energetski pretvarači i električne mašine

8/12/2019 Energetski pretvarai i elektrine maine

1/124


2/124

2 1

, . -

1.1.2

, . . - , . , . , . - , - . , .

, , .

1.1.3

- . , , , . , . - , , .

, - . - , - - . - ,


3/124

1.1 3

, , , . - , - . , - .

1.1.4

- . . - , - . -

, ,

, ,

, -

, -, - .

1.1.5

-

. , . - . - , - . - , , - -


4/124

4 1

. , , , , . . , , , , - .

1.1.6

- . - , 1.1. . - .

1.1. , , , - .

, , - . - . 1.1, - k A B. . , - . , - , - . N , - (1.1).


5/124

1.1 5

=

= N

k k k e iu p

1

(1.1)

, . , . m. , 1.1, - . - . - .

. M em, M m. , m . - .

mmm M p = (1.2)

. , pm . M m - , M em, , - . 1.1, . p e, (1.1), - , . , pe .

1.1.7

. - , , . - , , . - , - ,


6/124

6 1

. . , . , , .

1.2. - .

pe pm, , - . -

, , - . , - . , pm pe . , (- pe) - (- pm) .

1.2. .

1.2

. - ,


7/124

1.2 7

- , , , - .

, , - 1.3. .

(A) -

, , , , , , ,

. - .

(B) .

, - - . - m, M m. , .

(C) P m = m M m -

, - .

(D) 0,5

MW 1000 MW. . . . , . , - . , - u(t ). .

- . pe = ui. , - - M em. - . ( -


8/124

8 1

), . , M m, , - , M em - . - . , . 1.

() -

. -

6kV 25 kV, 50 Hz 60 Hz. - 2.

1 19. , , , - . ( - ) , . - . , - . -

, . . - . . . 400 V, -. 231 V. - - , - .

2 ,

, , . - . . .


9/124

1.2 9

750 kV, 1000 kV .

(F)

, , . . 10(20) kV, 10(20)/0,4 kV/kV 400 V - 231 V, . - , -

.(G)

, , , , , - , , , , , - , , , . - , , , - , , , , ,CD/DVD , . 8% - , - .

(H) , 70% - - , , . , - , , , - , . , - , -

, . - , - - .


10/124

10 1

1.3. .


11/124

1.3 11

1.3

. -, . - , .

( ) m. ,d m/dt = m, . m . . , - , .

- , - . SI , s -1, . f = /2 - (Hz). ,

mm n 54,9260 =

.

(1.3)

M em . - . M em - . M em . F , , , . 1.4 M em = FD , R = D/2 .

1.4 M em = FD , R = D/2 - .


12/124

12 1

M em M m, . , M em > M m, . , . - (1.4).

memm M M Ja

t

J ==d

d

(1.4)

1.4 . .

a = d m/dt - [rad/s 2] . , .

M em M m. J .

, J = J R + J RM - J R

J RM . 5 -


13/124

1.3 13

. - , R m. J = mR2.

(1.1): -

R m. .

(1.1): J RM = mR

2.

1.5. () (B). (C) .

1.3.1

, (u p , i p , p p = u p i p) - - (U p , I p , P p = U p I p), (IEC). - F , M . - M m -

. , . , s-1. . z - . ,


14/124

14 1

3. , uS iS . , uS iS . , . uS iS . - U S I S . [A] A. - ( ). sin, cos, rot, div, mod, d , , .

, , , F H B ,, . , B,

H , F .

. , - . , - .

, (SI) 1954. . . SI . , SI - . , W - F , l , 4. SI , W [J]= F [N] l [m], ,

3

. - space vector . . . " V " .

4 W = Fl , .


15/124

1.4 15

1 J = 1 N 1 m. , , Fl . - . , - . . V s = Wb, Nm rad/s = W, Nm rad = J, A =V, A H = Wb = V s, .

1.4

- . - . - , , , , - , . , - , , - .

- , . - , , . - . , , - ( ). -

. -

. . , . -


16/124

16 1

, , , , . , .

1.4.1

, , , , - . - , , , , - . - - , , .

1.4.2

. - , . , ( ) - . , , - . - , , , - .

1.4.3

, , . - . - M em( m) M em- m . -


17/124

1.4 17

- .

1.4.4

, - , , , . . , . . - . - . , . - , , -. , - ( ). - ( ) - . . - - - . - - .

. , , .

, .


18/124

18 1

1.4.5

- - . - u = Ri + d /dt , J d m/dt = M em M m. J R , m - ( ). , , -

, - . - , -. , , .

, . - , . , , E -

. , - , -. . , .

, . - - . , - .

1.5

- . , , - . -


19/124

1.5 19

, , , , - , . , . , . - , , - , - . - - , -

, , .

- . - . , - . - . -, . -

- , - . , , , , - . , - . . . . N , , . - , - .


20/124

20 1

, ( ), ( ) ( ). , , , - , , , . - -. , - - .

