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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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=========================导纳矩阵输出开始:=========================$ _- k! i8 R$ i( Y+ E) r. _7 Q
2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714
* u! m$ R2 Z7 z* E$ M0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 4 |7 B0 O1 Y2 ?2 N3 x+ ]& m2 J
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809
: D6 \) j7 z! N& C3 _- j1 D-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092
, ~0 [& D+ E- }% s% Q2 v#########################导纳矩阵输出完毕!#########################1 ~8 f; o! i9 x
1 @2 G' J0 W& P6 n% w; q$ J4 {
=========================初始功率向量输出开始:=========================
' d5 k. W! E4 y, B5 _1 n% \0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000 # E( T: q) Q+ q4 k5 k p# B9 L
#########################初始功率向量输出完毕!#########################* T) L4 [" d: |& \2 ~/ B# D
* |. l& l9 O& s7 S, V" M
=========================初始电压向量输出开始:=========================9 \. \. \. t; g% I4 L1 u5 p
1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000
! @/ |2 Q9 q9 Y% M& K/ G#########################初始电压向量输出完毕!#########################- \7 A3 @/ o; G5 F, {
, |$ Y/ @% ]: i: J===================Iteration k = 0 Begin=========================6 W: R/ @- ~8 j' U1 u3 K
P[0] = -0.145253 @ A/ N" D0 q- o) u! z
Q[0] = 0.37497
3 C! g/ a$ O# N( @3 c, zP[1] = 0.00000
' E: R2 T# E9 w5 W# t g' C( bQ[1] = -0.654348 Z3 J6 I- H& e2 Z# E
P[2] = 0.087152 Z. j, P2 |5 L3 F6 O" Z0 w
Q[2] = 1.10250
+ R. j4 r% K) j+ `: V" t8 ~误差向量 p、q:0 U0 `& Q' o: ?& t
0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000, # ~4 T$ K5 O1 H& }3 x
电流 aii、bii:) [8 R6 a( \% v! w1 k7 N
aii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
7 V/ D+ X* [" d* w% Q========================雅克比矩阵========================
; v" I/ o" k7 A-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000 / r) T$ e/ ~8 O# Q- W
-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000
4 K# c7 ~: b, A) ?; [1 ]4 X0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
) z& Y+ ~) `! U9 ~7 i5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000
& I# K4 ^8 {- |1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000
' Q/ p) @' `% k% {0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000 ( g ~' x0 \* ]/ C7 J
2 f: ^+ C- d" m; R8 x2 ?所求矩阵的逆矩阵为：
$ K; s) E4 j' U0 i2 q& J. |4 ?- S4 U-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 ' A$ X0 Q2 C9 |$ r
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524
, O, i2 a& I5 a+ N4 h, g6 G-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
5 V8 \4 w& c+ W1 ]& F, g, ^6 n-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524
* U! B* |* `3 _" [4 S8 U0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619
# ]6 I4 Z G' Q) b. e4 B- }-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965 % z3 @$ w$ i( O4 Z H+ D
方程的解:
* k. l' m) u0 G1 K+ `0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460
! N/ c8 Y3 P" ~/ e6 |1 @新的电压值(e+jf):# E$ [6 G5 Y) S3 G- k4 d2 L. s
0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946,
9 h, n. E! p% A===================Iteration k = 0 End =========================) E. V9 a/ E2 P( N2 }9 W/ Y4 \; P
===================Iteration k = 1 Begin=========================, k8 ^ x. C: ]6 K g
P[0] = -0.028350 ~; K# ^4 B% n# j# U3 O. x
Q[0] = -0.00268: \6 T5 Z$ N; F# X: F; v9 Z
P[1] = -0.46151. c2 Y7 `$ n: b3 c1 e u
Q[1] = -0.207946 W/ S2 C' _8 T: v( T8 p% I4 c. T1 u
P[2] = 0.20354
; R/ D# ?& u: H" j, i& o& eQ[2] = 1.10337
. }" K# |7 o% U误差向量 p、q:) y$ S1 F+ L: M( ^9 E8 J
0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787, ; g ]; U; C/ k/ }; z1 p
电流 aii、bii:. Y i1 Y0 [% k. u' O- @# U% p
aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000
. \. J; r. h0 _# j========================雅克比矩阵========================1 {) y; `8 r6 r N S
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 1 D2 Y% Z; C5 @* ]
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000 7 x$ F& e, F) v3 j
0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
% l9 ~! [' m8 f5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
9 |4 C& r: p9 C! s/ V1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000 # ~1 ~ v L8 P& \! W1 ?
