Mechatronic systems – El. machines – AC induction motors
INDUCTION (ASYNCHRONOUS) MOTORS
The induction motor is considered to be the workhorse of industry. It is an AC motor, either
three phase or (for low powers) single phase. Industrial (conventional) induction motors are
supplied from constant voltage and frequency industrial power grids for rather constant speed
operation. For variable speed drives induction motors are fed from converter at variable
voltage amplitude and frequency.
Induction motor consists of a stator (the fixed part) and a rotor (the moving part) mounted on
mechanical bearings and separated from the stator by an airgap.
Fig. 1. Design of AC induction machine
a2)
Fig. 2. Induction motor rotors
a) cage - type rotor b) wound (slip-ring) rotor
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Mechatronic systems – El. machines – AC induction motors
Fig. 3. Modern induction motor with surface cooling
Fig. 4. Cut of 3-ph. induction motor
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Mechatronic systems – El. machines – AC induction motors
MECHANICAL CHARACTERISTIC of AC INDUCTION MOTOR
Synchronous (no load) motor speed = speed of the rotating magnetic field n0 = ns.
With increasing of the load the induction motor speed is smaller.
Proportional rotor speed n decreasing relative to the speed of the rotating magnetic field n0 is
called slip
s = (n0 - n) / n0
and is usually given in percentage
s = (n0 - n) / n0 100
[%]
Nominal slip is in the range from 1 to 10%, average of about 5%. Small motors have a more
slip than large motors.
The normal course of mechanical characteristics of squirrel cage IM is shown in Fig. 5.
The motor area is in the range s = (0-1) corresponding to the speed range n = (0 to n0).
Nominal torque Mn is corresponding nominal (rated) speed sn.
Important is maximum torque Mmax.
Fig. 5. Mechanical characteristic of induction motor
Wound motors can increase slip by connection of external resistor to slip rings of the rotor
and thus move the mechanical characteristics according to Fig. 6.
Fig. 6. Mechanical characteristic of wound induction motor for different external rotor resistors
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Mechatronic systems – El. machines – AC induction motors
For practical use mechanical characteristic can be calculated using known simplified Klos
equation:
M=
2 M max
s sk
+
sk s
where slip s =
n0 − n
n0
 f 
60 f1
= n0 n  1 
p
 f1n 
where f1 is supply frequency and p number of pole pairs
and synchronous (no load) speed
n0 =
Max torque
M max =
(
3U 12
2ω0 R1 ± R12 + X K2
)
3U 12
≅±
2ω0 X K
and corresponding slip
smax = sk = ±
R2´
R12 + X K2
≅±
R2´
XK
The significance of parameters Mmax and sk you can see in fig. 5 and 7, and they can be
calculated from the nominal values.
For practical calculations we use the following relationship applies to the nominal supply
voltage and frequency:
Maximal torque M max n = M n ⋅ qM
2
Slip can be calculated from Klos equation: skn = sn  qM + qM − 1 


where
n −n
nominal slip sn = 0 n n
n0 n
torque overload qM = M max n /M n is known from motor catalog
Maximal torque and slip for general value of voltage and frequency can be calculated:
M max
U 
= M max n ⋅  1 
 U1n 
2
f 
⋅  1n 
 f1 
2
f 
sk = skn ⋅  1n 
 f1 
The equation shows that the torque of induction motor is proportional to the square of the
voltage, so that the induction motor is sensitive to supply voltage fluctuations.
The motor area is in the range s = (0-1) corresponding to the speed range n = (0 to n0).
The generator braking area is in the range s < 0 corresponding to the speed range n > n0.
The counter-current braking area is in the range s > 1 corresponding to the speed range n < 0.
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Mechatronic systems – El. machines – AC induction motors
Fig. 7. Mechanical characteristic of IM
Fig. 8. Stator and rotor currents I1, I2 = f(s)
Frequency control of induction motors
From the equation of mechanical characteristic (Klos) we can see the possibilities of
induction motor speed control.
The best way is by changing supply frequency = changing the synchronous speed, thus
getting shifted network characteristics versus speed. This option is the most ideal, because the
connection with the smallest losses. Recently, this method we use with available transistor
frequency converters.
Induced voltage depends on frequency and magnetic flux.
Ui1 = 4.44 N1 Φm. f = const. Φm. f
To maintain a constant magnetic flux, frequency and voltage have to be controlled together.
Frequency and voltage control
M max
U 
= M max n ⋅  1 
 U1n 
2
2
Φ 
f 
⋅  1n  = M max n ⋅  m 
 f1 
 Φn 
2
The above equation shows that the torque of an asynchronous motor is proportional to the
square of the voltage, so that the induction motor is sensitive to voltage fluctuations – see fig.
9.
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Mechatronic systems – El. machines – AC induction motors
Fig. 9. Mechanical characteristics of IM with the voltage changes
At a constant torque on the shaft M = const. it is necessary to maintain a constant magnetic
flux Φm, leading to the control voltage U and the frequency f together, for U / f = const.
At nominal frequency frequency ratio ν = f1 / f1n = 1, at the equivalent circuit in fig. 10, the
magnetizing reactance Xµ» |R1 + jX1σ | and also | j Xµ Iµ | > |R1 + jX1σ | I1, so voltage drop
across the stator winding can be neglected.
For substantially reducing the frequency f (ν < 0,1) νXµ. is decreas and starts to apply the
voltage drop across the stator resistance R1. The ratio R1/(2π f1 Lµ) will increase, so it is
necessary to control the stator voltage according to the relationship:
U1
f
= 1 .K f = ν .K f
U1n
f1n
where correction factor
Kf =
λ=
f1n
+ j (X µ + X 1σ )
f1
=
R1 + j ( X µ + X 1σ )
R1
λ2 +
1
ν2
λ +1
2
X µ + X 1σ
R1
Fig. 10. Equivalent circuit of IM
Fig. 11. Dependence Kf = f (ν) at frequency control
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Mechatronic systems – El. machines – AC induction motors
The dependence of the correction factor Kf on the frequency ratio ν = f1 / f1n for various λ is
plotted in fig. 11. In the equivalent circuit of the induction motor is therefore in frequency
control all reactance multiplied ν.
Mechanical characteristics are depicted in Fig. 12.a) assuming that the voltage is controlled by
the above formula
U1
f
= 1 .K f = ν .K f
U1n
f1n
In the case of regulating the voltage U1, proportional to the frequency f1 for low speed, the
dashed lines in mechanical characteristics are true.
When regulating speeds above base speed (ν>1), it would lead to a size greater than the
nominal voltage, therefore it is used the field weakening (decreasing of the magnetic flux)
similarly to the DC motor.
This weakening does not affect the no load speed (as in DC motor) but only on the course of
the torque.
At weakening it is maintained a constant nominal voltage U1= U1n. In this case, the motor
torque decreases according to the equation M=Mn/ν2. This control over both ranges
correspond to the mechanical characteristics shown in Fig. 12.b).
a) courses without weakening
b) courses with weakening
Fig. 12. Mechanical characteristics of IM with frequency control
In practice, courses without field weakening (fig. 12 a) for high speeds are not used. We use
field weakening acording to fig. 12 b).
ω0 in fig. 12 is no load speed at nominal frequency.
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