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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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txt |
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=========================导纳矩阵输出开始:=========================
, o) E' r! A4 x2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714
- _2 c, H; d* @* A' D* \0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000
& k# V' W6 r+ J+ ]$ x+ ~-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 " F9 x. F, q9 p, k# ^ x
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092
! a+ G! I7 X' F% x: k8 N* U#########################导纳矩阵输出完毕!#########################% Z2 Z& ?! O" B3 g
2 Q) m) O) A& r- y4 j+ V) W. }
=========================初始功率向量输出开始:=========================8 a0 t" o+ c8 j1 o9 X" O+ `- z+ m5 y
0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000
! T3 L: U" s* r4 u- }# @0 p#########################初始功率向量输出完毕!#########################
! Z, H6 ~' s; }$ `
6 h. V* l' w# `! G J& Z r=========================初始电压向量输出开始:=========================
5 R) y5 M" G; Z! n3 O6 Q1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000
" f$ a9 z, q# }& T; j#########################初始电压向量输出完毕!#########################
+ v! f+ z, b1 a# Q, \$ _6 Q2 w3 |# u
y( u9 L7 \7 c3 }5 L8 u===================Iteration k = 0 Begin=========================+ m0 N- k2 S% _* H
P[0] = -0.145257 u- x+ H* v4 l
Q[0] = 0.37497
' i0 C# J- v+ e ?% W; SP[1] = 0.000002 ~- D2 a7 E- D3 a4 A9 h& W/ D3 g- m
Q[1] = -0.65434
9 ~3 G n! h: g" D1 I" x. eP[2] = 0.08715
+ O+ G/ W1 p+ V; h7 BQ[2] = 1.10250# }5 h# W, C* y Y0 ~8 Y1 P
误差向量 p、q:# |5 c9 Q- f' v" M7 S
0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000, * c. P- C, X: P1 \' k
电流 aii、bii:- e" Y* N! Z1 d, |) |* [$ e
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000 # d2 p6 e. }2 N D; X5 z
========================雅克比矩阵======================== E- R8 }9 z+ ^7 Q# }' A1 J
-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000 * d( s) c+ o- P9 h# |8 i" E/ D0 C
-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000
7 m6 K* `% M; @' }8 { I' a) ~0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
# }9 z7 G0 j* N8 L) ^5 @5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000
8 U, m$ F0 g) U( ~1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 . T6 y1 |. ^5 u, @3 g* a
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000
; C) `) `. o$ h- w! y. D6 d' W8 E7 j2 ~# u* ?
所求矩阵的逆矩阵为：
4 T" G) |8 N5 `5 m& B1 p# u5 ?0 J-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 5 X7 W9 I6 [- d9 d# l
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 , N/ v' m: e2 k l" E; v; @
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612 ! G) J& ^8 h5 O* p( e
-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524 ( u1 f1 C& U( l
0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619
- x4 E& f# e, `+ q+ y1 F-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965
& C( v- D$ L# Y- N* o方程的解:
J" `: k! B n8 |6 H5 u9 N0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460 6 v4 w- d3 p3 Z w" I q
新的电压值(e+jf):
9 y- {, Y; C! x: _0 U b0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946, + u5 K* Z5 D/ g2 Z6 a/ S
===================Iteration k = 0 End =========================
8 b$ |4 {+ {, d/ g \===================Iteration k = 1 Begin=========================
/ {8 s1 J9 g, E4 p5 CP[0] = -0.02835
) h! l0 D; v+ i4 s6 PQ[0] = -0.002689 L, I2 a* @/ A" p3 S, N6 t5 A# }6 T
P[1] = -0.46151
# X8 N7 T, k" l0 jQ[1] = -0.20794
* G7 v! q" `0 s) f; w# mP[2] = 0.20354
0 y8 A0 c' }; S6 [' a2 cQ[2] = 1.10337
. H# E* x* |3 I* n1 K4 ^5 s误差向量 p、q:
$ }0 }& _$ G |/ L0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787, 2 s# |* J4 }: @& o3 u4 C
电流 aii、bii:
3 g9 T1 z/ l1 Y( \- \9 Zaii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000 & b1 M4 L I+ z- h3 z$ P
========================雅克比矩阵========================
! }; N s& o, I( A+ u4 P-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000
( ^! M D' ?+ Q s, O-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000 / @+ f h8 [# g, l/ m: o
0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000 1 Z- o! [! H6 w2 a
5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
