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夏道止老师《电力系统分析》N-R迭代过程 |
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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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=========================导纳矩阵输出开始:=========================
1 P$ h' q% m! g/ V! A+ @- r2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714
9 k/ {; |9 W6 q0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 ' S0 ?) P+ D6 u( s
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 4 ?4 W) k! k2 ] w$ x# q
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092
% C/ ?6 r e$ U8 p m, D" ]#########################导纳矩阵输出完毕!#########################
2 K# I- U6 @& ]% D$ P) }. @
9 ^! g; w& L; S! p% _$ d% B2 o=========================初始功率向量输出开始:=========================6 `% G4 B- ~! n
0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000 + ^$ P0 B% D2 J' z$ S0 v
#########################初始功率向量输出完毕!#########################
7 d, c8 L2 }/ i! B) o3 v# U4 P8 ?/ L8 N5 ?4 q" m
=========================初始电压向量输出开始:=========================) V* V/ o* ]! }! x% j+ n0 e
1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000 0 @- z( t3 n' K4 H+ z1 L2 A
#########################初始电压向量输出完毕!#########################
) @+ t: H" f0 x( y
) q$ d# B% q) c. t===================Iteration k = 0 Begin=========================+ L6 M. b; Z+ Z% t% e
P[0] = -0.14525
9 B- M7 _5 z, E. N; [Q[0] = 0.374970 [. D c# j7 w$ l$ e& r
P[1] = 0.00000
6 q: x. j% v0 T6 P4 n. PQ[1] = -0.65434, P4 h) l5 y6 K: _. H* h0 b- t" a0 x
P[2] = 0.08715
* t3 Q3 Y$ P% i+ {5 v/ o- |) _; x0 h, KQ[2] = 1.10250
* R/ x: J( e4 _6 g* }" b+ f% B% ~. G误差向量 p、q:
2 P1 B8 ?& r5 D' @# {* e' g0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000, 5 V) k0 r B# w" L+ m2 z. }
电流 aii、bii:$ K! U4 W$ D4 R4 Q/ ?
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000 / r3 m+ [. B+ ~* [4 D
========================雅克比矩阵========================* H2 j# j+ e$ Z! C
-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000 6 }( L. [; B; c: {( }
-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000 3 c8 _2 g6 j& h# i1 X: a6 X6 w
0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
0 i2 K7 j. Y4 p! T7 v5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000 6 \) d2 ?* B9 ^3 [; p0 A
1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 . s+ @9 ?/ c {1 t. B
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000
5 D2 R% V5 v; s, }# ?2 O9 ~2 k7 }& \% C
所求矩阵的逆矩阵为：- j( z3 f. q2 _
-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 r" P: h; A0 A4 O! d: t
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 # H' A+ [9 x& I+ s& |) X) o
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612 " @& u( w. E! B: P- r2 q. U) c
-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524 8 W1 R5 I- ~8 l
0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619
. _% u8 g0 I3 T( A1 E- H-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965
9 a2 M- s( K1 O! M4 J方程的解:
4 f) [) u+ n- Y2 C0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460
2 O! ]; \! [, G6 s2 E新的电压值(e+jf):
' T6 |" |5 d2 t" t: M0 f5 ~( B% n4 M2 @0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946,
4 e0 V7 Q4 }# a1 n. L===================Iteration k = 0 End =========================
7 o7 c0 S6 Y H* @===================Iteration k = 1 Begin=========================
: @* c. J' C3 d% n' z! kP[0] = -0.028353 x1 ?% _1 k* i% `* t6 K
Q[0] = -0.00268* [7 S# U7 R: E' c4 }
P[1] = -0.46151: ~; E' Z; k. H B+ c; k1 Z; p
Q[1] = -0.20794
5 K7 a7 v* @) r- E5 X7 m! pP[2] = 0.20354
: q/ o3 r( o* g- g- tQ[2] = 1.10337. d/ [: ~. A( {* j3 R/ N- M) F
误差向量 p、q:
- p% j9 L) H+ o; _0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787, ' J2 a) \1 D2 S2 X- Y1 Y% ~
电流 aii、bii:
" u* T* D# {% b6 baii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000 4 _; S" p' c! }' V0 U
========================雅克比矩阵========================