,

, , , - , . , , . , , .

- . , 5 - . ,

. -

, - . , - , - .

1.5.1

, - , -

-

5 , , ,

. - ( ) . . , .


21/124

1.5 21

. . , - . 2. - - , . , - . , , - ( ), . - , -

. , - , - - . , - . - . , , . - . - . , - . , - .

, - , , . , - , - . - , - .

1.5.2

. - , - , , - . - . -


22/124

22 1

.

. :

, - , . - - . , , , - . - .

, - 1 kHz. - - . - . -

. -

. , - .

, - .

1 GW. , - , - 50 Hz. - , -


23/124

1.5 23

, - .

- - , . - , .

: - ,

. - - . - - . , - ( ) - . , - ( ). - . - ,

, , - . - . - 50 Hz, . . , - , .

: - . - , - . . -


24/124

24 1

. , . , - . - - , , . , - , , .

. , . , . , .

:

, , . , - P, - - , M em = P / , - .

- . , - , . : - - .

, - - . ( ) .

- . -


25/124

1.5 25

, - . - . , - . - , .


26/124

2

. - . -

. , - . - , . , .

2.1

. - , - .

- , - Q v - .

( ) BvQ E Q F += (2.1) , -

. - B

. , (2.1) - .

2.1 l - i - B. F


27/124

28 2

i , l , B - . - 2.1, . - x, y, z, , .

2.1. .

( ) Bl i F i B B

il l

z

x

==

=,

,

(2.2)

, F = l B i. l B. y y, W m = F y. v y, pm = Fv y. , pm . , , pm , .


28/124

2.2 29

, , e. - e i ( pe = ei ) - ( pm = Fv y). , pe pm. .

2.2

- - . , .

2.2 . (A) . (B) - . (C) .


29/124

30 2

, 2.1. - .

, . , .

, - . 1 A , d = 0,1 m, - - .

(2.3).

T102T1,02

1104

267

0

=

==

d

I B

(2.3)

- , - l = 1 m (2.4).

N102 6== I Bl F (2.4)

, , 1 - , .

2.3

, . -

1 . S B. S C , . S , S - , = BS . , S .


30/124

2.3 31

2.3 , , . - l , v y . , F s. B z .

- E ind . . - Q, , (2.1), .

( ) ( ) ind E Q BvQ BvQ E Q F ==+= (2.5) , -

QE . F Q, B.

Bv E ind = (2.6)

2.3. - .

e - l . ,


31/124

32 2

E ind . , (2.7).

( ) Bvl E l e ind == (2.7) , x , -

z , - y . (2.8), a a e = lvB. e , - l .

lvB E l eivB E

ivvi B Bil l

ind xind

y z x

======

,

,,,

(2.8)

2.4

, 2.3, -

, e, - R. 2.4. - , i = e/ R. - , - R . - , . i- F m (2.2). F s , F m. - 2.4, - F sv ei.

e = lvB, , - u = Ri, R. , 2.4, , (2.9).

( ) yiilB Bl i F == (2.9)


32/124

2.4 33

, F s F m . . e, i = e/ R .

2.4. , - R .

, , - v , - .

ilB F F F F F F m sm sm s ====+

;;0 (2.10)

F s P m = F sv = ilBv. - e P e = ei = ilBv = P m. P e = e

2/ R > 0, - . , , , , ( P e = P m).

(2.1): , 2.4, - , ?

(2.1): , - - , .


33/124

34 2

2.5

e - . 2.5 - ( Fe >> o), . , .

2.5. , - .

. , , ( ) , , . ( ) - . - ( ) - . , .

, - . .

.

(2.2): ?


34/124

2.6 35

(2.2): -

. , . . - , , . . - , - .

2.6

2.6, - . . - B , B .

2.6. .

2.6 . , . , - .


35/124

36 2

, ( ) . , .

- , .

2.7

, -

E , 2.7. -, . - , - .

. . F . x, F x.

- , .

2.7. .


36/124

2.8 37

2.8

, , . 2.8, - = r 0. - 0.

r >1 . ,

x = a , . - , x = 0, . - 0 < x < a F - .

2.8. - .

U , E - E = U /d , d .

, U = Ed - , - . - D = r 0U /d , D = 0U /d . (2.11), S = ab .


37/124

38 2

( )[ ]r

r e

x xaa

Sd d U

Sd a x

d U

Sd a

xad U

W

+

=

=

+

=

2

0

2

0

2

0

21

21

21

(2.11)

U , - , F x W i = W e + W meh ( 2.19).

(2.12).

( )121

d

d 20

== r

e

aSd

d U

x

W F

(2.12)

F - . , p = we1 - we2, we1 we2 . w0 = 1 0(U /d )2, wd = 1 r 0(U /d )2, F (2.13), S d = bd = Sd /a .

( ) ( )a

Sd d U

S ww F r d d

== 1

21

2

00 (2.13)

(2.3): . -

Q , .

