4.1.4.1. 2 ( , .. ).
, 1 . 8.
. 8. I3.
4.1.4.2. I3 .
) R23 R2 R3
R23 = R2 R3/ (R2 + R3) (4.1.16)
R.
R. = R1 + R23 (4.1.17)
) I1
I1 = 1/ R. (4.1.18)
) R3
U3 = U23 = I1 R23 (4.1.19)
) 3
3 = U3/ R3 (4.1.20)
3) 3 , 2.
4) I3
I 3 = 3 + 3 (4.1.21)
I3.
2
4.2.1. , , .. , : ,
= 0, , J= 0.
, .. . J r. E r.,
E = Jr. (4.2.1)
r. = r. (4.2.2)
9; 9 .
) )
. 9. () ()
.
4.2.2. , 10.
. 10. 2
: 1 = 30 ; 2 = 16 ;
3 = 10 ; R1 = 2 ; R2 = 5 ; R3 = 3 ; R4 = 1 ; R5 = 8 ; R6 = 5 .
.
4.2.2.1 .
1) , , . 11.
. 11. .
2) :
I11 R11 - I22 R12 - I33 R13 = 11;
- I11 R21 + I22 R22 - I33 R23 = 22; (4.2.3)
- I11 R31 - I22 R32 - I33 R33 = 33,
R11 = R1 + R2 + R4 = 2 + 5 + 1 = 8 ; R22 = R2 + R3 + R5 = 5 + 3 + 8 = 16 ;
|
|
R33 = R4 + R5 + R6 = 1 + 8 + 5 = 14 ;
R12 = R21 = R2 =5 ; R23 = R32 = R5 =8 ; R13 = R31 = R4 =1 ;
11 = 1 2 = 30 - 16 = 14 ; 22 = 2 3 = 16 - 10 = 6 ; 33 = 0.
8I11 - 5I22 - I33 = 14;
- 5I11 + 16I22 - 8I33 = 6; (4.2.4)
- I11 - 8I22 + 14I33 = 0.
3) : 1, 2, 3.
8 -5 -1 14 -5 -1
= -5 16 -8 = 834; 1 = 6 16 -8 = 2708;
-1 -8 14 0 -8 14
8 14 -1 8 -5 14
2 = -5 6 -8 = 1758; 3 = -5 16 6 = 1198.
-1 0 14 -1 -8 0
4) :
I11 = 1 / = 2708/834 = 3,247 ;I22 = 2 / = 1758/834 = 2,108 ;
I33 = 3 / = 1198/834 = 1,436 .
5) :
I1 = I11 = 3,247 ; I2 = I11 - I22 = 3,247 2,108 = 1,139 ;
I3 = - I22 = - 2,108 ; I4 = I33 I11 = 1,436 3,247 = -1,811 ;
I5 = I33 I22 = 1,436 2,108 = - 0,672 ; I6 = I33 = 1,436 .
4.2.2.2 .
1) (. 11) I 1, I2, I3, I4, I5, I6 1, 2, 3.
2) .
I6 I1 I4 = 0;
I1 + I3 - I2 = 0; (4.2.5)
I4 + I2 I5 = 0.
3) ; .
I6 R1 + I2 R2 I4 R4 = E1 E2;
-I2 R2 I3 R3 I5 R5 = E2 E3; (4.2.6)
I4 R4 + I5 R5 + I6 R6 = 0.
4) , .
4.2.2.3 .
R4; R5; R6.
:
R46 = R4 R6/ (R4 + R5 + R6) = 0,357 ;
R45 = R4 R5/(R4 + R5 + R6) = 0,571 ; (4.2.7)
R56 = R5 R6/(R4 + R5 + R6) = 2,857 ;
4.2.2.4 .
1) U , . 11
U - I4 R4 + I1 R1 + 2 = 0 (4.2.8)
2) U
U = - 2 - I1 R1 + I4 R4 = -16 - 3,247 2 1,811 = -24,305 .
.
4.2.2.4 .
, , , , . (, ). .
1)
. = 1 I1 + 2I2 +3I3 (4.2.9)
. = 30 3,247 -16 1,139 10 2,108 = 58,1 .
2)
R = I1 R1 + I 2 R2 + I 3 R3 + I4 R4 + I5 R5 + I6 R6 (4.2.10)
|
|
R = 58,1 , .. , .
3
4.3.1. , , , , , , - . : /, /,- , .
= + jb =A e , (4.3.1)
,
b .
= (4.3.2)
= arc tg b/a (4.3.3)
= cos (4.3.4)
b = A sin (4.3.5)
4.3.2. :
) : , ;
) .
, , .
