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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:=========================
* ]0 d Q, G$ ?7 E7 ^( t2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714
& t7 i9 q! u9 L0 S3 ]& d- Q0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 . B) b+ w6 T: Y' e5 s& B
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 ( B) q; e8 x6 K* @
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092
/ F: \- f) H T: l#########################导纳矩阵输出完毕!#########################
, b6 k2 Y1 X* N5 G6 f
o( Y5 F; y. Y4 j- j=========================初始功率向量输出开始:=========================' h& a# Z/ w( T- |% R( h2 `3 t
0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000 * ?/ P1 {; C% K9 @9 y7 t$ v9 G$ ~
#########################初始功率向量输出完毕!#########################
5 x' q+ H3 g8 K2 @: u( g+ Y/ r0 }& b6 i$ B
=========================初始电压向量输出开始:=========================
5 S: g4 C% r" p1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000
! H/ e1 s2 ]( j: w' i; ^' ^/ G2 m#########################初始电压向量输出完毕!#########################0 C7 f7 o6 K% h+ _1 [
- P* C- k0 h) o+ J1 v$ M
===================Iteration k = 0 Begin=========================
Q' q) W0 n$ r2 Q* J8 QP[0] = -0.14525
1 d5 C- h! K: H( ~( x: S" P4 n3 fQ[0] = 0.37497
3 s' V7 ^8 K$ N4 T7 h* t5 ^3 Y+ F& ^P[1] = 0.00000 R, g! \% c/ O0 K
Q[1] = -0.65434% f! X2 v0 l5 \% |
P[2] = 0.08715
+ o t1 A- i, {# o" aQ[2] = 1.10250& S4 _# U! V* `- [$ d
误差向量 p、q:) C, Z: z. x$ x; e+ Z
0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000,
# m+ t% S M4 l. s m2 j3 u0 s" A电流 aii、bii:, a3 I/ E* l L
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
( x) u- U2 G- H! ]========================雅克比矩阵========================
' K! u( k- G) v; s. J$ b-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000
0 X$ g& `5 f5 H4 E-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000
" Y, h/ [+ X; |7 g% j$ U+ T5 y0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
! K% R5 Z8 V- j F; g3 z3 B5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000
' l& W' j/ o+ W% S+ m# ]1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 4 H" Y! _6 o1 K7 b" |8 I7 i- s
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000 % g) ?4 B. E! B
; |% ~9 `4 M; R
所求矩阵的逆矩阵为：
: Z% A+ Z" z, J-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 & ]3 y8 k7 W$ H0 k4 W4 {* a
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 . T- ^! u7 j( c# e C: m" E
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
z$ n/ [, O( A. U-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524 & v: \% M/ P" W& e
0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619 4 l [) m- O4 {2 B: n9 ?
-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965 # V# t. r& _2 x
方程的解:! A* N3 I3 @& P* o7 w; N1 W" I' i
0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460 / R- Y: d/ ?. P& P) [4 N% `. B. p
新的电压值(e+jf):
4 s& l1 Y) h% X) s6 q) [4 N& z( }0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946,
7 E0 [2 v2 d* o* d6 }4 z) p3 p$ {===================Iteration k = 0 End =========================, w$ U! \1 C1 l) H4 b2 b
===================Iteration k = 1 Begin=========================
9 A6 u9 O- u5 N: k* k- ~P[0] = -0.02835
. C s, Z2 p( S; A; T2 S* pQ[0] = -0.00268" y! h; l; \5 E2 U4 [& `5 r" R
P[1] = -0.46151. ~! C' x o& i) t |7 _
Q[1] = -0.20794
5 I+ r' y2 ~1 |, N1 z; nP[2] = 0.203547 N9 o3 W2 k, v; B8 w; s1 i/ S
Q[2] = 1.103374 S. u" ?9 g+ P: `3 Z4 ^
误差向量 p、q:: V- R" s! }1 k4 F
0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787,
# c* e3 x$ E+ z5 ]$ [. q; z电流 aii、bii:0 d( D! \: f. v3 x( v9 |% D. H7 o
aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000
: e* h) d+ O1 }0 e, e========================雅克比矩阵========================) M- R7 b1 E4 w: ~: C5 G