(2.3):

. - 1/ . U - . , Ed U , E =U /d .


38/124


39/124

40 2

( )2

0

2

0

2 11

21

dd

2

+=

+=

r r

r x xabd Q

x xa xbd Q

F

.

, . Q =CU ,

( ) ( )a

Sd d U

d bU

F r r 121

2 22

002

== ,

(2.12) (2.13). x, .

(2.4): 2.8

. E D - ? ?

(2.4):

, r . wed = 0 r E

2/2 r wev = 0 E 2/2 . -

wevV v + wed V d , wev wed , V v V d - , . - , V v - V d . wev < wed , . , , - . - Q , , E . - E , - . - W e( x),


40/124

2.9 41

( ) 0

22

221

b x xad Q

C Q

W r

e+

== ,

, Q , .

2.9

, , . - . - , , . , - , .

- . ( ).

-

. - , - . . , - . - .

. - -

, .


41/124

42 2

2.9. - .

2.10

o

. , - - . 2.10 - . , , - , . , - .

. - .

2.10. - .


42/124

2.11 43

- 50 Hz, - . - , - .

2.11

- . -

. , .

- - , 2.11. (S >> d 2), - E = U/d [V/m], U . D [As/m 2] E 0. . , . - .

2.11.1 ,

, - , E =U /d. D - Q/S . D E ( - ) 0.

d U

S ES Q E S Q

Dd U

E 000 ;; ====== (2.14)


43/124

44 2

2.11. - .

C - Q U . , - - .

d S

U Q

C 0 == (2.15)

- we . , . - we = 0 E 2. V =Sd , W = CU 2 = Q2/C .

( )

C Q

CU E Sd

V E V E DV wW V V V

ee

221

21

d21

ddd2

220

20

==

=

=

===

(2.16)


44/124

2.11 45

2.11.2 ,

2.12, - . . , F . , x, F x. , - W e - .

F

, . x. , . W e , . ( ) .

2.12 U . , C .

, . , Q = CU , Q. W i = U Q, W meh = F x. , - . , (2.17).

, , W e = W meh = W i.

2.12, , . , D , .

, - . - , W meh = - W e. - , (2.18).


45/124

46 2

( ) ( ) xd

S U CU E xd S xW e

==

=

-221

21

- 02

220

(2.17)

( ) ( )S xd Q

C Q

E xd S xW e0

222

0-

2221

-

==

=

(2.18)

2.12 . .

2.11.3

. - , , -

. 2.12 - . - W meh = F x W meh = - W e, W meh = W i. , x, - .


46/124

2.11 47

, 2.12 . - , (2.19).

emehemehi

i

W W W W W

QU W

=+===

0

(2.19)

F , - (2.20). W e x - , W e/ x W e( x) x = x x = 0.

0

2

0

2

2-

2dd

dd

S Q

S xd Q

x xW

F

xW

F

e

e

=

==

=

(2.20)

, . , - (2.21).

eeimehemehi

iei

W W W W W W W

W QU CU

W QU W

==+=

==

==

2

1

2

1

2;

2

(2.21)

F , - (2.22). W e x - , W e/ x dW e( x)/d x.

( )

0

2

0

2

0

2

20

20

2

222

-2-2dd

dd

S

QS

DS

E

xd

S U xd S U

x xW

F e

===

==

=+=

(2.22)

(2.20) (2.22) - , , - . , , - C . ,


47/124

48 2

=

==

C xQ

C Q

x xW

F e1

dd

21

2dd

dd 22

.

, , C - . ,

xC U

C U

x xW

F edd

22dd

dd 22 +=

+=+= .

(2.5): (2.20) F

, (2.22) . , Q. ? .

(2.5):

. . - . - , - . - D, - E = D/ 0. .

2.11.4

, . , - W meh , W meh =-W e. , W i , W e = W meh = W i.


48/124

2.11 49

2.13. .

, , . W e - we = 10 E 2 . - - . E max 30 kV/cm. , - , . - we .

, - W e(max) . , - , - .

, - , , - .

-, , - , , . , . - . - , - , .

2.13. (A), ( ), .


49/124

50 2

(2.6):

- . , , - E m = 30 kV/cm.

(2.6): -

. S , - d we(max) = 0 E m2. - W = Sd we(max) . (2.7):

f , - .

(2.7): f P sr = f W

= f Sd w e(max) .

2.11.5

- . . - , - . - . - - .

- . - . , - . , .

-


50/124

2.11 51

. 0 =8,85 10 -12 10 -11 , 0 = 4 10 -7 10 -6. wm = 0 H 2/2 - we = 0 E 2/2.

, - . , E max 30 kV/cm 3000 kV/m, H H max Bmax/0 1000 kA/m. - . , (10 3-10 4 ) .

2.11.6

- , - E H . - - - . - .

. , Wm 2. - . . - E H , .

