topic 8 acinduction

Jan-May 2010 Electrical Machines & Drives - ECNG 3010 8 -

Induction Motors

Most common of all motors.

“Workhorse” of industry.

Stator Three phase distributed winding.

Rotor Distributed three-phase winding. Cage of interconnected copper bars.

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Induction Motor

Salient features of an induction motor :

Simple and rugged construction.

Low cost and minimum maintenance.

High reliability and sufficiently high efficiency.

Needs no extra starting motor and need not be synchronized .

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No connection between primary and secondary.

Primary and secondary linked magnetically.

Rotor

Stator One set of three phase windings connected to supply→

primary or excitation (field) winding.

Single phase and three phase machines.

Introduction Induction Motor

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Rotor Induction Motor

Stator

Stator winding

Rotor

Squirrel cage

Squirrel-cageBrushless.Thick copper bars.Short circuited by rings.

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Jan-May 2010 Electrical Machines & Drives - ECNG 3010 8 - 5



Rotor Induction Motors

Wound RotorWindings - Double layer of distributed winding.Terminals connected throughoutslip ring.Secondary windings could be connected to electrical supply.

Rotor WindingStator

Stator winding

Brushes

Sliprings

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Rotor Induction Motors


Magnetic Field

Single turn of stator winding – DC supplyRotor

Current out of surface

Current into surface

Air gap

Stator

Magneticfield lines

0

Bf

δ

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Distributed Winding

Mmf of individual coils

Resulting mmf approximatedby a sine wave

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Distributed Winding


Distributed Winding

Multiple turns of stator winding

The effect of multiple turns is to concentrate the magnetomotive force in the center.

This can be approximated by a sinusoidal distribution of mmf and of flux.

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Distributed Winding


Distributed Winding

П

0 2 П

Field strength along the air gap

0,2П

Approximates a sinusoidal distribution in space П

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Energization with AC1

2

3

4

5

61

2

3

4

5

6

τ0 0,2τ

Sinusoidal flux distributionin the air gap,

a space function

F = kf N Imaxcos sin(ωt)πxτ

1

2

3

4

56

time

curr

ent

Sinusoidal currentwaveform,

a time function

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AC field as Two Rotating Fields

Fmax/2

Forward rotating

field

Fmax/2

Reverse rotating

field

Fmax cosӨ

-ӨӨ

MMF at instant ‘t’,a space functioncentered on the

winding axis

Instant ‘t’

time

current

Ө

Sinusoidal currentwaveform,a time function

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Stator with Balanced Three Phase AC

Direction of maximum mmfB phase coil

Direction of maximum mmfC phase coil

Direction of maximum mmfA phase coil

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F = kf N Imaxcos sin(ωt)πxτ

F = kf N Imaxcos πxτ -

2π3

sin ωt - 2π3

F = kf N Imaxcos πxτ +

2π3

sin ωt+ 2π3

A phase mmf :

B phase mmf :

C phase mmf :

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Fa = kf N Imaxcos sin(ωt)πxτ

= ½ kf NImax cosπxτ

- ωt + cosπxτ + ωt

Fb = kf N Imaxcos2π3

πxτ

- sin2π3

- ωt


- ωt + cosπxτ

+ ωt4π3

-

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Fc = kf N Imaxcos2π3

πxτ

+ sin2π3

+ ωt


- ωt + cosπxτ

+ ωt4π3

+

F = Fa + Fb + Fc = 3

2kf NImax cos

πxτ

- ωtTotal mmf


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reverse

reverse

reverse

forward

A

B C

The three reverse rotating fieldscancel each other.The three forward rotating fields add to each other.

The resultant is an mmf that is 3/2 times that of one phase and rotates.

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22


a’ a a’

a

a’ a

a

a’

a a’

a’a

Two polemachine

Four polemachine

Six polemachine

Only phase a winding is shown

Electrical synchronous speed in all cases is 2πf rad/secThis is the speed of the rotational magnetic flux.

i.e. one cycle produces movement of magnetic field fromcenter of a phase coil of center of a phase coil.

