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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:=========================# L1 O: z+ C) l/ L/ ~
2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714
5 ?) S9 g0 j' |6 r2 E4 g0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 4 _& H6 z. e* g6 c6 D' p& [
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809
, a4 a2 z0 t. ]2 L) R, Y: N-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092
; s- }( z5 Y$ g4 S#########################导纳矩阵输出完毕!#########################6 J9 K8 }: F9 w6 M0 D( p
" k$ g j7 Z% n- e/ K) G' Y. [- W1 X=========================初始功率向量输出开始:=========================
6 r8 C- P. f1 ~: D e; e" G3 M3 l0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000
3 O, v) V( h+ y3 B/ z' [#########################初始功率向量输出完毕!#########################
4 A. J, L) J. I( L* T5 M' L& q
z# E! d% u M4 ?1 p$ b7 p=========================初始电压向量输出开始:=========================8 Z- Z# V" A# R( Q7 P- }
1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000 0 o/ t W, S! s9 c) }3 g
#########################初始电压向量输出完毕!#########################
: T, W7 j: Y. ?6 _( H
7 U6 j1 M# ~3 ~5 x) b% Q$ k===================Iteration k = 0 Begin=========================, {0 Z" H D9 z- `( R. u; x4 |
P[0] = -0.145255 z4 z Y; Z: G n7 q% O
Q[0] = 0.37497" o2 Y9 J+ h. y* ~
P[1] = 0.00000
0 Y$ m5 O# V- U5 O; sQ[1] = -0.65434
' `% y3 R, E# V. @P[2] = 0.08715
* L# L: H3 o' H+ ~4 j. s+ s+ s: G) XQ[2] = 1.10250 L" [9 D2 H2 @7 w! a5 I
误差向量 p、q:
" O! y2 c, x5 n+ J0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000, % F; a" A$ Z: I# n6 {3 O" T4 L
电流 aii、bii:
' T7 h! M3 [: P! F4 w, Yaii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000 4 V8 m# O7 [; a: c; d
========================雅克比矩阵========================0 i" ]3 y/ T# d1 j( Z
-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000
1 r" V$ C, P( }# {! e, L$ t-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000
P0 r" w1 Q$ i; J, D% h0 K; ?' Y0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
: F! C( J' X% T0 N5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000
5 Y0 L. Y& _& S' @1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 ( q9 M/ ]1 T& E; }
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000
' t5 c3 ^" X0 R; ^; Z$ a' k D4 S# ]" R+ d9 g$ H
所求矩阵的逆矩阵为：
4 s* E; T3 @; A, f& ?) y( l5 q# W-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 V$ Y: ~6 Z+ [
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524 * l s8 U# Z. E3 K6 Z: C/ _
-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612 ! G( V4 d+ ?4 Q$ Q
-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524 . P" o, X0 o- v, L
0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619 ! ^% x7 f9 C6 J+ y, @! I: y& b1 `
-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965
' M/ _5 `9 y% U4 i方程的解:
. y, d" M8 {# M: E) w: x0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460 $ t1 ]4 j5 q* Z: q: ~$ G
新的电压值(e+jf):
- e: @5 `5 q5 Y6 s0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946, ) b( D9 T5 n. W/ M* O
===================Iteration k = 0 End =========================3 d7 S% p' T! R$ q- Y
===================Iteration k = 1 Begin========================= j# z) x0 U, g4 P
P[0] = -0.02835
8 B# [1 F3 x* V# S. m% yQ[0] = -0.002687 \0 B9 k( `' r
P[1] = -0.46151
' f$ [, C. t5 y0 q$ O3 K4 K; ]Q[1] = -0.20794
$ r( V6 k1 h `/ f. M: hP[2] = 0.20354
# G! h& a& y, ]3 s" m1 JQ[2] = 1.10337
0 K; K& W# g/ V, {) ~误差向量 p、q:
0 L8 v' R, Q$ W$ z0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787,
; J! [! t- i" D( R电流 aii、bii:9 V2 [' z& ?) D j, Y! i
aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000 * B8 |7 I& ?9 v/ ?
