3-phase induction machines

8/14/2019 3-Phase Induction Machines

1/22

Lecture 24 - EE743Lecture 24 - EE743

3-Phase Induction Machines

Torque Speed characteristics

Professor: Ali KeyhaniProfessor: Ali Keyhani


2/22

2

Importance of T-speed characteristics

s Torque speed characteristic of a motor is important from

the point of view of its applications to specific situations.

To calculate the torque produced by the machine, first, we

compute the motor power. The motor power, or the

mechanical power supplied to the load is

The electrical power inputted to the machine can be

calculated from the eq. circuit given below

lossesinem PPP =


3/22

3

Importance of T-speed characteristics


4/22

4

Machine Torque

s Power dissipated is

s Motor power Pem is

s Motor torque can be calculated from

{ }

+==s

RRIIVP

'2

1

2

1*

111 3~~

Re3

extrotor RRR

XaX

RaR

+==

=

2

22'

2

22'

2

( ) ( )'212

1221

2

1 33 RRIRaRIP +=+=

( ) 21'2

'21

'2

1

2

1

133 IR

s

sRR

s

RRIPem

=

+

+=

memem TP =2

1'2

13IR

s

sT

m

em

=


5/22

5

Machine Torque

s Since Tm can be written as

s Substituting for I1 in equation (3), we will have

( )ssyncm = 1

2

1

'23 I

s

RT

sync

em

=

( )

2'

21

2'2

1

2

12

1

XXs

RR

VI

++

+

=

( )2'212'

21

2

1

'

23

XXs

RR

Vs

RTsync

em

++

+=


6/22

6

Power calculations

s Figure 2 shows the plot of equation (3) for the values of slip

from zero to unity. In Fig.1 . This

corresponds to the normal range of the speed of an induction

motor from starting (m=0, s=1) to the synchronous speed (m=

sync, s=0)

( )extRRaR += 22'

2


7/22

7

smax and Tmax calculation

s To find smax first set derivative of (4) with respect to s

equal to zero.

s Which will results in

s substituting smax in (4) will result in Tmax

0=ds

dTm

( )2'2121

'2

max

XXR

Rs

++=

( )

+++

=2'

21211

2

max2

3

XXRR

VT

sync


8/22

8

Torque-speed characteristic

s Equation (5) shows that the slip at which the maximum torque

occurs is proportional to the rotor resistance. Equation (6) shows

that the maximum torque is independent of the rotor resistance


9/22


10/22

10

Torque-speed characteristic

s Case 1: sync and m are rotating in the same direction and

sync is rotating faster than m.

s Case 2: sync and m are rotating in the same direction and sync is rotating slower than m.

s Case 3: sync and m are rotating in different directions.


11/22

11

Torque-speed characteristic. Case 1.


sync is rotating faster than m. This case is the normal operation of the induction machine. Machine

operates as a motor. Note also in equation (7) sync and m are inthe same direction and the slip is positive for motor operation


12/22

12



sync is rotating slower than m. If the speed of the machine is increased beyond its synchronous

speed by an external prime motor, but still rotated in the same

direction as the stator field, the slip will be negative (s


13/22

13


s Case 3: sync and m are rotating in different directions. Suppose an induction motor is operating under normal conditions at

the same value of positive slip in stable region (0


14/22

14

Example 1

s On no-load a 3-phase delta-connected induction motor

takes 6.8A and 390W at 220V line to line. R1=0.1/phase,friction and windage losses are 120W. Determine Xm,and

Rm

of the motor equivalent circuit.

AII linephase 926.33

8.6

3===

LLphase VVV == 220 WRI phasephase 54.12 =

m

phase

RVWlossesCore

2

46.8854.13120390 ===

== 14.54746.88

2202

mR ==

110828.1

1 3

m

mR

G


15/22

15

Example 1

=== 11084.17

220

926.3 3

V

IY mm

=== 1

10746.17

1 322mm

mm GYXB = 35.56mX


16/22

16

Example 2

s The motor of the previous example take 30A and 480W at

36V line-to-line, when the rotor is blocked. Determine the

complete equivalent circuit of the motor. Assume that

X1=X2.

( ) eqeqeq XRZXX ==

==+ 0.2533.0

3/30

36 22

22'21

( )( )

eqRRR ===+ 533.03/30

3/4802

'21

== 433.01.0 '21 RsoR

== 12

21eqX

XX


17/22

17

Example 3

s An induction motor has an output of 30kW at =0.86. Forthis operating condition Pcoil,1=Pcoil,2=Pcore=Prot.Determine the slip

3,

0

inP

PEff=

WEff

PPin 884,34

86.0

000,3003, ===

WPloss 884,4000,30884,343, ==

M


18/22

18

Example 3

WPPPPP rotcoreRAG 663,33'20=+++=

3,

3,'2

AG

R

P

Ps = WP

R221,1

4884,4

'2

==

%6.3036.0663,33

221,1ors ==


19/22

19

Example 4

s A wound rotor six-pole 60Hz ind. motor has R2=0.8 andruns at 1152 rpm (s=0.04) at a given load. The load torque

remains constant at all speeds. How much resistance must

be inserted in the rotor circuit to change the speed to 960

rpm (s=0.2). Neglect the motor leakage reactance, X1 and

X2.

The air gap power function is:

( )2'212'

21

21

'2

'2

2'2 33

XXs

RR

V

s

R

s

RIPg

++

+

=


20/22

20

Example 4

s If (see eq. circuit ), the voltage, current,

air-gap power, and torque conditions remain the same, i.e

tconssR tan

'2 =

..

'

2 ConstTthenConstsR ==

2.004.0

''2

'2 insertRRR +=

=== 2.38.0)8.0(504.0

2.0 '2

'2

' RRRinsert


21/22

21

Example 5

s A 400V, 3-phase WYE connected motor has

, and

using the approx. eq. circuit. Determine the max.

electromagnetic power, Pd

( ) phasejZ /2.16.01 += ( ) phasejZ /3.15.0'2 +=

( )2'212'

21

1

21

1'2

XXs

RR

V

ZZ

VI

++

+

=+

= VV 2313

4001 ==

( ) 22

'2

5.25.0

6.0

231

+

+

=

s

I


22/22

22

Example 5

( ) ( )sfunctionIRs

sPsRIPP ggd =

===2'

2'2

'2

2'2

11

CBss

ssAPd

++

=2

2

( )

( )( )Bs

CBss

ssA

CBss

sA

ds

dPd +++

++

== 221022

2

2155.0

max=

dPats

( )( )

WCBss

ssAP

s

phased 962,6

155.0

22

2

max,, =++

==

WP phased 886,20962,633max,, ==

3-phase induction machines

Documents