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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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原创 |
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=========================导纳矩阵输出开始:=========================5 B1 `& W8 b3 z" P/ z# \
2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714 ) \1 k/ l4 }2 H; \
0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 $ } r: B' x9 Q6 _
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 # ?# J$ { a2 w! T4 a
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092
5 t9 T9 ?. P0 x, X, t% A9 v; J; K9 z$ D#########################导纳矩阵输出完毕!#########################! U- e1 N# U& u E
9 h0 _1 v; o" C- M9 t" o/ _% N=========================初始功率向量输出开始:=========================
; S2 J. M( E" {/ @, C! O0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000
$ L) N! R! o2 F6 k* Q# r#########################初始功率向量输出完毕!#########################- k/ A+ z3 ~9 {* D, P3 S
; Z* F @+ H7 x" H. z=========================初始电压向量输出开始:=========================7 B8 [; K7 W G' |4 s3 @+ G
1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000
S( M" p8 d; C9 \9 t4 c; E#########################初始电压向量输出完毕!#########################9 g- f4 l/ L5 Z) A1 _0 V1 W
( O) X0 D$ \* {& ~- g! k3 `
===================Iteration k = 0 Begin=========================# O4 m! \& Z7 L* e- g/ b. Q
P[0] = -0.14525
3 H4 b9 a" y+ J2 W, h) v* dQ[0] = 0.37497. w4 q+ ?: B9 g4 D( r0 n% B! O8 \
P[1] = 0.000007 r y6 @+ D3 E ]% L' M
Q[1] = -0.65434+ Q3 G3 `- _$ I V, ~0 y7 ^
P[2] = 0.087159 n1 W) w6 r m2 u
Q[2] = 1.10250
% f7 _( M5 y# \$ Z, P: ?3 [误差向量 p、q:
3 T& E$ W4 I# r. @- @% J0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000,
% s' ~9 T% j8 ?) c/ \" X) O' [电流 aii、bii:
2 W, @9 }, N4 E% e& P. v4 r8 Y9 qaii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000 ( u: {5 o# ?$ Y5 z
========================雅克比矩阵========================4 N0 P3 g- U2 l9 D
-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000 : e( ~3 ] q, F3 |
-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000 & z$ E! V1 ]( V u0 f C
0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000 8 h& Y3 ]0 r& e) I
5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000 + V# Z9 p! o) D, H! o
1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000
( |: j7 L; h. @( F2 y1 V0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000
: |! s3 c1 L ~% x! `3 t* m5 Z, C6 {7 Z! N* `* P
所求矩阵的逆矩阵为：/ @: }( `3 R$ n& B1 {- ]. D
-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 0 ?9 I4 C m4 K
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 9 A0 A; W: a7 a* [! J/ ?$ ^8 ]
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
% {8 t" E+ G# ^, h2 X* Y-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524
2 g% G W. Z" ]3 L0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619 3 O/ O5 Y" n; F3 l4 ]
-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965
% T6 z) n7 P8 ?0 J9 Q: y方程的解:4 J; [& N& O6 t8 A
0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460 & q& l: `# X- o/ }) ?- d
新的电压值(e+jf):
; ?( f, w8 k# E5 i3 M+ b0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946,
9 E6 D/ G G: ?" J( Q% e( G1 E===================Iteration k = 0 End =========================1 R6 Q) {. M1 y7 u' m3 q2 x4 Z0 W* Z
===================Iteration k = 1 Begin=========================6 |1 O. K( W7 e% O
P[0] = -0.02835* A! D0 z0 Z5 x( v$ X* j6 E! }
Q[0] = -0.002685 `8 n- P' |8 R1 d# r8 _
P[1] = -0.46151
5 v+ U% u5 S; i: l8 W6 xQ[1] = -0.20794
" }' S% f0 U/ m; B6 }, U# eP[2] = 0.20354& V7 K& ~( l5 k8 [
Q[2] = 1.10337
/ f! I8 x4 w" }误差向量 p、q:& B& k r6 j, C1 e5 Z0 f
0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787, 4 F: r6 n N. N! u' ]- l {# _
电流 aii、bii:- o8 Y7 S8 s' v' ~1 [
aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000
# b0 V- o1 Y9 r% c9 ^- u========================雅克比矩阵========================6 R% j% u6 _& L
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 8 }2 q* Y7 y" p6 Y/ [" b# q
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
2 Z5 N r) m ?$ B0 H$ m0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000 : K' x) c0 C1 S, e/ y( w
5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
