Chapter 4 Introduction to

Rotating Machines

1

4.1 Elementary Concepts

• Rotating machines: voltages are induced in windings or groups of coils by

– rotation of a magnetic field past a winding or rotation of a winding through the field,

– or by designing the magnetic circuit so that the reluctance varies with rotation of the rotor

• Since the flux linking a coil changes cyclically, a time-varying voltage is induced e = dl/dt

• A group such coils carrying AC currents is often called an armature winding

2

3

Stator of a 100-MVA three-phase

synchronous generator under

construction.(General Electric

Company.)

Armature of a dc motor. (Baldor

Electric/ABB)

In an AC synchronous machine,

the armature is typically on the

stator

In a DC machine, the armature

is located on the rotor

• DC and synchronous machines typically have field windings carrying DC to set up the main operating flux, usually located on

– the stator for DC machines

– the rotor of AC synchronous machines

• Some machines, especially motors, use magnets instead of field windings

• Induction machines do not have fields, but produce flux similarly to transformers

• Many types of machines exist, but very similar physical principles govern their performance

4

4.2 Introduction to AC and DC

machines

• AC machines:

– Synchronous machines: rotor currents are

supplied directly from the stationary frame,

through a rotating contact for example

– Induction machines: rotor currents are

induced in the rotor windings by time-variation

of stator currents combined to rotor relative

motion.

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• Field has a single pair

of poles, so it is a

two-pole machine

• Armature here has a

single coil of N turns

• Field is excited through

brushes contacting slip

rings, or by brushless

excitation system

• If the air-gap flux is

sinusoidal in space,

the induced voltage in

the armature is

sinusoidal in time, as

the machine rotates at

constant speed

6

Schematic view of a simple,two-

pole, single-phase synchronous

generator

7

Idealized flux distribution and waveform of generated voltage

• Two poles generator has electrical

voltage frequency synchronized with

mechanical speed

• 3600rpm = 60Hz

• Many machines have more than two poles. A four-pole synchronous machine, which will rotate at half the speed of a two-pole machine if the frequency is the same

• 1800rpm=60Hz

8

Idealized flux distribution and waveform of generated voltage

Four-pole single-phase

synchronous generator

• For convenience in analyzing machines

with more than two poles, define electrical

angle and electrical speed, as follows:

9

meme2

poles

2

poles

Non-salient pole Synchronous

Machine

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Salient pole x Non-salient

Salient pole:

• Large hydropower with low rpm speed

• High number of poles for frequency match

Non-salient pole:

• Steam and gas turbine with high rpm speed

• 2 or 4 poles for frequency match

• Best approximate “sin” air-gap flux 11

Salient pole x Non Salient

12

3-phase sychronous machine

• 3 set of coins desplaced by 120 electrical

degrees

13

Synchronous generator operation

1. Armature current creates magnetic flux

waves in the air-gap (rotating at

synchronous speed)

2. This flux reacts with the flux created at

the rotor by the field current

3. The tendency of these 2 flux to align

results in electromechanical torque.

4. On generator mode, the field flux pulls the

armature flux. 14

Synchronous motor operation

1. AC is supplied to armature winding at

stator, while DC is supplied to field

winding at rotor

2. Magnetic field at stator rotates at

synchronous speed.

3. Now, the armature flux pulls the field flux.

In both cases (gen. or motor), torque and

rotating voltage are produced. 15

Induction Machines

• Stator windings are essentially the same as a synchronous machine

• Rotor winding is electrically short-circuited and often has no external connections, deriving its excitation by magnetic induction

– Also called asynchronous machines

– Common construction for an induction motor uses the squirrel-cage rotor with no external connection

– Squirrel-cage induction motors are the most common type of motor used today

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• Cage rotor has bars that

are shorted by end rings

• Inexpensive to construct

and yet very rugged

• Rotor currents are

induced as the rotor slips

past the stator flux wave,

which rotates at

synchronous speed

• Flux wave set up by the

rotor currents rotates at

synchronous speed, and

interacts with the stator

flux to produce torque

• This machine is very

similar to a transformer,

but with rotation of

windings

17

Cutaway view of a 460-V, 7.5 hp

squirrel-cage induction motor.

18

DC Machines

• A simplified dc

generator armature

winding (a single coil of

N turns) is shown

– The commutator is a

cylindrical structure with

two segments attached

to the rotor, serving as a

mechanical rectifier to

convert the ac in the

armature coil to dc at the

stationary brushes

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Elementary dc machine

20

– DC in the field sets up a stationary flux

– The commutator causes armature flux to be fixed in space between the field poles

– Interaction of fluxes sets up torque

21

Air-gap flux

distribution and

voltage waveform

4.3 MMF of Distributed Windings

• Practical armature windings are usually

distributed, or spread over a number of

slots

• Consider one phase of an ac three-phase

two-pole winding (called a full-pitch

winding since each coil spans p radians)

• Fourier analysis gives the space

fundamental component of the MMF,

developed in Appendix B 22

23

The mmf of one

phase of a distributed

two-pole, three-

phase winding with

full-pitch coils.

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• The peak value of the space fundamental is given in the following equation, where kw is the winding factor that accounts for the distribution of the winding (see Appendix B for details)

a

phw

peak1ag ipoles

Nk4F

p

– The factor kw Nph is the effective number of

series turns per phase

– Typical values for kw are 0.85 to 0.90

• Consider the dc machine with an armature

winding distributed over many slots

– An approximation to the mmf is a sawtooth

wave

25

Cross section of a two-pole dc machine

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Current and mmf

wave of idealized

dc machine

current armature i

windingarmature through

paths parallel of numberm

windingarmature in

conductors of numberC

ipolesm2

CF

a

a

aa

peak1ag

4.4 Magnetic Fields in Rotating

Machinery • Machine with a uniform air gap and a single full-

pitch N-turn coil on a highly permeable iron core

27

Diagram of machine

28

p

g2

iN4H

peak1ag

MMF and field distributions

Space fundamental

field peak value:

4.5 Rotating MMF Waves

• Single-phase winding produces a pulsating

MMF that can be resolved into two equal

rotating waves, rotating in opposite directions

• Polyphase winding produces a rotating MMF

that has constant amplitude and constant

speed in steady state

• The figure on the next slide shows a

graphical explanation while the text gives a

mathematical derivation for the three-phase

case

29

30

The production of a rotating magnetic field by

means of three-phase currents

F is the resultant of vector addition of Fa+Fb+Fc

4.6 Generated Voltage

• Flux density is nearly

sinuosoidal in space

• Phase-a flux linkage:

31

pole per flux

tcosNk

p

epphwa

l

• Generated voltage

(constant flux in normal

steady state): tsinNke ephwea

DC Machines

• Commutator acts as a rectifier, giving

average voltage:

32

mpa

a

a

mpepa

m

C

2

polesE

paths parallel2

conductors active

m2

CN

Npoles

N2

E

p

p

p

4.7 Torque in Non-Salient-Pole

Machines

• Torque can be found from either a

coupled-circuit point of view, or from a

magnetic-field point of view

• Rotor current ir and stator current is with

angle between the magnetic axes

– Coupled circuit: T = (poles/2) Lsr is ir sin me

– Magnetic field: T (poles/2) Fs Fr sin dsr

Where dsr is angle between stator and rotor

MMF’s

33