! f* o3 j! P: d/ g1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000
G: `+ y$ M7 E0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000
- G; m6 ~* h# \; F% O c4 `
7 n* e+ Z6 Y" I0 M所求矩阵的逆矩阵为：2 J F6 P# s! {' {' z& }. ~
-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385
3 P' v) F6 j: A% {% H% O$ @5 @ U-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189
+ `/ c b5 ^9 i2 x8 L-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835 , V% N" `! C0 O6 g
-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893
$ e9 j7 z. \. F S9 X-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893 3 v1 D% J- E8 x2 m3 ^
-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892 ' Z, i3 ~' n! U
方程的解:9 [* n7 H2 _% o. G, {& v
0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815
' X) a- s& q9 G9 q新的电压值(e+jf):
4 Y3 h7 Y6 u4 f. v, h: L( F0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328, - N7 h4 l2 ]# T$ ~- N6 K
===================Iteration k = 1 End =========================
7 t( o' T2 T: b: d c% f===================Iteration k = 2 Begin=========================+ u( n) g) _+ j3 _. r
P[0] = -0.00050
6 S1 _( o' }/ E B" v/ FQ[0] = 0.00005
6 u& q6 K$ m/ y+ ~- P( s- FP[1] = -0.49877
! h& ?' ?: c% Z, [7 ^4 I4 pQ[1] = -0.29567
# u# v7 D @( | a+ M4 U& S+ D6 A1 PP[2] = 0.200718 A5 L( e# s2 U2 T( {: V
Q[2] = 1.10251
6 U1 |/ }# }, Y3 S误差向量 p、q:9 _1 Y2 e3 e6 X Y- M9 R
0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483, & n S" x; _3 b" l0 j4 S" Y
电流 aii、bii:( b6 X- Z2 A3 y4 S' `5 [! k
aii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000 9 Z4 b9 |9 q8 J- G
========================雅克比矩阵========================1 n2 B; @' Y! Q3 E3 S" i6 M
-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000
; N6 F+ E; F# x6 \, \, s7 F( C' g-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000 4 e# y' A. U* U% x* `* v
0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
% w- f) y3 z: \+ D' t5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000
# R3 h7 V* x$ p8 q1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000
1 U+ B; Q/ n8 y+ t0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 3 N& ]4 C3 t F8 X
; ?4 g p7 E: s- Y1 {
所求矩阵的逆矩阵为：" t: J: g7 ~9 [: H
-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342 8 P9 @8 B; s5 y
-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058
) `. W3 c7 ~7 S-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
. j+ `% D1 T. B4 [" S0 O-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145 6 v- D% x/ |8 C3 h$ }- T
-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835
3 R7 a8 @1 P( V2 H8 n! u' e6 W$ O; Y-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478
; w+ }. M, Y6 W3 R8 I. x H1 q方程的解:
8 p1 D. J5 Z" h3 B! v6 N0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432
% C* W+ ~4 [2 o7 w3 z1 [新的电压值(e+jf):
* c7 }" \2 Q2 G& ~+ r0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371, : l% F2 o w; |. g( @, o& b7 f
===================Iteration k = 2 End =========================- d# ^. h I" W3 o' G) d, Z2 l* @- m
===================Iteration k = 3 Begin=========================
' |0 F6 t& A" {" y# ?9 ?P[0] = -0.000002 B V$ l/ U" N
Q[0] = 0.00000
) \; f, i/ r9 Q+ }( A. [& o; uP[1] = -0.50000+ ~- a: h& w" K! I. D1 D
Q[1] = -0.29999. U; K: Z/ V- T% F
P[2] = 0.200084 W/ L4 G& q/ y: S2 [
Q[2] = 1.10250. R0 `4 g, n2 u9 P, E8 V
误差向量 p、q:% j7 k% g$ a! p& {8 M) k0 ^
0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019,
8 A9 Z7 |6 y1 |6 c' D$ Y电流 aii、bii:3 n: u) O; c6 R5 M" r; O- ^. V. F0 N; I
aii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 ( v! L F0 q# d( H4 O
========================雅克比矩阵========================
# D' ~. J6 K7 j u8 X-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000 " v7 v: i9 r9 C) k1 q4 X$ p; h
-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000 * |' f0 c, e- D# v; W
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
5 J; ]4 ]( P$ b9 x. ~% M2 r7 c5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000
/ H$ N7 V* y- t& Q1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000 ( I0 U( ]9 n+ A9 U
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000 : _% z" z1 Z. ^- Y% A
! @. }" x" e8 N1 O8 `8 _$ `1 ?
