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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:=========================1 D( M! c. [% k5 G% G' @
2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714 ; x3 _! t$ v0 c% i2 {5 ^
0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 9 x5 ^3 D/ C% [
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809
, t, W. `3 C7 f H+ t- b( ~4 p-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092 9 ?: U5 Z0 b7 i. I8 y6 c
#########################导纳矩阵输出完毕!#########################
_& w4 }2 T$ O! W1 H) n
$ W+ G) @" T8 w+ c: p5 F% Z2 u=========================初始功率向量输出开始:=========================
9 k- X* t8 y( `, y0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000
. Y4 W5 O( o" B2 N! |) `4 ?#########################初始功率向量输出完毕!#########################: o) v7 _& E' A/ i2 y3 }$ P
6 H) {& o: _7 H, o3 i; E
=========================初始电压向量输出开始:=========================
! M' a' Q4 m7 k% k- z: i1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000
x' k" U9 m" |/ W$ N$ ^#########################初始电压向量输出完毕!#########################
/ x) p* ?) y; i) }. E1 B' l3 }7 `3 A5 R( E
===================Iteration k = 0 Begin=========================
7 t4 V/ j7 H# |P[0] = -0.14525/ c/ Z6 a* `. L7 F: R7 e! }
Q[0] = 0.374976 Y2 k, Q1 Q" x( J6 ?" o
P[1] = 0.00000
8 u6 ?" C0 }3 ]Q[1] = -0.65434/ j [! k" K- K1 [# X1 B) o
P[2] = 0.08715: @( R; E9 r0 b N: |8 H6 y
Q[2] = 1.10250
& W q% @5 f9 y, e& ^; j误差向量 p、q:2 M! ]% W( z$ U# e- a1 b' C2 o
0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000, / |; @0 ]8 E% w! V. o, |' g' g. [
电流 aii、bii:2 r) Y! v7 r) U6 K5 S8 V9 E; k
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
2 y W' C) O$ p% [========================雅克比矩阵========================5 C; ^! Z/ W! r
-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000
# R. I8 I) U4 K" R-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000 ( f! ?2 P( ?6 ~* `+ y
0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
5 ?( c1 ?6 R1 G3 v7 Z4 e0 D3 \5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000 0 v. W, ]% Q- v" Y
1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 6 f- @! A: h1 E* w( C, z
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000
/ e& @" P! M. m0 K1 u& G( H& W3 n, i
7 s1 k( R9 s+ z' m- C+ K6 Q所求矩阵的逆矩阵为：
- v, A5 Q" [! Y# Q-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618
) F( e7 m0 h! l5 I8 f-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524
, j! S* l! z7 p-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
/ [! X& E" K" ~: ]9 t0 Y: e9 s6 S-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524
0 @: V, W- t2 K) T& B: u0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619
( e# q7 e W5 P! a8 I5 Z g-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965
# ^, z: s3 ]7 x, S. g方程的解:
# h0 H% j. ]' U0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460
3 k8 K, O% o6 s; b5 [$ |$ X新的电压值(e+jf):) u) t" o; g. a3 n$ {+ e
0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946,
6 _; @6 I- i% R) F===================Iteration k = 0 End =========================
# N c% y6 @/ ], p===================Iteration k = 1 Begin=========================
: }, ^$ B/ @" H- S8 gP[0] = -0.02835
% {+ W+ t9 S; k1 B% [$ o7 B2 LQ[0] = -0.00268" ?' I5 o& Q6 L! Z" T* u
P[1] = -0.46151( z4 u" [! Q6 p, G. y( v) k
Q[1] = -0.20794% _; B+ [; S7 n$ r+ b4 }; `- ]# a
P[2] = 0.20354
5 t' }1 S4 D# Z/ d6 n |Q[2] = 1.10337
2 O# {2 x( v L/ b3 [" J2 L2 T误差向量 p、q:7 q2 b* g* e& U, Y3 V
0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787,
$ d8 e" U9 k0 v电流 aii、bii:
' c* c, _0 E% Iaii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000
- k s( ?9 r8 L: d+ i1 L* O========================雅克比矩阵========================) W$ P* w5 ~( Y
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 ' N9 e4 P& O7 L% |2 c2 g& l! U6 g
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000 " [% K. d K3 a