- , , - . , - - . , -. , . -, . . ( )


51/124

52 2

,rott

D J H

+=

(2.23)

D - H . H , H - . H .

. , , -. , . , . . ( ),

,rott

B E

=

(2.24)

B ( - ) ,

E .

2.12

. - . .

. . .


52/124

2.12 53

2.12.1

2.14 - . - , , - U , . - AB l 1 U . AB, U . - AB , R.

2.14. - .

, i. l 1 2.14 AB. , B. F m - (2.25).

( ) Bl i F m = 1 (2.25) l 1 , -

F m = l 1iB. 2.14, - . , - v . F s, . , , v , - . .


53/124

54 2

Bil F F F F F F m sm sm s 1;;0 ====+

(2.26)

, E ind , . , e = eAB (2.27)

( ) ( )( ) Bvl E l e ind == 11 (2.27) ,

a a e = l 1vB. - e = eAB , 2.14. e = e AB > 0 A B.

, i = ( U - e)/ R. , i(t ) I =(U l 1vB)/ R. P i = Ui = ei + Ri

2 P AB = ei =l 1vBi, P = Ri2. - . P AB . - , F m F s, . , - P meh = F mv = l 1iBv. P meh - , - U , . P meh = F mv = P AB =ei = l 1vBi, P i (2.28).

222 Ri P Riv F RieiUi P mehmi +=+=+== (2.28)

, , . - e P e = e(-i) = - ei < 0. , - e , - ei = l 1vBi, P meh = F mv =ei. , - . - (2.29) .


54/124

2.12 55

v F ei m= (2.29)

, P = Ri2 . - , , - . - , , - . P - . , . - . , - , . , , , . R. , , , .

, 2.14 , - . 2.4 .

2.12.2

, . ( ) 2.15. ABCD, D L - , B. , 2.15, . m m = d m/dt . m = 0, - S = D L . I.

F 1 AB CD - . - L, F 1 = LIB. - BC DA, D, , . m=/2,


55/124

56 2

BC DA , , .

2.15. .

M em = DF 1. - m = d m /d t , (t = 0) P meh = M em m = DLIB m.

P meh - , I , .

. A1 D1 u = vA1 vD1. ABCD, u = RI + d /dt , S R . S . ABCD, , . 2.15 1.16, n. , S m - .


56/124

2.12 57

2.16. .

2.16, m - S . , . m, S n1. , ( m) = msin( m) = msin( mt ), m = BS m= /2. , u = RI + m mcos( mt ). , m = 0, (2.30).

222

22

RI P DLIB RI BS I RI

BS I RI I RI uI P

mehmm

mmmi

+=+=+==+=+==

(2.30)

, , . m = 0,

M em = m I = P meh/ m. m, K F 1,

2.16, K =( D/2) cos m. M em m (2.31)

mmem I M cos= (2.31)

(2.31) . - 2.15


57/124

58 2

. - , - .

, - 2.15 , . , .

2.12.3 -

2.15, e1 e2 . , - , - .

2.17. - .

2.17 , A1 D1. - S . S , n 2.15 2.16.

I (ABCD) n. m, 2.15 S .

S , , - . - . , . -


58/124

2.12 59

. 2.17, . Req = , e1 . , , - A1 D1 , - e1 .

, - . , .

. . , 2.15, . e1, (2.32).

t

edd

1 = (2.32)

e1


59/124

60 2

2.15 2.17. e1, (B) 2.17, - (2.32). , () (2.34). e2 = +d /dt - .

t

eedd

12 == (2.34)

2.13

- . , - . , , - . - , - ( a). 2.18.

2.18 , - . ( ) . , - ( ). - N , . , - . H Fe = B/Fe, - H 0 = B/0. - , - . Ni = H 0 , H 0 i =

H 0 / . B ,

i = B / ( 0). , . -


60/124


61/124

62 2

B( H ) .

0d =S

S B (2.35)

, -

. - . - , - , - . , . . - . - , , ( ) . . N = N . , - . .

, - .

(2.36). c S 2.19.

= S c S J l H dd (2.36)


62/124

2.13 63

2.19. S c .

, , - . - . , - J - S , , . (2.36) (2.37).

I l H c

=

d (2.37)

H B - (2.38).

( ) H B B = (2.38) , -

. , (2.39). 0 =4107 H/m . , B( H ) . , .

, B( H ) - B/ H - 0.

H H B r 0== (2.39)


63/124

64 2

2.13.2

2.19 . - S , c, B. , . S . - , , - = N , S .

2.13.3

. - B(H) 2.20. - B/ H = o, , Fe B(H) . B- H H , , B

. . - . . . H , - , - . - .

H ,

B = Fe H B = 0 H . .


64/124

2.13 65

2.20. . - , .

2 T, . - H , . - . , , B = 0 H.

2.13.4

-

. . H Ni, N i . Ni/ - . . , , , , (


65/124

66 2

). .

2.21. , , .