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000 ! C$ E# L! L. }' |* i
% N0 [) W8 Z$ E& W所求矩阵的逆矩阵为：
9 @/ i v _. m1 O+ S" r6 Z* \- f-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385
% l. L0 D# m/ D1 S-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189 0 H- Q+ z: T' Y- E8 a3 e
-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835
; _8 u3 [: S6 i* l* `1 m-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893 & N' K. [+ U/ [
-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893 I, @" s7 ?% y! B; b
-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892 0 L4 H" C" T+ B- \; b- N+ \
方程的解:& O5 o3 e! q4 k* ]7 |$ }
0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815
9 t8 ?# L6 O% w0 C3 I8 M/ E% `新的电压值(e+jf): _) m5 e, Y ~
0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328, 7 T7 N, y3 E; P" K% g; I
===================Iteration k = 1 End =========================" M) R" l# S. c3 S: N' L F3 U
===================Iteration k = 2 Begin=========================
/ V! ]- v4 ~% {P[0] = -0.00050
' g+ b* E. p& z1 p6 ?Q[0] = 0.00005
. X4 c; }* h9 v r3 B; {* r- B& [P[1] = -0.498779 N7 c# `- `6 P7 d5 m# [0 k
Q[1] = -0.29567
% \' |( i, F1 T9 b: rP[2] = 0.20071
6 ?+ o5 s" a2 i& m. e) N5 LQ[2] = 1.10251$ s5 u; J; G6 `. @2 A8 n2 c
误差向量 p、q:
: R8 e3 a5 b; F0 l' l0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483, : N8 V/ l. Z9 P
电流 aii、bii:
( W3 C$ e$ c. V4 q1 u6 f6 Paii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000 ; s- b9 o# D: `
========================雅克比矩阵========================+ F1 Y$ F4 P1 w/ N
-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000 * I4 ]9 [- Z( o$ {- K4 @
-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000
- v6 M% X3 F6 e! Z, ]3 v- i0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
; y; w$ \5 x- A& ?/ [$ G* e6 H3 ?5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000
0 z% O5 f0 F6 Z J7 ^, u3 D8 T1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000 4 q. Q- M! F1 q( Q8 }9 _
0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000
: M" @2 x& I; B; K/ ~( ?: u8 O9 a( s7 c3 p
所求矩阵的逆矩阵为：: A- T: r J _* o7 ]4 V
-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342 - n! ~# U) b/ Z2 A
-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058 % g# p0 y0 O9 b0 V# G
-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
4 U6 l/ H! J( W-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
: D! U9 Q- f8 i4 J( ^9 v$ {2 z-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835
; O) w7 I0 ^9 D-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478 7 x1 Q: ^6 s" l& D/ a7 J% P
方程的解:
' a8 r3 E$ O! s, m( n9 U0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432 $ T9 o) N# U% g( z) C7 K4 U2 o& u8 e
新的电压值(e+jf):
3 P' C( M9 {- t- V0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
$ C- H5 x; y9 F3 y===================Iteration k = 2 End =========================, T+ y! d: @( ?: j6 M5 k
===================Iteration k = 3 Begin=========================
s$ N, \) m2 s/ }7 ^& JP[0] = -0.00000
0 f; } I4 ]: V$ E" `* _) A5 W$ X: @: rQ[0] = 0.00000) u: w, S1 z g6 q
P[1] = -0.50000. {( k# g) w1 z2 j q
Q[1] = -0.299996 J1 ~" Q2 g5 R6 k; v& |4 c
P[2] = 0.200082 ~* T1 _0 B1 m3 v
Q[2] = 1.10250' r. Q9 h+ A8 f4 K! P# G! B( Q4 Z
误差向量 p、q:, q: V% \2 _# r- d! V# P1 k7 A ~0 U
0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, , N* d c* J5 G
电流 aii、bii:( c E0 ]5 Q& C. B$ P& G
aii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 ! I( j n" o: D0 I9 I p; P2 B
========================雅克比矩阵========================
* v& t# L0 A: p& I-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000
. T$ z) s$ ]) G0 ?1 e, F1 z-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
