Lecture 24 EE743

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Lecture 24 - EE743
3-Phase Induction Machines Torque Speed
characteristics
Professor Ali Keyhani
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Importance of T-speed characteristics

• Torque speed characteristic of a motor is
  important from the point of view of its
  applications to specific situations. To calculate
  the torque produced by the machine, first, we
  compute the motor power. The motor power, or the
  mechanical power supplied to the load isThe
  electrical power inputted to the machine can be
  calculated from the eq. circuit given below

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Importance of T-speed characteristics
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Machine Torque

• Power dissipated is
• Motor power Pem is
• Motor torque can be calculated from

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Machine Torque

• Since Tm can be written as
• Substituting for I1 in equation (3), we will have

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Power calculations

• Figure 2 shows the plot of equation (3) for the
  values of slip from zero to unity. In Fig.1
  . This corresponds to the normal range of the
  speed of an induction motor from starting (?m0,
  s1) to the synchronous speed (?m?sync, s0)

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smax and Tmax calculation

• To find smax first set derivative of (4) with
  respect to s equal to zero.
• Which will results in
• substituting smax in (4) will result in Tmax

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Torque-speed characteristic

• Equation (5) shows that the slip at which the
  maximum torque occurs is proportional to the
  rotor resistance. Equation (6) shows that the
  maximum torque is independent of the rotor
  resistance

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Torque-speed characteristic

• The machine is operating as a motor for the range
  of s for which the torque-speed curves are shown
  in fig.1 and fig.2. In this range, torque is
  positive and ?sync is greater than rotor speed
  ?m. Note that the torque is zero at slip equal
  to zero. As was state before, slip is given by
• Let us consider three different cases

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Torque-speed characteristic

• Case 1 ?sync and ?m are rotating in the same
  direction and ?sync is rotating faster than ?m.
• Case 2 ?sync and ?m are rotating in the same
  direction and ?sync is rotating slower than ?m.
• Case 3 ?sync and ?m are rotating in different
  directions.

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Torque-speed characteristic. Case 1.

• Case 1 ?sync and ?m are rotating in the same
  direction and ?sync is rotating faster than ?m.
• This case is the normal operation of the
  induction machine. Machine operates as a motor.
  Note also in equation (7) ?sync and ?m are in the
  same direction and the slip is positive for motor
  operation

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Torque-speed characteristic. Case 2.

• Case 2 ?sync and ?m are rotating in the same
  direction and ?sync is rotating slower than ?m.
• If the speed of the machine is increased beyond
  its synchronous speed by an external prime motor,
  but still rotated in the same direction as the
  stator field, the slip will be negative (slt0).
  This region (slt0) corresponds to the generator
  operation. For this region, torque is negative.
  This means that the mechanical power is required
  to drive the machine, which in turn delivers
  electric power at the stator terminals

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Torque-speed characteristic. Case 3.

• Case 3 ?sync and ?m are rotating in different
  directions.
• Suppose an induction motor is operating under
  normal conditions at the same value of positive
  slip in stable region (0ltsltsmax). Now we
  interchange any two terminals of the stator. This
  reverses the direction of the stator rotating
  field. The rotor speed ?m may now be considered
  as a negative with respect to that of the stator
  field. For this case, sgt1 and power loss in the
  variable resistance is negative, indicating
  that mechanical energy is being converted to
  electric energy. Both the power fed from stator
  and power fed from rotor are lost as heat in the
  rotor resistance. This region is called the
  braking region

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Example 1

• On no-load a 3-phase delta-connected induction
  motor takes 6.8A and 390W at 220V line to line.
  R10.1?/phase, friction and windage losses are
  120W. Determine Xm,and Rm of the motor equivalent
  circuit.

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Example 1
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Example 2

• The motor of the previous example take 30A and
  480W at 36V line-to-line, when the rotor is
  blocked. Determine the complete equivalent
  circuit of the motor. Assume that X1X2.

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Example 3

• An induction motor has an output of 30kW at
  ?0.86. For this operating condition
  Pcoil,1Pcoil,2PcoreProt.Determine the slip

M
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Example 3
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Example 4

• A wound rotor six-pole 60Hz ind. motor has
  R20.8? and runs at 1152 rpm (s0.04) at a given
  load. The load torque remains constant at all
  speeds. How much resistance must be inserted in
  the rotor circuit to change the speed to 960 rpm
  (s0.2). Neglect the motor leakage reactance, X1
  and X2.The air gap power function is

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Example 4

• If (see eq. circuit ), the voltage,
  current,air-gap power, and torque conditions
  remain the same, i.e

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Example 5

• A 400V, 3-phase WYE connected motor has ,
  and using the approx. eq. circuit. Determine
  the max. electromagnetic power, Pd

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Example 5