Готман В.И. Короткие замыкания и несимметричные режимы в электроэнергетических системах
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191
1
20Ȉ
ǻ
// 1,15//0,97 0,526
LL
L
xx x
6
.
2. Ɋɚɫɱɟɬ ɬɨɤɨɜ ɫɯɟɦɵ.
Ɉɩɪɟɞɟɥɢɦ ɫɢɦɦɟɬɪɢɱɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɬɨɤɨɜ ɜ ɫɯɟɦɚɯ ɨɬɞɟɥɶ-
ɧɵɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ:
1
1
1
1Ȉ
1, 4 3
0,565
(2 0,526)
()
La
L
L
j
j
jx x
6
'
c
E
I
;
1
21
2Ȉ
0,526
0,565 0,258
1,15
L
La La
L
x
x
'
II
;
0
0,526
0,565 0,307
0,97
L
I
,
ɱɬɨ ɩɨɡɜɨɥɹɟɬ ɪɚɫɫɱɢɬɚɬɶ ɬɨɤ ɜ ɧɟɩɨɜɪɟɠɞɟɧɧɵɯ ɮɚɡɚɯ ɥɢɧɢɢ:
2237
0,565 0,258 0,307 0,85 .
j
L
BLC
e II
D
aa
Ɇɨɞɭɥɶ ɷɬɢɯ ɬɨɤɨɜ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɢ ɩɨ ɜɵɪɚɠɟɧɢɸ (8.18), ɢɫ-
ɩɨɥɶɡɭɹ ɤɨɷɮɮɢɰɢɟɧɬ
1,1
m , ɬ. ɟ.
1,1
m
2
1,15 0,97
3 1 0,565 0,85
(1,1 5 0, 9 7)
.
3. Ɋɚɫɱɟɬ ɧɚɩɪɹɠɟɧɢɣ ɜ ɭɡɥɚɯ ɫɯɟɦɵ.
ɇɚɣɞɟɦ ɫɢɦɦɟɬɪɢɱɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɥɟɦɦɟ
L
c
,
ɭɱɢɬɵɜɚɹ, ɱɬɨ ɜ ɭɡɥɟ ɟ ɫɯɟɦ ɨɬɞɟɥɶɧɵɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɧɚɩɪɹɠɟ-
ɧɢɹ ɪɚɜɧɵ ɧɭɥɸ:
1 1345
( ) 0,565 (0,15 0,2 1,2) 0,876
L
aLa
jx x x j j
c
UI
;
2 2345
( ) 0,258 (0,15 0,2 0,35) 0,18;
L
aLa
jx x x j j
c
UI
0034
( ) 0,307 (0,57 0,2) 0,236
L
L
jx x j j
c
UI
.
ɇɚ ɛɚɡɟ ɧɚɣɞɟɧɧɵɯ ɡɧɚɱɟɧɢɣ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɧɚ-
ɩɪɹɠɟɧɢɣ ɨɩɪɟɞɟɥɹɟɦ ɮɚɡɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɭɡɥɟ
L
c
:
(0,876 0,18 0,236) 0,46
L
A
jj
c
U
;
240 90 120 90
90
32,56
0,876 0,18 0,236
1,085 ;
jj
j
LB
j
ee e
e
c
U
DD DD
D
120 90 240 90
90
147,44
0,876 0,18 0,236
1,085 .
jj
j
LC
j
ee e
e
c
U
DD DD
D
D
Ɋɚɫɫɱɢɬɚɟɦ ɫɢɦɦɟɬɪ
ɢ
ɦɟɫɬɟ ɪɚɡɪɵɜɚ:
12
L
aLa
' ' 'UU
U
ɢ ɫɢɦɦɟɬɪɢɱɧɵɟ ɫɨɫɬɚɜɥɹ
ɸ
11
L
aLa
c
'
UU
22
L
aLa
c
'
UU
00
L
L
c
'UU
U
ɇɚɩɪɹɠɟɧɢɟ ɮɚɡɵ
Ⱥ
ɥɹɸɳɢɟ ɨɩɪɟɞɟɥɢɬɫɹ ɬɚɤ:
(1,
LA
j U
ɢɥɢ ɱɟɪɟɡ ɜɟɤɬɨɪ ɩɚɞɟɧɢɹ
ɧ
L
ALA
c
'
UU
Ⱦɥɹ ɧɟɩɨɜɪɟɠɞɟɧɧɵ
ɯ
ɤɥɟɦɦɵ
L
c
ɢ L ɨɞɢɧɚɤɨɜ
ɵ
ɬɟɥɶɧɨɫɬɟɣ ɩɪɢɜɟɞɟɧɵ ɧɚ
ɪ
Ɋɢɫ. 8.10. Ʉ
ɩ
ɛ –
ɷɩɸ
ɪ
192
ɢ
ɱɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹ
1
01
ǻ
0,565 0,526 0,2
9
LLa
L
j
xjj
U
I
ɸ
ɳɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɤɥɟɦɦɟ L:
1
(0,876 0,297) 1,173;
La
jj
'
U
2
( 0,18 0,297) 0,117;
La
jj
'
U
0
( 0,236 0,297) 0,061
L
jj
U
.
Ⱥ
ɧɚ ɫɬɨɪɨɧɟ L ɱɟɪɟɡ ɫɢɦɦɟɬɪɢɱɧɵɟ
173 0,117 0,061) 1,351j
,
ɧ
ɚɩɪɹɠɟɧɢɹ ɜ ɦɟɫɬɟ ɪɚɡɪɵɜɚ
(0,46 3 0,297) 1,351.
