Energetski pretvarači i električne mašine
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Transcript of Energetski pretvarači i električne mašine
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8/12/2019 Energetski pretvarai i elektrine maine
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2 1
, . -
1.1.2
, . . - , . , . , . - , - . , .
, , .
1.1.3
- . , , , . , . - , , .
, - . - , - - . - ,
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1.1 3
, , , . - , - . , - .
1.1.4
- . . - , - . -
, ,
, ,
, -
, -, - .
1.1.5
-
. , . - . - , - . - , , - -
-
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4 1
. , , , , . . , , , , - .
1.1.6
- . - , 1.1. . - .
1.1. , , , - .
, , - . - . 1.1, - k A B. . , - . , - , - . N , - (1.1).
-
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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
. - , , . - , , . - , - ,
-
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6 1
. . , . , , .
1.2. - .
pe pm, , - . -
, , - . , - . , pm pe . , (- pe) - (- pm) .
1.2. .
1.2
. - ,
-
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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. - . ( -
-
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8 1
), . , M m, , - , M em - . - . , . 1.
() -
. -
6kV 25 kV, 50 Hz 60 Hz. - 2.
1 19. , , , - . ( - ) , . - . , - . -
, . . - . . . 400 V, -. 231 V. - - , - .
2 ,
, , . - . . .
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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% - - , , . , - , , , - , . , - , -
, . - , - - .
-
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10 1
1.3. .
-
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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 - .
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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 -
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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 - . ,
-
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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 , .
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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
- . - . - , , , , - , . , - , , - .
- , . - , , . - . , , - ( ). -
. -
. . , . -
-
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16 1
, , , , . , .
1.4.1
, , , , - . - , , , , - . - - , , .
1.4.2
. - , . , ( ) - . , , - . - , , , - .
1.4.3
, , . - . - M em( m) M em- m . -
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1.4 17
- .
1.4.4
, - , , , . . , . . - . - . , . - , , -. , - ( ). - ( ) - . . - - - . - - .
. , , .
, .
-
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18 1
1.4.5
- - . - u = Ri + d /dt , J d m/dt = M em M m. J R , m - ( ). , , -
, - . - , -. , , .
, . - , . , , E -
. , - , -. . , .
, . - - . , - .
1.5
- . , , - . -
-
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1.5 19
, , , , - , . , . , . - , , - , - . - - , -
, , .
- . - . , - . - . -, . -
- , - . , , , , - . , - . . . . N , , . - , - .
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20 1
, ( ), ( ) ( ). , , , - , , , . - -. , - - .
,
, , , - , . , , . , , .
- . , 5 - . ,
. -
, - . , - , - .
1.5.1
, - , -
-
5 , , ,
. - ( ) . . , .
-
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1.5 21
. . , - . 2. - - , . , - . , , - ( ), . - , -
. , - , - - . , - . - . , , . - . - . , - . , - .
, - , , . , - , - . - , - .
1.5.2
. - , - , , - . - . -
-
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22 1
.
. :
, - , . - - . , , , - . - .
, - 1 kHz. - - . - . -
. -
. , - .
, - .
1 GW. , - , - 50 Hz. - , -
-
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1.5 23
, - .
- - , . - , .
: - ,
. - - . - - . , - ( ) - . , - ( ). - . - ,
, , - . - . - 50 Hz, . . , - , .
: - . - , - . . -
-
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24 1
. , . , - . - - , , . , - , , .
. , . , . , .
:
, , . , - P, - - , M em = P / , - .
- . , - , . : - - .
, - - . ( ) .
- . -
-
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1.5 25
, - . - . , - . - , .
-
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2
. - . -
. , - . - , . , .
2.1
. - , - .
- , - Q v - .
( ) BvQ E Q F += (2.1) , -
. - B
. , (2.1) - .
2.1 l - i - B. F
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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 , .
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2.2 29
, , e. - e i ( pe = ei ) - ( pm = Fv y). , pe pm. .
2.2
- - . , .
2.2 . (A) . (B) - . (C) .
-
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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 .
-
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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 . ,
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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)
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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): , - - , .
-
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34 2
2.5
e - . 2.5 - ( Fe >> o), . , .
2.5. , - .
. , , ( ) , , . ( ) - . - ( ) - . , .
, - . .
.
(2.2): ?
-
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2.6 35
(2.2): -
. , . . - , , . . - , - .
2.6
2.6, - . . - B , B .
2.6. .
2.6 . , . , - .
-
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36 2
, ( ) . , .
- , .
2.7
, -
E , 2.7. -, . - , - .
. . F . x, F x.
- , .
2.7. .
-
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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 .
-
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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 .
-
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-
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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),
-
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2.9 41
( ) 0
22
221
b x xad Q
C Q
W r
e+
== ,
, Q , .
2.9
, , . - . - , , . , - , .
- . ( ).
-
. - , - . . , - . - .
. - -
, .
-
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42 2
2.9. - .
2.10
o
. , - - . 2.10 - . , , - , . , - .
. - .
2.10. - .
-
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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)
-
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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)
-
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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).
-
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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, - .
-
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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 . ,
-
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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.
-
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2.11 49
2.13. .
, , . W e - we = 10 E 2 . - - . E max 30 kV/cm. , - , . - we .
, - W e(max) . , - , - .
, - , , - .
-, , - , , . , . - . - , - , .
2.13. (A), ( ), .
-
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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
- . . - , - . - . - - .
- . - . , - . , .
-
-
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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 , .
- , , - . , - - . , -. , . -, . . ( )
-
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52 2
,rott
D J H
+=
(2.23)
D - H . H , H - . H .