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 & H) c+ v6 R; F! _6 u% x
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
8 v8 p- f; R& m3 g& K0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
6 f5 q& E, R: p9 b5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000 / s* T, [% s% i4 K
1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000
' E) C) d2 D. Q0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000
- m7 I6 y7 P) G+ [# B+ a4 g( a$ H" H1 ?, B$ G1 U4 Z
所求矩阵的逆矩阵为：! }' T0 j9 `& ~9 P. n" ^& c+ Z
-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385
: Z7 M- ?; P1 i+ N& k8 n6 |# w1 s-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189 `8 `; M ]$ }% A# v7 w
-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835 7 }% p6 H9 @6 e/ H
-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893 ' H4 s9 \# Z9 i7 ^1 C
-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893
+ j1 r, k/ l3 l" k. p; _/ Y-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892 ( `' H3 M& h6 j. H" U% {
方程的解:
4 A0 Z5 C/ ~- s. Z$ p$ B0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815 # A7 v% v4 ^7 m2 e
新的电压值(e+jf):
G% `5 A* c+ V U0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328,
- u- n) E2 K! X1 ]; {===================Iteration k = 1 End =========================9 Y* C6 L% S, m# x( {4 c) @
===================Iteration k = 2 Begin=========================/ m" q9 y- \3 l. l( B6 ~# d6 U9 y
P[0] = -0.00050
5 F' `8 Y$ }3 r% V4 T% oQ[0] = 0.00005
' Q: ]: t# S4 b/ R4 aP[1] = -0.49877
& k8 s, ?+ G& {- U1 v+ \Q[1] = -0.29567% i! R" U9 y9 O: ^5 e( s
P[2] = 0.20071
& \ J1 Z a9 x; k! ?Q[2] = 1.10251/ {* \4 H" y- c2 {, b, M; ^1 F
误差向量 p、q:
5 ?; k9 u% L+ q, g0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483,
$ Z t+ D& U: @, J$ o5 z9 L电流 aii、bii:+ y* b% [7 H# @" c
aii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000
3 {6 r2 m" S1 z# D; u x========================雅克比矩阵========================5 B1 S/ v3 W* d* Y3 g& {9 H
-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000 1 S! P+ E& I& @9 d! K4 n C/ n
-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000
- _1 ^* t" q# C* ~0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
6 J8 L: J( v1 ^5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000 8 y: Q, T& |! Y1 v+ u4 h! o: K
1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000 9 |, \8 _0 \& x% {6 s4 g
0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000
! A: ?% ^) i* o# t$ V! ` ]# M, G/ h8 M! U8 P) D
所求矩阵的逆矩阵为：% Y1 k( K0 {( B2 W
-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342
5 B, I& {: H; U/ N/ Z4 ?-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058 6 y- \$ y1 H5 }/ U$ F
-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965 a# V! ~1 y0 E8 {
-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
7 A Q4 C# d3 h3 _$ o7 E-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835 / y9 _, y' [9 q9 a. s$ N. F4 @8 Z
-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478 + p! s$ _1 P$ z5 R6 h
方程的解:* ^( R! o. o4 t
0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432 3 R) w* G" M8 K# ?7 l1 m6 D
新的电压值(e+jf):
$ M$ u. p! q7 _/ q/ N; R- r! e* N0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371, 9 w: R- O7 T8 S; Y/ c
===================Iteration k = 2 End =========================
# V. X- T% y/ z% j4 I4 X0 r===================Iteration k = 3 Begin=========================
% X4 {. O3 O4 g7 r' M2 xP[0] = -0.00000. \! p8 g4 q5 z! U$ D
Q[0] = 0.00000
+ e7 Y0 ?" D' L1 l2 I1 ]P[1] = -0.500001 Z9 `3 G' y) F8 b# r6 V
Q[1] = -0.29999
% |& J" Z$ ~5 F' j+ [# qP[2] = 0.20008
7 C/ h6 V- ^ b' z/ p4 [Q[2] = 1.10250* S& `2 Z# u: U" l% ~) y6 I
误差向量 p、q:: s0 ]$ }% `: @) G! F* F9 w1 L
0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, 2 N. Q2 E4 c' y. k$ ?
