Lecture Electromechanical energy conversion: Introduction to Rotating machines - Nguyễn Công Phương

This chapter include all of the following content: Elementary concepts, introduction to AC and DC machines, MMF of distributed windings, magnetic fields in Rotating machinery, rotating MMF Waves in AC machines, generated voltage,...

Nguyễn Công Phương

ELECTROMECHANICAL ENERGY

CONVERSIONIntroduction to Rotating Machines

I Magnetic Circuits and Magnetic Materials

II Electromechanical Energy Conversion

Principles

III Introduction to Rotating Machines

IV Synchronous Machines

V Polyphase Induction Machines

VI DC Machines

VII.Variable – Reluctance Machines and Stepping

Motors

VIII.Single and Two – Phase Motors

IX Speed and Torque Control

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

Elementary Concepts (1)

• In rotating machines, voltage are generated in windings

or groups of coils by rotating these windings

mechanically through a magnetic field:

– By mechanically rotating a magnetic field past the winding, or

– By designing the magnetic circuit so that the reluctance

varies with rotation of the rotor.

• A set of such coils connected together is typically

referred to as an armature winding.

• In AC machines (e.g synchronous or induction), the

armature winding is typically on the stationary –

portion of the motor (referred to as the stator).

• In DC machines, the armature winding is on the

rotating portion of the motor (referred to as the rotor).

Elementary Concepts (2)

to produce the main operating flux in the machine

is called field winding

– For a DC machine, it is on the stator.

– For a synchonous machine, it is on the rotor.

– Sometimes it is a permanent magnet.

known as eddy currents, in the electrical steel.

machines, such as variable reluctance machines and stepper motors.

Synchronous Machines (1)

• A simple, two – pole, single –

phase synchronous generator.

• The field – winding,

producing a single pair of

magnetic poles, is excited by

direct current conducted to it

by means of stationary carbon

brushes which contact rotating

slip rings or collector rings.

• The single, low – power field

winding on the rotor; the high

– power, typically multiple –

phase, armature winding on

Field winding Armature – winding magnetic axis

Synchronous Machines (2)

• The two coil sides (of the

armature winding) a & –a

placed in diametrically

opposite narrow slots on the

inner periphery of the stator

• The conductors forming the

coil sides are parallel to the

shaft of the machine

• The rotor is turned at a

constant speed by a source

Field winding Armature – winding magnetic axis

Synchronous Machines (3)

• The flux – linkages of the

armature winding change with

time.

• If the flux distribution is sinusoidal

& the rotor speed is constant, then

the resulting coil voltage will be

sinusoidal in time.

• The frequency (Hz, cycles per

second) of the coil voltage is the

same as the speed of the rotor

(revolutions per second).

• The electric frequency of the

generated voltage is synchronized

with the mechanical speed the

Induction Machines

• Synchronous machines:

– Stator winding: AC current

– Rotor winding: DC current

• Induction machines:

– Stator winding: AC current

– Rotor winding: AC current

– The rotor does not itself rotate synchronously

DC Machines (1)

• A very elementary two

– pole DC generator.

• The two coil sides a &

–a are placed at

diametrically opposite

points on the rotor with

the conductors parallel

Copper commutator segments

DC Machines (2)

• The voltage induced in an

individual armature coil is AC

rectification is required.

• Commutator: a cylinder formed

of copper segments insulated

from each other by mica or

some other highly insulating

material & mounted on (but

insulated from) the rotor shaft.

• Stationary carbon brushes held

against the commutator surface

connect the winding to the

external armature terminals.

• Commutation is the reason why

the armature windings of DC

machines are placed on the

Copper commutator segments

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

Fundamental Fag1

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

AC Machines (6)

1

2

3 4 5

6 7

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

DC Machines (1)

Magnetic axis of armature winding

Magnetic axis of field winding

π

=

4 Magnetic Fields in Rotating Machinery

a) Machines with Uniforms Air Gaps

b) Machines with Nonuniform Air Gaps

5 Rotating MMF Waves in AC Machines

Machines with Uniform Air Gaps

F H

g

=

1 1

4

cos 2

ag peak

Ni H

g

π

=

Machines with Uniform Air Gaps

Machines with Uniform Air Gaps

(3)

Ex.

Given a four – pole synchronous AC generator with a smooth air gap has a

distributed rotor winding with 263 series turns, a winding factor of 0.94, and an air gap of length 0.7mm Find the rotor – winding current to produce a peak, space – fundamental magnetic flux density of 1.6T in the machine air gap?

