ENERGY CONVERSION ONE (Course 25741)

CHAPTER SEVEN INDUCTION MOTORS … (Induced Torque…)

…INDUCTION MOTOR INDUCED-TORQUE 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 INDUCED-TORQUE 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 INDUCED-TORQUE EQUATION

• A typical induction motor torque-speed characteristic curve

…INDUCTION MOTOR INDUCED-TORQUE EQUATION

• A plot of speed above & below normal range shown below:

INDUCTION MOTORTORQUE-SPEED CURVE

• Torque-speed characteristics curve provides several important information

1- induced torque of motor is zero at syn. Speed2- 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 MOTORTORQUE-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 MOTORTORQUE-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 MOTORTORQUE-SPEED CURVE

• Induced Torque & Power Converted versus motor Speed in r/min (4 pole induction motor)

INDUCTION MOTORTORQUE-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