% O- e8 A4 i1 X# v4 F& \- X# z+ G7 C- H1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000 X0 N. p4 O# T; [8 V+ s( c
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000 3 y# z8 W$ Z4 O9 i7 ]
- v/ t( s$ ?" Z1 q
所求矩阵的逆矩阵为：
6 C! z3 d/ H) O* G" w-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385 1 p- f( H; Z R4 a4 Q
-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189 & r" C$ k& \. d0 r4 c% i
-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835 0 V" Y1 Z/ `1 f( Y! l( c" K
-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893 8 q3 k$ Y# @7 E
-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893
$ A3 ~: J2 ^+ C! @; f-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892 9 v+ ]+ J6 B( V1 L
方程的解:% c. a; S. C$ L3 h9 O, k2 T# n
0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815
/ @8 [1 \8 a( C5 I新的电压值(e+jf):
3 b' N7 y, s/ z" F# S) G0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328,
# u/ E; h! ^& b, d2 @, T===================Iteration k = 1 End =========================/ |4 V- w( |% a' }# o
===================Iteration k = 2 Begin========================= E K# f/ z( C
P[0] = -0.00050' \0 R. R; }) K; y2 ^/ u0 d% K
Q[0] = 0.00005* P7 O5 k6 C0 a2 H8 z
P[1] = -0.49877% f2 V+ H0 C% v- t0 S3 C
Q[1] = -0.29567
$ w$ z0 A5 x; e/ u4 I- V$ ZP[2] = 0.20071
) Y/ x( f1 G0 k% pQ[2] = 1.10251+ t6 s3 A C/ `$ ~& K. H
误差向量 p、q: t; j1 K1 z3 w, J; q
0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483,
. X# Q) n; L2 M7 ]. p电流 aii、bii:: C7 T9 R. I5 v7 p4 Q ~9 e
aii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000
/ o4 h$ a1 w. o; k" ]( x========================雅克比矩阵========================
7 a8 l7 l) ^# N% U" b& q-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000
: z) x. }( Z u' K& p-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000 % ?: \6 X; |1 y+ W* z
0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
( Q$ a f. |1 [3 w6 v. M* o. C4 z5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000
! {% k7 E# v1 D8 D h/ x1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000 / S* Y+ b, t) r$ f" R3 v
0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000
6 s, N! z# W' S1 r
+ x5 T5 E% z- f所求矩阵的逆矩阵为：6 n7 d* w. \# K6 C
-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342
# g- O. A9 K9 C( S2 ^8 c. j-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058 & R8 P8 F4 m, ^8 V+ r. T
-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965 ( ?8 y8 }* o9 p: J$ ?
-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
( w0 w2 B% G. F. P$ f-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835 " s+ }; A/ [# B/ o
-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478
/ {' t' z/ s! q* V1 h/ l. Z方程的解:% l0 X) `3 y* v) f4 G6 M$ T& u* O$ \
0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432 ' a |, M! } E' f! D
新的电压值(e+jf):
4 f: Q4 h- K, }0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
' d( J; Q! B8 o- I' ?' K% `===================Iteration k = 2 End =========================. l) e3 a& D3 B- c
===================Iteration k = 3 Begin=========================
T4 o: J# a$ X/ R1 yP[0] = -0.00000 \2 G& m6 c) E7 L5 u; A3 i1 ^
Q[0] = 0.00000# }8 k A7 j5 I$ t; W. i v
P[1] = -0.50000: r1 N% U6 \2 i$ b9 X0 b. n! a
Q[1] = -0.299991 }; P% m# O) I9 `. A' p9 m+ t9 w
P[2] = 0.20008
; A4 M; v4 V4 d3 b; u* rQ[2] = 1.10250* k5 O( L7 a$ A$ e) s4 Z# T% M
误差向量 p、q:! Z: `# M- j2 M/ N [ x
0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019,
+ b( J9 c" s$ t' t- J电流 aii、bii:
! }* b1 t. o- ^* J5 w& |aii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 ) z2 Q5 A/ f- ]9 p- G b* X
========================雅克比矩阵========================( g0 E% }8 A4 B+ O, w
-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000
3 n5 c+ Z8 X, F7 x$ I( {-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
& ~) [9 l4 z# r, v8 ^1 m/ v& J0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
0 B4 Q/ n* l3 I5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000
: }$ i" b8 I+ }2 B, a1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000
$ v6 Z. ^7 w" \$ r0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000
) e+ n+ @' J, h$ N3 O& S( b n/ c( }' y) b( `2 K" g# ?
