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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:=========================
. L0 A2 ?# R6 O2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714
3 T) P3 ?' a" X2 q+ h0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 6 M2 h- ]6 I5 S7 Q5 S
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 0 M0 }/ w2 Z& B
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092 9 ^4 m& U0 i9 K4 H
#########################导纳矩阵输出完毕!#########################$ |+ h! n+ f9 J
9 Q: {0 l# I m- W! X- j- H; ~& h; p=========================初始功率向量输出开始:=========================( S2 k7 n$ z( G5 Q% b2 I
0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000 & b% ^! q5 B% {- G& ^/ @
#########################初始功率向量输出完毕!#########################4 f/ A5 s) k' H0 z3 w) l6 N! M
7 `! a5 [# f( P=========================初始电压向量输出开始:=========================
: f& V* K. g. {2 N% v1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000 $ ]% Q4 g( S# I c
#########################初始电压向量输出完毕!#########################9 f o2 a% S+ C0 w$ U1 m
( u- q9 ~% @/ B* i$ i8 r, A===================Iteration k = 0 Begin=========================5 I9 V% T }" Q# x9 O; c2 q
P[0] = -0.14525* P! ~3 P+ V8 _/ c
Q[0] = 0.37497
8 d6 c* b; f- s# f4 |( Y* W: t' |P[1] = 0.000007 p# x! j, P: B( P2 I# R+ n
Q[1] = -0.654344 c9 j- n: S/ A2 P: a( z3 `6 T0 A% b
P[2] = 0.08715
3 H3 c3 f6 Y7 Q5 l: gQ[2] = 1.10250$ u% M- v3 s/ H" }3 j/ b2 i
误差向量 p、q:
8 m6 n- r5 H7 \7 V b0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000, ; V4 z: B" |- o7 {7 ?: G" e# f3 z
电流 aii、bii:5 ?& J0 H8 C# F, k% w% a
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
& ^" D+ I7 f' E' u========================雅克比矩阵========================
$ [1 H6 l4 i4 K" E-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000
3 d2 G+ R2 v4 | ?-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000 . ?+ n0 p7 `; \3 f; ^6 C
0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000 & {' w; b5 `# p# V; j
5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000 - |' P% X; [ k5 O' b
1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 " o* i) i L v9 ?2 t a
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000
' r$ o5 k5 }. O" y! ]; u0 K4 T! E: `- T C" }
所求矩阵的逆矩阵为：
1 S0 R7 _+ j! R( ?-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 # ?$ X9 `1 k+ X, V
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 : g! x9 X' |, d% J6 T- y
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
, w1 k, D( I$ M+ Z: G3 l-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524 ; x3 B6 }2 p H( j6 Y1 i
0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619 , H0 @- e# e6 m" D2 l; h- p
-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965
3 |6 {( }# n9 g8 B( {7 Q8 _, u2 T方程的解:
, _/ q, j7 g1 i, r" G# k7 Y3 ~% |0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460 4 i; [& @+ V P! `
新的电压值(e+jf):
8 @4 n4 @" o/ V3 k1 F, `0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946, 1 Q! L0 B0 }; a3 ~
===================Iteration k = 0 End =========================
+ `" R7 D0 t) W% a9 D V. Y% U) t===================Iteration k = 1 Begin=========================; h/ _5 p/ i' Z6 _1 \; F5 Q
P[0] = -0.02835
4 F0 R& V9 n0 J8 ?: ?Q[0] = -0.00268
& o$ e$ V, ^( c" GP[1] = -0.46151
8 o! @1 g: Q; B% \5 i2 G. DQ[1] = -0.207946 w1 c' I2 P6 \( A. f; ~ I. ~2 v, c/ A
P[2] = 0.20354
! A4 `, B& f0 D& M% {$ vQ[2] = 1.103374 l5 k- Y6 V2 R4 \8 r3 F
误差向量 p、q:
, j$ Q* X8 E0 U1 o0 ?/ O0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787,
* o# t% f4 v$ E2 D电流 aii、bii:- { f: @8 L0 K) o- g- }
aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000 # ]/ A9 S8 z3 o1 Q
========================雅克比矩阵========================$ q7 ^+ k& ?% I
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000
7 c9 m% p( p2 x7 K' E$ [* }-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
