Three Phase Induction Motors Study Notes for SSC JE & Other AE JE Exams

3-Phase Induction Machine

• A 3-phase induction motor (IM) is also called an asynchronous AC motor, that supplies power to the rotating device through electromagnetic induction.
• A 3-phase induction motor is also called a rotating transformer because, in an induction motor the stator is essentially the primary of the transformer, and the Rotor (rotating part) is the secondary side.
• Induction motors are widely preferred for industrial motors due to their rugged construction. Absence of brushes and the ability to control the speed of the motor.
• It is a single excited AC machine.
• The stator winding of a 3-phase induction motor is directly connected to the AC source, whereas its rotor winding receives its energy from the stator through induction (i.e., transformer action).

Type of Rotor 

• Squirrel cage rotor
• Wound Rotor

Squirrel-Cage Rotor

the rotor winding of the squirrel-cage induction motor consists of single copper or aluminium bars placed in the slots and short-circuited by end rings on both sides of the rotor. Most single-phase induction motors have a Squirrel-Cage rotor. For cooling of motor One or 2 fans are attached to the shaft of the Rotor.

Figure: Squirrel-cage rotor

Wound Rotor

• In the wound rotor(slip-ring rotor), an insulated 3-phase winding wound for the same number of poles as the stator similar to the stator winding is placed in the rotor slots. For speed control of the motor, the ends of the rotor winding are brought to three slip rings on the shaft, this type of connection is possible in the star-connected rotor winding. usually for large 3-phase induction motors.
•  wound rotor motors are expensive and require more maintenance of the slip rings and brushes as compared to squirrel cage rotors, so it is not so common in industrial applications.
• Rotor has a winding the same as stator and the end of each phase is connected to a slip ring.

Figure: Wound Rotor

Principle Of Operation of 3-Phase Induction Motor

The basic principle of operation of induction machine is mutual induction.

It is singly excited motor (voltage is applied to the stator only) but voltage is induced in the rotor winding through mutual induction.

When a 3-ϕ supply is given across the start it produces an RMF rotating at N_s (Synchronous speed). It sweeps pass the rotor and cut the rotor conductor which will induce emf. As the rotor is essentially closed, it results in current and torque and makes the rotor to rotate in the direction of RMF according to Lenz’s law. The rotation of the rotor is in such a way to oppose the relative speed between RMF and the rotor. Actually, the rotor wants to catch the RMF and to rotate at synchronous speed. But it could not catch it and runs at a speed N slightly less than N_s. As in slips Back N_s by a slip speed (N_s – N).

Some important Definitions

Slip

It is the difference of speed between the stator (synchronous speed) and the rotor speed expressed as the fraction of synchronous speed N_s.

Slip Speed

It is the difference of speed between the stator (synchronous speed) and the rotor speed.

Slip speed, sN_s = N_s - N

Frequency of Rotor Current or E.M.F.

Rotor frequency, f_r = sf

Where, s = slip

 f = supply frequency

Rotor E.M.F.

The rotor emf is directly proportional to the frequency. At standstill, this frequency is equal to supply f but at running condition, it is equal to (sf).

Hence induced emf in the rotor at running condition will be s-times the induced emf at standstill.

Rotor inductance (X₂)

Rotor power factor

Torque in Induction Motor

The relative speed between stator field and rotor field is zero.

A steady torque is generated by the interaction of both fields.

T_e ∝ F₁ F₂ Cos ϕ

where, F₁ → Stator field produced by induced voltage in stator (E₂)

F₂ → rotor field produced by induced current in rotor (I₂’)

Cos ϕ → angle between stator and rotor field

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Running torque

Let the motor run at speed N with the slip (s) & delivering

full load torque ‘T_f’

Condition for maximum running torque

Slip at which maximum torque (T_m) occurs 

By putting the value of s_m in running torque

Torque Slip Characteristics of Induction Motor

Torque equation is given by

Low slip region

For high slip region

Figure: Torque Slip Characteristics of 3-phase Induction motor

In an operating region, the torque-slip characteristic is essentially a straight line. It has good speed regulation.