. B( H ) . - . , , - . -,

. - .

(2.37), H c, 2.21, Ni. F =

Ni , H . -


66/124

2.13 67

F . F = Ni - H , . 2.21, F nk , .

S . - , H c Ni - .

, , = BS . = N .

. S = S 0 =S Fe , SB Fe = SB0, B Fe = B0, B0 - B Fe - . H 0 = B0/0, - H Fe = B Fe / Fe = B0/ Fe . (2.40), l -, l 0 .

Nil H l H Fe =+ 00 (2.40) H 0 = B0/0 H Fe = B Fe / Fe = B0/ Fe

(2.40), (2.41), B Fe = B0.

F Nil B

l B

Fe

==+ 00

00

(2.41)

= BS , - F (2.42).

R

F

S l

S l

F

S l

S l

Ni

Fe Fe

=

+

=

+

=

0

0

0

0

(2.42)

, 2.22, E . - R = F/R


67/124

68 2

i = E / R . - . - .

F - c. , i = U/R , = F/R , R . , - Ni . - , -

. - . , F R i, U R . (2.42) " " , .

l , S R = l /(S ). - . , , - , - Rk = l k /(S k k ), (2.43).

=

=n

k k k

k

S l

R1

(2.43)

2.22. .


68/124

2.13 69

S - , (2.44), c . S ( x) ( x) x, c, . - S ( x), ( x), x , S ( x) S ( x + x), ( x) ( x + x). R x/(S ). , (2.44). (2.44) S ( x) ( x).

( ) ( )= c xS x x

R

d

(2.44)

N , = N . (2.45), .

=

===== k

ii

i

S l

N R N

R Ni

i N

i N

i L

1i

22

(2.45)

2.13.5

wm . , BH /2. , - , V (2.46) - .

( )

===

V V V me V BH V B H V wW d2

1ddd

(2.46)


69/124

70 2

d V = S dl , S d l , c. - , . , B /S . - , (2.46) . -

dl , - .

( ) ====ccc

S V

e l H l H l BH S V BH W d2d

2dd

21

d21 (2.47)

, c

Ni, - (2.48). - .

2

21

22d

2 Li

i Nil H W

ce ==

==

(2.48)

(2.8): , 2.21, -

. .

(2.8): , -

R = l 0/(S o). L = oSN 2/ l 0.

2.13.6

. - 2.23 , N 1 N 2. . -


70/124

2.13 71

- . , 1, n1 2.22, c, n, - . , 1 = N 1 . n2 c. S n, 2 = - N 2 . ,

- .

2.23. .

1 = N 1 2 = - N 2 , , . , N 1 N 2, 1/ 2 . , - . N 1 N 2.


71/124

72 2

- . , . , | 1 / 2| N 1/ N 2. k 1. , - 1.

2.14

, . - ( ) . B . . .

2.24. . , - .

2. 14 .1

- . B = f ( H ) . B - T , 2.24, B = f ( H ) .


72/124

2.14 73

( ) T - . - . - .

p H B = f ( H ) - . - V

H H S V B H V W == d , (2.49) S H B = f ( H ) . -

H H S V f P = . (2.50)

H H

H S f V P

p ==1 .(2.51)

S H - H m Bm. - Bm H m, Bm

2,

211 m H H B f p = . (2.52)

H H 1 ,

2m H H B f p = . (2.53)

2. 14 .2

. - - - . - - .


73/124

74 2

2.25 - B Bm . C , - S C l C . , - RC = l C /( S C ).

( ) t BS t BS t t

e mC mC cossind

ddd === (2.54)

2.25. . -

- .

- , E Bm 2 f Bm. , , I C E / RC 2 f Bm/ RC . , (2.55), - RC I C .


74/124

2.14 75

C

m

C

mC C C C R

B R B

R I R P 222

2 ~~~

(2.55)

- - .

22mV V B f p = , (2.56)

V .

2. 14 .3

(2.57). p Fe W/kg. m - P Fe= p Fem.

222mV m H V H Fe B f B f p p p +=+= (2.57)

, - p Fe , - P Fe - .

2. 14.4

- . , - . .

, , . .

, - . - -


75/124

76 2

- .

- , , - . RC (2.55) .

, ( ) , 2.26. , -

.

2.26. .

, . , - . .

- 50 Hz - 0,2 mm 0,5 mm. ( , ) - , - .


76/124


77/124

78 2

( )

t B x x E

t Bl x x E l l d E e

m

mC

cos)(

,cos22

=

===

(2.58)

2.27. - .

- E - J = E . , ,

( ) .cos)( t B x x E x J m ==


78/124

2.14 79

. ,

( ) ( ).cos)()( 22

2 t B x x J

x E V P

x p m Fe ===

=

P 1 Fe al H - (2.59).

( ) ( )

( ) 2232223

2

0

2

cos12

cos21

==

===

mm

V

a

m Fe Fe

Bak t Bl H a

dxt B xl H dV x p P

(2.59)

k H l , cos 2 t , 0,5. (2.59) - - a.