========================雅克比矩阵========================- K/ v9 A S9 o
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000
% X6 B/ z% k+ D& Q-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
* }. R @5 k+ G# |' Z0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
5 X5 |: J' A5 ?% ^; M8 A5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
/ V# j1 p! M: c: Q; L2 [1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000
& b3 {" {6 c5 ?1 d$ s: `0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000 : F8 ^$ R# s# Q0 k! j! ^8 I
# L# [! i, i4 c所求矩阵的逆矩阵为：
$ p5 v- Z* T9 @7 T: u4 _-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385
6 v0 A* o* s$ J K; v-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189
% h# s8 J* R. i-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835
: }- p; v' E9 d1 p2 d# R-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893 1 z3 v9 J& w2 N# X
-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893
) s% p$ v4 @% r5 \* B5 ^/ v9 a-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892
1 c( D& [2 r3 {/ K- V% Q: M T3 m+ j方程的解:
@5 _7 l4 ]% @ t. ^0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815
) b. A% m6 E; W6 q& _0 b- @. M- [新的电压值(e+jf):& A% G/ y1 A C
0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328,
; }- q7 F* Z; A( [===================Iteration k = 1 End =========================- J" x, ?* i6 B$ H4 Z
===================Iteration k = 2 Begin=========================0 {2 R0 e& S" [- W5 {! I0 g( E1 o: D' @
P[0] = -0.00050% R! g1 a& O$ \# r
Q[0] = 0.00005
' ^$ l; b4 }& NP[1] = -0.49877
6 r! f* C" m# T- y7 F2 cQ[1] = -0.29567
' Z* j1 X' t5 p+ b; lP[2] = 0.20071
0 A# h$ q0 M% }/ x: T }Q[2] = 1.102514 s% f. O, `4 G m' N
误差向量 p、q:
5 a7 a" u e" D0 j0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483, " A) q; d5 M) c) }. w( a+ d# ~ a% r
电流 aii、bii:; m- H" O9 J# y t3 E; d
aii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000 - h: ^& v1 [0 j- s3 s# _) C; h
========================雅克比矩阵========================
! [# K4 _, s* z5 v; w; c-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000 & u E$ x2 E$ m& x$ N8 a
-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000
2 x2 X* O2 `; F0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000
8 ~' e7 d8 N2 B6 J( {5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000
9 a" H, H7 b% |" c6 g1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000
; c1 C+ K5 n# w* v( B0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 + x3 l& O7 W0 A: h' o4 \
6 O- A. q' h+ g& q
所求矩阵的逆矩阵为：
' y5 u. w7 M' G! ]-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342 ; R7 W$ }+ T; i) X$ s, S- B
-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058 # M L: |7 W) L9 }9 M3 ^
-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
- j2 I: C5 k) V( U-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145 s, d% {) @ R' |
-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835 ) g" ?3 H/ j0 d
-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478 & }" A% f0 J6 I- [ |/ Z- Z2 d% V
方程的解:
# x% \8 B# z1 Z0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432 0 c1 w0 c: ?( p; Y: {0 d/ d
新的电压值(e+jf):
- i: o, R. T# g4 ]- e# h) d; s0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
3 j8 ^0 n7 a0 R! M* g; ?===================Iteration k = 2 End =========================
& T- e" c' q4 u===================Iteration k = 3 Begin=========================$ A. D, @/ p) a" g/ b
P[0] = -0.00000
1 E9 n. A7 w' b" q0 |. L& OQ[0] = 0.000003 F: c, _) U+ p Y6 q' p' d& Y& J3 E
P[1] = -0.50000
( I' ?) P9 O0 S5 T. j, p! aQ[1] = -0.29999) W9 m4 U- ]) e. u
P[2] = 0.20008
0 @ A+ s" N; M( ?% t$ A- D5 B$ `Q[2] = 1.10250
5 j) I4 x! Y' m* `误差向量 p、q:1 h$ d' f' c* x" ^! m6 }
0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, 9 N9 ~" n4 k0 X( y6 K
电流 aii、bii:
# y: ?2 E/ R. a; Uaii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000
1 d) U+ y U2 d% @4 C, r$ h. j========================雅克比矩阵========================, O0 p, ~2 L, y+ c