0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
9 ]% z, F8 N! G8 @; I5 k- A6 l5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
; W& @7 W# c5 B: d( k1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000 # {6 M7 q4 `3 T8 e
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000 $ Y# t/ U* G" R6 m4 X4 s+ P
# I+ s( @( e6 k4 N4 O
所求矩阵的逆矩阵为：
5 o% z% z6 l: x/ s2 F-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385 G; o( P, p( U, }/ N# K
-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189 3 H. S @' y2 K" z
-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835 - J4 j) V) H' w5 L( J; c& y& d" f. g
-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893
- d$ G/ O5 U7 A+ y-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893 $ f: i3 G' Y+ X% n' m8 N. t8 x
-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892
; w7 P# Z( c6 j# g0 d! g- s方程的解:
: ^2 A9 ~+ Y4 H! E# z0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815 $ Q, P* p6 x& e; [( n, g% s3 K1 l
新的电压值(e+jf):
8 `. f$ I) s: V0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328, 2 {' M" l! \7 b* u' C4 b6 F
===================Iteration k = 1 End =========================$ }1 L) A8 r9 v j
===================Iteration k = 2 Begin=========================4 V# o7 s7 P' j
P[0] = -0.00050
/ _2 q: |3 v, s$ qQ[0] = 0.00005- Z" ^' \/ S- I# C
P[1] = -0.49877
: o" g: l! ~" ]8 xQ[1] = -0.29567
) e% v. A; j8 J$ qP[2] = 0.20071
2 Y4 [) X O+ ?! W3 @Q[2] = 1.10251
' z ] K5 k1 D9 r b3 s误差向量 p、q:- e2 N$ w# }8 v1 L4 G9 b+ X
0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483,
7 p# t& g" V$ o电流 aii、bii:
8 P5 E' [; Z& X- R* E! N1 m7 Waii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000
# I! }. k- _) C========================雅克比矩阵========================+ [0 P) U& w# o
-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000
. e) f. Q- G/ E) B3 [. a A-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000 ; g; T7 I9 K9 r1 ?: \5 ]$ \% ~5 c
0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
4 ?* `7 l7 K9 M; ?9 w/ [3 K5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000 & F+ S' J, X5 v9 e3 ^3 ]
1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000
9 }% m! J5 j7 K( c0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 4 m& l: c; W' y6 a/ k: `2 }& i% y
( v4 H* G" E5 U# n* s# E所求矩阵的逆矩阵为：
# N' y3 m# H, A1 H8 W-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342 - b- n, O) x5 A: D/ O4 C
-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058 7 z; c( ]! o5 V- T/ L% P
-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
- ?4 \7 g. z' B" n3 K7 p-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
. r& f L0 k8 |8 T8 v9 |-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835
+ a# _5 ]. V9 H" J: _3 L. K0 d, r-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478
* s/ A7 W$ m/ t$ c% i方程的解:
& L( o5 e2 a) `& T7 t. r2 W: o* H0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432
! G2 e1 P6 `8 c9 E% L8 `新的电压值(e+jf):
, h2 w* h( j8 t3 w1 E0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371, 0 E- I1 I' K. [) W$ v; x( M* ^& a" b
===================Iteration k = 2 End =========================
, q# K6 c+ b4 N9 S8 n===================Iteration k = 3 Begin=========================
: y3 p5 s0 X# y& rP[0] = -0.00000. u/ d8 o1 J6 B8 E$ N2 t$ x, s/ I
Q[0] = 0.00000! s, e* k4 ^' y/ c5 J* }
P[1] = -0.50000" N/ I2 p+ b' a* q9 ?8 A
Q[1] = -0.29999
4 Q1 f7 V2 W* FP[2] = 0.20008
. R5 H( ]9 O4 M. K$ `& [Q[2] = 1.102505 o. t' b9 P$ n
误差向量 p、q:
, [5 H6 G2 O, _- p0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, / `7 p h! F# G; {. |
电流 aii、bii:
' m' C) s. ^ V% w6 j& q! A0 paii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 / ?" B. L" m0 [1 ~. Q
========================雅克比矩阵========================
) x/ M( K$ r" G: o$ Q-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000 / s' s' r7 D4 k