4.3.3. f
= 2f (4.3.6)
4.3.4.
)
L = L () (4.3.7)
C = 1/ C () (4.3.8)
) , . 4.3.1 .
:
- = 100 ; = 650;
= 100 j65 ,
(4) (5);
- R, L
R = 3 ; L = 9 ; = 5 .
Z = R + j (L ) = 3 + j (9 5) = 3 + j 4
c (4.3.1) (4.3.3).
6.
6 -
.
, | ||
) , . .
) , , , . 7. .
7 - .
, .
4.3.5. S , .
S = , (4.3.9) , . , = 3 + j4, = 3 - j4.
.
( ).
|
|
,
S = I, (4.3.10)
,
= S cos ; (4.3.11)
Q = S sin , (4.3.12)
- .
, .
, .
4.3.6. , () n-
P. = I n Rn, (4.3.13)
In , ;
Rn , .
, (. . 4.3.5).
4.3.7.
= m sin ( t + ) (4.3.14)
- , - (. ).
4.3.8. .
.12 , 7, I' U', I" U".
. 12.
7 -
, | 1 | I'1 + jI"1 | I1 e | I1 |
2 | I'2 + jI"2 | I2 e | I2 | |
3 | I'3 + jI"3 | I3 e | I3 | |
4 | I'4 + jI"4 | I4 e | I4 | |
5 | I'5 + jI"5 | I5 e | I5 | |
6 | I'6 + jI"6 | I6 e | I6 |
7
, | 1 = R1 | U'1 + j U"1 | U1 e | U1 |
2 = C2 | U'2+ jU"2 | U2 e | U2 | |
3 | U'3 + jU"3 | U3 e | U3 | |
R3 | U'R3 + jU"R3 | UR3 e | UR3 | |
C3 | U'C3 + jU"C3 | UC3 e | UC3 | |
4 = R4 | U'4 + jU"4 | U4 e | U4 | |
5 | U'5 + jU"5 | U5 e | U5 | |
R5 | U'R5 + jU"R5 | UR5 e | UR5 | |
5 | U'L5 + jU"L5 | UL5 e | UL5 | |
6 = R6 | U'6 + jU"6 | U6 e | U6 |
. 13 , :
1. : (+1) , (j) .
2. , , mI mU. , 4 ( 210297 ) 40 U = 500 : mI = 5 /, mU = 50 /.
3. mI mU , ; , .. .
, , I = 40 = 20 + j34,6 U = 500 = 433 + j 250 :
- /I / = 40 / 5 / = 8 ; I = 20 / 5 / = 4 , I = 34,6 / 5 / = 6,9 ;
- / U / = 500 / 50 / = 10 ; -
|
|
U = 433 / 50 / = 8,66 ; U =
= 250 / 50 / = 5 .
, 7.
7 - ,
, 1/ | , | , | , | ||
1 | mI= 5 / | ||||
2 | |||||
3 | |||||
4 | |||||
5 | |||||
6 | |||||
1 | mU=50 / | ||||
2 | |||||
6 | |||||
1= R1 | |||||
R1 | |||||
2 = C2 | |||||
3 | |||||
R3 |
7
C3 | mU=50 / | ||||
4 = R4 | |||||
5 | |||||
R5 | |||||
L5 | |||||
6 = R6 |
4. , . , .
, , . 3 , : (+1) 30 , .. , 8 ; , (+1) 4 , (j) 6,96 , .
(. 13) : , .
5. , . , ,
(. 12):
- 1, 4 6 1, 4 6 ;
- R5 I5, L5 5 90 ;
- 1 5 6;
- 111 3, 6 5 6.
, .
. 13. . 12.
4
4.4.1 , . , - , , , .
4.4.2 , U. = 660 . : RA = 8 ; XLA = 6 ; RB = 6 ; XBC = 8 ;
RC = 23 ; XCL = 15,3 . R0 =1 .
:
1) :
) ;
) ;
2) :
) ;
) ;
3) , :
) ;
)
4) :
) , ;
) .
. . 14.
:
) ;
) ;
. 14.
.
.
1) .
|
|
U0
0 = ( Y A + Y + Y )/(Y + Y + Y + Y 0), (4.4.1)
, , , ;
Y , Y , Y Y 0 , , .
.
U. U.
U. = U./ (4.4.2)
,
U = U = U = 660/ = 380 .
, :
= 380 = (380 + j0) ;
= 380 = (-190 j328) ;
= 380 = (-190 + j328) ;
Z = 8 + j6 = 10 ;
Y = 1/ Z = 1/ 10 = 0,1 = (0,08 j0,06) ;
Z = 6 j8 = 10 ;
Y = 1/ Z = 1/10 = 0,1 = (0,06 + j0,08) ;
Z = 23 + j15,3 = 27,6 ;
Y = 1/ Z = 1/27,6 = 0,0362 = (0,03 j0,02) ;
Z 0 = 1 + j0 = 1 ;
Y 0 = 1/ Z 0 = 1/1 = 1 .
(4.4.1)
)
0 = ( 380 0,1 + 380 0,1 + 380 0,0362 ) /
/( 0,08 j0,06 + 0,06 + j0,08 + 0,03 j0,02 + 1) = (38 + 38 +
+ 13,7 ) / 1,17 = 32,48 + 32,48 + 11,75 = = 26 j19,5 +12,7 j30 + 0,752 + j11,75 = 39,45 j37,75 = 54 .
)
0= ( 380 0,1 + 380 0,1 + 380 0,0362 ) /
/( 0,08 j0,06 + 0,06 + j0,08 + 0,03 j0,02) = (38 + 38 +
+ 13,7 ) / 0,17 = 223,5 + 223,5 + 80,9 =
= 178 j134 + 87 j205 + 5,17 + j80,74 = 270 j258 = 372 .
2)
. 0
. = - 0 (4.4.3)
)
.= - 0 = 380 - 39,45 + j37,75 = 340,5 + j37,75 = 348 ;
. = - 0= -190 j328 - 39,45 + j37,75= -229,45 - j290,25=370 ;
.= - 0 = -190 + j328 - 39,45 + j37,75 = -229,45 + j365,75=433 .
)
. = - 0 = 380 - 270 + j258 = 110 + j258 = 280 ;
. = - 0 = -190 j328 - 270 + j258 = - 460 j70 = 464 ;
. = - 0 = -190 + j 328 - 270 + j258 = - 460 + j586 = 745 .
3) ,
, .. I. = I.;
I. = I.; I. = I.;
Y ,
= Y (4.4.4)
)
. = . = . Y = 348 0,1 = 34,8 =
= (30 j17,8) ;
. = . = . Y = 370 0,1 = 37 =
= (9,35 j35,7) ;
. = . = . Y = 433 0,0362 = 15,7 =
= (0,45 + j15,6)
0 = 0 Y 0 = 54 1 = 54 .
0 = . + . + . = 30 j17,8 + 9,35 j35,7 + 0,45 + j15,6 = 39,8 - j37,9 = 54 .
.
)
. = . = . Y = 280 0,1 = 28 =
= (24,2 + j13,95) ;
. = . = . Y =464 0,1 = 46,4 =
(- 21,9 j40,9) ;
. = . = . Y = 745 0,0362 = 27 =
= (- 2,3 + j26,95)
0 = 0 Y 0 = 0, ..
.
4)
S. . .
S = . . (4.4.5)
- , .
: . = 9,35 j35,7 = 37 : . = 9,35 + j35,7 = 37 .
.
(4.4.5)
S = . = 348 34,8 = 11696 = (9357 + j7017) ;
S = . = 370 37 = 13690 = (8214 j10952) ;
S = . = 433 15,7 = 6785 = (5647 + j3757) .
S = S + S + S = 9357 + j7017 + 8214 j10952 + 5647 + j3757 = (23218 j178).
, ..
= 9357 ;
= 8214 ;
= 5647 ;
= + + = 9357 + 8214 + 5647 = 23218 ;
Q = 7017 ;
Q = -10952 ;
Q = 3757 ;
Q = Q + Q + Q = 7017 -10952 + 3757 = -178 .
. = I . R., (4.4.6)
I. ;
R. .
= I . R. =(34,8) 8 = 9357 ;
= I . R. = (37) 6 = 8214 ;
= I . R. = (15,7) 23 = 5647 .
4)
os
os = a/, (4.4.7)
;
.
, , , .
os = /S = 9357/11696 = 0,8, os = R/Z = 8/10 = 0,8
os = /S = 8214/13690 = 0,6, os = R/Z = 6/10 = 0,6
os = /S = 5647/6785 = 0,8323, os = R/Z = 23/27,6 = 0,8333
( os ).
os . . = /S = 23218 / = 23218/23218,7 =1,0
8.
8 -
0, | 39,45 j37,75 | 54 | |||
, | . | 340,5 + j37,75 | 348 | ||
. | -229,45 - j290,25 | 370 | |||
. | -229,45+ j365,75 | 433 | |||
() , | . = . | 30 j17,8 | 34,8 | 34,8 | |
. = . | 9,35 j35,7 | 37 | |||
. =
: 2016-12-31; !; : 537 | : : , , |
: 0.259 .