. , , -. , . , . . ( ),
,rott
B E
=
(2.24)
B ( - ) ,
E .
2.12
. - . .
. . .
-
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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 , - . .
-
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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) .
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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,
-
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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 - .
-
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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
-
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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 , , - . - . , . -
-
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2.12 59
. 2.17, . Req = , e1 . , , - A1 D1 , - e1 .
, - . , .
. . , 2.15, . e1, (2.32).
t
edd
1 = (2.32)
e1
-
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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). , . -
-
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-
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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)
-
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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)
-
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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 . .
-
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2.13 65
2.20. . - , .
2 T, . - H , . - . , , B = 0 H.
2.13.4
-
. . H Ni, N i . Ni/ - . . , , , , (
-
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66 2
). .
2.21. , , .
. B( H ) . - . , , - . -,
. - .
(2.37), H c, 2.21, Ni. F =
Ni , H . -
-
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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
-
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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. .
-
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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)
-
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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. . -
-
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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.
-
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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 ) .
-
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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
. - - - . - - .
-
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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 .
-
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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
- . , - . .
, , . .
, - . - -
-
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76 2
- .
- , , - . RC (2.55) .
, ( ) , 2.26. , -
.
2.26. .
, . , - . .
- 50 Hz - 0,2 mm 0,5 mm. ( , ) - , - .
-
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-
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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 ==
-
8/12/2019 Energetski pretvarai i elektrine maine
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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)
-
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80 2
(2.61) - N 2 N , . - , - . , .
, a , . 50 Hz
0,2 mm. - , , , , - .
, , B . , . , . ,
, - .
2. 15
( ) . - , . . - . , . - , . - .
-
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80/124
2.15 81
2.15.1
. - , , . , ( ). , . , - . - , . 2.28 .
2.28. . () . (B) . (C) - . (D) F em .
-
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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.
-
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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).
-
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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, , - .
-
8/12/2019 Energetski pretvarai i elektrine maine
84/124
2.15 85
2.31. .
2. 15.4
, . , - 2.33. , , . - , , . ( , ) .
, , . , , , - . - ( ), . 2.32. , .
-
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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.)].
-
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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.
-
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87/124
88 2
2.36 . , , . - , . - , , . , - , - .
. ,
- , , . . , . - , . - . . - .
-
, . . - . , H Fe . , - , - 2.34. Ni =2 H o . , , - , , , . . . , , - , , .
, - , . , -
-
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2.15 89
- . 2.34.
, - . . , - ( 6 ), . ( ).
2.34. .
2. 15.6
, , - . -
- . , - , . - . - . -
-
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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 -
-
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2.15 91
. P eG , iG.
P mG . . P mG P mG . P CuG P FeG . . - P eG = uiG,
.
2.36. .
- . , - , . - , . ,
. , . , , - , .
- . , -
-
8/12/2019 Energetski pretvarai i elektrine maine
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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.) ]
-
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2.15 93
2.37. . (A) - . (B) . (C) .
2.38. - .
Ni = 2 H o , ,
-
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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 -
-
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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 ,
-
8/12/2019 Energetski pretvarai i elektrine maine
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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, ). , .
-
8/12/2019 Energetski pretvarai i elektrine maine
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-
8/12/2019 Energetski pretvarai i elektrine maine
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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. - .
-
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98/124
2.16 99
2.16.1
- . - , , . - , - , - , , - .
, , , , .
, - -, - , .
P e - , P m ( ) ,
P Cu, P Fe , P m - . 2.40.
? ? ,
. - . , . , , ( , , ).
, . , - . , , - ( ) . , , -
-
8/12/2019 Energetski pretvarai i elektrine maine
99/124
100 2
, , .
, ( ). , , , . - , - . , . . -
, , - , R, L, C, - ( Ri = u, i = C du/dt, u = Ldi/dt ). - , , RLC - , .
: - , , - ,
( ) . , - , , .
, . - . -, .
- .
- . - E = U/d . , - , . -
-
8/12/2019 Energetski pretvarai i elektrine maine
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2.16 101
, - dV /dt . , , - . , - , - E = U/d ( ). , , - ( - ) . - , -
, . - , - .
, - ( dV /dt ) , , , E = U/d . - , . , . , , 10,000 , , -
, . - , . U/f , (PWM) .
, . , . , - - , , - . , - , - . , - .
-
8/12/2019 Energetski pretvarai i elektrine maine
101/124
102 2
: - .
, ( , ), - . , .
, - , -
. - . , . , , , , - , .
2.16.2
, - . :
, , , -
.
- . , , , . u L=L di/dt iC =Cdu/dt, . -
-
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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 - . .
-
8/12/2019 Energetski pretvarai i elektrine maine
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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 . , , .
-
8/12/2019 Energetski pretvarai i elektrine maine
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-
8/12/2019 Energetski pretvarai i elektrine maine
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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 - -
-
8/12/2019 Energetski pretvarai i elektrine maine
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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
-
8/12/2019 Energetski pretvarai i elektrine maine
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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 - , . . - .
-
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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 , , . , , . - .
-
8/12/2019 Energetski pretvarai i elektrine maine
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 - . - . -
-
8/12/2019 Energetski pretvarai i elektrine maine
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
+=+=
-
8/12/2019 Energetski pretvarai i elektrine maine
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
==
-
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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
-
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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 ),
-
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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
-
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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 = ,
-
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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 == ,
-
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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.
-
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-
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120 2
2.42 .
2.16.11
- , , - , - .
(2.42). -. , - , - - k F m,
2m F m k p = (2.87)
- . , , - .
, 2.42, - , . . - m. -
-
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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