LA
jj
'
U
ɯ
ɮɚɡ ȼ ɢ ɋ ɮɚɡɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɫɨ
ɵ
. ɗɩɸɪɵ ɧɚɩɪɹɠɟɧɢɣ ɨɬɞɟɥɶɧɵɯ ɩɨ
ɫ
ɪ
ɢɫ. 8.10, ɛ.
ɩ
ɪɢɦɟɪɭ 8.2: ɚ
– ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ
;
ɪ
ɵ ɧɚɩɪɹɠɟɧɢɣ ɩɪɢ ɪɚɡɪɵɜɟ ɨɞɧɨɣ ɮɚɡɵ
ɹ
ɠɟɧɢɹ ɜ
9
7
ɟ
ɫɨɫɬɚɜ-
ɫɬɨɪɨɧɵ
ɫ
ɥɟɞɨɜɚ-
ɉɭɧɤɬɢɪɨɦ ɩɨɤɚɡɚɧ
ɨ
ɪɟɠɢɦɟ. ȼ ɦɟɫɬɟ ɪɚɡɪɵɜɚ
ɬɟɥɶɧɨɫɬɟɣ ɦɟɧɹɸɬ ɫɜɨɣ ɡ
ɧ
ɬɟ ɪɚɡɪɵɜɚ ɩɪɟɞɫɬɚɜɥɟɧɵ
ɧ
ɉɪɢɦɟɪ 8.3. ɋɯɟɦɚ
ɡɭɟɦɨɣ
ɋ
E
= const. Ɂɚ ɥɢɧ
ɟ
ɬɪɟɯɮɚɡɧɨɟ ɤɨɪɨɬɤɨɟ ɡɚɦ
ɵ
ɫɥɟɞɭɸɳɢɯ ɭɫɥɨɜɢɣ: ɧɚɥ
ɢ
ɮɚɡ ɪɟɚɤɬɨɪɚ ɡɚɤɨɪɨɱɟɧɚ.
Ɋɢɫ. 8.11. Ʉ ɩɪ
ɢ
ɛ –
ɫɯɟɦɚ ɡɚ
ɦ
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ.
ɉ
ɜɚɬɟɥɶɧɨɫɬɟɣ ɨɞɢɧɚɤɨɜɵ
ɢ
ɧɵɯ ɟɞɢɧɢɰɚɯ ɩɪɢ ɩɪɢɧɹɬ
ɵ
ɧɢ 6 ɤȼ).
Ɋɟɲɟɧɢɟ
1. ɉɪɢ ɧɚɥɢɱɢɢ ɪɟɚɤ
ɬ
1
0,x
6
ɢ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɬɪɟɯɮɚɡɧɨ
ɝ
3
K
I
ɢ ɜ ɢɦɟɧɨɜɚɧɧɵɯ
–
3
1,
K
I
2. ɉɪɢ ɨɬɫɭɬɫɬɜɢɢ
ɪ
1
x
6
ɢ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɬɪɟɯɮɚɡɧɨ
ɝ
3
K
j
j
I
3. ɉɪɢ ɭɫɥɨɜɢɢ ɡɚɤɨɪ
ɚ
Ɂɚɤɨɪɚɱɢɜɚɧɢɟ ɮɚɡɵ
ɪɟɚɤɬɢɜɧɨɫɬɢ x = –0,366 ɩ
ɪ
ɡɚɯ. Ɋɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ
193
ɨ
ɪɚɫɩɪɟɞɟɥɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɧɨɪ
ɦ
ɧɚɩɪɹɠɟɧɢɹ ɨɛɪɚɬɧɨɣ ɢ ɧɭɥɟɜɨɣ ɩɨ
ɫ
ɧ
ɚɤ. ȼɟɤɬɨɪɧɵɟ ɞɢɚɝɪɚɦɦɵ ɧɚɩɪɹɠɟɧ
ɢ
ɧ
ɚ ɪɢɫ. 8.3.
(ɪɢɫ. 8.11, ɚ) ɩɢɬɚɟɬɫɹ ɫɢɫɬɟɦɨɣ, ɯɚ
ɪ
ɟ
ɣɧɵɦ ɪɟɚɤɬɨɪɨɦ ɧɚ ɫɬɨɪɨɧɟ 6 ɤȼ ɩɪ
ɨ
ɵ
ɤɚɧɢɟ. Ɉɩɪɟɞɟɥɢɬɶ ɡɧɚɱɟɧɢɹ ɬɨɤɨɜ
ɢ
ɱɢɟ ɪɟɚɤɬɨɪɚ; ɨɬɫɭɬɫɬɜɢɟ
ɪ
ɟɚɤɬɨɪɚ;
ɢ
ɦɟɪɭ 8.3: ɚ –
ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦɚ
;
ɦ
ɟɳɟɧɢɹ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ
ɉ
ɚɪɚɦɟɬɪɵ ɫɯɟɦ ɩɪɹɦɨɣ ɢ ɨɛɪɚɬɧɨɣ
ɩ
ɢ
ɩɪɟɞɫɬɚɜɥɟɧɵ ɧɚ ɪɢɫ. 8.11, ɛ ɜ ɨɬɧ
ɨ
ɵ
ɯ ɛɚɡɢɫɧɵɯ ɭɫɥɨɜɢɹɯ (
ɛ
I
= 9,16 ɤȺ ɧ
ɬ
ɨɪɚ
125 0,19 0,366 0,681
ɝ
ɨ ɄɁ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ
c
1
1,0 8
1, 5 9
0,681
jE
jx
6
59 9,16 14,6
ɤȺ.
