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夏道止老师《电力系统分析》N-R迭代过程 |
| 内容简介: |
夏道止老师《电力系统分析》N-R迭代过程 |
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电力 |
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txt |
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=========================导纳矩阵输出开始:=========================
# x- m4 q# I2 d9 F J2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714 5 O; H% h) u# s4 R
0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000
9 T2 i: {9 C7 T-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 # L( |+ J! u# `# O
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092 , H" }5 L M; S9 K4 E/ C6 b$ F: t
#########################导纳矩阵输出完毕!#########################, t4 S; {- O- @5 g& l, f9 D
8 m& ]/ J$ o$ c1 `
=========================初始功率向量输出开始:=========================, Y& _& Z, {5 r
0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000 ( X- ~! e+ D- c
#########################初始功率向量输出完毕!#########################
p5 O/ q' h% i2 d: @6 Z* V5 t5 ?$ B& r- N# c( q% r7 l
=========================初始电压向量输出开始:=========================
1 w3 i0 O3 s) T0 D% S% Y1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000
0 Y9 c% p- C$ }5 B0 b) s' s#########################初始电压向量输出完毕!#########################; E6 [5 A- Y9 V5 V7 m, q' W0 I
9 F/ \) h1 F$ k& P: Q
===================Iteration k = 0 Begin=========================! g% o! \7 D8 p& R5 y2 i9 G
P[0] = -0.14525# b3 g5 w6 o$ M M& C# E
Q[0] = 0.37497! X; W& W% M2 e! l: n- Y" u( w# g% C
P[1] = 0.00000
. \" h. e" `( Y) I0 Y; c- ?+ m+ GQ[1] = -0.65434# ?1 o7 Y7 G# a1 t$ V8 g( r6 a
P[2] = 0.08715
7 x0 Q; G: Z7 J0 b8 XQ[2] = 1.10250
4 u) Y5 u5 u* a/ e; ?7 P' ^误差向量 p、q:, B- e; Q( W% T( S1 k& f o3 v+ N' y
0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000,
" ~1 y" H) d3 f% H5 T0 ?- @& \电流 aii、bii:: ?1 R0 G' p" L; G
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
0 V* S% L: ]+ ~0 `! t( e! {========================雅克比矩阵========================
5 S+ V* v' e" a9 Q& y: m4 _-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000 ! v* W2 k* W) f) y0 E' q
-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000 : {9 G+ u1 Y( N/ G
0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
1 F9 \0 J8 m0 _/ j5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000
& u* j8 b7 ?, [( ?1 Y% f# x' l2 F1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 H& E. V/ @( j7 b" W7 L& G
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000 7 [# t& T" U. r% p
T J2 @ s" O {/ Q; d3 M
所求矩阵的逆矩阵为： u. e/ ^8 x! y! e3 z& j% J' k
-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 9 |3 Q/ b( P, a$ e9 i5 G
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 1 ` \7 p/ I' T6 G# T. i
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
y- J/ x0 z9 ?/ B5 P-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524 , U. r9 A/ ?3 y* k6 q
0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619 5 f, A( O0 E' g/ k7 [" C3 J4 E
-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965 " z, I3 p2 U; l) a" S* |
方程的解:+ [) `. G- L! F. s- n& d+ {
0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460
. O( R2 ?% R1 R1 \$ O$ x; U新的电压值(e+jf):
1 D, v; ]+ ~( e, Z: I0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946, ( _- f9 V# t6 w. O
===================Iteration k = 0 End =========================
! s6 Y& ?* v* v( \: O- L! N+ L7 J# }===================Iteration k = 1 Begin=========================
2 n/ g. m; o D$ |9 N' H% oP[0] = -0.02835
4 l. f/ d# N' R5 o9 _ u+ MQ[0] = -0.00268
^/ H. U$ F" ?9 Q; F" |% \* IP[1] = -0.46151
2 _& S' y% A" U+ B9 gQ[1] = -0.20794& ?: a- ` X, N+ f- F
P[2] = 0.20354
# z3 p2 Q8 y0 p( NQ[2] = 1.10337
8 t7 g) L+ ? y! L' `误差向量 p、q:
, V7 @- |5 n& i& h4 A0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787,
1 V0 K, c: N; g6 x9 {电流 aii、bii:- w7 o9 I; a# M1 j) d2 M, P
aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000
! Q0 |; h. m! S$ [ B" i========================雅克比矩阵========================) j/ ~; f% T! J7 G8 m6 Q
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 ( _/ H' }1 g0 j% U7 t8 T) b1 u
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
9 U7 w- _4 H! C; f0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
9 b1 q3 @. F8 F" v9 j5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000 ' r$ h$ @# E! _, X E0 {$ J6 H
1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000
! u, o6 ~$ S2 U; u/ d+ G# C9 p$ P0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000
{% A" A- _& c* [6 |
0 K. ^; Q9 J$ u3 [4 }所求矩阵的逆矩阵为：4 K) ^+ Q$ j* {1 R+ W/ k
-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385
" B7 Z6 P& S- [ T+ b7 D6 N-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189 ( h5 @: ]# K* ?
