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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:=========================
" j9 w& I# R+ S: \4 W2 l% N2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714 2 C. d' W# i B- _$ H, E
0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 3 l% {1 d( B }: X- O
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 - F/ N1 ~! |+ I- A1 x+ O6 [
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092
' S% l0 f6 U0 y0 [- u5 f#########################导纳矩阵输出完毕!#########################* v m- M: \, a' c# b+ Q" e
5 p- J+ C; g% G1 t% {" h+ K=========================初始功率向量输出开始:========================= m$ C; r6 U9 a% b& S
0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000
+ Z+ S! i: o# d: ~5 @# A#########################初始功率向量输出完毕!#########################
0 I) N" K5 S# V/ U6 c0 i8 T
7 j* ~$ t( L7 \8 W6 P6 h' B; b) h=========================初始电压向量输出开始:=========================0 \- v2 _% A% L$ [) y9 C
1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000 3 x5 b% U2 l/ ?# V, X" R: R
#########################初始电压向量输出完毕!########################## c! z/ ]2 b* w4 `' a
6 R+ D. g8 P1 g; J& l! F* ^
===================Iteration k = 0 Begin=========================6 |7 W4 `1 P$ V+ l# U
P[0] = -0.14525
7 p: Z# `" p4 t ^Q[0] = 0.37497
) K1 e$ h! G3 a4 { L& R7 jP[1] = 0.000003 D7 K. g* D( l3 t# u
Q[1] = -0.65434, X4 v2 v; ^7 B" B7 H4 w
P[2] = 0.08715 U9 |* Q: Z7 z0 J; m4 F
Q[2] = 1.10250$ o, p. u3 v+ o& n
误差向量 p、q:
6 T L1 a1 w/ j2 e' }0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000,
?* y" K) a$ @' N0 R0 M G! c电流 aii、bii:2 g/ F L& ~$ n+ B8 R8 F7 `
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
) {' Z& m3 c$ q: e2 X========================雅克比矩阵========================
& A* p5 m+ I6 P6 Z/ x-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000
+ H9 g6 A" w$ ]5 J-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000
N9 _6 ^" m. p1 A6 y4 U0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000 8 z/ _! n. \; k; R' H
5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000 / h# g/ W/ U# @" ^& T
1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 0 ]3 Z \! E; C
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000 7 x6 Q2 i ~. d8 c: S
9 v4 [4 Y* u7 l8 e
所求矩阵的逆矩阵为：
- G6 r* i' I$ ~' d: _4 }-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 0 X- _+ ~/ ]: D5 r) \4 x0 k A8 o. ~
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 * w& [2 |8 ~) _1 x
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
+ x _2 \+ `6 F, g-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524
0 A8 _- r: b( J3 ?0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619 3 d- h; ~! O a: W8 Q3 ?, c
-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965 i$ W) L* _( f' i
方程的解:" K3 ]# ^. L& B3 @
0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460 ; M9 p) u1 v5 E( ]! E
新的电压值(e+jf):
5 f' S5 o* I6 h# J4 \) j$ q0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946,
" }, b, F2 `! i! D. m. q7 u7 Q( m- J# y===================Iteration k = 0 End =========================
5 ~9 o6 _; f& U( c3 _) X===================Iteration k = 1 Begin=========================$ G9 {+ ]0 _4 i& [
P[0] = -0.02835
" c" b% t1 _& `6 X2 ]+ _, `" JQ[0] = -0.002688 w6 H& a/ Z* A/ O7 T: U
P[1] = -0.46151
. y1 @0 c$ _* n9 @3 K6 sQ[1] = -0.20794$ P% V% F* K- u1 E, u6 z. T$ V9 o ?& D
P[2] = 0.20354$ W8 ^: z9 S8 j& L% W' q0 C
Q[2] = 1.10337# K9 D8 k9 g4 s9 g
误差向量 p、q:( A) ?( |4 n$ a
0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787, & d! f9 N; M# L1 u/ N
电流 aii、bii:
% p+ G/ H; X+ |# a, \1 h2 F @aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000
; M, j9 V0 C' Y; z- N========================雅克比矩阵========================" E8 Z' _ c, {4 R1 }% \1 b5 D
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 , l* \1 G" v; z/ p% [1 {
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
" G5 n, [2 [$ C% |/ }0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
. _2 C# }6 B$ z5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
" ~: l% u% i$ O3 q3 L( M" X1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000 # @" N n. f4 }8 j' z! d
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000
, K! t2 r4 F+ d/ z0 _/ E4 B4 S2 e, V b/ X" I
所求矩阵的逆矩阵为：( G/ l, J/ g, G4 n
-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385 + z5 r) |6 f' a" K$ J% ?