ɪ
ɟɚɤɬɨɪɚ ɜ ɫɯɟɦɟ
0,125 0,19 0,315,
ɝ
ɨ ɄɁ ɜ ɢɦɟɧɨɜɚɧɧɵɯ ɟɞɢɧɢɰɚɯ
C
ɛ
1
1, 0 8
9,16 31,4
0,315
j
E
I
j
x
6
ɤȺ.
ɚ
ɱɢɜɚɧɢɹ ɨɞɧɨɣ ɮɚɡɵ ɪɟɚɤɬɨɪɚ.
ɪɟɚɤɬɨɪɚ ɷɤɜɢɜɚɥɟɧɬɧɨ ɜɤɥɸɱɟɧɢɸ ɜ
ɷ
ɪ
ɢ ɭɫɥɨɜɢɢ ɧɚɥɢɱɢɹ ɪɟɚɤɬɨɪɚ ɜɨ ɜɫɟɯ
ɡɚɢɦɫɬɜɭɟɦ ɢɡ ɬɚɛɥ. 8.1 ɞɥɹ ɧɟɫɢɦɦɟ
ɬ
ɦ
ɚɥɶɧɨɦ
ɫɥɟɞɨɜɚ-
ɢ
ɣ ɜ ɦɟɫ-
ɪ
ɚɤɬɟɪɢ-
ɨ
ɢɫɯɨɞɢɬ
ɄɁ ɞɥɹ
ɨɞɧɚ ɢɡ
ɩ
ɨɫɥɟɞɨ-
ɨ
ɫɢɬɟɥɶ-
ɚ ɫɬɭɩɟ-
ɷ
ɬɭ ɮɚɡɭ
ɬɪɟɯ ɮɚ-
ɬ
ɪɢɢ L
(1)
.
194
ɍɱɢɬɵɜɚɹ, ɱɬɨ ɪɟɡɭɥɶɬɢɪɭɸɳɚɹ ɪɟɚɤɬɢɜɧɨɫɬɶ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚ-
ɬɟɥɶɧɨɫɬɢ ɪɚɜɧɚ ɛɟɫɤɨɧɟɱɧɨɫɬɢ (
0
x
6
f
), ɞɨɩɨɥɧɢɬɟɥɶɧɚɹ ɪɟɚɤɬɢɜɧɨɫɬɶ,
ɜɤɥɸɱɚɟɦɚɹ ɜ ɫɯɟɦɭ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ, ɛɭɞɟɬ ɫɨɫɬɚɜɥɹɬɶ
3
1
2
0,366
// //0,681 0,149
33
L
x
xx
6
'
§·
§·
¨¸
¨¸
©¹©¹
.
ɇɚɯɨɞɢɦ ɫɢɦɦɟɬɪɢɱɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɬɨɤɨɜ ɮɚɡɵ Ⱥ:
1
1
1
1
1, 0 8
2,03
(0,681 0,149)
()
La
L
j
j
jx x
6
6
'
E
I ;
1
21
2
( 0,149)
2,03 0,444
0,681
L
La La
x
x
'
6
II
.
ɇɚɢɛɨɥɶɲɢɣ ɬɨɤ ɛɭɞɟɬ ɜ ɮɚɡɟ Ⱥ (ɜ ɤɨɬɨɪɨɣ ɭɫɥɨɜɧɨ ɨɬɫɭɬɫɬɜɭɟɬ
ɪɟɚɤɬɨɪ):
12ɛ
( ) (2,03 0,444) 9,16 22,66
L
La La
I II I
ɤȺ;
ɬɨɤɢ ɜ ɮɚɡɚɯ ȼ ɢ ɋ ɫɨɫɬɚɜɥɹɸɬ ɨɤɨɥɨ 17 ɤȺ.
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚɤɨɪɚɱɢɜɚɧɢɟ ɨɞɧɨɣ ɮɚɡɵ ɪɟɚɤɬɨɪɚ ɩɪɢ ɡɚɞɚɧɧɵɯ
ɭɫɥɨɜɢɹɯ ɩɪɢɜɨɞɢɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɬɨɤɚ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɜ 1,55 ɪɚɡɚ.
8.5. ȿɝɩɤɨɩɠ ɢɛɧɶɥɛɨɣɠ ɨɛ ɢɠɧɦɹ
ɋɥɨɠɧɵɟ ɜɢɞɵ ɩɨɜɪɟɠɞɟɧɢɣ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɜɨɤɭɩɧɨɫɬɶ ɧɟ-
ɫɤɨɥɶɤɢɯ ɧɟɫɢɦɦɟɬɪɢɱɧɵɯ ɡɚɦɵɤɚɧɢɣ ɢɥɢ ɩɪɨɞɨɥɶɧɨɣ ɧɟɫɢɦɦɟɬɪɢɢ
ɨɬɞɟɥɶɧɵɯ ɭɱɚɫɬɤɨɜ ɜ ɫɢɫɬɟɦɟ. ȼɨɡɦɨɠɧɨ ɢ
ɨɞɧɨɜɪɟɦɟɧɧɨɟ ɜɨɡɧɢɤɧɨɜɟ-
ɧɢɟ ɩɪɨɞɨɥɶɧɨɣ ɢ ɩɨɩɟɪɟɱɧɨɣ ɧɟɫɢɦɦɟɬɪɢɣ ɜ ɪɚɡɥɢɱɧɵɯ ɤɨɦɛɢɧɚɰɢɹɯ.