所求矩阵的逆矩阵为：
7 C8 z0 Z0 U2 h- I: ?- {-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 9 v" U' b7 q. C% K( z6 j2 I6 [
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 / v! D7 e" @& E
-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084 & k! M! C: e: y, L: G/ D
-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109
1 M# x' \4 m( E( o$ Q) Z-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826
p. _1 r+ q- v8 o-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453 ! I) `, G4 M/ B& x0 t9 Z
方程的解:
# J$ g( Y$ `' e/ F9 `0.000004 0.000013 0.000008 0.000014 0.000001 0.000027
0 S$ i* Q0 h1 O" x新的电压值(e+jf):
! O1 u' Z. i/ d' X5 e6 b; N6 h: w' p0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373, . m, K: ~! y% [( v5 O- G
===================Iteration k = 3 End =========================
) t$ [6 U. \& i; x- [" q; g===================Iteration k = 4 Begin=========================, H# l L) R! D8 X6 _
P[0] = -0.000006 O; Q0 p) d5 x2 {. D0 b# I3 ?2 e
Q[0] = -0.00000
* @4 f" R7 W; ~8 |/ B4 }- \& I/ _P[1] = -0.50000
* w/ P: K4 e W7 r( X v2 h, W& Q7 C$ qQ[1] = -0.30000+ e) u: U9 Z7 v% h% p4 |* A& F. l
P[2] = 0.20001# a5 N) Z! C3 s; w5 B# z# d
Q[2] = 1.10250
( ?$ K! z9 d* u9 s1 w% j7 o误差向量 p、q:2 p* K6 B4 H. F3 j
0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000,
5 }1 K4 o d3 r9 A( K, P2 b. C* L电流 aii、bii:0 l2 |( O& h9 ^7 k5 P8 E+ I
aii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000 0 \' ~$ L! V. h' ?) P/ T' r! D
========================雅克比矩阵========================5 s0 D3 f+ z/ U! j9 w3 ?
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000 - A1 d8 _0 Z* S1 G1 P) G1 Y
-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 % \ f$ |- l+ g/ {' j& o& U* J
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 7 B/ N/ ?4 z( @
5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000
' k3 w1 v2 [( V* D1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000 + d* e" Q6 h U* B# x: P
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 8 Z0 Q4 A: ^$ ?) q% g; z6 D
5 P- [0 r' T( C5 E. [ p1 k( @
所求矩阵的逆矩阵为：
" M) p$ B7 e/ M-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 8 @# M6 f! a# {' }- p) G U) |; v
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
3 u1 p" w L# ?0 \6 t-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084
, d4 ^8 p) ?) c8 d-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108
% a# f0 t6 O1 B4 C5 t, i8 r: N-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825 9 ]8 p8 d7 e& Q
-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452
; m) U0 _* ]9 p方程的解:
1 H5 h. X/ f& g' r$ ]: f0.000000 0.000001 0.000000 0.000001 0.000000 0.000002
+ i! b" b$ D ~' t" S新的电压值(e+jf):
7 t" h2 {1 o" b" Y7 @0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374,
3 m' b4 O4 I7 U* i' ?===================Iteration k = 4 End =========================
& N0 r) r, ]9 Y2 m7 Q% ? u' {===================Iteration k = 5 Begin=========================
N6 @3 \/ [+ f- qP[0] = 0.000005 k" s) ^8 ]! S0 x
Q[0] = -0.00000
7 l3 ?2 N5 \ ]6 @P[1] = -0.50000
. U8 e9 U# f; C" y, wQ[1] = -0.300002 q$ L' o7 t* S
P[2] = 0.20000* R2 R% t9 M7 v
Q[2] = 1.102505 L( }3 h# Z+ d6 {
误差向量 p、q:# X7 x1 m. ?0 v9 b& Q
-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000, : R F2 c% P4 D, ~9 m
=================k=5时，结果收敛=======================; h- v; P8 p2 M$ E! D" b9 U
================牛顿法计算共耗时:0秒:609毫秒========= |
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