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ENERGY CONVERSION ONE
(Course 25741)
CHAPTER SEVEN
INDUCTION MOTORS … (Induced Torque…)
…INDUCTION MOTOR INDUCEDTORQUE EQUATION
ZTH=RTH+jXTH = jXM(R1+jX1)/[R1+j(X1+XM)]
• Since XM>>X1 and XM+X1>>R1 , Thevenin
resistance & reactance can be approximated as:
RTH ≈ R1 ( XM/ [X1+XM] ) ^2
XTH ≈ X1
• resulting equivalent circuit:
…INDUCTION MOTOR INDUCEDTORQUE EQUATION
• The current I2 obtained as follows:
I2= VTH / (ZTH + Z2)=VTH/[RTH +R2/s + j XTH +j X2]
• Magnitude of current:
I2= VTH /√(RTH+R2/s)^2+(XTH+X2)^2
• Air gap power
PAG = 3 I2^2 R2/s=
3 VTH^2 R2/s / [(RTH+R2/s)^2+(XTH+X2)^2]
and rotor induced torque is:
Tind=PAG/ ωsync
Tind=3VTH^2 R2/s / {ωsync [(RTH+R2/s)^2+(XTH+X2)^2]}
a plot of torque as function of speed (& slip) shown in
next figure:
…INDUCTION MOTOR INDUCEDTORQUE EQUATION
• A typical induction motor torque-speed
characteristic curve
…INDUCTION MOTOR INDUCEDTORQUE EQUATION
• A plot of speed above & below normal range
shown below:
INDUCTION MOTOR
TORQUE-SPEED CURVE
• Torque-speed characteristics curve provides several important
information
1- induced torque of motor is zero at syn. Speed
2- torque-speed curve is nearly linear between no load and full
load. In this range rotor resistance is much larger than its
reactance so rotor current, rotor magnetic field & induced
torque increase linearly with increasing slip
3- there is a maximum possible torque that cannot be exceeded
(pullout torque) is 2 to 3 times rated full-load torque of motor
(calculated in next section)
4-starting torque on motor is slightly larger than its full-load torque,
so this motor will start carrying any load that it can supply at full
power
5- Note: that torque on motor for a given slip varies as square of
applied voltage. This is useful in one form of induction motor
speed control that will be described
INDUCTION MOTOR
TORQUE-SPEED CURVE
6- if rotor of induction motor driven faster than sync.
Speed, direction of Tind reverses & machine become
Gen. converting Pmech to Pelec
(discussed later)
7- if motor turning backward relative to direction of
magnetic fields, induced torque will stop machine very
rapidly & will try to rotate it in other direction
since reversing direction of magnetic field rotation is
simply a matter of switching any two stator phases,
this fact can be used as a way to very rapidly stop an
induction motor
act of switching two phases in order to stop motor
very rapidly is called plugging
INDUCTION MOTOR
TORQUE-SPEED CURVE
• Power converted to mechanical in an induction
motor:
Pconv=Tindωm
• Note: peak power supplied by induction motor
occurs at a different speed than maximum
torque; and of course no power is converted to
mechanical form when rotor is at zero speed
INDUCTION MOTOR
TORQUE-SPEED CURVE
• Induced Torque & Power Converted versus
motor Speed in r/min (4 pole induction motor)
INDUCTION MOTOR
TORQUE-SPEED CURVE
• Maximum (Pullout) Torque in induction motor
• Tind=PAG/ωsync maximum possible torque occurs when
air gap power is maximum
• Since air-gap power = power consumed in R2/s
maximum induced torque will occur when power
consumed by this resistor is maximum
• If angle of load impedance is fixed, maximum power
transfer theorem states :
maximum power transfer occur when magnitude of
that impedance = source impedance magnitude
• Equivalent source impedance:
Zsource=RTH+jXTH+jX2
• So maximum power transfer occurs when:
R2/s=√RTH^2 + (XTH+X2)^2