Lecture 15 Induction Machines: Principle of

Operation and Equivalent Circuit Model

ECE 492/592 Electric Motor Drives

Introduction to Induction Machines

•

Induction Machines are also called–

Asynchronous machines

–

Rotating transformer•

Main properties–

90% of industrial motor drives

–

Rugged and reliable–

Low maintenance (no brushes)

–

Inexpensive–

Relatively high power density

Induction motor construction

•

Stator construction (same as for the synchronous machine)–

Three windings spatially removed 120 degrees from each other–

Excited by a balanced three phase voltage

•

Rotor construction–

Rotor consists of a winding wound in the rotor slots–

The current in the rotor is induced from the stator winding

Introduction to Induction Machines•

Induction Machine types–

Squirrel cage: rotor winding are shorted; rotor windings are typically copper bars

–

Wound rotor: a winding on the rotor that can be accessed externally through the slip rings

–

We will investigate the squirrel cage induction machine

Squirrel cage (source: daviddarling.info) Wound rotor (source: tpub.com)

Review of Rotating Magnetic Field of the Stator

•

The diagram illustrates how the stator circuit (stator windings) sits on the stator of a simple two pole motor.

•

Each phase winding is capable of producing flux as defined by the right hand rule. If we excite the windings with a 3-phase voltage source, the resulting current through the coils will produce a time varying flux (vectors) by each phase.

c

b

a

The flux vector’s magnitude will be sinusoidal. The sum of the three flux vectors will result in a Net Flux ΦN

. As an example lets examine the flux at time t1

.

max( ) sin 0a t t

max( ) sin( 120 ) 240b t t

max( ) sin( 240 ) 120c t t

( ) ( ) ( ) ( )N a b ct t t t

1 1 1 1 max3( ) ( ) ( ) ( ) 302N a b ct t t t

2 max3( ) 302N t

2 max3( ) 902N t

What results is a rotating magnetic field with a constant magnitude which produces a rotating flux ΦN

.

Review of Rotating Magnetic Field of the Stator (cont)

Rotor Behavior

•

When we excite the stator with a balanced current, a current will be induced in the rotor

•

As a result of the interaction between the two currents, a force will be produced in the motor

Faraday's EMF Lawe Blu

Lorent's ForceF Bli

•

Look back to example from lecture 1

Transformer Model•

Since the induction machine at zero speed (locked rotor condition) is a form of a three-phase transformer with a shorted secondary we will review the transformer model

•

We will assume that both the primary (stator) and the secondary (rotor) are Y-connected

•

We will then investigate a single phase of the motor and realize the other two phases will behave identically with a 120 degrees offset

Ideal Transformer Model

V

+

-

R’

I1

V

+

-

E2

+

-

R

I2

+

-

E1

I1

N1 N2

Ideal Transformer

1 1

2 2

N VN V

1 2

2 1

N IN I

21

2'

NR RN

Practical Transformer Model

R1

: winding resistanceX1

: winding inductive reactance (leakage)RC

: core loss (eddy currents, hysteresis)Xm

: magnetizing reactance of entire transformerIm

: magnetizing current

Primary circuit model Secondary circuit model

E2

: Induced voltage X2

: inductive reactance (leakage)R2

: winding resistance

Developing the Induction Motor Model from the Transformer Model

•

Looking at the rotor circuit, we see that the induced emf

is a function of the rate of change of flux seen be the rotor winding

•

If the rotor is moving at some speed in the same direction as the flux vector, the speed of change in flux will be reduced

2

For stationary rotor 0

where is the synchronous electrical speed

The frequency of the induced voltage is

For moving rotor 0

where is the induced voltage on the

r

e e

e

r

r e r r

dEdt

dE Edt

rotor winding

The frequency of the induced voltage is e r

Developing the induction motor model from the transformer model

•

We want to find the relation between E2 and Er

Er=sE2

sX2

R2

Ir+

-

2

2

,

The parameter is defined as the motor slip

e r e r

e rr

e

d dE Edt dt

E sE

s

Developing the induction motor model from the transformer model

2 2 2

2 2

2 2 2 2

r r

r

E sE I jsX RsE EI

jsX R jX R s

Er=sE2

sX2

R2

Ir+

-

Induction Motor Equivalent Circuit

V

+

-

R1 X1

I1

E2

+

-

X2

R2/sIr

Rc

+

-

E1Xm

I

Im

2' 12 2

2

NR RN

Reflected rotor circuit parameters

2' 12 2

2

NX XN

' 22

1r

NI IN

Assumption: Im

<<I1

, then I1

≈I’2

and the stator and rotor windings are now in series.

'1 2eqR R R

'1 2eqX X X

V

+

-

R1 X1I1

E1=E’2

X’2 R’2

I’2

Rc

+

-

Xm

Im

R’2 (1-s)s

Rewrite the reflected stator resistance: this is done to ease power flow computation.

' ''2 22 (1 )R RR s

s s

Induction Motor Equivalent Circuit

Component related to the rotating rotor