1. Magnetic field due to an electric current
Review: Electromagnetism
Magnetic field due to an electric current
When a conductor carries an electric current, a magnetic field is produced around that conductor.
Right Hand Rule

2. Magnetic field of a solenoid
If a coil is wound on a steel rod and connected to a supply, the steel becomes magnetized and behaves like a permanent magnet.
Grip Rule if solenoid is gripped with the right hand, with fingers pointing in the direction of current, then the thumb outdtretched parallel to the axis of the solenoid points in the direction of the magnetic field inside the solenoid.
Solenoid with a steel core

3. Force on a conductor carrying current across a magnetic field
F (force on conductor, N) = B (flux density, T) x L (length, m) x I (current through conductor, A)
Left Hand Rule: First finger: Flux
Second finger: Current
Thumb: Mechanical Force

4. Electromagnetic induction
When a conductor cuts or is cut by a magnetic flux, an emf is generated in the conductor and a magnitude of the generated emf is proportional to the rate at which the conductor cuts or is cut by the magnetic flux. Ex : transformer

5. Direction of induced e.m.f
Two methods:
Fleming’s right hand rule - If the first finger of the right hand be pointed in the direction of the magnetic flux and if the thumb be pointed in the direction of motion of the conductor relative to the magnetic field, then the second finger, held at right angles to both the thumb and the first finger, represents the direction of the emf.
b) Lenz’s law
Fleming’s right hand rule

6. INDUCTION MACHINE
The induction machine is the most rugged and the most widely used machine in industry. Like dc machine, the induction machine has a stator and a rotor mounted on bearings and separated from the stator by an air gap. However, in the induction machine both stator winding and rotor winding carry alternating currents. The induction machine can operate both as a motor and as generator
As motors, they have many advantages. They are rugged, relatively inexpensive, and require very little maintenance. They range in size from a few watts to about 10,000 hp. The speed of an induction motor is nearly but not quite constant, dropping only a few percent in going from no load to full load.
The main disadvantages of induction motors are:
· The speed is not easily controlled.
· The starting current may be five to eight times full-load current.
· The power factor is low and lagging when the machine is lightly loaded

7. INDUCTION MOTOR CONSTRUCTION
Two different types of induction motor which can be placed in stator:
a) squirrel cage rotor
b) wound rotor
Squirrel Cage rotor
Wound rotor

8. Types of rotor
Squirrel cage rotor – consists of conducting bars embedded in slots in the rotor magnetic core, and these bars are short circuited at each end by conducting end rings. The rotor bars and the rings are shaped like squirrel cage.
Wound rotor – carries three windings similar to the stator windings. The terminals of the rotor windings are connected to the insulated slip rings mounted on the rotor shaft. Carbon brushes bearing on these rings make the rotor terminals available to the user of the machine. For steady state operation, these terminals are short circuited.

9. Squirrel Cage Rotor

10. Wound Rotor
Most motors use the squirrel-cage rotor because of the robust and maintenance-free construction.
However, large, older motors use a wound rotor with three phase windings placed in the rotor slots.
The windings are connected in a three-wire wye.
The ends of the windings are connected to three slip rings.
Resistors or power supplies are connected to the slip rings through brushes for reduction of starting current and speed control

11. Induction Motor Components

12. BASIC INDUCTION MOTOR CONCEPT
A three phase set of voltages has been applied to the stator, and three phase set of stator currents is flowing. These produce a magnetic field Bs, which is rotating in a counterclockwise direction .
The speed of the magnetic field’s rotation is

13. The rotating stator fields Bs induces a voltage in the rotor bars.
The rotor voltage produces a rotor current flow, which lags behind the voltage because of the inductance of the rotor.
The rotor current produces a rotor magnetic field BR lagging 900 behind itself, and BR interacts with Bnet to produce a counterclockwise torque in the machine

14. THE CONCEPT OF ROTOR SLIP
The voltage induced in a rotor depends on the speed of the rotor relative to the magnetic field.
Slip speed is defined as the difference between synchronous speed and rotor speed
where
nslip = slip speed of the machine
nsync = speed of the magnetic fields
nm = mechanical shaft speed of motor
Slip is the relative speed expressed on a per unit or a percentage basis

15. CONTINUED… In term angular velocity (radians per second, rps)
If the rotor turns at synchronous speed, s = 0
while if the rotor is stationary/standstill, s = 1.

16. THE ELECTRICAL FREQUENCY CONCEPT
Like a transformer, the primary (stator) induces a voltage in the secondary (rotor) but unlike a transformer, the secondary frequency is not necessary the same as the primary frequency.
If the rotor of a motor is locked, then the rotor will have same frequency as the stator.
The rotor frequency can be expressed

17. EXERCISE 1
A 208V, 10hp, 4 pole, 60Hz, Y connected induction motor has full load slip of 5%.
Calculate,
nsync (Ans:1800rpm)
nm (Ans: 1710rpm)
fr at the rated load (Ans: 3 Hz)
Shaft torque at the rated load (Ans: 41.7Nm)

18. THE EQUIVALENT CIRCUIT OF AN INDUCTION MOTOR
R1 = Per phase stator winding resistance
jX1 = Per phase stator leakage reactance
VP = Per phase terminal voltage
RC = Core resistance
jXM = Magnetizing reactance
ER = Rotor voltage
RR = Rotor resistance
jXR = Per phase rotor leakage reactance

19. THE ROTOR CIRCUIT MODEL
The greater the relative motion between rotor and the stator magnetic fields, the greater the resulting rotor voltage and rotor frequency. The largest relative motion occurs when the rotor is stationary. (locked rotor or blocked rotor condition)
jXR0 = blocked rotor rotor resistance
ER0 = Locked rotor voltage

20. THE FINAL EQUIVALENT CIRCUIT
In an ordinary transformer, the voltages, currents, and impedances on the secondary of the device can be referred to the primary side by means of the turn ratio of the transformer:
The transformed rotor voltage becomes
The rotor current becomes
The rotor impedances becomes
Referred rotor resistance and reactance

21. THE FINAL EQUIVALENT CIRCUIT

22. POWER FLOW DIAGRAM
When the secondary windings in an induction motor (rotor) are shorted out, so no electrical output exists from normal induction motors. Instead, the output is mechanical.
The relationship between input and output powers are shown below:

23. POWER AND TORQUE IN INDUCTION MOTOR
Stator Copper Loss,
Core Losses,
Air Gap Power,
Rotor Copper Loss,
Developed Mech. Power,
Output power,
Developed Torque,

24. Separating the rotor copper losses and the power converted in Induction motor equivalent circuit

25. The derivation of the induction motor induced-torque equation
The induced torque in induction motor is:
Air gap power:
Total Air gap power:
Air gap power is the power crossing the gap from the stator circuit to the rotor circuit. It is equal to the power absorbed in the resistance R2/s.

26. Continued…
If I2 can be determined, then the air gap power and the induced torque will be known.
To solve circuit above, we use thevenin’s theorem:

27. Continued…

28. THEVENIN’S EQUIVALENT CIRCUIT