INDUCTION MOTOS An induction motor ha the ame phyical tator a a ynchronou machine, with a different rotor contruction. There are two different type of induction motor rotor which can be placed inide the tator. One i called a cage rotor, while the other i called a wound rotor. 1
BASIC INDUCTION MOTO CONCETS Induction motor operation i baically the ame a that of amortieur winding on ynchronou motor. A three-phae et of voltage ha been applied to the tator, and a three-phae et of tator current i flowing. Thee current produce a magnetic field B, which i rotating in a counterclockwie direction. The peed of the magnetic field' rotation i given by n ync 120 f e Where f e i the ytem frequency and i the number of pole. It i the relative motion of the rotor compared to the tator magnetic field that produce induced voltage in a rotor bar. The rotor current flow produce a rotor magnetic field B. Due to induced torque rotor accelerate. There i a finite upper limit to the motor' peed, however. If the induction motor' rotor were turning at ynchronou peed, then the rotor bar would be tationary relative to the magnetic field and there would be no induced voltage. And the rotor would low down a a reult of friction loe. An induction motor can thu peed up to near-ynchronou peed, but it can never exactly reach ynchronou peed. Note that in normal operation both the rotor and tator magnetic field B and B rotate together at ynchronou peed n ync while the rotor itelf turn at a lower peed. 2
The Concept of otor Slip The voltage induced in a rotor bar of an induction motor depend on the peed of the rotor relative to the magnetic field. Two term are commonly ued to define the relative motion of the rotor and the magnetic field. Slip peed: Slip, which i the relative peed expreed on a per-unit or a percentage bai. Thi equation can alo be expreed in term of angular velocity ω 3
It i poible to expre the mechanical peed of the rotor haft in term of ynchronou peed and lip. The Electrical Frequency on the otor An induction motor work by inducing voltage and current in the rotor of the machine, and for that reaon it ha ometime been called a rotating tranformer. Like a tranformer, the primary (tator) induce a voltage in the econdary (rotor), but unlike a tranformer, the econdary frequency i not necearily the ame a the primary frequency. At n m = 0 rpm, the rotor frequency f r = f e, and the lip = 1. At n m = n ync the rotor frequency f r = 0 Hz, and the lip = 0. For any peed in between, the rotor frequency i directly proportional to the difference between the peed of the magnetic field n ync and the peed of the rotor n m. Since the lip peed i defined a n lip 120 f r nlip n fr nync nm nync 120 120 120 120 f r f e ync 4
THE EQUIVALENT CICUIT OF AN INDUCTION MOTO It i poible to derive the equivalent circuit of an induction motor from a knowledge of tranformer and from what we already know about the variation of rotor frequency with peed in induction motor. The otor Circuit Model The larget voltage induced in rotor at = 1 (locked rotor condition) E 0 The mallet voltage induced in rotor at = 0 (locked rotor condition) E 0 The magnitude and frequency of the voltage induced in the rotor at any peed between thee extreme i directly proportional to the lip of the rotor. The magnitude of the induced voltage at any lip will be given by the equation E E 0 With a rotor inductance of L, the rotor reactance i given by 5
where X 0 i the blocked-rotor rotor reactance ( f r f e ). The rotor current flow can be found a Notice from Equation that it i poible to treat all of the rotor effect due to varying rotor peed a being caued by a varying impedance upplied with power from a contant-voltage ource E0. The equivalent rotor impedance from thi point of view i 6
The Final Equivalent Circuit In an ordinary tranformer, the voltage, current, and impedance on the econdary ide of the device can be referred to the primary ide by mean of the turn ratio of the tranformer. Exactly the ame ort of tranformation can be done for the induction motor' rotor circuit. If the effective turn ratio of an induction motor i a eff, then the tranformed rotor voltage become E E a E eff 0 I I a eff Z a jx eff 0 a eff X a X 0 eff 0 7
OWE AND TOQUE IN INDUCTION MOTOS The tator copper loe in the three phae are given by 3I 2 SCL The core loe are given by o the air-gap power can be found a 2 2 3E core 3E Gc c AG in SCL core Look cloely at the equivalent circuit of the rotor. The only element in the equivalent circuit where the air-gap power can be conumed i in the reitor /. Therefore, the air-gap power can alo be given by AG I 2 3 8
The actual reitive loe in the rotor circuit are given by the equation 3 2 I CL After tator copper loe, core loe, and rotor copper loe are ubtracted from the input power to the motor, the remaining power i converted from electrical to mechanical form. Thi power converted, which i ometime called developed mechanical power, i given by conv AG CL 3I 3I 2 1 3I 1 2 1 conv 3I 2 2 Notice that the rotor copper loe are equal to the air-gap power time the lip: CL AG Therefore, the lower the lip of the motor, the lower the rotor loe in the machine. Alo, power converted conv AG CL conv AG AG conv 1 AG 9
Finally, if the friction and windage loe and the tray loe are known, the output power can be found a out conv F& W mic The induced torque T ind in a machine wa defined a the torque generated by the internal electric-to-mechanical power converion. Thi torque differ from the torque actually available at the terminal of the motor by an amount equal to the friction and windage torque in the machine. The induced torque i given by the equation T ind conv m Thi torque i alo called the developed torque of the machine. The induced torque of an induction motor can be expreed in a different form a well T T ind ind 1 AG AG 1 10