ɇɚɢɛɨɥɶɲɢɣ ɩɪɚɤɬɢɱɟɫɤɢɣ ɢɧɬɟɪɟɫ ɩɪɟɞɫɬɚɜɥɹɸɬ ɨɞɧɨɜɪɟɦɟɧɧɨɟ
ɤɨɪɨɬɤɨɟ ɡɚɦɵɤɚɧɢɟ ɜ ɞɜɭɯ ɬɨɱɤɚɯ ɫɯɟɦ ɷɥɟɤɬɪɨɫɧɚɛɠɟɧɢɹ ɫ ɢɡɨɥɢɪɨ-
ɜɚɧɧɨɣ ɧɟɣɬɪɚɥɶɸ ɢ ɨɞɧɨɜɪɟɦɟɧɧɨɟ ɤɨɪɨɬɤɨɟ ɡɚɦɵɤɚɧɢɟ ɧɚ ɡɟɦɥɸ ɫ
ɪɚɡɪɵɜɨɦ ɬɨɣ ɠɟ ɮɚɡɵ ɜ ɫɢɫɬɟɦɟ ɫ ɡɚɡɟɦɥɟɧɧɨɣ ɧɟɣɬɪɚɥɶɸ. Ȼɨɥɟɟ ɫɥɨɠ-
ɧɵɟ ɜɢɞɵ ɩɨɜɪɟɠɞɟɧɢɣ ɦɚɥɨɜɟɪɨɹɬɧɵ.
ɉɨɥɭɱɢɦ ɪɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ
ɞɥɹ ɞɜɨɣɧɨɝɨ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ.
ɋɱɢɬɚɟɦ, ɱɬɨ ɜ ɩɪɨɢɡɜɨɥɶɧɵɯ ɬɨɱɤɚɯ Ɇ ɢ N ɬɪɟɯɮɚɡɧɨɣ ɫɟɬɢ ɩɪɨ-
ɢɡɨɲɥɢ ɨɞɧɨɜɪɟɦɟɧɧɵɟ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ ɮɚɡ ȼ ɢ ɋ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ
(ɫɦ. ɪɢɫ. 8.12, ɚ).
Ɋɢɫ. 8.12. Ⱦɜɨɣɧɨɟ ɡɚɦ
ɵ
ɛ
– ɫɢɦɦɟɬɪɢ
ɱ
Ⱦɥɹ ɭɩɪɨɳɟɧɢɹ ɩɨɥ
ɚ
ɦɟɧɬɵ ɫɯɟɦɵ ɱɢɫɬɨ ɢɧɞɭɤ
ɬ
Ⱥɧɚɥɨɝɢɱɧɨ ɩɪɨɫɬɨ
ɦ
ɜ ɪɚɡɞ. 7.3, ɝɪɚɧɢɱɧɵɟ ɭɫɥ
ɨ
M
A
I
NA
I
ɢ ɞɨɩɨɥɧɢɬɟɥɶɧɵɦ ɭɫɥɨɜɢ
ɥɹɟɬɫɹ ɪɚɜɟɧɫɬɜɨ:
ɉɪɢɧɹɜ ɧɟɩɨɜɪɟɠɞɟ
ɧ
ɳɢɟ ɢɡ ɝɪɚɧɢɱɧɵɯ ɭɫɥɨɜ
ɢ
ɫɬɚɜɥɹɸɳɢɦɢ ɬɨɤɨɜ (ɪɢɫ.
8
195
ɵ
ɤɚɧɢɟ ɧɚ ɡɟɦɥɸ: ɚ –
ɩɪɢɧɰɢɩɢɚɥɶɧɚɹ ɫɯɟɦ
ɚ
ɱ
ɧɵɟ ɫɨɫɬɚɜɥɹɸɳɢɟ ɬɨɤɨɜ ɜ ɦɟɫɬɚɯ ɄɁ
ɚ
ɝɚɟɦ, ɱɬɨ ɡɚɦɵɤɚɧɢɹ ɦɟɬɚɥɥɢɱɟɫɤɢ
ɟ
ɬ
ɢɜɧɵɟ.
ɦ
ɭ ɨɞɧɨɮɚɡɧɨɦɭ ɡɚɦɵɤɚɧɢɸ, ɪɚɫɫɦɨɬ
ɪ
ɨ
ɜɢɹ ɜ ɨɛɟɢɯ ɬɨɱɤɚɯ ɢɦɟɸɬ ɫɥɟɞɭɸɳɢ
ɣ
0, 0, 0;
MC MB
IU
0, 0, 0
NB NC
IU
,
ɟɦ ɞɚɧɧɨɝɨ ɜɢɞɚ ɩɨɜɪɟɠɞɟɧɢɹ, ɨɱɟɜ
ɢ
.
MB NC
II
ɧ
ɧɭɸ ɮɚɡɭ Ⱥ ɡɚ ɨɫɧɨɜɧɭɸ, ɡɚɩɢɲɟɦ
ɜ
ɢ
ɣ ɫɨɨɬɧɨɲɟɧɢɹ ɦɟɠɞ
ɭ
ɫɢɦɦɟɬɪɢɱɧ
ɵ
8
.12, ɛ):
ɚ
;
ɟ
ɢ ɷɥɟ-
ɪ
ɟɧɧɨɦɭ
ɣ
ɜɢɞ:
(8.27)
(8.28)
ɢ
ɞɧɨ, ɹɜ-
(8.29)
ɜ
ɵɬɟɤɚɸ-
ɵ
ɦɢ ɫɨ-
I
I
2Mɚ
I
2Na
I
12
M
bMb
UU
U
12Nc Nc
UU
U
Ⱦɨɩɨɥɧɢɬɟɥɶɧɨ ɢɡ ɫɨɨɬɧɨ
ɫɜɹɡɶ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬ
ɚ
ɞɥɹ ɬɨɱɟɤ M ɢ N
ɉɪɢɜɟɞɟɧɧɵɟ ɫɨɨɬɧ
ɨ
ɫɬɚɜɥɹɸɳɢɟ ɬɨɤɨɜ ɜɫɟɯ ɬɪ
ɟ
ɦɟɠɞɭ ɫɨɛɨɣ ɩɨ ɦɨɞɭɥɸ ɢ
ɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɬɨɤɨɜ
ɜ
ɜɢɟɦ (8.34).
ɋɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɨ
ɬ
ɡɚɦɵɤɚɧɢɢ ɦɨɝɭɬ ɛɵɬɶ ɩɪ
ɢ
Ɉɧɢ ɩɨɡɜɨɥɹɸɬ ɭɫɬɚɧɨɜɢɬ
ɶ
M ɢ N ɞɥɹ ɫɯɟɦ ɡɚɦɟɳɟɧɢ
ɹ
ɧɨɫɬɟɣ.
Ɋɢɫ. 8.13. ɋɯɟɦɵ ɡɚɦɟ
ɳ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ
ɫ
196
120
;
Mb Mb M
II
120
;
Nc Mc N
I
II
1
,
Mɚ
Ia
2
01
;
M
Mɚ
IIa
2
1
,
N
ɚ
Ia
01
;
NNɚ
IIa
2
0120
0;
MMaMaM
U
UUUaa
2
01 20
0
NNa NaN
U
UUUaa
.
ɲɟɧɢɹ (8.29), ɫ ɭɱɟɬɨɦ (8.30)–(8.33
)
ɚ
ɜɥɹɸɳɢɯ ɬɨɤɨɜ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬ
ɟ
11
.
Na Mɚ
IIa
ɨ
ɲɟɧɢɹ ɩɨɤɚɡɵɜɚɸɬ, ɱɬɨ ɫɢɦɦɟɬɪɢ
ɱ
ɟ
ɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɜ ɬɨɱɤɚɯ M ɢ
ɨɬɥɢɱɚɸɬɫɹ ɬɨɥɶɤɨ ɮɚɡɚɦɢ; ɫɜɹɡɶ ɫɢ
ɦ
ɜ
ɨɛɨɢɯ ɦɟɫɬɚɯ ɡɚɦɵɤɚɧɢɹ ɨɩɪɟɞɟɥɹɟ
ɬ
ɬ
ɞɟɥɶɧɵɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɩɪɢ
ɞ
ɢ
ɜɟɞɟɧɵ ɤ ɜɢɞɭ, ɩɪɟɞɫɬɚɜɥɟɧɧɨɦɭ ɧɚ
ɪ
ɶ
ɫɜɹɡɶ ɦɟɠɞɭ ɬɨɤɚɦɢ ɢ ɧɚɩɪɹɠɟɧɢɹɦ
ɢ
ɹ
ɩɪɹɦɨɣ, ɨɛɪɚɬɧɨɣ ɢ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞ
ɳ
ɟɧɢɹ ɩɪɹɦɨɣ (ɚ), ɨɛɪɚɬɧɨɣ (ɛ), ɧɭɥɟɜɨɣ
ɫ
ɬɟɣ ɩɪɢ ɞɜɨɣɧɨɦ ɡɚɦɵɤɚɧɢɢ ɧɚ ɡɟɦɥɸ
(8.30)
(8.31)
(8.32)
(8.33)
)
, ɢɦɟɟɦ
ɟ
ɥɶɧɨɫɬɢ
(8.34)
ɱ
ɧɵɟ ɫɨ-
N ɪɚɜɧɵ
ɦ
ɦɟɬɪɢɱ-
ɬ
ɫɹ ɭɫɥɨ-
ɞ
ɜɨɣɧɨɦ
ɪ
ɢɫ. 8.13.
ɢ
ɜ ɭɡɥɚɯ
ɨɜɚɬɟɥɶ-
(ɜ)
197
ɉɨɥɧɵɣ ɚɧɚɥɢɡ ɞɜɨɣɧɨɝɨ ɡɚɦɵɤɚɧɢɹ ɬɪɟɛɭɟɬ ɪɚɫɱɟɬɚ 12 ɩɚɪɚɦɟɬ-
ɪɨɜ ɜ ɬɨɱɤɚɯ ɄɁ (ɬɪɢ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɧɚɩɪɹɠɟɧɢɹ ɢ ɬɪɢ
ɫɨɫɬɚɜɥɹɸɳɢɯ ɬɨɤɚ ɞɥɹ ɤɚɠɞɨɣ ɬɨɱɤɢ). Ⱦɥɹ ɷɬɨɝɨ ɧɟɨɛɯɨɞɢɦɨ ɪɟɲɢɬɶ
12 ɭɪɚɜɧɟɧɢɣ, ɫɜɹɡɵɜɚɸɳɢɯ ɧɚɡɜɚɧɧɵɟ ɩɟɪɟɦɟɧɧɵɟ. ɉɟɪɜɵɟ ɫɟɦɶ ɭɪɚɜ-
ɧɟɧɢɣ ɩɪɟɞɫɬɚɜɥɹɸɬ ɝɪɚɧɢɱɧɵɟ ɭɫɥɨɜɢɹ (8.27)–(8.29). Ʉ ɧɢɦ ɧɭɠɧɨ ɞɨ-
ɛɚɜɢɬɶ 5 ɭɪɚɜɧɟɧɢɣ ɜɬɨɪɨɝɨ ɡɚɤɨɧɚ Ʉɢɪɯɝɨɮɚ, ɡɚɩɢɫɚɧɧɵɯ ɞɥɹ ɫɯɟɦ ɪɚɡ
-
ɥɢɱɧɵɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ (ɫɦ. ɪɢɫ. 8.13).