2.26( ) a = A. ,

(2.59) P hom (2.60).

322 A Bk P mhom = (2.60)

N ( ) a = A/ N , 2.26(B). - a , , 2.26 ( ). P 1 Fe , (2.59). -

N , P lam A = aN (2.61).

2222

322

N P

a A Bk N A

Bk N P hommmlam ==

=

(2.61)


79/124

80 2

(2.61) - N 2 N , . - , - . , .

, a , . 50 Hz

0,2 mm. - , , , , - .

, , B . , . , . ,

, - .

2. 15

( ) . - , . . - . , . - , . - .


80/124

2.15 81

2.15.1

. - , , . , ( ). , . , - . - , . 2.28 .

2.28. . () . (B) . (C) - . (D) F em .


81/124

82 2

2. 15.2

. m. - M em , m - P em = M em m. - P em . . 2.29.

2.29. , - .

, , . m - em. , ( M em > 0), - ( , ) , M m. , em>0 , - m>0 . .

memm M M

t J =

dd

(2.62)

- . , . , em , . , , M m 2.29.


82/124

2.15 83

em , . - P em . - , P em - .

2. 15.3

, , - , , . -. , ( ). . , - . . . , , , - . , . - ( , ) . i a N F = Ni.

R . , - . , .

- . , . 2.30 ( ) - . - . . - . , .

- .

2.30, - (C) - . . , 2.30 (E).


83/124

84 2

2.30. - . (A) 2 . (B) .(C) . (D) - . (E) .

- , , .

. - , .

2 2.30 - , . - , . .

, - - . H - , . B Fe < 1,7 T

H Fe = B Fe / Fe 0, , - .


84/124

2.15 85

2.31. .

2. 15.4

, . , - 2.33. , , . - , , . ( , ) .

, , . , , , - . - ( ), . 2.32. , .


85/124

86 2

2.32. . (A) . (B) .(C) .

2.33, (B) 3 . ( 2.33). , , . , , . 2.33, , .

2.33. .

3 [ = slot (eng.), cava (it.) = tooth (eng.) dente (it.)].


86/124

2.15 87

( 2.33). - , . , 2.33 (D) 4. - (D) .

- , ( F 2.33). - ( C - ) (D).

. . - . . .

. - . N N .

(2.9):

? ? (2.9):

, - . , . , , . , .

2. 15.5

, , , - , . -

4 end turns, eng.


87/124

88 2

2.36 . , , . - , . - , , . , - , - .

. ,

- , , . . , . - , . - . . - .

-

, . . - . , H Fe . , - , - 2.34. Ni =2 H o . , , - , , , . . . , , - , , .

, - , . , -


88/124

2.15 89

- . 2.34.

, - . . , - ( 6 ), . ( ).

2.34. .

2. 15.6

, , - . -

- . , - , . - . - . -


89/124

90 2

- .

, P eM = ui M . - P eM i M - ( ). , - ( , P FeM ) ( , P CuM ). - M em m. , P mM . P mM = M em m - P mM = M m m -

. , P eM -, P mM , P FeM + P CuM + P mM - . = P mM / P eM - , . 2.35.

2.35. .

, .

2.36. P mG, , , -.

2.36, . ( 2.35), , P m -


90/124

2.15 91

. P eG , iG.

P mG . . P mG P mG . P CuG P FeG . . - P eG = uiG,

.

2.36. .

- . , - , . - , . ,

. , . , , - , .

- . , -


91/124

92 2

. , - , , - .

. , . , .

. , .

2. 15.7

, 5. 0,5 mm , .

( ) . , . Fe>> 0, H , - je H o . H - (2.63) - .

==C

H l H Ni F 02d (2.63)

H o (2.63)

, - 2.38.

5 [airgap (eng.) traferro (it.) entrefer (fr.) ]


92/124

2.15 93

2.37. . (A) - . (B) . (C) .

2.38. - .

Ni = 2 H o , ,


93/124

94 2

. , - . , , 0.5 1 mm, - .

2.15.8 ,

- . - . , - -.

. . 2.37 2.38. . , . . /

, - / . 2.33 - . - , - , , - . 2.39, W i, W meh W m , - , . -

2.13.2 . ( 2.39 ), - u N d /dt = 0, - . , - , dW meh = -d W m. - . d x -


94/124

2.15 95

dW meh = F d x, F . L( x) - . , R , , . - d x (2.64), i .

2.39. , . () - , = const. (B) , I =const .

Li L L L

LiW m d21

d22

d21

dd 2222

2 ==

=

=

(2.64)

dW meh = -d W m, (2.65).

== mmeh W x F W ddd

x L

i F dd

21 2=

(2.65)

( 2.39 B), - I . d x, dW i = u I dt ,


95/124

96 2

u = d /dt . (2.66).

ddd I t I uW i == (2.66)

, - (2.67).

im W I L I LI W d21

d21

d21

21

dd 22 ===

=

(2.67)

6 dW m = d W meh = d W i/2. (2.65), .

