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

Nguyễn Công Phương

ELECTROMECHANICAL ENERGY
CONVERSION
Introduction to Rotating Machines


Contents
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
sites.google.com/site/ncpdhbkhn

2


Introduction to Rotating
Machines
1. Elementary Concepts
2. Introduction to AC and DC Machines
3. MMF of Distributed Windings
4. Magnetic Fields in Rotating Machinery
5. Rotating MMF Waves in AC Machines

6. Generated Voltage
7. Torque in Nonsalient – Pole Machines
8. Linear Machines
9. Magnetic Saturation
10.Leakage Fluxes
sites.google.com/site/ncpdhbkhn

3


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).
sites.google.com/site/ncpdhbkhn

4

Elementary Concepts (2)
• Second winding(s) carrying DC currents and used
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.

• The time – varying flux tends to induce currents,
known as eddy currents, in the electrical steel.
• There are no windings on the rotor of some
machines, such as variable reluctance machines
and stepper motors.
sites.google.com/site/ncpdhbkhn

5


Introduction to Rotating
Machines
1.
2.

Elementary Concepts
Introduction to AC and DC Machines
a)

AC Machines
i.

ii.

b)

3.
4.
5.
6.
7.
8.
9.
10.

Synchronous Machines
Induction Machines

DC Machines

MMF of Distributed Windings
Magnetic Fields in Rotating Machinery
Rotating MMF Waves in AC Machines
Generated Voltage
Torque in Nonsalient – Pole Machines
Linear Machines
Magnetic Saturation
Leakage Fluxes

sites.google.com/site/ncpdhbkhn

6

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
the stator

Armature – winding
magnetic axis

θa
Field
winding

−a
a
Rotor
N – turn
armature

winding

sites.google.com/site/ncpdhbkhn

Stator
Flux paths

7


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
of mechanical power
connected to the shaft

Armature – winding
magnetic axis

θa
Field
winding

−a
a
Rotor
N – turn
armature
winding

sites.google.com/site/ncpdhbkhn

Stator
Flux paths

8


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
name “synchronous”.
• 3000 rpm 50 Hz.
sites.google.com/site/ncpdhbkhn

Armature – winding
magnetic axis

θa
−a
a

Stator

9


Synchronous Machines (4)

− a1

θ ae =

poles
θa
2

poles n
fe =

×
2
60

a1

a2

B
1
0.8
0.6
0.4

−a1

a1

−a 2

a2

2π

π

0.2
0

4π

2π

-0.2

θ a , mechanical radians

−a 2

θ ae, electrical radians

-0.4
-0.6
-0.8
-1
0

2

4

6

8

10

12

sites.google.com/site/ncpdhbkhn

10


Synchronous Machines (5)
Salient/projecting/concentrated
windings
− a1

fe =

Nonsalient/cylindrical/distributed
windings

poles n
×
2
60

N

a1

a2

S

− a2

Hydroelectric generator

sites.google.com/site/ncpdhbkhn

Steam/gas turbin generator
11


Synchronous Machines (6)
−c
a

b

−c
b

N

a

−a

c

S

N

−b

−b′

S
−b
c

−a

c′

N

S
− a′

b′

a′
a

−c′

−a a ′
−c′ −a′
−c

c
sites.google.com/site/ncpdhbkhn

c′

−b′

−b

b′
b
12


Introduction to Rotating
Machines
1.
2.

Elementary Concepts
Introduction to AC and DC Machines
a)

AC Machines
i.
ii.

b)

3.
4.
5.
6.
7.
8.
9.

10.

Synchronous Machines
Induction Machines

DC Machines

MMF of Distributed Windings
Magnetic Fields in Rotating Machinery
Rotating MMF Waves in AC Machines
Generated Voltage
Torque in Nonsalient – Pole Machines
Linear Machines
Magnetic Saturation
Leakage Fluxes

sites.google.com/site/ncpdhbkhn

13


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

sites.google.com/site/ncpdhbkhn

14


Introduction to Rotating
Machines
1.
2.

Elementary Concepts
Introduction to AC and DC Machines
a)

AC Machines
i.
ii.

b)

3.
4.
5.
6.
7.
8.
9.
10.

Synchronous Machines
Induction Machines

DC Machines

MMF of Distributed Windings
Magnetic Fields in Rotating Machinery
Rotating MMF Waves in AC Machines
Generated Voltage
Torque in Nonsalient – Pole Machines
Linear Machines
Magnetic Saturation
Leakage Fluxes

sites.google.com/site/ncpdhbkhn

15


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
to the shaft.
• The rotor is normally
turned at a constant

speed by a source of
mechanical power
connected to the shaft.