ȼɵɪɚɠɚɹ ɜɫɟ ɧɟɢɡɜɟɫɬɧɵɟ ɱɟɪɟɡ ɬɨɤ
1
M
a
I
, ɩɨɥɭɱɚɟɦ ɞɥɹ ɧɟɝɨ ɪɚɫ-
ɱɟɬɧɭɸ ɮɨɪɦɭɥɭ
2
1
111
(3 )
MA NA
Ma
H
MND
jx x x x
EE
I
a
, (8.35)
ɝɞɟ
222 0
3.
D
HMNMN
xxxxx
(8.36)
Ɍɨɤɢ ɩɨɜɪɟɠɞɟɧɧɵɯ ɮɚɡ ɜ ɦɟɫɬɟ ɡɚɦɵɤɚɧɢɹ ɜɵɱɢɫɥɹɟɦ ɩɨ ɫɨɨɬ-
ɧɨɲɟɧɢɸ
2
1
3.
M
BMaNC
IIIa
(8.37)
Ɋɚɫɱɟɬɧɵɟ ɜɵɪɚɠɟɧɢɹ ɞɥɹ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɧɚɩɪɹ-
ɠɟɧɢɣ ɜ ɬɨɱɤɚɯ M ɢ N ɭɞɨɛɧɨ ɩɪɟɞɫɬɚɜɢɬɶ ɱɟɪɟɡ ɬɨɤ
2
01
M
Ma
IIa
ɢɥɢ
00
()
NM
II
:
2
1011
;
Ma MA M H M
jxx
ªº
«»
¬¼
UE Iaa +a
(8.38)
22
20 22
;
Ma M H M
jxx
ªº
«»
¬¼
UIaa a
(8.39)
2
012
;
MMaMa
UUUaa
(8.40)
22
1011
;
Na NA M H N
jxx
ªº
«»
¬¼
UE Iaa a
(8.41)
2
20 22
;
Na M H N
jxx
ªº
«»
¬¼
UIaa a
(8.42)
2
012
.
NNaNa
UUUaa
(8.43)
ȼɟɤɬɨɪɧɵɟ ɞɢɚɝɪɚɦɦɵ ɬɨɤɨɜ ɢ ɧɚɩɪɹɠɟɧɢɣ ɜ ɦɟɫɬɚɯ ɄɁ ɩɪɢɜɟɞɟ-
ɧɵ ɧɚ ɪɢɫ. 8.14. Ʉɪɢɬɟɪɢɟɦ ɩɪɚɜɢɥɶɧɨɫɬɢ ɪɚɫɱɟɬɚ (ɩɨɫɬɪɨɟɧɢɹ ɞɢɚ-
ɝɪɚɦɦ) ɹɜɥɹɟɬɫɹ ɩɟɪɩɟɧɞɢɤɭɥɹɪɧɨɫɬɶ ɜɟɤɬɨɪɨɜ
00NM
UU ɢ
0
M
I
.
ɇɚɢɛɨɥɶɲɟɟ ɨɫɬɚɬɨɱɧɨɟ ɧɚɩɪɹɠɟɧɢɟ ɢɦɟɟɬ ɡɞɨɪɨɜɚɹ ɮɚɡɚ Ⱥ; ɧɚɩɪɹɠɟɧɢɟ
ɩɨɜɪɟɠɞɟɧɧɵɯ ɮɚɡ ȼ ɢ ɋ ɜ ɦɟɫɬɟ ɢɯ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ ɪɚɜ-
ɧɨ ɧɭɥɸ ɢ ɩɨ ɦɟɪɟ ɭɞɚɥɟɧɢɹ ɨɬ ɄɁ ɜɨɡɪɚɫɬɚɟɬ.
ɋɯɟɦɚ ɧɭɥɟɜɨɣ ɩɨɫɥ
ɪ
ɚɰɢɸ, ɱɬɨ ɢ ɫɯɟɦɚ ɩɪɹɦ
ɨ
ɫɱɢɬɵɜɚɟɦɚɹ ɫɟɬɶ ɪɚɛɨɬɚɟ
ɬ
ɬɪɚɥɹɦɢ. ɗȾɋ, ɜɯɨɞɹɳɢɟ
N
E
ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɪɟɨɛɪ
ɚ
Ɋɢɫ. 8.14. Ⱦɜɨɣɧɨɟ ɡɚɦ
ɵ
ɧɚɩɪɹɠɟɧɢɣ ɜ
ɉɪɢɦɟɪ 8.4. ɂɫɯɨɞɧ
ɵ
ɜɨɜɚɧɵ ɢɡ [1].
ɉɪɢ ɨɞɧɨɜɪɟɦɟɧɧɨɦ
ɧɨ ɜ ɬɨɱɤɚɯ M ɢ N ɫɯɟɦɵ,
ɩ
ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɢ ɮɚ
ɡ
Ɋɚɫɱɟɬɵ ɩɪɨɜɟɞɟɦ ɞ
ɥ
ɝɟɧɟɪɚɬɨɪ ɞɨ ɜɤɥɸɱɟɧɢɹ ɜ
ɥɨɜɢɹɯ ɧɚɱɚɥɶɧɨɟ ɡɧɚɱɟɧɢ
ɟ
ɬɨɪɚ ɪɚɜɧɨ ɟɝɨ ɧɚɩɪɹɠɟɧɢ
ɸ
198
ɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɩɪɢɨɛɪɟɬɚɟɬ ɬɭ ɠɟ
ɤ
ɨ
ɣ (ɨɛɪɚɬɧɨɣ) ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ, ɤ
ɨ
ɬ
ɫ ɡɚɡɟɦɥɟɧɧɵɦɢ (ɤɨɦɩɟɧɫɢɪɨɜɚɧɧɵ
ɦ
ɜ ɫɯɟɦɭ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬ
ɢ
ɚ
ɡɨɜɚɧɢɹɦɢ, ɩɪɢɜɟɞɟɧɧɵɦɢ ɜ [1, ɩɪɢɥ.