. , W m . , , . - H B. W m - , -

Bmax< (1,7 2) T. , - ( 2.39) ( ). - , .

6 dW m = d W meh = d W i/2 - , , - . L( x) -

x , /i . , - (2.66) (2.67) dW m = d W meh = d W i/2. - , B( H ) . , , L = /i =

f ( x, ). , .


96/124


97/124

98 2

Bmax 1,7 T, B - . 1 Bmax2/ o. - W m(max) 1 LD Bmax2/ o, 2.

2. 16

. - ( ), ( ), , - . - . - , , - , . -. 2.40 P e, - P m, P Cu , P Fe , - P m W m.

2.40. - .


98/124

2.16 99

2.16.1

- . - , , . - , - , - , , - .

, , , , .

, - -, - , .

P e - , P m ( ) ,

P Cu, P Fe , P m - . 2.40.

? ? ,

. - . , . , , ( , , ).

, . , - . , , - ( ) . , , -


99/124

100 2

, , .

, ( ). , , , . - , - . , . . -

, , - , R, L, C, - ( Ri = u, i = C du/dt, u = Ldi/dt ). - , , RLC - , .

: - , , - ,

( ) . , - , , .

, . - . -, .

- .

- . - E = U/d . , - , . -


100/124

2.16 101

, - dV /dt . , , - . , - , - E = U/d ( ). , , - ( - ) . - , -

, . - , - .

, - ( dV /dt ) , , , E = U/d . - , . , . , , 10,000 , , -

, . - , . U/f , (PWM) .

, . , . , - - , , - . , - , - . , - .


101/124

102 2

: - .

, ( , ), - . , .

, - , -

. - . , . , , , , - , .

2.16.2

, - . :

, , , -

.

- . , , , . u L=L di/dt iC =Cdu/dt, . -


102/124

2.16 103

- p = ui , - .

-, - . - ( H 2 E 2),

.

, . ( )

222mV m H V H

Fe Fe B f B f p pm

P p +=+==

- , .

. , ( - ). B/ H - B/ H . 1,2 T, -

. ,

- - . N - . .


103/124

104 2

2.16.3

2.41 N ( ) . . ( ), - ( ). , - .

, - . ,

u = Ri + d /dt = 0. , d /dt = 0, . - , (u d /dt ).

2.41. N ( ). 1 i , 2 N - .

(2.68), u i . , , .


104/124


105/124

106 2

2.42. - .

(A) - . - e = + d /dt , (u e )/ R. , , . (A) - -, . - . , - , . , , (e = +/- d /dt ).

2.16.5

(2.69). - N , k -

t i Ru k k k k d

d += ,(2.70)

uk , ik , Rk k , , k- , - . k k , k - -


106/124

2.16 107

. ik k - Lkk . i j j k - Lk .

N N - .

[ ][ ],,...,...,,

,...,...,,

121

121

N N k T

N N k T

uuuuuu

iiiiii

==

(2.71)

,

[ ] N N k T ,...,...,, 121 = , (2.72)

R

=

N

k

R

R

R

R

R

R

0000

0000

0000

0000

0000

3

2

1

(2.73)

. (2.74), N (2.69). ,

t i Ru

d

d+= .(2.74)

-

. k - , - Lkj , .

N Nk k kk k k k i Li Li Li L +++++= ......2211


107/124

108 2

, , (2.75), , (2.76).

=

NN N

kk k

N k

L L

L L

L

L L

L L L L

L

...

...

....

...

.

1

1

33

2221

111211

(2.75)

i L = (2.76)

- , .

Lij = L ji, , L = LT .

. - ( ) ( ). ,

. - . - - . - 2.6, - - .

2.16.6

, . - , . 2.43 - , . . - .


108/124

2.16 109

- . , , . - , . - , - . -

. Lm =L SR = L RS , . - , . - 2.41, 2x2. - - LS L R. - , -, /2. ,

RS

m

L L Lk = .

. N R , , LS = L R,

Lm = kLS = kL R. k < 1, - . ,

( ) S mS S Lk L L L == 1 , , . , , . - .


109/124

110 2

2.43. .

, 2.43,

.

,

m R R

mS S

+=+=

( S ) ( R)

Rm

S mm += .

- ,

.,

Rm R R Rm R R R R

S mS S S mS S S S

N N N N N N N N

+=+==+=+==

S , R - . - . -


110/124

2.16 111

, . 2.43,

R

R R

S

S S i

Li

L

== , .

S

S m R

R

RmS

RS SRm i N

i N

L L L ==== .

. , .

.

