М=
5) Найдём обратную матрицу:
|
|
1 |
2 |
3 |
4 |
5 |
6 |
7 |
|
8-7 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |
|
8-6 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
|
5-1 |
1 |
1 |
1 |
0 |
0 |
0 |
0 |
|
1-2 |
0 |
1 |
1 |
0 |
0 |
0 |
0 |
|
2-3 |
0 |
0 |
1 |
0 |
0 |
0 |
0 |
|
5-4 |
0 |
0 |
0 |
1 |
0 |
0 |
0 |
Мg =
6) Построим вторую матрицу инциденции:
|
|
8-7 |
8-6 |
5-1 |
1-2 |
2-3 |
5-4 |
7-5 |
6-5 |
5-3 |
3-4 |
|
6-5 |
0 |
1 |
0 |
0 |
0 |
0 |
0 |
1 |
0 |
0 |
|
5-3 |
0 |
0 |
-1 |
-1 |
-1 |
0 |
0 |
0 |
1 |
0 |
|
3-4 |
0 |
0 |
1 |
1 |
1 |
-1 |
0 |
0 |
0 |
1 |
N=
7) Матрица N*Lв:
|
0 |
1.5 |
0 |
0 |
0 |
0 |
0 |
3 |
0 |
0 |
|
0 |
0 |
-2 |
-2 |
-3 |
0 |
0 |
0 |
1 |
0 |
|
0 |
0 |
2 |
2 |
3 |
-1.9 |
0 |
0 |
0 |
1.8 |
Аварийный режим
a=[0 -1 1 0 0 0 0 0 0;0 0 -1 1 0 0 0 0 0;0 0 0 -1 1 0 0 0 -1;0 0 0 0 -1 0 0 1 0;-1 1 0 0 0 1 0 -1 0;0 0 0 0 0 -1 1 0 0;0 0 0 0 0 0 -1 0 1;0 3 2.7 5 3.5 0 0 4 0;0 -3 -2.7 -5 0 2.5 2 0 1]
a =
0 -1.0000 1.0000 0 0 0 0 0 0
0 0 -1.0000 1.0000 0 0 0 0 0
0 0 0 -1.0000 1.0000 0 0 0 -1.0000
0 0 0 0 -1.0000 0 0 1.0000 0
-1.0000 1.0000 0 0 0 1.0000 0 -1.0000 0
0 0 0 0 0 -1.0000 1.0000 0 0
0 0 0 0 0 0 -1.0000 0 1.0000
0 3.0000 2.7000 5.0000 3.5000 0 0 4.0000 0
0 -3.0000 -2.7000 -5.0000 0 2.5000 2.0000 0 1.0000
b= [-0.7;-0.7;-0.8;-0.9;-0.7;-1;-0.7;0;0]
b =
-0.7000
-0.7000
-0.8000
-0.9000
-0.7000
-1.0000
-0.7000
0
0
c= [-0.7;-0.5;-0.6;-0.7;-0.3;-0.3;-0.7;0;0]
c =
-0.7000
-0.5000
-0.6000
-0.7000
-0.3000
-0.3000
-0.7000
0
0
a1=inv(a)
a1 =
-1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 -1.0000 0.0000 0.0000
-0.7838 -0.5891 -0.2287 -0.1220 0 -0.1040 -0.1871 0.0305 -0.0416
0.2162 -0.5891 -0.2287 -0.1220 0 -0.1040 -0.1871 0.0305 -0.0416
0.2162 0.4109 -0.2287 -0.1220 0 -0.1040 -0.1871 0.0305 -0.0416
0.0915 0.1738 0.3263 -0.3593 0 0.1483 0.2670 0.0898 0.0593
-0.1248 -0.2370 -0.4450 -0.2373 0 -0.7477 -0.5459 0.0593 0.1009
-0.1248 -0.2370 -0.4450 -0.2373 0 0.2523 -0.5459 0.0593 0.1009