ɵ
ɤɚɧɢɟ ɧɚ ɡɟɦɥɸ:
ɚ, ɜ – ɜɟɤɬɨɪɧɵɟ ɞɢɚɝɪɚ
ɦ
ɬɨɱɤɚɯ M ɢ N; ɛ – ɬɨ ɠɟ ɬɨɤɨɜ ɜ ɬɨɱɤɟ M
ɵ
ɟ ɞɚɧɧɵɟ ɞɥɹ ɧɚɫɬɨɹɳɟɝɨ ɩɪɢɦɟɪɚ ɩ
ɨ
ɡɚɦɵɤɚɧɢɢ ɧɚ ɡɟɦɥɸ ɮɚɡ ȼ ɢ ɋ ɫɨɨɬ
ɜ
ɩ
ɪɟɞɫɬɚɜɥɟɧɧɨɣ ɧɚ ɪɢɫ. 8.15, ɚ, ɨɩɪɟɞɟ
ɡ
ɧɵɟ ɧɚɩɪɹɠɟɧɢɹ ɜ ɦɟɫɬɚɯ ɩɨɜɪɟɠɞɟɧ
ɢ
ɥ
ɹ ɧɚɱɚɥɶɧɨɝɨ ɦɨɦɟɧɬɚ ɜɪɟɦɟɧɢ, ɫɱ
ɢ
ɫɟɬɶ ɪɚɛɨɬɚɥ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ. ɉɪɢ
ɟ
ɫɜɟɪɯɩɟɪɟɯɨɞɧɨɣ ɗȾɋ ɫɢɧɯɪɨɧɧɨɝ
ɨ
ɸ
ɜ ɧɨɪɦɚɥɶɧɨɦ ɪɟɠɢɦɟ.
ɤ
ɨɧɮɢɝɭ-
ɨ
ɝɞɚ ɪɚɫ-
ɦ
ɢ) ɧɟɣ-
ɢ
,
M
E
ɢ
1].
ɦ
ɦɵ
ɨ
ɡɚɢɦɫɬ-
ɜ
ɟɬɫɬɜɟɧ-
ɥɢɬɶ ɬɨɤ
ɢ
ɹ.
ɢ
ɬɚɹ, ɱɬɨ
ɷɬɢɯ ɭɫ-
ɨ
ɝɟɧɟɪɚ-
ɂɫɯɨɞɧɵɟ ɞɚɧɧɵɟ
Ƚɟɧɟɪɚɬɨɪ Ƚ: S = 37,
5
Ɍɪɚɧɫɮɨɪɦɚɬɨɪ Ɍ1:
S
/Y '
-11.
Ɍɪɚɧɫɮɨɪɦɚɬɨɪ Ɍ2:
S
(ȼ-ɋ)
10,5
K
U
%,
0
//YY
'
Ʌɢɧɢɹ Ʌ: L = 12,5 ɤɦ
ɋɢɫɬɟɦɚ ɋ: ɢɫɬɨɱɧ
ɢ
123
0xxx
.
Ɋɢɫ. 8.15. ɋɯɟɦɵ ɤ ɩɪɢɦ
ɟɪ
ɩɪɹɦɨɣ (ɨɛɪɚɬɧɨɣ) ɩɨɫɥɟɞɨɜɚ
ɬ
Ɋɟɲɟɧɢɟ. Ɋɚɫɱɟɬ ɩɪ
ɨ
ɷɥɟɦɟɧɬɵ ɤ ɫɬɨɪɨɧɟ ɥɢɧɢ
ɢ
ɦɟɳɟɧɢɹ (ɪɢɫ. 8.15, ɛ, ɜ):
x ɝɟɧɟɪɚɬɨɪɚ:
2
37
0,143
37,5
d
x
cc
199
5
ɆȼȺ, U = 6,3 ɤȼ,
d
x
cc
= 0,143 | x
2
.
S
= 25 ɆȼȺ,
B ɇ
/37/6,3UU
ɤȼ,
K
U
S
= 40 ɆȼȺ,
ȼɋɇ
/ / 115/37/UUU
'
-12, 11.
,
1
x
= 0,4 Ɉɦ/ɤɦ,
0
x
= 1,45 Ɉɦ/ɤɦ.
