Induction Motor Starting & Running Conditions for GATE EE Electrical Machines

The synchronous speed of induction motor,

At full load, slip 
We know that slip is directly proportional to load, hence at half load slip will be 0.025
At half load rotor speed, Nr  = Ns (1 - s) = 1000 (1 - 0.025) = 975 rpm

At starting slip, S=1
Current Drawn α voltage

Rotor phase voltage at standstill, 
R₂ = 0.04 Ω
X₂ = 0.6 Ω
X_r = sX₂ = 0.04 × 0.6
= 0.024 Ω
E_r = sE₂
= 0.04 × 714.286 V
= 28.57 V

When 3-ϕ induction machine working as an induction generator, then 
Slip (s) = 
Where, 
Ns = Synchronous speed
Nr = Rotor speed
Frequency of rotor current = s × f
Where s is the slip
f is the supply frequency
Calculation:
Given that,
Supply frequency (f_s) = 60 Hz
Rotor current frequency (f_r) = 5 Hz
Number of poles = 4
Synchronous speed, 

We know that,
f_r = (s) f_s
⇒ 5 = (s) (60)

To work as an induction generator, rotor speed should be slip speed greater than synchronous speed, therefore 

⇒ N_r = 1950 rpm

We have, R₂ = 0.5 Ω, X₂ = 2.5 Ω
At maximum torque, R₂ = sX₂  
Where s is the slip.

Impedance at maximum torque,

= 0.707 Ω          (∵ Xr = sX2)
Standstill phase voltage in rotor is
E2=230V ( ∵ Delta connection)
Now rotor induced emf is
E_r=sE₂=0.2×230
= 46 V
Rotor current per phase, 

⇒ s²mt - 4s_mt + 1 = 0
⇒ s_mt = 3.73 (or) 0.27
s_mt = 3.72 is not valid.
So, s_mt = 0.27

⇒ r'₂ = 0.2 x 0.27 = 0.054Ω
External resistance that must be inserted in the rotor circuit
= r'₂ - r₂ = 0.054 - 0.04 = 0.014Ω
Without external resistance,
Power factor = 
With external resistance,
Power factor 
Percentage improvement in power factor

Exact Equivalent Circuit

Here, R₁ is the winding resistance of the stator
X₁ is the inductance of the stator winding
R₀ is the core loss component
XM is the magnetizing reaction of the winding
R₂/s is the power of the rotor, which includes output mechanical power and loss of rotor
Important:
If we draw the circuit with refereed to the stator then the circuit will look like

Here all the other parameters are same except R₂’ is the rotor winding resistance with referred to stator winding. R₂(1-s) / s is the resistance which shows the power which is mechanical power output or useful power. The power dissipated in that resistor is the useful power output or shaft power.
Explanation:

We redraw the given circuit as

Given V_g=210V,s=0.05
Air gap voltage is the voltage across AB, i.e.

Hence, torque = 

Methods used to start a three-phase cage-type induction motor:

DOL starter:

• The direct on line (DOL) starter method of an induction motor is simple and economical.
• In this method, the starter is connected directly to supply voltage.
• It also  referred as Full Voltage Starting.
• In this method, small motors up to 5 hp rating are started to avoid the supply voltage fluctuation.

Star-delta starter:

• The star-delta starter method of starting three-phase induction motors is very common and widely used among all the methods.
• In this method, at stating motor in star connection and runs at delta connected stator windings.
   

Auto-transformer starter:

• The Autotransformer is used in both the type of the connections, i.e., either star connected or delta connected.
• The autotransformer is used to limit the starting current of the induction motor.
• This method is used for the high rating of squirrel cage induction motors. So, this method is most suitable for a 20 hp squirrel cage induction motor.
• The auto-transformer starter is expensive compare to the “direct on line” (DOL) starter

Slots in Induction motor:

• The speed of the induction motor is inversely proportional to the load torque. In semi-closed and closed slots, the air gap between the stator and rotor is small as compared to open slots. As the air gap is small, the requirement of magnetizing current to establish the flux in the air gap is less.
• It results in improved power factor In order to semi-closed slots or totally closed slots are used in induction motors.
• Among all the three types of slots, semi-closed type slots are preferred for induction machines as semi-closed slots having the partial advantages of open type and partial advantages of closed type slots.
• Open-type slots are generally preferred for synchronous and dc machines.
• In general, closed type slots are used in low hp motors, to control the starting current, as the leakage reactance offered by closed type slots is very high compared to other types of slots.
• Large size induction motors use open slots so that already prepared and properly insulated coils can be easily inserted in open slots.
• In order to improve the power factor semi-closed slots or totally closed slots are used in induction motors.

The direct on line (DOL) starter method of an induction motor is simple and economical. In this method, the starter is connected directly to supply voltage. By this method, small motors up to 5 HP rating are started to avoid the supply voltage fluctuation.

The star-delta starter method of starting three-phase induction motors is very common and widely used among all the methods. In this method, the motor runs at delta connected stator windings. It is also used for motors of 5-15 HP rating.

The Autotransformer is used in both the type of the connections, i.e., either star connected or delta connected. The autotransformer is used to limit the starting current of the induction motor. This method is used for the high rating of squirrel cage induction motors. So, this method is most suitable for motors having ratings of more than 15 HP.