% M+ ?5 F; O, q @6 y' ^0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 / K! L/ D- u- `0 @* }, Z# |
5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000 * W; n- L* ^' i8 O. G
1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000 " K5 o$ l. \. S
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000 & X; k; e4 a7 t, ^- P& A! \* ]
: c- n) N9 n: j# n% D所求矩阵的逆矩阵为：
0 Y% f% ]: ^1 e' X$ [ p-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393
5 J; B+ r9 x( w) v8 b# @-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
: D/ _( X$ C. {7 W m-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
( d% p h# g1 c4 E3 K-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109
. o2 d' A7 E6 c8 G-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826
( ^! j/ T8 [7 ~1 p& t& R4 |-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453 8 y, Z; y5 m% ]* z& O8 c' f) R
方程的解:
2 q7 y; Y1 ]5 p6 K+ e- A T0.000004 0.000013 0.000008 0.000014 0.000001 0.000027
, h7 p! b0 O1 `. A新的电压值(e+jf):+ @$ W/ v, ?/ M
0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373,
4 _+ [3 a0 P1 J0 m/ E' y===================Iteration k = 3 End =========================
9 @) I: L% V0 F$ `. j7 T9 o===================Iteration k = 4 Begin=========================
+ Q; T+ ~8 ?5 i5 D8 D; dP[0] = -0.00000
2 ]( [; ]$ p1 Y$ }0 m; E8 RQ[0] = -0.000004 i& x, `* x7 c0 S9 Q: T
P[1] = -0.50000
8 s" ]' W3 X+ R1 t0 v. GQ[1] = -0.30000
" m C# z& g9 G( rP[2] = 0.200011 T/ K1 _' q$ X4 m$ o4 m/ v
Q[2] = 1.10250
) ^6 H- s$ y4 L% [, ?% j误差向量 p、q:
4 R. g8 t2 B4 m2 C9 o" `% A0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000,
# t. ?6 y# t3 E3 A D6 J电流 aii、bii:
9 S7 k' O" { N0 c- ~6 u& ]# C* xaii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000 0 ~6 u @: F6 E/ R8 G" L
========================雅克比矩阵========================2 A J, h5 V- _% N9 O, y' F2 A# Z
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000
7 s6 L2 R J' L9 d4 _* X/ {-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 + R3 g2 Q8 F7 a. { K
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
% g4 e7 ^6 @" H9 [5 v5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000 6 p3 E$ C3 E: v" c, D A
1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000 ( ]3 n2 K8 F% b& ^
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 & Y8 i. L7 w: z, D4 I* [
, e8 p [- G/ R
所求矩阵的逆矩阵为：
) Y) B! k1 }3 ?4 i) V4 n2 l$ m; O-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 6 L7 a- F- P$ K$ I% w, H
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 6 I. I; n; R. Y% ^
-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 6 G8 |$ x# K8 M* ~! p- T
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108 % s9 N) C: E# c
-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825 1 ~9 { e/ B9 }5 Q
-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452
, @" g+ R% p1 W4 K3 l方程的解:+ A" H# M. w* E" L3 P0 G
0.000000 0.000001 0.000000 0.000001 0.000000 0.000002
?/ n0 l# R, p& j新的电压值(e+jf):4 [7 D6 x: ^$ n4 K7 I; C
0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374,
/ Z# Z) H1 ~: l1 d! X===================Iteration k = 4 End =========================
( g! y5 o. K7 \) b; b===================Iteration k = 5 Begin=========================0 t) \& F3 X+ |8 D9 V' K9 D$ [1 W* D
P[0] = 0.00000! D" J) ^# z9 B; `9 k3 \
Q[0] = -0.00000* O) k! J2 p- e, p
P[1] = -0.50000
! ^' `/ l' w) k' J& ]Q[1] = -0.30000
( Y$ ]. l2 E! I6 e/ ~+ {0 D3 {P[2] = 0.200007 x5 I+ a1 T: q3 J( V, h8 r
Q[2] = 1.10250 c$ v% D5 I! V$ W+ G5 e2 l
误差向量 p、q:
" B0 r2 R" N" q7 x1 Q! i-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
- Y/ m. O# _; j=================k=5时，结果收敛=======================
7 r& D+ [# _( r% r1 M================牛顿法计算共耗时:0秒:609毫秒========= |
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