Separating the otor Copper Loe and the ower Converted in an Induction Motor' Equivalent Circuit art of the power coming acro the air gap in an induction motor i conumed in the rotor copper loe, and part of it i converted to mechanical power to drive the motor' haft. It i poible to eparate the two ue of the air-gap power and to indicate them eparately on the motor equivalent circuit. AG CL conv 1 I I 2 1 AG 3I 2 AG 3I 1 2 2 AG 3 3 er-phae equivalent circuit with the rotor copper loe and the power converted to mechanical form eparated into ditinct element i 11
The Derivation of the Induction Motor Induced-Torque Equation (Torque Speed Characteritic) It i poible to ue the equivalent circuit of an induction motor and the power flow diagram for the motor to derive a general expreion for induced torque a a function of peed. The induced torque in an induction motor i given by Equation T T ind ind m AG conv The air-gap power i the power croing the gap from the tator circuit to the rotor circuit. And ince the air-gap power i AG I 2 3 If can be determined, then the air-gap power and the induced torque will be known. I Although there are everal way to olve the equivalent circuit for the current, perhap the eaiet one i to determine the Thevenin equivalent of the portion of the circuit to the left of the X' in the figure. 12
Since c X m Below figure how the open terminal ued to find the Thevenin voltage. 13
Z V m TH V Z Z m The magnitude of the Thevenin voltage V TH V X m ( X X ) 2 2 m Figure how the input circuit with the input voltage ource killed. The two impedance are in parallel, and the Thevenin impedance i given by ZZ m ZTH Z Z m ZTH TH jxth 14
The reulting equivalent circuit i hown in Figure From thi circuit, the current I i given by I VTH VTH Z Z / j( X X ) TH TH TH The magnitude of thi current I V TH 2 2 / ( X X ) TH TH The air-gap power AG 3 I 2 2 3 VTH / 2 2 TH / ( TH ) X X 15
The rotor induced torque T ind V 2 AG 3 TH / 2 2 TH / ( XTH X ) 16
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Maximum (pullout) Torque in an Induction Motor Since the induced torque i equal to AG /ω the maximum poible torque occur when the air-gap power i maximum. Since the air-gap power i equal to the power conumed in the reitor, the maximum induced torque will occur when the power conumed by that reitor i maximum. efer to the implified equivalent circuit in Figure / In a ituation where the angle of the load impedance i fixed, the maximum power tranfer theorem tate that maximum power tranfer to the load reitor / will occur when the magnitude of that impedance i equal to the magnitude of the ource impedance. The equivalent ource impedance in the circuit i Z j( X X ) ource TH TH o the maximum power tranfer occur when ( X X ) 2 2 TH TH Solving Equation for lip, we ee that the lip at pullout torque i given by 18
max ( X X ) 2 2 TH TH Notice that the referred rotor reitance appear only in the numerator, o the lip of the rotor at maximum torque i directly proportional to the rotor reitance. The value of the maximum torque can be found by inerting the expreion for the lip at maximum torque into the torque equation T max 3V 2 TH 2 ( X X ) 2 2 TH TH TH 19
DETEMINING CICUIT MODEL AAMETES The No-Load Tet The no-load tet of an induction motor meaure the rotational loe of the motor and provide information about it magnetization current. The tet circuit for thi tet i hown in Figure 20
In thi motor at no- load condition, the input power meaured by the meter mut equal the loe in the motor. The rotor copper loe are negligible becaue the current i extremely mall [becaue of the large 1 load reitance, o they may be neglected. The tator copper loe are given by So the input power I 3I 2 SCL in SCL core F& W tray 21
The current needed to etablih a magnetic field i quite large in an induction motor, becaue of the high reluctance of it air gap, o the reactance X m will be much maller than the reitance in parallel with it and the overall input power factor will be very mall. With the large lagging current, mot of the voltage drop will be acro the inductive component in the circuit. The equivalent input impedance i thu approximately V Z X X eq m I _ nl The DC Tet for Stator eitance To perform the tet, the current in the tator winding i adjuted to the rated value, and the voltage between the terminal i meaured. V 2I DC DC 22
The Locked-otor Tet Thi tet correpond to the hort-circuit tet on a tranformer. In thi tet, the rotor i locked or blocked o that it cannot move, a voltage i applied to the motor, and the reulting voltage, current, and power are meaured. Since and X are o mall, almot all the input current will flow through them, intead of through the much larger magnetizing reactance X M. 23
Therefore, the circuit under thee condition look like a erie combination of, X, X,. After a tet voltage and frequency have been et up, the current flow in the motor i quickly adjuted to about the rated value, and the input power, voltage, and current are meaured before the rotor can heat up too much. The locked-rotor power factor F co in 3VI L L The magnitude of the total impedance in the motor circuit at thi time i Z L V I V L 3I L The impedance Z L L L Z L jx co jz L in L Since the reactance i directly proportional to the frequency, the total equivalent reactance at the normal operating frequency can be found a f X X X X rated L L ftet 24