-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
, L+ @) Q0 D! Z& W0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 , L& B- U+ \. t F5 M. i. W1 g7 {* o
5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000 4 L1 X Z; ?6 G0 A# J8 H
1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000 ; q# V1 C9 n9 Q) Y- G( G. A
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000
. W/ ?+ {6 o+ U, E" Z9 U* I
) q4 |+ Q/ \8 a所求矩阵的逆矩阵为：
2 p! B4 r/ A: T9 O; Q4 @0 h" ?& v-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393
6 ]; Z. p& \/ m' X* c- A" }-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 3 ]# E2 z* _' r! t6 M) W" `& k# g
-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
8 z6 J) Z l& l# l-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109 , C3 c9 f1 A( z: J
-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826 ) V5 F: p' ~2 r8 L( @+ }! A/ D# w2 v
-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453
+ l2 s/ J: \6 P方程的解:
- F) k/ _6 ? ]: \4 w( i3 ]3 e6 G* I0.000004 0.000013 0.000008 0.000014 0.000001 0.000027
/ K; e% v0 h/ k/ T, t" `新的电压值(e+jf):3 M1 F5 H0 W$ H+ M" k
0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373,
$ n4 [3 F* u3 h===================Iteration k = 3 End =========================
2 v Q2 D( ~/ e* d6 M) I$ M===================Iteration k = 4 Begin=========================
& v7 Q1 r7 a6 s4 O/ |& XP[0] = -0.00000
2 d/ s: C) e" ?7 y9 C! ?Q[0] = -0.000005 N+ u y& \. j# y+ |
P[1] = -0.50000. H/ }; y2 O' }" k9 D% V1 ]
Q[1] = -0.30000
" s' U. S% @. t; @' q7 W3 PP[2] = 0.200010 D) v3 E* r5 s5 C
Q[2] = 1.10250. {+ B4 d$ j. L( n
误差向量 p、q:
) X5 L% ]% |& E$ B' X9 M; l! H0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000, 1 L6 [$ K: \7 @6 [$ o/ b
电流 aii、bii:
8 s1 j5 S8 f" s/ D- M- f. h, ^aii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000 ) T! L. v" \3 V! j7 \9 F; |
========================雅克比矩阵========================3 P7 t+ S$ z8 H2 d, _: g* ~# }- a# }
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000 0 j2 u ?2 }8 Q; N4 y7 U* i
-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 # b: @1 {; U) @( W1 k ~$ H
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 . s2 F* D1 t+ S: ?6 w& z; T
5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 1 ~" E/ m# K1 G( z6 ]# r
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
8 Y, v7 P/ `' M1 a0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 ' ~' ~( X5 S+ K) M- y9 F: i6 m3 N. o
3 `+ |" G, P; ~! q8 K$ b所求矩阵的逆矩阵为：8 {, c# T3 Y9 e$ h: G0 r6 M
-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393
, ~' H. K3 K+ n1 c-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 ( [7 q U8 L- ]$ C8 Z5 |$ D
-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 1 @; k" L' `+ s+ R
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108
" T: k0 F: M* Z3 r* B r+ N5 J-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825 6 `! G% c+ q! I4 ^% @* Y+ z
-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452
9 @# d+ S0 U# S/ O& s方程的解:
- R! t- Y: n& S* e0.000000 0.000001 0.000000 0.000001 0.000000 0.000002 & e- B& k3 I# D: N" V
新的电压值(e+jf):* I6 \" J; V' U$ M1 z
0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374,
& c. p& [1 G( g7 s& o5 H' h9 o===================Iteration k = 4 End =========================
! y) @8 I5 K3 @' d3 n% G; d===================Iteration k = 5 Begin=========================2 e% W+ T* c* q/ ?$ @
P[0] = 0.00000( u G7 J# c3 O! T5 @9 k
Q[0] = -0.00000+ f, n9 S! X& j/ v3 [( K
P[1] = -0.50000
% Q- \0 z4 C! CQ[1] = -0.30000! Y- U D' L( i% |
P[2] = 0.200006 g3 b: ]- J1 L M( n0 Y. q
Q[2] = 1.10250& m$ W+ ?: A: Y" J. H+ H' V
误差向量 p、q:, x2 i0 J! Z/ @- s- e1 v
-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000, % v+ {7 b- t u6 e6 T# E) } S3 {
=================k=5时，结果收敛=======================3 e) P% A5 [0 k
================牛顿法计算共耗时:0秒:609毫秒========= |
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