induction machines: 1-phase induction motors 2021. 1. 21. · induction machines: 1-phase induction...

Induction Machines: 1-phase Induction Motors

Principle of Operation Equivalent Circuit Power and Torque Starting Methods and Types Testing

1


Video


Magnetic Field Production & Distribution

. enc

H dl I

.c

H dl Ni

g2g

NiH M 2NiM

p

g gH H Ni

S N

3

Magnetic Field Production & Distribution


i

et

cos( )m ei I t

sM

4


Rotor ReactionAt standstill, the rotor fieldwill always be shifted by 180o

from the stator field at all instances.

sMrM

sins rT kB B

sin180os rT kB B

T zero

5


Double Rotating Field Theory

cosM kNI

cos( )m eI I t

cos( )cosm eM kNI t p sM

fM

bM

cos( )2m

f eIM kN t p

cos( )2m

b eIM kN t p

[cos( ) cos( )]2m

e eIM kN t p t p

60s

fnp

60s

fnp

6



snnsnn

1s

s

n ns sn

2 2ss

n ns sn

7



1

2

1112

m m

m c

V VjV Vj

1 212m m m

V V V

1 2T T

fZ bZ

f bZ Z Z 1 2m mI I 1 2g gP P

1 2netT T T zero

8


Torque-Speed Characteristics9


Motor Starting

MM

AM

M AN N M AX X

cM cAA A M AR RA M

A M

R RX X

sinst M AT I I

M

A

10


Motor Starting

MM

AM

cos( )M Mm eI I t

cos( )A Am eI I t

cosM M MM kN I

cos( 90 )oA A AM kN I

cos( )cosM M Mm eM kN I t p

cos( )cos( 90 )oA A Am eM kN I t p

MA

11


Motor Starting

cos( )cos cos( )sin ]t M Mm e A Am eM kN I t p kN I t p

[ cos( ) cos sin [cos( ) cos( ) sin( )sin( )]]t M Mm e A Am e eM k N I t p N I p t t

[cos( ) cos( )] cos( )[sin( ) sin( )]2 2

sin( )[cos( ) cos( )]2

M Mm A Amt e e e e

A Ame e

kN I kN IM t p t p t p t p

kN I t p t p

[ sin( )][cos( )] cos( )sin( )2 2

[ sin( )][cos( )] cos( )sin( )2 2

A Amt M Mm A Am e e

A AmM Mm A Am e e

kN IkM N I N I t p t p

kN Ik N I N I t p t p

12


Equivalent Circuit at running conditions

aI zero

1

2

1112

mm

am

II jII j

1 212m m m

I I I

1 212m m m

V V V

13


Equivalent Circuit at running conditions

aI zero

fZ

bZ

1 1

mm

f b

VIR jX Z Z

14


Power Flowcosin m m mP V I

21 1cu mP I R

2gf m fP I RfZ

bZ

2gb m bP I R

2: :

1 : : (1 )gf cuf dfP P P

s s2: :

1 : 2 : (1 (2 ))gb cub dbP P P

s s

2 2 2cu cu f cu bP P P

(1 )( )d df db gf gbP P P s P P

out d mechP P P outoutPT

15


Motor Types1. Split-phase (resistance-start) Motor

16


Motor Types1. Split-phase (resistance-start) Motor

17


Motor Types2. Capacitor-Start Motor

18


Motor Types2. Capacitor-Start Motor

250 W (1/3 hp) motor, 4-poles, 110 V, 60 Hz

19


Motor Types3. Capacitor-Run Motor

20


Motor Types4. Capacitor-Start, Capacitor-Run Motor

21


Starting Winding DesignAt starting (n=0, s=1)

MM

VIZ

A

A

VIZ

MM

VIZ

AA C

VIZ jX

22


Starting Winding Design

VV

AI

M MI R

MI

AI

A

MMA

V V

M MI R

A AI R

A AI R

( )A C AI X X

M MI XM MI X

A AI X

MI

23


Starting Winding Design1. Design of Resistance-Start Motors

For max. starting torque:

A AI R

M MI R

V

M MI XA AI X

sinst AT I

sinA AI X

COA

B

A Add

A

R RABBC X

24


Starting Winding Design2. Design of Capacitor-Start Motors

For max. starting torque:

M MI R

V

A AI R

sinst AT I

sinA AI R

COA

B

C A

A

X XBCAB R

( )A C AI X X

25


Testing: 1. Locked Rotor (Standstill)Test Voltage is adjusted such that stator current ≤ full load currentMain winding only is connected

NLW1 2LR cu cuW P P

'1 2LRR R R

2LR LRW I R

'1 2 2

LRRR R

LRV

LRI

LRLR

LR

VZI

2 2LR LR LRZ R X

'1 2LRX X X

'1 2 2

LRXX X

0n

1s mm

26


Testing: 1. Locked Rotor (Standstill)Test To get the standstill impedances of the main and auxiliary windings, this test is performed on each winding individually.

'1 2M mR R R

'1 2M mX X X

''1 2A aR R R

''1 2A aX X X

M M MZ R jX A A AZ R jX

mm aa

27


Testing: 2. No-Load Test

1NL mech cuW P P

'2 2

1 1( )4cu NLRP I R

mechP

0s NLI

NLV

NLW

NLNL

NL

VZI

2 2NL NL NLZ R X

'2

1 2 2NLXXX X

'2

12 ( )2NLXX X X

28

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induction machines: 1-phase induction motors 2021. 1. 21. · induction machines: 1-phase induction...

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