' x9 b; B/ {0 g3 E-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 ) l& j2 R/ ^0 u
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
9 [( A+ u( g# F5 k9 z6 `- w+ B% _! q0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000 ! m7 P& Y. `5 n$ V- F' M; p& H
5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000 & `; ^2 i) g3 ]2 g) V
1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000 7 ]7 D5 K. t/ |3 U2 E" u* h% T
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000 5 k; U) P8 P9 D" _
+ A/ y% J# E V4 \所求矩阵的逆矩阵为：$ R+ W& H# T; U
-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385
% T9 e q" u. U8 W5 _, f-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189
6 ] h1 T5 P$ G1 x-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835
0 q" a1 f. ?: H9 k; d- q-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893
* }/ v- l6 R# e( X5 i9 i-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893
3 {4 P- |1 |) H; _' b-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892 9 n- ]. N$ ^0 u" ?: ~
方程的解:, V" f# u7 h0 U9 d! w3 s3 a: i
0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815
' _" I" U( v5 l% l% u新的电压值(e+jf):( g9 I/ N {% `3 c0 @
0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328,
( W& K3 T: ~' ]===================Iteration k = 1 End =========================* i, Y9 K8 j l$ d. ]
===================Iteration k = 2 Begin=========================& Z# T8 z" _# t
P[0] = -0.00050
' T/ Q1 | T: z. sQ[0] = 0.00005
) R/ N5 s* j( r1 t( MP[1] = -0.49877
8 X- H% Y0 ?# r0 ?, K2 k3 zQ[1] = -0.29567
2 N; u8 C8 h( _3 O! d5 z5 k& RP[2] = 0.20071
1 h. e9 d" H3 |$ h7 s* EQ[2] = 1.10251
3 z f: \2 J" q5 ~5 N, ]6 }3 b误差向量 p、q:( |5 V4 ?- Y. Z" j
0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483, 2 \: A7 `7 b0 u8 V* ]
电流 aii、bii:
2 F5 k, q& T0 F; Y6 i& Z7 kaii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000 5 q: h, ]( U9 ^. F. [% Q# {: D
========================雅克比矩阵========================
+ ^# o9 H- {1 I/ ~# ?-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000
( j1 c& z, D$ o" z2 X3 H4 N-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000
2 _# P; i5 w; i* E* [9 [0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
. h3 o# U$ S/ j% S# B5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000 6 M' c% H2 P4 q5 f
1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000
; L& G) J4 r- k- ]0 c0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 7 c& Y7 x9 z% J" ^5 Q/ }/ p/ w
4 @. k+ l8 ^9 r# O: v G& W9 Q* c4 m8 F; J
所求矩阵的逆矩阵为：
( h$ c# m# }+ o" Q/ e-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342
7 d5 o1 h9 z( g. J3 v3 Q-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058
g2 b6 R G6 B5 O' T-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
8 C% n9 \) }0 C; u+ _& O: o) H M-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
! B N# [4 Q7 n: E( b& @( j0 [-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835
& j* { L$ w$ E-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478 , F- b+ X) M5 v- N# ~
方程的解:4 a4 c/ T& H/ o* i
0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432
( t$ ]& `! y/ i3 J新的电压值(e+jf):0 G" G: X* f+ M% _4 U/ _
0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
8 Q3 t1 ^2 @6 \1 ]' n2 {; j===================Iteration k = 2 End =========================
% f7 \- h: P5 s) C2 m===================Iteration k = 3 Begin=========================
. i7 N+ N" F1 _. Q: `' YP[0] = -0.00000
d+ E; E. w$ ^0 KQ[0] = 0.000004 d; H$ m. O5 d* F( X- S
P[1] = -0.500002 u4 z4 a3 e! {8 X: ]
Q[1] = -0.299999 y$ z5 }0 F% b+ ^
P[2] = 0.20008
3 v+ G9 m' W1 {" A; S; YQ[2] = 1.10250
, J" T, _$ n3 w" k7 G. l9 U5 _误差向量 p、q:& E9 u) U* z9 y
0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, 4 f/ n/ q8 M* y' C, x7 v( m
电流 aii、bii:# P6 R. G9 ?6 w" H# B# U1 x" m! M
aii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000
7 c/ \# a' Y2 }$ K& N/ E) b========================雅克比矩阵========================