( @2 |+ E O2 M+ `% x0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000 % r$ w. }3 c: I
5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
- @' i( x2 a2 C! ?$ _$ A1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000 # o' n% C" K. r1 `+ r0 a
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000
/ z) @# G$ L' _' W5 j6 ~
3 u1 D( U9 p, c5 A% K& b5 ^所求矩阵的逆矩阵为：
: }. m7 Q) E; g) w" ~6 ]9 L-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385
9 a' g, t" ?' ?; F A-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189
8 {4 r- K, E9 i( {# A-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835
7 L7 X6 l* H" d8 A- s( P-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893
" [" C' D. d1 d/ m8 C6 @8 R-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893 & G$ W9 A' u9 x
-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892
6 y5 Z' r9 p3 o- T* h, b! A8 A3 r% {$ d方程的解:
' x# K$ n1 n4 \+ X0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815
9 e) i. o: a* M9 ~' [* ~新的电压值(e+jf):
; b" r/ p, d. e# e* B2 G: p0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328,
- ? T0 ~; }* Z! [===================Iteration k = 1 End =========================' c' I3 e4 X% P3 H6 {% o
===================Iteration k = 2 Begin=========================4 v7 E3 A+ p& \& Q* u. _4 O; A, }
P[0] = -0.00050
1 O _! C G8 G' h/ U7 v0 _0 Q6 |+ nQ[0] = 0.000058 W# v& r2 m$ F9 w" i6 b5 _. j$ `+ _
P[1] = -0.49877
$ x' p' o/ Q o( N# l2 e7 sQ[1] = -0.295671 s2 E* r! q4 c5 w
P[2] = 0.20071* _0 S+ m! R7 D; i7 [2 a
Q[2] = 1.10251 C2 m: H5 o5 W. t6 j
误差向量 p、q:
- L T7 B$ s0 z! K8 x1 k0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483,
L& v8 G% V- U! F' {电流 aii、bii:
0 b( U6 r7 Q8 n2 |! vaii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000 9 J) E# J& b( a) C% h; \4 i
========================雅克比矩阵========================
8 S. R5 h. n* j-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000
+ W8 [: n( k+ ~/ r-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000
' N& {3 K- q4 G# b! ^0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000 / j( i3 b' j1 q' s: H) J5 k9 @ r
5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000
N2 J% C+ {( b- |' M/ m- O1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000
% \4 x% T& O" Q2 s2 g6 X0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 ; K9 x8 h4 D& Q, J4 _% F# M$ _
/ r* x7 |& a5 e所求矩阵的逆矩阵为：5 V, h0 L2 L( b1 V
-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342 & t2 H! r& q* \7 J; f' a
-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058
# g$ A1 d/ D; K7 C7 C6 d-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
6 h# J# a( }" `5 p6 Y, ]+ q-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
7 Y4 m6 U! s; W `/ @# b9 e-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835 3 c' Q# Z- {$ A, t) Y% _8 K* @ Z6 T
-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478 ( X3 d3 @" _0 H) @( L1 H0 s
方程的解:/ ]( i# n" k: m3 O& W
0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432
8 d7 A$ i- R' m0 e8 v新的电压值(e+jf):
# ?) D% Q7 A" q+ d6 K2 ]* S6 h0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
( q: Y0 Q! D' T k: @8 J===================Iteration k = 2 End =========================
' y7 F6 u0 I* n( }& ^" o' H2 s# ?===================Iteration k = 3 Begin=========================8 |( ~5 p: U7 O; J3 W0 B
P[0] = -0.00000$ S3 X5 N! c$ ^( v) N$ r
Q[0] = 0.00000) m" A5 x9 r$ _
P[1] = -0.50000
/ f3 ]( F r( A. g$ d6 `Q[1] = -0.29999
1 w9 X$ Q! t7 ^2 XP[2] = 0.20008
8 A9 z5 @8 Z+ W$ o5 x2 }+ lQ[2] = 1.10250- W8 s0 M3 _* u6 ]9 A% @
误差向量 p、q:1 N. |2 C" e6 P6 p
0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019,
, o( ^. G0 n( e/ V7 Z/ @电流 aii、bii:3 C/ W$ E$ n! {
aii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 * W5 E% m: }$ t
========================雅克比矩阵========================
3 z/ B- J9 s% R ]-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000 ) p3 t6 K- r2 L; u4 k