Rotation

sites.google.com/site/ncpdhbkhn

N

Armature coil,
N turns

−a
−
Carbon
brush

+
a

Copper
commutator
segments

S
16


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
rotor.

Rotation

sites.google.com/site/ncpdhbkhn

N

Armature coil,
N turns

−a
−
Carbon
brush

+
a

Copper
commutator
segments

S
17


Introduction to Rotating
Machines
1. Elementary Concepts
2. Introduction to AC and DC Machines
3. MMF of Distributed Windings
4. Magnetic Fields in Rotating Machinery
5. Rotating MMF Waves in AC Machines
6. Generated Voltage
7. Torque in Nonsalient – Pole Machines
8. Linear Machines

9. Magnetic Saturation
10.Leakage Fluxes
sites.google.com/site/ncpdhbkhn

18


MMF of Distributed Windings
Flux lines

N – turn coil
carrying current i

Magnetic axis
of stator coil

θa
Ni
2
−

Ni
2

Fundamental Fag1

0

π

θa
Rotor surface
Stator surface

sites.google.com/site/ncpdhbkhn

19


Introduction to Rotating
Machines
1. Elementary Concepts
2. Introduction to AC and DC Machines
3. MMF of Distributed Windings
a) AC Machines
b) DC Machines

4. Magnetic Fields in Rotating Machinery
5. Rotating MMF Waves in AC Machines
6. Generated Voltage
7. Torque in Nonsalient – Pole Machines
8. Linear Machines
9. Magnetic Saturation
10. Leakage Fluxes
sites.google.com/site/ncpdhbkhn

20


AC Machines (1)

Fag (t ) = M 1 cos(ωt + ϕ1 ) + M 2 cos(2ωt + ϕ 2 ) + M 3 cos(3ωt + ϕ 3 ) + ...
= Fag1 (t ) + Fag 2 (t ) + Fag 3 (t ) + ...

4 Ni
Fag 1 (t ) =
cos θ a
π 2
Ni
2
−

Ni
2

Fundamental Fag1

0

π

θa
Rotor surface
Stator surface

sites.google.com/site/ncpdhbkhn

21


AC Machines (2)

Space – fundamental mmf wave

a

θa

Axis of phase a

Axis of phase a

2 N cia
−π

−a

π
0

sites.google.com/site/ncpdhbkhn

θa

22


AC Machines (3)
a

θa

Magnetic axis
of stator coil
Axis of phase a

θa
−a

4 Ni
Fag 1 (t ) =
cos θ a
π 2

4 k w N ph
 poles 
Fag 1 (t ) =
ia cos 
θa 
π poles
 2

sites.google.com/site/ncpdhbkhn

23


AC Machines (4)
(F )

ag 1 22.5o

(F )

ag 1 −22.5o

(F )

ag 1 7.5o

4 2 N cia
=
cos(θ a − 22.5o )
π 2
4 2 N cia
=
cos(θ a + 22.5o )
π 2

(F )

(F )

= ( Fag1 ) 22.5o + ( Fag1 ) −22.5o

ag 1 total

112.5o

a

67.5o

θa
22.5o

4 2 N cia
=
cos(θ a − 7.5o )
π 2
4 2 N cia
=
cos(θ a + 7.5o )
π 2

ag 1 −7.5o

o
82.5
97.5
o

+ ( Fag 1 )7.5o + ( Fag1 ) −7.5o

Axis of phase a

−a

−112.5
o
−97.5o −82.5

o

−67.5o

= 4.88 N cia cos θ a
sites.google.com/site/ncpdhbkhn

24


AC Machines (5)
(F )

ag 1 total

= 4.88 N cia cos θ a

→ ( Fag 1 ) peak = 4.88 N cia

o
82.5
97.5
o

112.5o

a

67.5o

θa
22.5o

4 kw N ph
 poles 
Fag 1 (t ) =
ia cos 
θa 
π poles
 2

Axis of phase a

→ ( Fag 1 ) peak

4 k w N ph ia
=
π poles

N ph = 8 N c ; poles = 2
→ kw = 0.96

−a

−112.5
o
−97.5o −82.5

sites.google.com/site/ncpdhbkhn

o

−67.5o

25