-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189 ; K+ k0 G. K6 [7 K! l a6 q
-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835
8 O$ ^; J+ D6 D+ `( V-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893
6 X2 T4 B; O$ T-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893 # o0 Y0 T" Y5 W) X, R* }: o
-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892
' }# f2 d& l% U7 `8 C方程的解:1 X B y5 L! b0 p/ Y E
0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815 & s. l! f) ~3 M" m
新的电压值(e+jf):
. }- Y3 m2 Q+ Q0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328, . n- y: l- ]# Y3 ]: v/ E- z
===================Iteration k = 1 End =========================0 }) m: d/ O4 C2 |$ p0 A I
===================Iteration k = 2 Begin=========================
. a# f3 O$ k" s1 VP[0] = -0.000508 x, l0 C6 |% x- W1 F8 m1 ]
Q[0] = 0.000055 B& g3 p" T3 o' S3 D5 k W/ A8 x
P[1] = -0.49877% R! X" `& l6 ]3 r. G
Q[1] = -0.29567. D" a5 i0 ~& ]0 E1 s1 t1 J
P[2] = 0.20071
% {: k$ W7 _# ^3 ^" k% rQ[2] = 1.10251- F3 r% g7 O: J! Z
误差向量 p、q:
5 |2 e; E' C5 q4 K( Q/ o ~0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483, 0 a/ h7 R. T8 a9 O0 T
电流 aii、bii:: `1 m( N* s! N& G9 z' [/ Z
aii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000 6 ] H# w) {, [8 }) D
========================雅克比矩阵========================8 ~5 e9 i+ P: d. b* ^
-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000
1 ]1 I6 h. O. q# \: k4 s$ W1 U-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000 8 N3 e. B( F: F+ p/ O I% V
0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
7 x% l$ J- p6 e5 D5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000 2 t/ J" s% S8 s) J3 @3 P
1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000 : C7 e# z. r; d F+ L4 [! |! s
0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 " T9 j( p7 U$ n! k' Z6 X
_2 I, ^$ y, A* s/ K. V& D0 U7 m
所求矩阵的逆矩阵为：: `2 `$ @ d3 R, X
-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342
) D; `. \) F/ q-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058
0 v, g7 U# n1 N- M-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965 6 U* n! r; j9 n8 p; p$ V
-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
' Y1 R8 {' p+ q# e$ f* a4 j-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835
C" W3 H' D9 b% j-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478 / f, ?& A, |" e- L' B
方程的解:
, R0 K' |; s( w0 J* b) G0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432
4 i, J; K7 Q- ^- E& C9 q! `$ |新的电压值(e+jf):
* d& G) g* T1 C# |3 B) |0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
2 ] D: |; G u5 S===================Iteration k = 2 End =========================
4 F: l: P8 A& h5 E* F===================Iteration k = 3 Begin=========================
6 Y6 o# }3 J" e! A3 Z& N# o6 I6 a' MP[0] = -0.00000" N+ M; K# |6 J( k3 i* |) {
Q[0] = 0.00000; G2 |0 B+ F( s: i5 k; m
P[1] = -0.500003 T9 ~! d: r4 Y% s
Q[1] = -0.29999
7 u% t. f7 i4 S$ V* XP[2] = 0.20008/ |; Z; w+ f5 b& A0 a& T
Q[2] = 1.10250+ G# @2 E; x! ]! }! K
误差向量 p、q:
! U3 p+ |6 k. U0 e# p A0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, / Q7 t; j2 G7 T5 p& Z
电流 aii、bii:
- r- f5 ]/ T2 k% xaii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 : G4 x3 W# h- `. e; E
========================雅克比矩阵========================% O1 } Q+ R1 J# n
-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000
- U6 ^5 G# _- F5 n7 }9 y-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000 8 v6 Z; ~2 j+ y( G2 x& u8 R; l
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
! R9 s ^" v' j3 x5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000
6 p) ]6 Y* X: a. E1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000
* [' r8 @! e6 }2 c+ g0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000
5 Z+ r7 Z& A* T* T' Z
8 |, g$ f* d4 X0 D0 q3 ~所求矩阵的逆矩阵为：
8 j) A! g/ U% n2 f3 @- D7 `, d-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 ) s; c* C! S; T* F* F" a
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
% H2 B6 Y1 F* U1 `& }-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084 3 K4 V% A! ]4 P
-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109 3 S: o5 Y8 a+ h
-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826 , M9 v" i _$ M0 Q O2 ^ N! t
-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453 ' A5 x3 i9 |! M' f& X2 d0 h: W
方程的解:
6 {/ B3 Y" ?% I9 T3 W7 W: `( B; L0.000004 0.000013 0.000008 0.000014 0.000001 0.000027 3 T+ S$ B' m3 a. _" k* t4 Z- q
新的电压值(e+jf):
& |2 v$ h# \/ P0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373, ' Y$ R5 t/ o+ ]
===================Iteration k = 3 End =========================3 t( r' ~; j6 ]6 b& b
===================Iteration k = 4 Begin=========================' {, C O: k# T: m6 B2 u
P[0] = -0.00000& }0 S1 v; F" \0 \- f, {
Q[0] = -0.00000
& n2 ~2 F5 \1 q5 u9 KP[1] = -0.50000
% `2 k) e+ m/ t; b' E! l. O7 zQ[1] = -0.30000
2 n+ M6 U# E* a7 n d; |$ I) tP[2] = 0.20001( @& w2 T. t$ R h# P3 j
Q[2] = 1.10250
$ Z# {6 U- M9 G! |误差向量 p、q:0 s7 w/ s; o9 D9 s/ v3 Q0 K: @
0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000,
]( I: E8 |0 k y- H4 [3 s电流 aii、bii:; Z; G' O% ]. | C( H% @) n) w+ J
aii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000 ( e) g! ?7 u* `
========================雅克比矩阵========================# V7 ~( [6 D) f: `, L
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000 3 l" ~, F6 N) U ^. g' D
-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000
3 n; J* T. X" |1 |. C, G, q* k6 C0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
7 R7 U# Q1 ~& n& V& e& [4 Q/ w" h5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 I7 j4 f- E( K& V
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
O! q5 A: S$ p8 N; G3 A0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000
% c2 V6 a4 b% ^/ i
) n5 q; n8 Y4 e/ k5 p; P1 z所求矩阵的逆矩阵为：+ o2 ]$ ~$ o1 m
-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393
" h3 A* ~7 ?# X-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
. k" ^1 Y B: Q+ h$ }8 ^-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 3 T" U8 @& L8 K$ v- A
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108
0 i: [& j& h# ]( c0 P/ t-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825 7 t. U# m+ o' E, }2 g* w7 h$ J I
-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452 8 A. ~/ h* _/ k9 ~9 \
方程的解:
7 F; e6 L0 j7 b( H0.000000 0.000001 0.000000 0.000001 0.000000 0.000002 6 }0 X% Y+ Q2 r* L% s& |
新的电压值(e+jf):
4 D" `" X# G. E e" s, R; ^0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374, p; i) C. c* F6 u) `- a+ m
===================Iteration k = 4 End ========================= h- N) H9 h- ^' z7 J, H
===================Iteration k = 5 Begin=========================
4 C6 w' A) [4 h8 W) [$ dP[0] = 0.00000, W$ i8 _2 _: v9 k1 X" W, a( G
Q[0] = -0.00000
! k# I4 ~" Z( Z! w& JP[1] = -0.50000' B0 }* g3 h8 w
Q[1] = -0.30000 i- |- m$ D/ ^+ r- C6 i- Z: A
P[2] = 0.200009 s+ f5 H7 q! r! M2 W9 M5 R
Q[2] = 1.102509 C* C% s9 E# M/ G& L9 Q! p8 c7 A
误差向量 p、q:
& T, b4 k; s8 |-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000, ; `, B" @5 o2 e, V
=================k=5时，结果收敛=======================9 q) ]5 s2 I9 Q$ r
================牛顿法计算共耗时:0秒:609毫秒========= |
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