ɢ
ɤ ɛɟɫɤɨɧɟɱɧɨɣ ɦɨɳɧɨɫɬɢ;
C
U
=
ɟɪ
ɭ 8.4: ɚ –
ɢɫɯɨɞɧɚɹ ɫɯɟɦɚ
; ɛ –
ɫɯɟɦɚ
ɡ
ɚɦɟ
ɳ
ɬ
ɟɥɶɧɨɫɬɢ;
ɜ –
ɬɨ ɠɟ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚɬ
ɟɥ
ɨ
ɜɟɞɟɦ ɜ ɢɦɟɧɨɜɚɧɧɵɯ ɟɞɢɧɢɰɚɯ, ɨɬ
ɧ
ɢ
. Ɋɚɫɫɱɢɬɚɟɦ ɩɚɪɚɦɟɬɪɵ ɷɥɟɦɟɧɬɨɜ
5,22
Ɉɦ,
6,3 37
21,4
6,3
3
E
cc
ɤȼ;
K
= 8 %,
10,5
ɤȼ,
=
115 ɤȼ,
ɳ
ɟɧɢɹ
ɟ
ɥɶɧɨɫɬɢ
ɧ
ɟɫɹ ɜɫɟ
ɫɯɟɦ ɡɚ-
200
x ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ Ɍ1:
2
Ɍ1
37
0,08 3,2
25
x
Ɉɦ;
x ɬɪɚɧɫɮɨɪɦɚɬɨɪɚ Ɍ2:
2
T2
37
0,105 3,6
40
x
Ɉɦ;
x ɥɢɧɢɢ Ʌ:
1
0,4 12,5 5x
Ɉɦ,
0
1,45 12,5 18,5x
Ɉɦ;
x ɫɢɫɬɟɦɵ ɋ:
C
115 37
21,4
115
3
E
ɤȼ.
ɇɚ ɪɢɫ. 6.44, ɛ ɩɨɤɚɡɚɧɚ ɫɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶ-
ɧɨɫɬɢ, ɝɞɟ ɭɤɚɡɚɧɵ ɪɟɚɤɬɢɜɧɨɫɬɢ (ɜ Ɉɦɚɯ) ɜɫɟɯ ɷɥɟɦɟɧɬɨɜ ɢ ɗȾɋ (ɜ ɤɢ-
ɥɨɜɨɥɶɬɚɯ) ɢɫɬɨɱɧɢɤɨɜ. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ ɨɛɪɚɬɧɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ
ɫɨɜɩɚɞɚɟɬ ɫɨ ɫɯɟɦɨɣ ɩɪɹɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ ɩɪɢ ɢɫɤɥɸɱɟɧɢɢ ɢɡ
ɧɟɟ ɗȾɋ. ɋɯɟɦɚ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ (ɫɦ. ɪɢɫ. 8.15, ɜ) ɫɨɞɟɪɠɢɬ
ɬɨɥɶɤɨ ɨɞɢɧ ɷɥɟɦɟɧɬ (ɥɢɧɢɹ).
Ɉɛɴɟɞɢɧɹɹ ɧɚɱɚɥɚ
ɝɟɧɟɪɢɪɭɸɳɢɯ ɜɟɬɜɟɣ, ɩɨɥɭɱɚɟɦ «ɬɪɟɭɝɨɥɶɧɢɤ»
ɫɨɩɪɨɬɢɜɥɟɧɢɣ, ɜ ɤɨɬɨɪɨɦ ɫɬɨɪɨɧɚ
11
M
ɇ
ɪɚɜɧɚ ɩɥɟɱɭ
Ƚ 1
ȿɆ
, ɢ ɫɬɨ-
ɪɨɧɚ
11
NH
ɪɚɜɧɚ ɩɥɟɱɭ
1C
NE
. ɉɪɟɨɛɪɚɡɨɜɚɧɢɟ «ɬɪɟɭɝɨɥɶɧɢɤɚ» ɫɨ-
ɩɪɨɬɢɜɥɟɧɢɣ
111
Ɇ
HN
ɜ ɷɤɜɢɜɚɥɟɧɬɧɭɸ «ɡɜɟɡɞɭ» ɞɚɟɬ ɪɟɚɤɬɢɜɧɨɫɬɢ
ɷɥɟɦɟɧɬɨɜ ɫɯɟɦɵ ɩɪɹɦɨɣ (ɨɛɪɚɬɧɨɣ) ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ:
12
2,47
Ɇ
Ɇ
xx
Ɉɦ,
12
1,0 6
NN
xx
Ɉɦ,
12
1, 7 8
ɇ
ɇ
xx
Ɉɦ.
ɉɨ (8.36) ɧɚɯɨɞɢɦ
D
x
= 3 1,78 + 2,47 + 1,06 + 18,1 = 27 Ɉɦ.
ɉɪɢɧɢɦɚɹ
21,4
A
j E
ɤȼ, ɩɨ ɜɵɪɚɠɟɧɢɸ (8.35) ɧɚɯɨɞɢɦ ɬɨɤ ɩɪɹ-
ɦɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɢ
2
30
1
21,4(1 )
1,0 3
(3 1,78 2,47 1,06 27)
j
Ma
j
e
j
I
D
a
ɤȺ.
Ɍɨɤɢ ɨɛɪɚɬɧɨɣ ɢ ɧɭɥɟɜɨɣ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɬɟɣ ɫɨɫɬɚɜɥɹɸɬ:
150
21
1, 0 3
j
M
aMa
e II
D
a ɤȺ,
2
01
1,0 3
M
Ma
j IIa
ɤȺ.
Ɋɚɫɫɱɢɬɵɜɚɟɦ ɬɨɤ ɜ ɦɟɫɬɚɯ ɤɨɪɨɬɤɨɝɨ ɡɚɦɵɤɚɧɢɹ ɧɚ ɡɟɦɥɸ (ɨɧ ɠɟ
ɹɜɥɹɟɬɫɹ ɬɨɤɨɦ ɜ ɡɟɦɥɟ):
0
33,09
M
BNCM
j III
ɤȺ.
Ⱦɥɹ ɫɢɦɦɟɬɪɢɱɧɵɯ ɫɨɫɬɚɜɥɹɸɳɢɯ ɧɚɩɪɹɠɟɧɢɣ ɜ ɬɨɱɤɟ Ɇ ɩɨ ɜɵ-
ɪɚɠɟɧɢɹɦ (8.38)–(8.40) ɢɦɟɟɦ: