Induction machines

Question 1

What is the difference between T_d and T_out and what are their Eqns.?

Answer 1

• T_d is the internal torque generated by the internal electrical to mechanical power conversion
• T_d = p_d/w_m=(1-S)P_g/(1-S)w_sync=P_AG/w_sync
• T_out is the torque at the terminals of the motor including the friction losses
• T_out= p_out/w_m

Question 2

What are all the rules for T_d?

Answer 2

• T_d=P_AG/W_sync=3I₂²*R’₂/S/W_sync

Question 3

Draw the graph of the torque speed charactristics and label it?

Answer 3

Question 4

Describe the torque speed charactristics curve and explain what we can understand from it?

Answer 4

• The torque at synchronous speed is zero (N_S)
• There is a torque called pullout torque that is the maximum torque that can’t be exceeded and is 2 to 3 times higher than thefull load torque
• There is a linear region where the resistance is much greater than the reactance so the torque increases linearly with the slip
• The starting torque is higher than the full load torque
• If the rotor is driven faster than synchronous speed it will run as a generator

Question 5

What are the conditions for the motor operation of the induction machine?

Answer 5

• 0
• P_AG=+ve
• P_d=+ve

Question 6

What are the conditions for the generator operation of the induction machine?

Answer 6

• An external prime mover is used to rotate the rotor at speed higher than synchronous speed
• S<0
• P_AG=-ve
• P_d=-ve

Question 7

What are the conditions for the brake operation of the induction machines?

Answer 7

• Used to stop moving shafts by switching the two phases of the stator to switch the direction of tha magnetic field.
• 1
• P_AG=+ve
• P_d=-ve

Question 8

What is the Eqn of the slip at maximum torque?

Answer 8

Question 9

What is the Eqn of the maximum torque?

Answer 9

Or we can use the eqn of the starting torque and substitute S by S_max

Question 10

How is the line voltage speed control method achieved and what are its properties?

Answer 10

• Can be done by using an autotransformer which is expensive
• Or by adding a resistance to the stator winding which would decrease the effeciancy
• Adding a reactance to the stator winding which would decrease the PF
• Decreasing the Supply voltage decreases the maximum torque
• Only used for speeds less than the base speed
• Provides limited range of speed control
• Only used for small driving fans

Question 11

What are the properties of the Rotor resistance speed control?

Answer 11

• Achieved by adding a resistance to the rotor circuit
• Only used for speeds lower than base speed
• Can only be used with wound rotor machines
• Decreases effeciancy and increases losses
• Wide range of speed control
• Increasing R_a decreases n_m
• Maximum torque is kept constant
• Cheap

Question 12

What are the properties of supply frequency speed control method?

Answer 12

• Changing supply frequency changes the synchronous speed so the curve can be shifted to right or left
• As the frequency increases n_m increases
• Motor speed can be controlled from 5% to 200% the base speed
• Wide range of speed control
• Can be used with squirel cage and slip ring machines
• expensive
• complicated

Question 13

What is the Eqn of T_start and at which conditions?

Answer 13

At S=1

Question 14

What are the general properties of the induction machines?

Answer 14

• Mostly used as generators
• called induction because the volt is induced in the rotor winding rather than being connected by a wire
• Doesn’t need Dc field current to operate the machine
• Generators only used for the wind turbine

Question 15

What are the advantetges of the induction machine that makes it widely used?

Answer 15

• Easy to be maintained
• Self exciting
• Rugged device
• Cheaper than synchronous machines
• Singly excited as power is only supplied to stator
• Wide range of power

Question 16

Describe the construction of the slip ring rotor?

Answer 16

• Has 3 phase windings similiar to stator
• The rotor winding terminals are connected to slip rings that turn with the rotor
• Windings are short circuited externally
• Called slip ring rotor because it has slip rings connected to it

Question 17

Describe the concstruction of the squirel cage rotor?

Answer 17

• Consists of copper bars slightly longer than the rotor, which are pushed into slots
• The ends are welded to copper end rings to short circuit to allow flow of current

Question 18

Describe the theory of operation of the induction machine?

Answer 18

• A three phase supply is applied to the stator
• This creates a magentic field with speed: N_S=120(F_e)/P
• This magnetic field induces a current in the rotor winding
• Having a current carrying wire and a magnetic field creates a magentic field for the rotor
• A torque is produced due to the interaction between the two magnetic field speeds
• Rotor magnetic field speed is N_r
• The direction of rotation is the same as the magnetic field

Question 19

At which speeds can the induction motor run and can it run at synchronous speeds? why?

Answer 19

If the rotor runs at synchronous speeds there will be no relative speed between the two magnetic fields and so the induced voltage will be zero which means that there will be no current and so no rotation. If the rotor is below the synchronous speed then the magnetic field will cut the rotor windings and torque is produced.

Question 20

What is the Eqn of the slip?

Answer 20

S=N_s-N_m/N_s

S=1 at standstill

S=0 at synchronous speed

Question 21

What are the Eqns of the rotor frequency?

Answer 21

f_r=Sf_s

f_r=(P/120)*(n_s-n_m)

Question 22

When does the largest relative motion occur and what is the Eqn of the of the induced voltage at that point?

Answer 22

• The largest relative motion occurs when the rotor is at standstill (n_m=0) this is called locked rotor or blocked rotor
• E_R0=4.44*N_R*Ø*f_r
• N_R is number of turns of stator winding

Question 23

What is the Eqn of the induced volt at any slip?

Answer 23

E_R=SER0

Question 24

What is the eqn of the reactance in case the frequency is changed?

Answer 24

• X_R=SX₀
• X_R=2πf_rL_r
• X₁/X₂=f₁/f₂

Question 25

What needs to be done if the frequency of the machine is changed? And what will happen to the values of the reactances?

Answer 25

Question 26

Draw the equivalent circuit of the induction motor?

Answer 26

Question 27

Draw the power flow diagram of the induction motors. Label it and state the eqns and the power ratio?

Answer 27