0.0915 0.1738 0.3263 0.6407 0 0.1483 0.2670 0.0898 0.0593
-0.1248 -0.2370 -0.4450 -0.2373 0 0.2523 0.4541 0.0593 0.1009
b1=a1*b
b1 =
5.5000
1.4887
0.7887
0.0887
-0.4586
1.9526
0.9526
-1.3586
0.2526
c1=a1*c
c1 =
3.8000
1.2280
0.5280
0.0280
-0.3266
1.2454
0.9454
-1.0266
0.2454
b1=diag(b1)
b1 =
5.5000 0 0 0 0 0 0 0 0
0 1.4887 0 0 0 0 0 0 0
0 0 0.7887 0 0 0 0 0 0
0 0 0 0.0887 0 0 0 0 0
0 0 0 0 -0.4586 0 0 0 0
0 0 0 0 0 1.9526 0 0 0
0 0 0 0 0 0 0.9526 0 0
0 0 0 0 0 0 0 -1.3586 0
0 0 0 0 0 0 0 0 0.2526
c1=diag(c1)
c1 =
3.8000 0 0 0 0 0 0 0 0
0 1.2280 0 0 0 0 0 0 0
0 0 0.5280 0 0 0 0 0 0
0 0 0 0.0280 0 0 0 0 0
0 0 0 0 -0.3266 0 0 0 0
0 0 0 0 0 1.2454 0 0 0
0 0 0 0 0 0 0.9454 0 0
0 0 0 0 0 0 0 -1.0266 0
0 0 0 0 0 0 0 0 0.2454
s=sqrt(b1*b1+c1*c1)
s =
6.6851 0 0 0 0 0 0 0 0
0 1.9299 0 0 0 0 0 0 0
0 0 0.9492 0 0 0 0 0 0
0 0 0 0.0931 0 0 0 0 0
0 0 0 0 0.5630 0 0 0 0
0 0 0 0 0 2.3160 0 0 0
0 0 0 0 0 0 1.3421 0 0
0 0 0 0 0 0 0 1.7029 0
0 0 0 0 0 0 0 0 0.3522
t=s*1000/(sqrt(3)*35)
t =
110.2749 0 0 0 0 0 0 0 0
0 31.8344 0 0 0 0 0 0 0
0 0 15.6571 0 0 0 0 0 0
0 0 0 1.5350 0 0 0 0 0
0 0 0 0 9.2875 0 0 0 0
0 0 0 0 0 38.2039 0 0 0
0 0 0 0 0 0 22.1393 0 0
0 0 0 0 0 0 0 28.0900 0
0 0 0 0 0 0 0 0 5.8098
i max= 110.2749А.
Iэкв= 48,57 А, следовательно, сечение проводов принять АС-50 r0=0.65 Ом/км и х0=0,392Ом/км
Расчёт баланса мощности в сложнозамкнутой сети
Р1=Р5-1-Р1-2=1,489-0,789=0,7
Q1=Q5-1-Q1-2=1,228-0,528=0,7
S1=0,7+j0,7
Р2=Р1-2-Р2-3=0,789-0,089=0,7
Q2=Q1-2-Q2-3=0,528-0,028=0,5
S2=0,7+j0,5
Р3=Р2-3+Р7-3 –Р3-4==0,089+0,253+0,459=0,801
Q3=Q2-3+Q7-3-Q3-4=0,028+0,245+0,327=0,6
S3=0,801+j0,6
Р4=Р3-4-Р5-4= -0,459+1,359 = 0,9
Q4=Q3-4-Q5-4= -0,327+1,027= 0,7
S4= 0,9+j0,7
Р5=Р8-5-Р5-1 – Р5-6 +Р5-4=5,5-1,489-1,953-1,359=0,699
Q5=Q8-5-Q5-1-Q5-6 +Q5-4=3,8-1,228-1,245-1,027=0,3
S5=0,699+j0,3
Р6=Р5-6-Р6-7=1,953-0,953=1
Q6=Q5-6-Q6-7=1,245-0,945=0,3
S6=1+j0,3
Р7=Р6-7-Р7-3=0,953-0,253=0,7
Q7=Q6-7-Q7-3=0,945-0,245=0,7
S7=0,7+j0,7