所求矩阵的逆矩阵为：- I/ |3 |/ W6 j, e. k* N
-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 ! o0 x" c; h" F/ b8 F
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
! f9 q! Q3 M7 H* p" t# C-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084 / K3 g, i/ d! \* p
-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109 2 L# z% o3 _4 Z% F2 j, `
-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826
1 g4 J. x; s g8 @; v- J-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453
; \5 w' a; y6 [方程的解:# B6 B, {& z! h$ T
0.000004 0.000013 0.000008 0.000014 0.000001 0.000027 - M( V. X$ u, \; L
新的电压值(e+jf):
$ h, ~# R5 Y- u' f' D0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373, ) Q2 }) q- M/ p$ l Y8 y" q4 m
===================Iteration k = 3 End =========================' w# a) Z; B) l+ p
===================Iteration k = 4 Begin=========================* t" k& L/ q* J1 s( I- B* \$ b
P[0] = -0.000001 |$ l9 C) y: H5 M- d7 ~
Q[0] = -0.00000
. J0 ?5 g* z0 A) F( z& CP[1] = -0.50000
, l) x$ e7 Z( h8 n: z$ U1 v2 QQ[1] = -0.300005 b8 S7 n9 `' b# f1 s1 _% D
P[2] = 0.20001/ `5 E; [. M) n& \4 ]) D
Q[2] = 1.10250
* W9 p. W1 ]( ^' x* A4 D误差向量 p、q:
/ p+ k8 j3 ?# _6 T3 F& s& H0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000, 1 w1 D( B0 w) B# t, \3 j! Y
电流 aii、bii:
( E% ~* g( s1 M5 ~# k: baii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000
- P9 ~7 k% V$ n, Z1 m7 {+ U) W========================雅克比矩阵========================0 @( B! K% r' R+ Y
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000 6 u/ K7 [. T; ?2 ~. h
-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000
) D1 v% q; ~2 x( J2 w0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
1 Q9 n. L. N+ `. d( n5 U! D5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 " T% ^% f9 X2 P
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
" d6 O4 h3 H4 P0 k0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 " t) N4 v. P9 M0 `. ?+ _7 \# W
" _; q2 j- I5 `
所求矩阵的逆矩阵为：2 d- _7 ~% q* }! t) ^ v( r% u
-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 , |6 e' Q6 r% G
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
s; o3 B$ l6 v/ r* v# H4 W-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 + a! l0 l& a5 [. b: Y A
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108
) p9 x5 a: T0 ]5 B% X7 T2 W-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825
% ~+ `3 k6 {) L2 \-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452
4 a: _! P0 l6 l' t. F5 E" Z4 G方程的解:
1 d4 _" g! ~: E/ z4 k0.000000 0.000001 0.000000 0.000001 0.000000 0.000002 , _8 L) W/ `6 E( @$ k/ ?' j. l
新的电压值(e+jf):
: Y: H( y8 ~9 ]+ o* p0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374,
+ l7 W- S9 d/ @0 Z( T* d7 `" O5 c===================Iteration k = 4 End =========================
6 N) x' n+ w& [===================Iteration k = 5 Begin=========================
; n% t: d! \- w8 u) f! pP[0] = 0.00000
1 O1 i/ f' h# {# D* i' fQ[0] = -0.000008 n. }- G8 f# z$ [& z! U
P[1] = -0.50000
6 c( x) _5 ~$ g6 S2 FQ[1] = -0.30000
6 \! c( {4 f. j& i. i5 w2 NP[2] = 0.20000
2 x8 B# [7 V/ TQ[2] = 1.10250' N/ M2 D7 u. e2 h# ]7 o! Q4 [# ~
误差向量 p、q:4 `( n A$ a4 | d! Q4 K; f
-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
' C- T9 U- u- I$ W- M" y=================k=5时，结果收敛=======================) Y4 w B) Z) C) o
================牛顿法计算共耗时:0秒:609毫秒========= |
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