21 IM Equivalent Circuits

8/15/2019 21 IM Equivalent Circuits

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Induction Motor Introduction

and Equivalent Circuit


2/22

UCF Induction Machine - IntroductionA machine with only armortisseur windings is called an

induction machine.

No DC field current is required to run the machine. Rotor

voltage is induced in the rotor windings rather than being

physically connected by wires.

Induction machine has the same physical stator as a

synchronous machine with a different rotor construction.

Induction machines can be operated as either motors andgenerator. However, they are primarily used as induction motors.

Induction machines are by far the most common type of motor

used in industrial, commercial or residential settings.


3/22

UCF IM Stator

Stator for a 2hp induction machine

http://www.ece.ualberta.ca/~knight/ee332/induction/basics/construction.html


4/22

UCF IM RotorTwo types of rotors for induction machine:

Cage Rotor

Wound Rotor


5/22

UCF Cage RotorA cage (or squirrel-cage) rotor consists of a series of conducting bars

laid into slots carved in the face of the rotor and shorted at either end

by large shorting rings.

skewed


6/22

UCF Wound Rotor (1)A wound rotor has a complete set of three phase windings usually Y-connected.

The ends of three rotor wires are tied up to slip rings on the rotor’s shaft, where

extra resistance can be inserted into rotor circuits for control.


7/22

UCF Wound Rotor (2)

skewed


8/22

UCF IM Basic Concepts: electrical frequency on stator

synchronous speed in revolution/second/ 2

120 synchronous speed in rpm

60: mechanical speed or speed of the rotor

: stator's magnetic field,

e

esync

sync esync

m

S

f

f f P

f f n

Pn

B rotates at synchronous speed

: rotor's induced magnetic field, rotates at synchronous

speed, follows at steady state

R

S

B

B

But the rotor will not follow BS.


9/22

UCF Concept of Rotor Slip

%100

sync

msync

f

f f s

syncm nsn )1(

)1(

)1(

syncm

syncm

f s f

s

P

f n

P

f n f

esync

esync

syn

120

2/60


10/22

UCF Rotor Electrical Frequency

: rotor electrical frequency

: speed (rev/s) of relative to the rotor/ 2

r

r slip R

f

f f P

B

Since BR follows BS, we have:

sync m slip f f f

slip sync m sync f f f sf

60

slip

slip

n f

2 2r slip sync e

P P f f sf sf

2 120

slip

r slip

n PP f f


11/22

UCF Example 1

details in im1.m


12/22

UCF Equivalent Circuit of Induction Motor (1)

meff e N f E 44.41

stator copper loss

meffRe R

RmeffRe

meffRr R

N f E

sE N sf

N f E

44.4

44.4

44.4

0

0

effR

eff

R

eff N

N

E

E n

0

1

RI

From Bnet

leakage


13/22

UCF Equivalent Circuit of Induction Motor (2)

Re R

R Re Rr Rr R

L f X

sX Lsf L f L X

2

22

0

0

0

0

0 / R R

R

R R

R

R R

R R

jX s R jsX R jX R

EEE

I


14/22

UCF Equivalent Circuit of Induction Motor (3)1:eff n

per phase equivalent circuit

0

2

2

2

2

Reff

Reff

X n X

Rn R


15/22

UCF Thevinin Equivalent Circuit

Thevinin equivalent circuit M c

M c M c M

jX R

X jR jX R Z

//

11

11

11

)(

)//(

jX R Z

jX R Z

jX R Z Z

M

M

M TH

TH TH TH jX R Z

VV

11 jX R Z

Z

M

M TH


16/22

UCF Induction Motor Power Flow


17/22

UCF Example 2

details in im2.m


18/22

UCF Power and Torque (1)

2

2

2

I n I

Rn R

eff R

Reff


19/22



20/22



21/22

UCF

Per Phase Equivalent Circuit with Rotor Loss and

Converted Power Separated


22/22

UCF Example 3

details in im3.m

21 IM Equivalent Circuits

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