-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000
8 y( j% W$ n- M F: r, [) t-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
% |8 H1 u4 g( X0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 4 ?8 S( P" l" }5 A4 b: c9 ?3 I
5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000
H3 \8 B \. ~. b1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000 4 z0 Z7 A# G, ^$ Y9 W8 J: w
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000
+ O5 [# v) ?! S0 U3 Y* J Q- G9 R; U7 I S) I7 @
所求矩阵的逆矩阵为：
1 n) x0 X# g4 q4 K-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 # G/ |- j) D7 Q6 @
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
$ n7 W$ _$ O% X: W4 y/ y3 h' x-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
: T( K- m# v* V) C$ L/ ~ Y* o$ x-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109 & s5 ^( J$ y$ ]% A' I
-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826 + { f1 E! Q! D4 W1 d* @
-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453 : u0 t- O& Q1 l, B: j$ l* I% M- |" a
方程的解:4 Z, J2 a4 u2 l
0.000004 0.000013 0.000008 0.000014 0.000001 0.000027 / a s0 Y- b8 t1 b; V1 x
新的电压值(e+jf):! Y! G5 a+ f5 x
0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373, - l7 g2 `& U7 w
===================Iteration k = 3 End =========================! ?2 c3 q8 U% [3 Q0 b( R9 T
===================Iteration k = 4 Begin=========================" P+ F( J4 T+ Z! N0 s; \
P[0] = -0.00000
& n6 l% l4 G8 M( Q Q" [! RQ[0] = -0.00000
" C; W4 u! a: Q, a$ a( L5 zP[1] = -0.500004 r8 @! {& Q1 u; h/ T
Q[1] = -0.30000
1 r& G* `1 ?. Y1 @* z& gP[2] = 0.20001. n4 s4 u9 z4 r% J
Q[2] = 1.10250
4 O$ ~5 ?0 h0 ~1 I误差向量 p、q:/ O) B6 h. F0 D) x9 p" d
0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000,
( ~2 j* h" `/ a" j" { X5 I {7 ^- ?0 M电流 aii、bii:+ Q7 `! X- D2 R/ O# F% \
aii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000 ! H& I( M: H& v5 T2 A$ l F
========================雅克比矩阵========================- A& v% j" p& b0 F
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000 ) E6 R0 b h7 b5 O# K
-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000
2 @0 W1 l7 ?- b0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 / C' ]$ n: B. g6 H& O( P
5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000
! I/ a& @. I5 q3 D2 W1 T. P- c1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000 , }7 B0 E. w$ L' X6 p k
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 - ~( J4 t) d' O+ ?# T
# A% l& C0 `8 @# Z( q( f/ s2 ]
所求矩阵的逆矩阵为：
# D1 }- O8 k5 u; k-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 , G1 B2 G3 ?/ k, D9 f- k& e1 {* J
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 : {4 F2 E) D% t$ Z# k+ I7 O" V
-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084 8 U& r- u9 p# D: i3 z
-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108 |8 @/ }- e' M
-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825
0 X- c$ A2 c5 P) ~9 t6 e9 {-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452
5 H t; S" d) ^0 F6 {+ P方程的解:
6 q1 o2 V& A8 K- C3 G; s6 {0.000000 0.000001 0.000000 0.000001 0.000000 0.000002 ) ~' O. I0 t) V8 z# f0 S- A* P
新的电压值(e+jf):
* Q2 \" t( y3 ?3 M6 J) [9 P0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374,
/ L* H, X! ~) V; s* g) n===================Iteration k = 4 End =========================! F% f7 n& z% L
===================Iteration k = 5 Begin=========================
, p6 O. e9 [& ^4 S9 aP[0] = 0.00000
, k( N; w. t" a. c' G- S+ x1 V* kQ[0] = -0.00000
3 X* B# V" }, p8 C* d7 }P[1] = -0.50000
/ [+ i5 U) S1 ~4 L, x a0 d- [# T9 UQ[1] = -0.300003 A- o/ C- L4 W
P[2] = 0.20000* f$ b7 P' F: E6 ^, H& Y# D
Q[2] = 1.10250
- N% Z4 N9 u0 W, y9 n" \误差向量 p、q:
g) R. l O- @ t0 s3 H6 |-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
6 m2 @/ `! i4 z* p7 b7 g=================k=5时，结果收敛=======================
2 W; |3 O8 s/ v( T. U, w: c================牛顿法计算共耗时:0秒:609毫秒========= |
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