AC Machines Fundamentals

Introduction

• Synchronous machines: Motors and generators whose magnetic field is supplied by a separate dc power supply.

• Induction machines: Motors and generators whose magnetic field is supplied by magnetic induction

transformer action.

Voltage Induced in a simple Rotating Loop

abab vBle sin

sin).( vBllBvein

cdcd vBle sin

SN

r

Vcd

Vab

a b

b

ad

c

l

+ -

tvBLein sinsin2 max

c d

B

0 dabc ee

B

r

F

ab

B B

Induce Torque in current Carrying Loop

cdcdcd rilBrF sin)sin)((

sin2rilBind

i

dFilBBliF )(

ababab rilBrF sin)sin)((

l

b

a

c

d

0 dabc sloopind BkB

a b

c d

Bloop

BS

Rotating Magnetic Field

• If three set of currents each of equal magnitude and differing in phase by 120º flow in 3 phase winding, then it will produce a rotating magnetic field of constant magnitude.

905.1

240)240sin(

120)120sin(

0sin

'

'

'

Mnet

Mcc

Mbb

Maa

BB

TtBB

TtBB

TtBB

a’

a0t

Resulting net magnetic field

Apply three set of currents to the stator will produce magnetic field intensity H and magnetic flux B as follows:

Baa’

Bbb’

Bcc’

b

b’

c’

c

Bnet

The relation between the Electrical Frequency and Mechanical Speed

• The rotating magnetic flux in stator (Bnet or Bs) can be represented by one North and one South pole (2 pole machine). These magnetic poles complete one mechanical rotation around the stator for each electrical rotation.

meme ff ,

For 4-pole machine, the mechanical pole move halfway around the stator in one electrical cycle:

mememe ff 2,2,2

P

fn

Pnf

Pf

Pf

P

mm

e

mememe

120

120

2,

2,

2

/

In general:

MMF and flux distribution on AC Machine

• The flux in a real machine doesn't behave in a simple manner assumed above since there is ferromagnetic rotor in the center of machine with small air gap between rotor and stator.

– The reluctance of air gap is much higher than the reluctance of either the rotor and stator. So the flux density vector B takes the shortest possible path across the air gap and jumps perpendicularly between the rotor and stator.

How to produce sinusoidal voltage ? The flux density must vary in sinusoidal manner.

The most straight foreword way to achieve a sinusoidal variations of m.m.f along the surface of air gap is to distribute the turns of the windings that produce the m.m.f in closely spaced slots and to vary the number of conductors in each slot in sinusoidal manner.

360

coscc Nn

180

Fractional pitch winding is also used to reduce harmonics and get sinusoidal waves

Induced voltage in AC Machine

• The magnitude of flux density at a point around the rotor is given by :

cosMBB

)cos( tBB M

• The magnitude of flux density at a point around the stator is given by :

BM

a-b

c-d

lBvein ).(

Airgap

a

b

c

d

ttvBLeee mdcbain coscos2 tNe cin cos

For N number of coil in each slot

Induced volt in 3 phase coils

)120sin()(' tNte cbb

tNe ctaa sin)('

)240sin()(' tNe ctcc

RMS voltage in three phase stator:

KfNE cA 2

Induce torque in AC Machine

sin

sin2

netRind

netRind

SRSind

BkB

BkB

BkBrliB

AC Machine Power Flow and Losses

Sync. Generator

Induction Motor