( )10

→ =

37

1.6

π π

4 Magnetic Fields in Rotating Machinery

a) Machines with Uniforms Air Gaps

b) Machines with Nonuniform Air Gaps

5 Rotating MMF Waves in AC Machines

Machines with Nonuniform Air Gaps

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

a) MMF Wave of a Single – Phase Winding

b) MMF Wave of a Polyphase Winding

c) Graphical Analysis of Polyphase MMF

MMF Wave of a Single – Phase

MMF Wave of a Single – Phase

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

a) MMF Wave of a Single – Phase Winding

b) MMF Wave of a Polyphase Winding

c) Graphical Analysis of Polyphase MMF

=

cos( ) 2

o max

1

cos( ) 2

cos( 120 ) 2

o max

1

cos( ) 2

cos( 120 ) 2

=

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

a) MMF Wave of a Single – Phase Winding

b) MMF Wave of a Polyphase Winding

c) Graphical Analysis of Polyphase MMF

Graphical Analysis of Polyphase

MMF of phase b MMF of phase c The total MMF

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

Nf – turn

field coil

r

θ

Phase b magnetic axis

Phase c magnetic axis

+

−

e

N – turn coil

AC Machines (2)

2 2

d d

Nf – turn

field coil

r

θ

Phase b magnetic axis

Phase c magnetic axis

+

−

e

N – turn coil

Nf – turn

field coil

r

θ

Phase b magnetic axis

Phase c magnetic axis

+

−

e

N – turn coil

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

Copper commutator segments

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

6 Generated Voltage

7 Torque in Nonsalient – Pole Machines

a) Coupled – Circuit Viewpoint

b) Magnetic Field Viewpoint

8 Linear Machines

9 Magnetic Saturation

10 Leakage Fluxes

Coupled – Circuit Viewpoint (1)

λ λ

Coupled – Circuit Viewpoint (2)

v R i

dt

λ λ

Coupled – Circuit Viewpoint (3)

Coupled – Circuit Viewpoint (4)

Coupled – Circuit Viewpoint (5)

Coupled – Circuit Viewpoint (6)

Coupled – Circuit Viewpoint (7)

=

o o

Coupled – Circuit Viewpoint (8)

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

6 Generated Voltage

7 Torque in Nonsalient – Pole Machines

a) Coupled – Circuit Viewpoint

b) Magnetic Field Viewpoint

8 Linear Machines

9 Magnetic Saturation

10 Leakage Fluxes

Magnetic Field Viewpoint (1)

• Currents in the machine windings create

magnetic flux in the air gap.

• Torque is produced by the tendency of

the two component magnetic fields to

line up their magnetic axes.

• Mutual flux: produced by the stator &

rotor winding, crosses the air gap &

links both windings.

• Rotor leakage flux & stator leakage

flux: some of the flux that does not cross

the air gap.

• Only the mutual flux is of direct

concern in torque production.

Magnetic Field Viewpoint (2)

r sr

sr s

F F

δ δ

=

sin sin

s sr

sr r

F F

δ δ

g

=

20

Coenergy density of the air-gap :

2 Hag

µ

2

0 ( ) Average coenergy density :

Magnetic Field Viewpoint (3)

Average coenergy density :

4

sr

F g

4

sr

F

Dlg g

4 sr

Dl F g

sin 2

Magnetic Field Viewpoint (4)

sr is the electrical space – phase angle between the rotor & stator mmf

waves.

• The torque T acts in the direction to accelerate the rotor.

• When δ sr is positive, the torque is negative & the machine is operating as a generator.

• When δ sr is negative, the torque is positive & the machine is operating as a motor.

• The torque is proportional to the peak values of the stator– & rotor–mmf

waves F s & F r , and to the sine of the electrical space – phase angle δ sr

Magnetic Field Viewpoint (5)

r sr

sr s

F F

δ δ

=

sin sin

s sr

sr r

F F

δ δ

F F g

Magnetic Field Viewpoint (6)

Ex.

A 2400 r/min, four – pole, 50 Hz synchronous motor has an air – gap length of 1mm The average diameter of the air – gap is 27 cm, & its axial length is 32 cm The rotor winding has 800 turns & a winding factor of 0.976 The maximum rotor current is

18A, the maximum Bsr = 2T, find the maximum torque & power output?

Magnetic Field Viewpoint (7)

(average value of B over a pole) (pole area)

Torque in Nonsalient – Pole Machines

The torque is proportional to the product of the magnitudes

of the interacting fields, and to the sine of the electrical

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

Linear Machines (1)

• The most widely known use of linear motors is

in the transportation field:

– The moving vehicle: the AC “stator”, and

– The rails: the conducting stationary “rotor”.

• Also in the machine tool industry & in

robotics.

• The analysis of linear machines is quite similar

to that of rotating mchines:

– Angle displacement, and

– Torque force.

w ph ag

cos cos( 120 ) cos( 120 )

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines

Magnetic Saturation

magnetic flux is increased, they begin to saturate.

characteristics of the machines.

analytical results.

typically presented in the form of an “open –

circuit characteristic” or ”magnetization curve” or

”saturation curve”.

4 Magnetic Fields in Rotating Machinery

5 Rotating MMF Waves in AC Machines