(例)建立图示网络的状态方程。 l2 ∧t① u 2 LI s2 R 2 解 10 12 38 选择一个正常树(支路1,2,3,4,5,6)
例1 解 建立图示网络的状态方程。 C1 + − us R1 R2 R3 L1 L2 C3 C2 R4 s1 i s2 i 4 2 1 5 6 3 7 8 9 10 11 12 选择一个正常树（支路1,2,3,4,5,6）
2 9 38 5 R;氵L,氵i ,R, C 1:00:00:0:00:1:00:1 10:00:0:00:-1:10-1 00:0001 01:00:0-11:0:010 …………………………………………………………… 00:01:0 0:000氵0 ………………… 02 0:00 0:-1:00:0 3456789101112
4 2 1 5 6 3 7 8 9 10 11 12 ⎥⎥⎥⎥⎥⎥⎥⎥⎦⎤ ⎢⎢⎢⎢⎢⎢⎢⎢⎣⎡ = 0 0 0 0 0 1 1 0 -1 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 -1 1 0 0 1 0 0 1 0 0 0 0 0 0 -1 1 0 -1 1 0 0 0 0 0 0 0 1 0 0 1 f s t t t s Ll Rl Cl u C R L i Q 1 2 3 4 5 6 7 8 9 10 11 12
Qn=0]Q12=[]Q:=[00]Q1= 21 22 Q23 24 00 31 32 Q3=0Qa=] 01Q2=1Q=0]Q4=0 R2 R10 R 0 R 3 0 R 4 0 R C=C 3 0
[ 0 0 ] Q11 = [ 1 ] Q12 = [ 0 0 ] Q13 = [ 1 ] Q14 = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = - 1 1 0 0 Q21 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 0 - 1 Q22 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 0 1 1 0 Q23 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 0 - 1 Q24 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 1 0 0 0 Q31 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 0 1 Q32 [ 0 ] Q33 = [ 0 ] Q34 = [1 0 ] Q41 = [ - 1 ] Q42 = [ 0 ] Q43 = [ 0 ] Q44 = ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 3 2 0 0 R R R t ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 3 1 0 0 C C C t [ ] C l = C 2 ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 2 1 0 0 L L L e ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ = 4 1 0 0 R R R l ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 3 2 1 0 0 1 R R Rt ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 4 1 1 0 0 1 R R Rt
C1+C,0 CM=C+Q24C, 224 LM=Lu+Q4, L, Q42 -Q4 Lu-L,Q4=L+L,I G10 A1=-Q2RQ23=R1 0-G A12=Q23RQ3R232-22=-Q2 A2=Q2-Q32GQ3Q23=10 A2=Q32 G Q32=[10] R20 R 0R20
⎥⎦⎤ ⎢⎣⎡ + = + = 3 1 2 24 24 0 0C T C C C M Ct Q ClQ [ ] 42 42 42 42 1 2 - t l - l t L L T t t T L M = Ll l + Q L Q Q L L Q = + [ ] [ ] [] 2 3 2 32 1 22 32 33 23 1 21 22 32 33 32 22 22 1 12 23 2 -1 1 23 1 11 23 - 0 1 0 0 - 1 0 -1 0 0 1 0 0 -R R R R -G G T T l T T t T T =⎥⎦⎤ ⎢⎣⎡⎥⎦⎤ ⎢⎣⎡ = − = = − = ⎥⎦⎤ ⎢⎣⎡ = − = − = ⎥⎦⎤ ⎢⎣⎡− = − = = − − − − A Q G Q A Q Q G Q G Q A Q R Q R Q Q Q A Q R Q
0 Q23R Q13 Bm=er3r'Q33R, Q31-q2l B1=Q12-QG3GQ13= B2=-Q3GQ1=1 R20T00 0R2‖10 BM=-Q2cr es/C 0 2=L,QA-Q L, Q4=L O
[ ] [ ] [] 0 0 1 0 0 0 0 0 -1 0 1 1 -1 0 0 0 0 3 2 31 1 22 32 33 13 1 21 12 32 33 31 21 1 12 23 13 1 11 23 =⎥⎦⎤ ⎢⎣⎡⎥⎦⎤ ⎢⎣⎡ = − = = − = ⎥⎦⎤ ⎢⎣⎡ = − = ⎥⎦⎤ ⎢⎣⎡ = − = − − − − R T R T l T T t T T B Q G Q B Q Q G Q G Q B Q R Q R Q Q B Q R Q 0 2 11 24 14 ⎥⎦⎤ ⎢⎣⎡ = − = T C l ' B Q C Q 22 41 42 t t 41 [ ] L1 0 T l l ' B = L Q − Q L Q =