2. Total impedance of circuit becomes minimum which is equal to R i.e Z = R.
  3. Circuit current becomes maximum as impedance reduces, I = V / R.
  4. Voltage across inductor and capacitor cancels each other, so voltage across resistor Vr = V, supply voltage.
  5. Since net reactance is zero, circuit becomes purely resistive circuit and hence thevoltage and the current are in same phase, so the phase angle between them is zero.
  6. Power factor is unity.
  7. Frequency at which resonance in series RLC circuit occurs is given by