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Synchronous Speed


Synchronous Speed


Synchronous Speed

a’ a a’

a

a’ a

a

a’

a a’

a’a

Two polemachine

Four polemachine

Six polemachine

Mechanical synchronous speed =

60*f/(p/2) rpm

For a machine energized from a 60 Hz system,mechanical synchronous speed is :

2 pole machine: 3600 rpm4 pole machine: 1800 rpm6 pole machine: 1200 rpm

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Rotor Phenomena - Slip

Stator Field

Direction of rotation

Direction of torque on rotor

• Voltage is induced in the rotor conductors (current because short-circuit).

• Interaction of stator field and rotor currents produces a torque on rotor.

• What if rotor rotates at synchronous speed?

• Speed depends on torque.

Rotor slip ‘s’ is defined as :s = 1 – nr /ns

Where ns and nr are mechanical synchronous speed and rotormechanical speeds, respectively.

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Definition of Slip

slip = s =ωs – ωm ωs

= ns - nm

ns

; ωs= (4Πf/p) rad/sec

; ns =120f

prpm

We can manipulate to get :

nm = ns(1 – s)

ωm = ωs(1 – s)

Slip speed = ns - nm

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Equivalent Circuit of Induction Machine

Rotorfield

Stator field

Torque

Rotor at stand – still

• Stator field at Ns.

• Slip s = 1.

• Rotor frequency f.

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Induction machine behaves like a transformer : there is a primary winding and a secondary winding.

At stand – still, the voltage induced in the rotor winding is proportional to turns ratio: E2 = E1 (N2/N1)

The only difference is that the secondary winding is short – circuited.

N1 : N2

E2im

I1

I2

R1 Xl1 R2 Xl2

ic

E1

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Rotorfield

Stator field

Torque

Rotor turning

• Stator field at Ns.

• Slip s.

• Rotor frequency sf.

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Relation Between Frequency and Slip

Rotor @ speed N2

Synchronous speed N1

Slip speed = N1 – N2

Internal voltages (e.m.f.) & current in rotorhave a frequency f2

f2 =N1 – N2

N1

f1 = sf1

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Rotor Phenomena – Slip

Induction machine action is similar to that of a transformer.

Stator current frequency : f Rotor current frequency : sf

When the induction machine acts as a motor, ‘s’ is positive, i.e. the rotor speed is always less than the mechanical synchronous speed.

When the induction machine acts as a generator, ‘s’ is negative. i.e. the rotor speed is always greater than the mechanical synchronous speed.

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As the rotor begins to turn, the frequency of induced voltages becomes sE2, since according to transformer theory the induced voltage is proportional to the frequency.

The leakage inductive reactance also changes to sXl2

sE2im

I1

I2

R1 Xl1 R2 sXl2

ic

E1

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Three versions of rotor current

sE2

I2

R2 sXl2

E2

I2

R2/s Xl2

E2

I2

R2 Xl2

I2=sE2

R2 + jsXl2

=E2

(R2 /s)+ jXl2

=E2

(R2 +jXl2) +R2(1 – s )/s

R2(1 – s)/s

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E2im

I1

I2

R1 Xl1 R2 Xl2

ic

E1

N1:N2

R2(1 – s)/s

E2im

I1

I2

R1 Xl1 R’2 X’l2

icE1R2’(1 – s)/s

Impedancesreferred to theprimary side

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Equivalent (per phase) Circuit

V1

R1 jX1 R’2 jX’2

R’2(1-s)/sRc jXm

Statorwinding

Airgap

Rotorwinding

Mechanicalload

I’2

I1

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Comparing with Transformer

Equivalent circuit Similar to a transformerPer phase equivalent circuit

E’2Im

I1

I’2

R1 jX1

R’2

jX2

Iw

E1

Io

Rfw jXm

Air gap

V1

np ns

Higher relation |Io| / |I1| than transformers

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Motor output power

(1-s)Pg = |I2|2(1-s)R2/s

Power Flow Through an Induction Motor

Pin

Motor core loss

|Iw|2RFW

Primary copper loss

|I1|2R1

Air-gap power

Pg = |I2|2R2/s

Secondary copper loss

|I2|2R2

Friction and Windage PowerTFWN

Power delivered to load

TLN

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E2

Im

I1

I2

R1 Xl1 R’2 X’l2

E1R2’(1 – s)/s

A possible simplification is to neglect core loss component in the circuit.

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topic 8 acinduction

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