Lecture 5

AC Machines and Rotating

magnetic field

AC generator and motor

Rotating magnetic field in a 3-phase coil stator

If two magnetic fields are present in a machine, .then a torque will be created which will tend to line up the two

magnetic fields. If one magnetic field is produced by the stator of an ac machine and the other one is produced by

the rotor of the machine, then a torque will be induced in the rotor which will cause the rotor to turn and align

itself with the stator magnetic field. If there were some way to make the stator magnetic field rotate, then the

induced torque in the rotor would cause it to constantly "chase" the stator magnetic field around in a circle.

How to produce a rotating magnetic field in a three-phase stator?

Three-phase stator

How can the stator magnetic field be made to rotate?

The fundamental principle of ac machine operation is that if “a three-phase set of currents, each of equal magnitude

and differing in phase by 120°, flows in a three-phase winding, then it will produce a rotating magnetic field of

constant magnitude.”

A set of currents are applied to the 3-phase stator coils

Flux densities resulting from these currents are;

The direction of the magnetic field vector is given by the

right-hand rule: If the fingers of the right hand curl in the

direction of the current flow in the coil, then the resulting

magnetic field is in the direction that the thumb points

Electrical Angle

Mechanical Angle

Electrical Cycle = 360o

The Relationship between Electrical Frequency and the Speed of Magnetic Field Rotation

In general, if the number of magnetic poles on an ac machine stator is P, then there are P/2 repetitions of the winding

sequence a-c' -b-a' -c-b' around its inner surface, and the electrical and mechanical quantities on the stator are related by

The resulting mechanical speed of the stator magnetic fields in revolutions per minute (nsm)is given by

𝒏𝒔𝒎 = 𝟔𝟎𝒇𝒔𝒎 =𝟏𝟐𝟎𝒇𝒔𝒆𝑷

Өse : synchronous electrical angle, (rad)

Өsm : synchronous mechanical angle, (rad)

fse : synchronous electrical frequency, (Hz)

fsm : synchronous mechanical frequency, (Hz)

ωse : synchronous electrical frequency, (rad/sec)

ω sm : synchronous mechanical frequency, (rad/sec)

Reversing the Direction of Magnetic Field Rotation

If the current in any two of the three coils is swapped, the direction of the magnetic field 's rotation will be reversed.

This means that it is possible to reverse the direction of rotation of an ac motor just by switching the supply connections on any

two of the three coils.

Synchronous and Induction Machines

• In this machine, the rotor is short-circuited (squirrel cage rotor type) or

closed through an external impedance (wound rotor type). The stator

rotating magnetic flux goes to the rotor inducing currents in the rotor

windings; which in turn create magnetic fields in the rotor. Hence, the

rotor will start to rotate in the direction of the rotating stator magnetic

field, however, with a speed (nrm) slower than synchronous speed(nsm).

The difference, or "slip," between the rotor speed and synchronous speed

varies from about 0.5 to 5.0% .

• The induction machine's essential character is that it is created solely by

induction without the need of external sources.

• They involve a degree of 'slip' in order that the current may be produced

due to the relative movement of the stator field and the rotor ( nrm < nsm )

• In this machine, the rotor winding is fed with an

external DC supply with the help of slip rings. A rotor

with permanent magnets can also be used. Thus, the

rotor has a constant magnetic field. The N pole of the

rotor will move toward the S pole of the magnetic field

of the stator, and vice versa. This magneto-mechanical

attraction creates a force which will drive the rotor to

follow the stator rotating magnetic field in a

synchronous manner

• Synchronous machine rotor always runs at a speed (nrm)

equal to its synchronous speed. nrm = nsm= 120f/P

In both asynchronous (induction) and synchronous machines, the stator has axial slots which consist of 3-phase stator winding

wound for a specific number of poles. 3-phase AC power is supplied to the stator to create a magnetic field in the stator rotating with

synchronous speed (nsm=𝟏𝟐𝟎𝒇𝒔𝒆

𝑷)

Short-circuited rotor

Synchronous Machine Induction (Asynchronous) Machine

• How to produce a rotating magnetic field in a machine stator?

• How to reverse direction of rotation of an AC motor

• What are the main differences between a synchronous and an induction machine