IEV 411 Starting method

winding current

%

mains current % torque % interruption starting time critical

-22-18 direct - - - no no

-22-26 series-parallel 1/2 1/4 1/4 yes no

-22-19 wye-delta 1 ⁄ √3 1/3 1/3 yes no

-22-20 auto-transformer

α α2 α2

-22-21 with 2 switches

α α2 α2 yes no

-22-22 with 3 switches

α α2 α2 no no

-22-23 stator inductance

α α α2 no yes

-22-25 stator resistance

α α α2 no yes

Table 1 Classical starting methods

jXml

(jx ml)

(jx 2!)

jX'2!

(jx 1!)

jX1!R'2/s

(r2/s)

R1

(r1)

I1

(i1)V1

(v 1)

I'2(i2)

Iml

(iml)

E1

+

_

+

_

jXm

(jx m)

(jx!)

jX!

R/s

(r/s)

I1

(i1)

V1

(v 1)

I

(i)

Im

(im)

+

_

X = X + X = (1+ )X = Xm l ml l ml l!!

lX1 !

!

"

X = X (1+ )+X' (1+ ) =! ! !l l 2 l! !

2

R = (1+ ) R'

= ' /(1+ )

!

!

l 2

2 l

2

I I

(a) (b)

s/r

til

1

2

3

11x

!

(b)

im il

i

v l

(a)

tmin

tmax

tpo

0

n n-1

2 1 0

0s1s2 sosns =1n+1

t

s

! " "r r sy= /

(c)

r =0,052

0,05 0,15 0,35

0,7 1,4 2,8

(b)

r =0,052

A

B

C

D

E

0,05

0,1

0,2

0,4

0,8

(a)

2

1

01 0,5 0

s

t

Ru

Ru

Ru

(a)(b)

!r

w

!r

0

!"

#!

"#

!"

#

rr

2rr

4rr

8rr

rr

2rr

4rr

16rr

20rr

24rr

32rr

rr

2rr

4rr

!"

#

II

III

Ib

Ia

t

!"

"r

rsy

=/

1

-1 1

-1

1 > > 0!

l > s > : motoring!

Pem1

sPem1

!Pem1

(1-s)Pem1

P =(s- )Pj2 em1!

P2

Pm

Pm

P =(s- )Pj2 em1!

P2!P

em1

sPem

1

(1-s)Pem1

Pem1

s > 1 > : reverse braking!

Pem1

Pm P2

(1-s

)Pem

l

!P

eml

(s-

)P!

eml

Pj2

s > 1 > 0 > : reverse braking!

P2

!Pem1

Pem1

(1-s)Pem1

Pm

P =(s- )Pj2 em1!

l > s > : motoring!

0 > > s : generating!

Pem1

Pm

P2

sPem1

(1-s)Pem1

!Pem

1

P =(s- )Pj2 em1!

! > s : generating

Pem1

Pm

P2

Pj2

(1-s)Pem1!Pem1

(s- )P! em1

(here s > 0)

0 > !

Pem1

sPeml

P2"!Pem1

(1-s)Pem1

positive sign references :(URS primary, GRS secondary)

(here s < 0)

Pem1

P =(s- )Pj2 em1!:

adjustableDC source

Eg

Em

s001

00

s

! " "r r sy= /

E =K. . (1-s)g sy#$$" %

E = k.E = k.s.E'm 2 1

!"

#

1

(a) (b)

P <0

P >0

P >0

(P >0)

m

eml

2

em2

P >0

P >0

P >0

(P >0)

m

eml

2

em2

P <0

P <0

P <0

(P <0)

m

eml

2

em2

P <0

P <0

P <0

(P >0)

m

eml

2

em2

P <0

P >0

P <0

(P >0)

m

eml

2

em2

P >0

P >0

P <0

(P >0)

m

eml

2

em2

P >0

P >0

P <0

(P <0)

m

eml

2

em2

P <0

P <0

P >0

(P >0)

m

eml

2

em22

2

1

1 0

0

!

!

!"#$%&!"$!"$%'

!"(%'

2

10

1

1

0

2

-1(b)

(a)

(0)

(c)

)

s

s

s

generator

generatormotorreverse braking

reverse braking motor motor0>!

1> >0!

( c)

!r

w

!r

(b)

!r

w

!r

(a)

slip energyconversion 50Hz

(a) (b)