Power Flow in Induction Motor

Power Flow Diagram of Induction Motor explains the input given to the motor, the losses occurring and the output of the motor. The input power given to an Induction motor is in the form of three-phase voltage and currents. The Power Flow Diagram of an Induction Motor is shown below.

Figure: Power Flow Diagram of Induction Motor

Losses in Three-Phase Induction Motor

There are two types of losses that occur in a three-phase induction motor. These losses are:

1. Constant or fixed losses,

2. Variable losses.

Constant or Fixed Losses

Constant losses are those losses which are considered to remain constant over the normal working range of an induction motor. The fixed losses can be easily obtained by performing  no-load test on the three-phase induction motor. These losses are further classified as-

(i)   Iron or core losses,

(ii)  Mechanical losses,

(iii) Brush friction losses.

Iron or Core Losses

Iron or core losses are further divided into hysteresis and eddy current losses. Eddy current losses are minimized by using lamination on core. Since by laminating the core, area decreases and hence resistance increases, which results in decrease in eddy currents. Hysteresis losses are minimized by using high grade silicon steel. The core losses depend upon frequency of the supply voltage. The frequency of stator is always supply frequency, f and the frequency of rotor is slip times the supply frequency, (sf) which is always less than the stator frequency. For stator frequency of 50 Hz, rotor frequency is about 1.5 Hz because under normal running condition slip is of the order of 3 %. Hence the rotor core loss is very small as compared to stator core loss and is usually neglected in running conditions.

Mechanical and Brush Friction Losses

Mechanical losses occur at the bearing and brush friction loss occurs in wound rotor induction motor. These losses are zero at start and with increase in speed these losses increase. In three phase induction motor the speed usually remains constant. Hence these losses almost remain constant.

Variable Losses

These losses are also called copper losses. These losses occur due to current flowing in stator and rotor windings. As the load changes, the current flowing in rotor and stator winding also changes and hence these losses also change. Therefore, these losses are called variable losses. The copper losses are obtained by performing blocked rotor test on three phase induction motor.

The main function of induction motor is to convert an electrical power into mechanical power. During this conversion of electrical energy into mechanical energy the power flows through different stages.

This power flowing through different stages is shown by power flow diagram. As we all know the input to the three-phase induction motor is three phase supply. So, the three-phase supply is given to the stator of three phase induction motor.

Electrical Power input to the stator, P_in = √3V_LI_Lcosφ

Where,

P_in = electrical power supplied to the stator of three phase induction motor

V_L = line voltage supplied to the stator of three phase induction motor

I_L = line current

Cos Φ = power factor of the three-phase induction motor.

A part of this power input is used to supply stator losses which are stator iron loss and stator copper loss. The remaining power i.e. (input electrical power – stator losses) are supplied to rotor as rotor input.

So, rotor input P₂ = P_in – stator losses (stator copper loss and stator iron loss).

Now, the rotor must convert this rotor input into mechanical energy, but this complete input cannot be converted into mechanical output as it has to supply rotor losses. As explained earlier the rotor losses are of two types rotor iron loss and rotor copper loss. Since the iron loss depends upon the rotor frequency, which is very small when the rotor rotates, so it is usually neglected. So, the rotor has only rotor copper loss.

Therefore, the rotor input must supply these rotor copper losses. After supplying the rotor copper losses, the remaining part of Rotor input, P₂ is converted into mechanical power, P_m.

Let P_c be the rotor copper loss,

I₂ be the rotor current under running condition,

R₂ is the rotor resistance,

P_m is the gross mechanical power developed.

P_c = 3I₂²R₂

P_m = P₂ – P_c

Now this mechanical power developed is given to the load by the shaft but there occur some mechanical losses like friction and windage losses. So, the gross mechanical power developed must be supplied to these losses. Therefore, the net output power developed at the shaft, which is finally given to the load is P_out.

P_out = P_m – Mechanical losses (friction and windage losses).

P_out is called the shaft power or useful power.

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