电流 aii、bii:
1 z& T5 ^- |& p% J5 r, p2 Oaii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 / c1 f- D' G$ E- X& w
========================雅克比矩阵========================6 v1 U( a# r( d' X& I7 f, i
-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000
9 B3 N% u8 Y" A( \+ s$ y-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
( Q% _: C7 n( Z, u) a- K' t0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 ; t% M4 ~& c/ J5 O" ~" ?: ~2 X
5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000 : e0 M5 {6 w D4 L
1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000 , j% g; J# M5 U1 i) Y5 h. X4 m' M0 h
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000
, A0 h) J$ C- h7 J( o1 L: g
t3 Z6 `. k# q- B9 m7 V: m所求矩阵的逆矩阵为：
" d# n1 v) G* L8 W7 l-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393
& Z0 ^% Z' Y" \) f2 d6 k3 J-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
# ^. x- N/ F1 Y. k* J/ ]0 W0 }-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
- d& T- J# Y/ E( [1 \-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109 + L; ^9 \: K; C- N9 y0 a4 d
-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826
% I2 ^& E: |% ]8 a. H-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453
# Y3 d3 ~: p X& N, B2 W方程的解:
; v, ?6 o6 C% ]* i0.000004 0.000013 0.000008 0.000014 0.000001 0.000027
$ T% ]7 J4 H8 R3 Y0 A* K新的电压值(e+jf):
a) X' S/ {9 X0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373, 5 L- u s* e3 j! ?) r
===================Iteration k = 3 End =========================( M( R, k( l( y5 G) T
===================Iteration k = 4 Begin=========================
: ~; Q. g4 H; S7 N. x) R Y3 TP[0] = -0.00000
5 w0 y- o. l' ^7 zQ[0] = -0.00000
3 T5 R3 Q+ A7 l$ s* a' [P[1] = -0.50000$ E V9 y! o6 E! A
Q[1] = -0.300002 E" ^9 {# Y9 ^9 E
P[2] = 0.20001
, i* ~! i+ `, a5 ]Q[2] = 1.10250. W! k3 b; \0 J! }
误差向量 p、q:' V( a3 y3 G& i
0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000,
" y+ A" P+ g0 d- w电流 aii、bii:
+ T- v- I5 M+ d6 D/ h: h, S4 Faii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000
* y) R7 _8 M6 J& a========================雅克比矩阵========================
5 n3 t' O5 d9 f7 p3 Q* p-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000
& S( k" h) P6 ~-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 V& }0 y$ V! e8 P# d6 O
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 % R7 R) ^8 R! |/ O
5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 * I7 J, d' k) z' o0 L8 C7 {
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
7 n! ~% @2 G w/ o- w9 N4 k, ?0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000
7 \8 @( ?% g/ z/ c9 R
& t8 {( F; o `2 ?; s7 r( [9 r所求矩阵的逆矩阵为：
; f: k4 j1 j# M-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393
4 Y+ r. F* ^2 J3 [+ T1 f-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
1 ?% `' W0 L: ~. c8 J-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 + B1 _& r, e/ t
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108 4 r3 P6 v, G S9 n3 q
-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825
5 J$ E" }, {! c; e N' p-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452 $ Y$ `0 \$ d# ]. L
方程的解:
! I; @. C, g$ _( u6 k& }6 Y0.000000 0.000001 0.000000 0.000001 0.000000 0.000002 9 f; t+ r) e. G
新的电压值(e+jf):( C2 z# Y* B' m& s2 b
0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374, 1 g% q: W* L# d. o& ~) T: E$ m
===================Iteration k = 4 End =========================
8 q: r1 @1 J1 U p# I$ ^1 L! B===================Iteration k = 5 Begin=========================
; x8 Y* C7 u# aP[0] = 0.000001 l# O1 A2 H' i* J, V* `4 u
Q[0] = -0.000009 z4 Q; C7 v- c" i6 z+ o
P[1] = -0.50000
; Q5 C. `6 B$ nQ[1] = -0.300005 `; l; ~: h5 W$ m
P[2] = 0.200007 q0 c B7 ^! {
Q[2] = 1.10250# e8 g1 y# b9 Z0 q) ?: S2 b, h; m
误差向量 p、q:* p% [+ s) G3 k4 G
-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000, , S* E ?* h; c$ F
=================k=5时，结果收敛=======================
6 U6 k3 M& I! t+ c================牛顿法计算共耗时:0秒:609毫秒========= |
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