,

RmS

R RSR

S

R

R

R Rm R

R

R R Rm R

R

S m R

S S RS

R

S

S

S S mS

S

S S S mS

S

L L N N

L L N N

i

N

i

N N L

L L N N

L L N N

i

N

i

N N L

+=+=

=+

=+

=

+=+=

=+

=+

=

, . . , ( - ) , - ,

.,

Rm R

S mS

L L L L L L

+=+=


111/124

112 2

2.16.7

. - , . , . -

= B H wm d . , , = B/ H =

const, wm = BH = H 2.

wm - . - . , , L1i1

2 + L2i22 + L12 i1 i2.

, . - ( BH ) dV . d V = d S d x, ( BH ) dS d x = ( B dS )( H d x). ( B dS ) ,

( H d x) - , . , i Li2.

N , -

( ) = =

=== N

i

N

j jiij

V V m ii LV B H V wW

1 1m 2

1ddd .

, Lii - . Lij - .

[ ][ ].,...,...,,

,,...,...,,

121

121

N N k T

N N k T iiiiii

==


112/124

2.16 113

(2.77), L - .

i LiW T m 21=

(2.77)

(2.11): L1 L2.

( L1 L2)0,5 ?

(2.11): L12= k ( L1 L2)

0,5, k

. 1, , . 1, ( L1 L2)

0,5 .

(2.12):

= j k

k j jk m ii LW 2

? - .

(2.12): - . , 2W m = L1 i1

2+ L2 i22+2 L12 i1 i2 = L1 i1

2+ L2 i22+2 k ( L1 L2)

0,5 i1 i2. a =( L1)

0,5 i1 b = ( L2)

0,5 i2, 2 W m = a

2+ b2+ 2 k ab. . - , , 2W m 0 k = 1, k < 1. k = 1, 2 W m = (a+b)2, .

2.16.8

N , . pk = uk ik


113/124

114 2

iuuiiu p T T

k k k e === . (2.78)

- , 2.74, , .

( )

t

i Lii

t

Lii Ri

i Lt

i Rit

i Ri p

T T T

T T e

d

d

d

ddd

dd

++=

=

+=

+=

(2.79)

, . Rk , ik , Rk ik

2. N -

i Rii R p T

k k k Cu == 2 (2.80)

R N x N , , -.

. (2.77), - (2.81).

+

+

=

=

==

t i

Liit

Lii L

t i

i Lit t

W p

T T T

T mwm

dd

21

dd

21

dd

21

21

dd

dd

(2.81)

pwm . (2.81) , - . . ( , 1x1) s =

sT , ( L jk = Lkj, L = LT ),


114/124

2.16 115

=

=

=

t i

Lit i

Lii Lt

ii L

t i T T T

T T T

dd

dd

dd

dd

.

(2.81), (2.82).

+

=

t i

Liit

Li p T T wm d

ddd

21

(2.82)

(2.82) - . -

. - . , - . i - (2.82) . , . , .

pwm pe , pCu , pC -

. ( - 2.33), . - ( 2.34), .

wmCueC p p p p =

(2.79), (2.80) (2.82),

( )

.dd

dd

21

dd

dd

+

++=

t i Lii

t Li

i Rit i

Liit

Lii Ri p

T T

T T T T C


115/124

116 2

it

Li p T C d

d21= .

(2.83)

, - . - . , - m m = d m/dt , (2.84),

i L

it

i L

iit

Li p

m

T mm

m

T T C

d

d

2d

d

d

d

2

1

d

d

2

1 === .(2.84)

(2.84) - - m.

, - . ,

pC ( ), ( ). - , - , . , 2.34, - , , .

2.16.9

. - m m. N , . - , L .

t m

m dd = ,


116/124

2.16 117

( ) ( )m f t f L 21 == . -

. . - M em, - M em, . , . M em - .

, M em , m, pC = M em m . , M em - , .

, M em , pC = M em m . - - . , M em - , - .

. , (2.84)

memm

T mC M i

Li p =

=

dd

21

,

M em , (2.85) .

i L

i M m

T em d

d21= (2.85)

N . - . (2.67), - , ,

memmehm M W W ddd == ,


117/124

118 2

m

mem

W M

dd= .

(2.77), -

= i Li M T

mem 2

1dd

.

, - . -

m.

i L

i M m

T em d

d21=

- m. - , - . .

N , (2.86).

= =

=

N

k

N

j m

jk jk em

Lii M

1 1 d

d

21

(2.86)

(2.13):O

.

(2.13): , m

. m =0, . - , . , - m =0. , /2 /2- m.


118/124


119/124

120 2

2.42 .

2.16.11

- , , - , - .

(2.42). -. , - , - - k F m,

2m F m k p = (2.87)

- . , , - .

, 2.42, - , . . - m. -


120/124

2.16 121

2mV Fe k p = .

, -

mV m

Fe Fe k

p M == .

p m = k F m2, -

7. -

, . - , -

3m F m k p = .

2.16.12

J . - , R m, - J = mR 2/2. - J m W mehA = J m

energetski pretvarači i električne mašine

Documents