; c D3 u9 |" d- l9 i1 `) y-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000 8 m1 ~- J" I; N% c5 J
-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000 ! a6 A, {% c3 X+ L# _
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
\' K9 |9 x. i* t$ s5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000 4 t8 @+ m& P" M/ K: n
1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000
) T0 _+ j g' u6 y& |) M0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000 1 L0 C) \7 T, e) v# }# z
( m+ ^. D# p S4 y) c5 q; ~# l所求矩阵的逆矩阵为：
v( P, r7 j- D/ ^* K; R- V+ D-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 1 O$ t, d/ k$ A. X. O
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
5 ~5 Q. X3 a; h* ^. ^% o-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
9 P9 b! C, e) @5 ^1 U/ }+ u2 ?, r-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109 ' `- ~" g% T1 f, k1 E/ `
-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826 ! C$ B! Q: L" {0 p. I
-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453
3 K$ M6 K/ G9 X" H* o& B, i. `方程的解:- s# j% H- Y; G l7 N
0.000004 0.000013 0.000008 0.000014 0.000001 0.000027
5 [( N- w" N1 R* M/ R新的电压值(e+jf):5 a- B9 E, _8 ~# [, B
0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373, ( \! s7 `* x* V+ i
===================Iteration k = 3 End =========================
' G! G I) c1 ?4 ^/ U& T' @3 c===================Iteration k = 4 Begin=========================& _$ w% r/ x% X, |/ p7 `5 H- E- \
P[0] = -0.00000
" f; m. X! y" i/ FQ[0] = -0.00000" Q0 ^3 U* S+ q7 S/ T: P
P[1] = -0.50000
. f$ }' U C$ L5 m% SQ[1] = -0.30000
% Y( p5 p d- YP[2] = 0.20001( B! C z& v. w" e* p
Q[2] = 1.10250. x0 W [" }2 ?( t! P
误差向量 p、q:
& U' t& W: D/ ]" Z) k5 K. _5 g0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000, ; t2 i* u) m$ U- s& Y
电流 aii、bii:
; Z7 g8 A" R. `, S# u& S& {. vaii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000
8 S- k: K- X+ I! K========================雅克比矩阵========================/ C) A5 K! \4 {4 _* @
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000
, }! ~, X: o4 n4 G3 X. _-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 ( \* ? O: _ D. B: Z8 J
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
! S1 I% X# g0 U$ S: a* T! U5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 $ G6 C- V. j D
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
' r; z7 k0 Q9 v( B' s4 R, d0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000
$ e8 g' W0 r7 @" z' \$ b$ P) {, b% i; O$ z3 k1 z/ l0 G
所求矩阵的逆矩阵为：9 F9 j- `9 N# [, v4 j( }3 T: @
-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 2 \' z8 Z6 r/ E- Z/ f5 Y
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 5 r {, b" k# x3 V* D2 K
-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 5 K' k# m4 O) |+ P- h4 E
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108 $ Y. p1 v$ |( U% \; w8 ^/ h/ p
-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825
0 s% N" _9 m7 {0 G, K+ A-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452 " }9 M3 h, C7 o" @
方程的解:
6 k; P: U5 l* y+ L0.000000 0.000001 0.000000 0.000001 0.000000 0.000002
( @5 E9 ~+ z- e8 U新的电压值(e+jf):* e* y* J4 B6 I5 l/ X: r W7 `
0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374, # }! L& a# Q1 L. o! ^% G( r
===================Iteration k = 4 End =========================3 p: U4 E4 m, V# m
===================Iteration k = 5 Begin=========================- k0 Z% g8 R! m9 P9 c- j
P[0] = 0.000005 p6 i) r& z8 q! w9 W% o* q
Q[0] = -0.00000$ @; s) d5 ]% A8 [/ h, I
P[1] = -0.50000
5 ~! m1 n: m- d7 S+ D0 k" cQ[1] = -0.30000$ [" n" F- Q; W' t& X1 X; o
P[2] = 0.20000
) [! G; h8 c) DQ[2] = 1.10250
: G! H. [9 }$ u误差向量 p、q:
- ^ J1 N& i% L; O1 F) _2 A7 D-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
3 w3 @1 u8 `9 F=================k=5时，结果收敛=======================
& ^' i$ P0 _! V( x================牛顿法计算共耗时:0秒:609毫秒========= |
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