-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835 0 O+ g4 ]+ o1 C5 h8 f" P
-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893 " e5 }2 R. N( r" ^, P
-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893
+ r n3 t& c7 y-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892 * Z l& u8 ?- @! v5 {3 i
方程的解:- {$ ~0 z7 ?% K" E
0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815 1 ]* O# V7 Y" Z9 n) s
新的电压值(e+jf):
* i4 L! b3 u2 Y/ J0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328,
) {' I# Y3 C- v% d===================Iteration k = 1 End =========================
" F& S0 }, g" K" {===================Iteration k = 2 Begin=========================
5 I+ ^9 o/ F" }! IP[0] = -0.00050
5 l7 r$ z$ H5 v# |1 y4 I* \. KQ[0] = 0.00005, q- \- y w K; o/ z" b# a! |
P[1] = -0.49877
$ R4 h, x0 h; aQ[1] = -0.29567+ V3 F4 x) ? ~5 G0 |
P[2] = 0.20071
. F3 s- y0 }% D2 k7 c& KQ[2] = 1.10251/ v Z: g! w; n$ q4 ^2 `
误差向量 p、q:% }' o7 p9 F f0 c
0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483,
) k+ N' u5 I( ?9 _7 b电流 aii、bii:
- r- w% o: k4 P$ c9 V% j+ F2 q/ Yaii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000 0 Q1 Q! R3 C3 u5 `) X
========================雅克比矩阵========================& R9 j9 ~- @* w( {% a! [
-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000 . F' g) @+ S) |( `3 ~1 d- m1 D3 A
-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000
! w* W( Q; }' a" g6 L, z0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000 / [% G, @. r* `* M" Z& ^! P
5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000 " F" M1 {. T$ t% o4 F' d5 n
1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000 . c2 j; }9 S& r3 ?8 c; a+ ?
0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 * ~& o% w/ p: w
8 X/ k1 H* f9 i% A# g8 z2 y$ i: B
所求矩阵的逆矩阵为：
) Y; |6 T4 D+ n- g2 [-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342
- q1 [" j. l1 ]) T) P-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058
3 |0 r6 x/ x5 N5 @& Y-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
. B* A5 R4 A) p, d7 l, e% r, ^-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
/ Q3 ~+ F- z* p g4 D-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835 # k% z8 v8 d/ e2 @4 R; C2 D
-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478 ; w! c, F! L; y: M$ C) w- \5 [
方程的解: l+ B1 D2 U$ u' E5 w8 [$ r
0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432
7 g i) T; `0 ]6 T" G2 c( V新的电压值(e+jf):
1 ?; i9 X- p$ d1 h' I2 P0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
R& t3 X" d+ i===================Iteration k = 2 End =========================
! M2 s, a' m1 L7 @+ a; x===================Iteration k = 3 Begin=========================
5 X) k, w$ M5 LP[0] = -0.00000
- ?: G0 z' P4 \3 z9 `0 }# vQ[0] = 0.00000: @2 k: c* i: J2 v1 ?( x
P[1] = -0.50000
# }1 v5 M9 {" A6 e6 b- NQ[1] = -0.29999
# D* \( X5 s8 \2 \2 ?P[2] = 0.20008
/ V7 C. M3 i& p* cQ[2] = 1.10250) q% [* w2 T/ v/ b8 D* {
误差向量 p、q:
7 ?. ~; m2 @" z4 g0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019,
. {/ x: }( w x! u电流 aii、bii:
1 d1 h: ?/ \. p8 f6 Z0 Taii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 . D i; h6 R/ b- T% E' r1 _- R8 K
========================雅克比矩阵========================# Q# w2 w8 y3 k) D. t2 d1 t1 S* h
-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000 * c) z& F% k8 { O
-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
0 b9 x5 w( `$ k; B6 l- J9 Z+ p0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 4 ]$ F5 p. C8 n, e2 v2 X& ]9 Z
5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000