-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
# Y2 {9 R, ?& Z4 d% _+ f0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 ' J9 i) k: B4 [/ I3 R2 n8 y/ V
5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000 5 r( n+ T( z* \
1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000 ( A4 C& p! J2 y6 f
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000 8 e V6 j6 ^3 ?% e+ R& K
+ o& [ O( d4 {. m" E: }2 N所求矩阵的逆矩阵为：0 z/ z/ m4 ]+ n* v' @* F8 Z5 |6 N
-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393
6 }3 a7 o0 N" ?-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 + }1 Q6 { b9 p9 a. {: N6 I
-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084 ) B% ^ ?$ k6 x% ]# E8 I0 C0 a
-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109
9 V* X* ~7 A8 j4 f. w-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826
7 _$ g. ^2 N& B: w: r& I/ e& J-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453 , Z6 a) e6 u4 y2 w) f; @* s
方程的解:8 _$ F7 h" M! }2 X5 Y# m9 [
0.000004 0.000013 0.000008 0.000014 0.000001 0.000027
- l0 z" t1 Y0 J新的电压值(e+jf):# [8 B/ I3 K4 f# t$ N2 H
0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373, $ f; }& j5 G) W, {2 f7 F3 r& L
===================Iteration k = 3 End =========================
+ V1 K* o5 L9 `7 o: ]# m; n @5 m7 c===================Iteration k = 4 Begin=========================& |" j( @/ `* `4 C
P[0] = -0.00000" p+ A# X& r! g3 u
Q[0] = -0.00000
& r/ A2 V' k' M2 K' TP[1] = -0.50000
J- ~) T5 L( [5 D, q* @Q[1] = -0.30000
& T% a% h1 o8 z$ `) CP[2] = 0.20001* E" ~' J m0 [7 t; M- C0 p
Q[2] = 1.102508 q r8 _. s. h9 o/ a# M# }
误差向量 p、q:
. x( q, {) O' ?& a0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000, ! d n; m! s% H4 F; _0 c6 [; ]
电流 aii、bii:
5 {% x7 H# R3 A1 l0 o* u6 O2 Daii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000 : b3 N4 V1 @9 `8 }+ H+ q
========================雅克比矩阵========================
/ W& G; W2 Z2 Z8 m' Z-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000 4 i, p; ^/ p$ ?3 W
-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 ! O/ ^" e; w5 g$ u% l0 k% u
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 ' r$ J. C4 P8 Q0 a0 g: w- z' C- n" @
5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 ) c: t. y7 {0 `1 n0 a4 A' z
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
9 b- v* A+ c6 v0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 6 [2 k2 e4 L1 S3 ] x( m
4 q6 @# ^; Z* h% s7 |所求矩阵的逆矩阵为：3 T4 Q5 M$ O$ b0 ~# Y5 y
-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 0 m. C7 y9 e! N2 F7 W
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
$ ~$ R- n" e4 J-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084
3 s# h r) m9 |; s6 r-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108 / x7 |1 h Z, Q# g0 H
-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825
0 _; ^& N7 T# Z-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452 4 v/ B4 J5 |% y4 d Y! \, S
方程的解:: P& ]6 ~# A# Y Y0 w
0.000000 0.000001 0.000000 0.000001 0.000000 0.000002
5 e i# z# L, ]9 G4 d& C1 s, G新的电压值(e+jf):- s- F; f; b+ i
0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374,
2 j( F) i6 @ O* C4 j===================Iteration k = 4 End =========================) Z) N0 s4 T. B
===================Iteration k = 5 Begin=========================% ~) z- o7 [& O B% c
P[0] = 0.00000
5 W6 i) m5 ]; d& g3 S3 ZQ[0] = -0.000007 W( p1 e) s* z* c
P[1] = -0.50000
( p' u4 a C+ W* o' a- ~Q[1] = -0.30000
3 ~& z; y; e3 | f/ M1 @P[2] = 0.20000
! n; x; a# ^- M& YQ[2] = 1.10250; [( I1 |0 s t' h; W! q* V: [( o
误差向量 p、q:; V; v* l4 K0 J& _& n
-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
( C! S" e- J' | o: u' z=================k=5时，结果收敛=======================; _% B. T* n# u" v: K$ k1 I
================牛顿法计算共耗时:0秒:609毫秒========= |
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