Study Notes For Three-Phase Induction Machines - 2 | Electrical Machines for Electrical Engg. - Electrical Engineering (EE) PDF Download

STARTING OF 3-PHASE INDUCTION MOTORS
There are two important factors to be considered in starting of induction motors:

• The starting current drawn from the supply, and
• The starting torque. 

The starting current should be kept low to avoid overheating of motor and excessive voltage drops in the supply network. The starting torque must be about 50 to 100% more than the expected load torque to ensure that the motor runs up in a reasonably short time.

• At synchronous speed, s = 0, and therefore , R₂/s = ∞ ⇒ so I₂' = 0.The stator current therefore comprises only the magnetising current i.e. I1 = Iφ and is quite therefore quite small. 
• At low speeds, R₂'/X + jX₂ = ∞ is small, and therefore I₂' is quite high and consequently I₁ is quite large.
• Actually the typical starting currents for an induction machine are ~ 5 to 8 times the normal running current.

Hence the starting currents should be reduced. The most usual methods of starting 3-phase induction motors are:

• Rotor resistance starting For slip-ring motors
• For squirrel-cage motors

(i)   Direct-on -line starting
(ii)  Star-delta starting
(iii) Autotransformer starting.

Rotor Resistance Starting

• By adding eternal resistance to the rotor circuit any starting torque up to the maximum torque can be achieved; and by gradually cutting out the resistance a high torque can be maintained throughout the starting period.
• The added resistance also reduces the starting current, so that a starting torque in the range of 2 to 2.5 times the full load torque can be obtained at a starting current of 1 to 1.5 times the full load current.

Direct-On-Line Starting

• This is the most simple and inexpensive method of starting a squirrel cage induction motor. The motor is switched on directly to full supply voltage. The initial starting current is large, normally about 5 to 7 times the rated current but the starting torque is likely to be 0.75 to 2 times the full load torque.
• To avoid excessive supply voltage drops because of large starting currents the method is restricted to small motors only.
• To decrease the starting current cage motors of medium and larger sizes are started at a reduced supply voltage.

Star-Delta starting

• This is applicable to motors designed for delta connection in normal running conditions. Both ends of each phase of the stator winding are brought out and connected to a 3-phase change -over switch.
• For starting, the stator windings are connected in star and when the machine is running the switch is thrown quickly to the running position, thus connecting the motor in delta for normal operation.
• The phase voltages & the phase currents of the motor in star connection are reduced to 1/√3 of the direct -on -line values in delta. The line current is 1/3 of the value in delta.
• A disadvantage of this method is that the starting torque (which is proportional to the square of the applied voltage) is also reduced to 1/3 of its delta value.

Auto-Transformer Starting

• This method also reduces the initial voltage applied to the motor and therefore the starting current and torque.The motor,which can be connected permanently in delta or in star, is switched first on reduced voltage from a 3-phase tapped auto -transformer and when it has accelerated sufficiently, it is switched to the running (full voltage) position.
• The principle is similar to star/delta starting and has similar limitations. The advantage of the method is that the current and torque can be adjusted to the required value, by taking the correct tapping on the autotransformer. This method is more expensive because of the additional autotransformer.

Starting Torque: The torque developed the motor at the instant of starting is called starting torque.

where,
N_s = Synchronous speed in RPS
E₂ = Rotor emf per phase at standstill
R₂ = Rotor resistance per phase
X₂ = Rotor reactance per phase at standstill

• Condition for maximum starting torque
  R₂ = X₂
• Starting torque, T_st ∝ (supply voltage)²
  T_st ∝ V²
  
  Torque Under Running Conditions
  
  Key Points
• Condition for maximum torque under running conditions R₂ = sX₂
• Slip corresponding to maximum torque  s = R₂/X₂
• Maximum torque

 
Full Load Torque and Maximum Torque


S_f = Slip corresponding to full load torque
Note. In general,

Starting Torque and Maximum Torque


Rotor Torque and Breakdown Torque: The rotor torque at any slip s can be expressed in .terms of the maximum torque

where, T_b = Maximum (or breakdown) torque
sb = Breakdown or pull out slip
No Load Test:
Power input = P₀
No load current = I₀ (average of 3 ammeter reading)
Voltage = V₀ (line to line voltage)

I_m = I₀ sin φ₀
I_c = I₀ cos φ₀
R_o = V_o/I_o  &  X_o = V_o/I_m
and
Rotation loss
Note: This test gives rotational losses and X0

Blocked Rotor Test: The shaft of the motor is clamped so that it cannot move and rotor winding is short-circuited.
V_BR = Stator voltage (line to line) required to circulate I_BR when rotor is blocked.
I_BR = Stator current (average of three ammeter reading)
P_BR = Total copper loss on full load at standstill
Blocked rotor impedance
Blocked rotor resistance
Blocked rotor reactance
Note: 

Speed Control of Induction Motors: The rotor speed of an induction motor is given by
N_r = (1 – s)N_s and  N_s = 120f/P
also
Speed Control by Frequency Changing: The synchronous speed of an induction motor is given by

The synchronous speed and therefore, the speed of the motor can be controlled by varying the supply frequency. The emf induced it the stator of the induction motor is given by


Speed Control by Pole Changing: The number of stator poles can be changed by (a) multiple stator windings, (b) method of consequent poles and (c) Pulse-Amplitude Modulation (PAM).

• Sometimes induction machines have a special stator winding capable of being externally connected to form two different number of pole numbers. Since the synchronous speed of the induction machine is given by ns = f.s/p (in rev./s).

where p is the number of pole pairs, this would correspond to changing the synchronous speed.With the slip now corresponding to the new synchronous speed, the operating speed is changed.

• This method of speed control is a stepped variation and generally restricted to two steps. If the changes in stator winding connections are made so that the air gap flux remains constant, then at any winding connection, the same maximum torque is achievable. Such winding arrangements are therefore referred to as constant-torque connections.
• If however such connection changes result in air gap flux changes that are inversely proportional to the synchronous speeds, then such connections are called
• constant-horsepower type.

Speed Control by Slip Changing: There are three ways of controlling slip. (i) Voltage control, (ii) Rotor-resistance control, (iii) Secondary foreign voltage control, and (iv) Speed control by cascade arrangement.

Voltage control
From the torque equation of the induction machine, we can see that the torque depends on the square of the applied voltage. The variation of speed torque curves with respect to the applied voltage is shown in figure below. These curves show that the slip at maximum torque remains same, while the value of stall torque comes down with decrease in applied voltage. The speed range for stable operation remains the same.

• Further, we also note that the starting torque is also lower at lower voltages. Thus,even if a given voltage level is sufficient for achieving the running torque, the machine may not start. This method of trying to control the speed is best suited for loads that require very little starting torque, but their torque requirement may increase with speed.

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Rotor Resistance Control
From the expression for the torque of the induction machine, torque is dependent on the rotor resistance. The maximum value is independent of the rotor resistance. The slip at maximum torque is dependent on the rotor resistance. Therefore, we may expect that if the rotor resistance is changed, the maximum torque point shifts to higher slip values, while retaining a constant torque. Figure below shows a family of torque-speed characteristic obtained by changing the rotor resistance.

• The resistors connected to the slip-ring brushes should have good power dissipation capability. Water based rheostats may be used for this. A ‘solid-state’ alternative to a rheostat is a chopper controlled resistance where the duty ratio control of of the chopper presents a variable resistance load to the rotor of the induction machine.