7 N$ @0 Z E+ w2 g$ o, o4 s1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000
# ?: M1 l, L* d# x( _* E0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000 + K; ]6 q, O: u- U1 |& a
* P4 y0 P7 ^' M% X0 t5 N所求矩阵的逆矩阵为：
2 i. C( ^+ P, I* a; m5 h2 j3 E( M-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 4 G& W2 ?9 R7 Y% Z
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 . v8 S0 w$ W, p; A6 C
-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
- x0 S+ k( A* e* w8 b-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109
! T. T1 a! g. `- S-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826
, ~8 \7 }6 @+ G6 t% k, q) B-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453
3 p: Z, x$ A- W! c$ b5 W; @) ?4 Q方程的解:
7 }3 j! y1 y R* j, }7 Z- w P- m! o0.000004 0.000013 0.000008 0.000014 0.000001 0.000027 5 h! b% @+ Y# _# _3 d0 T& ~
新的电压值(e+jf):
! B$ |% }7 y4 c& {+ [0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373,
6 ~: l' v h# I: B===================Iteration k = 3 End =========================& e8 x5 }/ g F
===================Iteration k = 4 Begin=========================
% J% L8 s' O: hP[0] = -0.00000( p& N: {8 n4 L" e9 `
Q[0] = -0.00000* G! [3 X; [& F: H6 Y* p, N o* Y
P[1] = -0.500006 P, ?0 q; _/ ~5 X
Q[1] = -0.30000
' L" G/ k/ v& j T+ o9 OP[2] = 0.20001
4 n( E9 M: b1 @- C! `( h) y$ kQ[2] = 1.10250
% M) V" l3 t+ v误差向量 p、q:
7 w8 e$ V* m& u# {# i0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000, 7 T$ Y, S x# g4 m" k
电流 aii、bii:9 {2 B' u' ~# n: T% d3 ? n# ^" s/ Z
aii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000
/ g+ V3 M# ~/ ?3 L========================雅克比矩阵========================
! M5 P& _( ]/ j1 c-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000 I& b( b9 u2 T" Y
-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 , f/ h$ {$ |% y( j
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
1 g6 l) [( |1 `3 }, C5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 3 \5 [8 O& \ D& G# i6 T* \
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
% u) D5 V- _7 S2 S+ D5 N8 @0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000
: Z3 [5 {2 w! E H. H% Z. F" c ^) T- f! U- T% l
所求矩阵的逆矩阵为：' c8 {' e8 Y# C0 X3 `& X
-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 7 K1 J9 g& `% n
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
4 g% Q0 U2 }7 a" r3 a3 p-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 - Y* V6 u; j- i3 D7 Z9 y- w
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108 2 d( h' u5 v: t
-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825 . R1 j$ q( A4 ?% a/ c
-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452 ) u* o7 ]- _* d
方程的解:9 {/ C8 F/ r/ Q, K* U
0.000000 0.000001 0.000000 0.000001 0.000000 0.000002
# w+ R9 a1 P6 p4 \& x! ?# R3 h$ ~( @新的电压值(e+jf):+ x } Y4 B$ I! p
0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374, 5 V* }. }' @" b1 n3 t! P8 ^
===================Iteration k = 4 End =========================2 R- H) d$ x, C7 \2 N
===================Iteration k = 5 Begin=========================" q- U7 A! m l0 U0 F6 v
P[0] = 0.00000
2 K4 Z) b, o2 C' E5 x; |3 I, MQ[0] = -0.00000
7 H5 V) I* t7 C- v% e+ kP[1] = -0.500003 E1 T: v3 D `6 K1 X
Q[1] = -0.30000
# E& I1 r" _, s3 b9 YP[2] = 0.20000
# b/ t2 p: T2 x; @Q[2] = 1.102501 J, ~: a! H( ?6 B
误差向量 p、q:
5 N# ~! q5 H5 K; c-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
+ w/ @2 C8 n( ~. U* f5 W=================k=5时，结果收敛=======================
7 d6 m$ y0 P# D8 {0 x================牛顿法计算共耗时:0秒:609毫秒========= |
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