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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:=========================; \: {# q, \2 f% c% i! `9 e
2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714 - o; L: U( x( C% V
0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000
( O* c+ g! g6 c; A1 {1 y-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809
9 B, R6 W+ T5 I9 s2 X-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092 8 X8 I( O8 s" D& u: t' r
#########################导纳矩阵输出完毕!#########################5 G6 r2 u7 [' X
, ?/ ?! o. D: T7 U ^( O=========================初始功率向量输出开始:=========================+ d3 r( X: }( q+ c
0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000
) _! j+ P: E; g# R3 N#########################初始功率向量输出完毕!#########################
+ j( _8 p# M. f( M5 _9 E2 V
& z( v: _1 [4 H. }+ [=========================初始电压向量输出开始:=========================
7 U2 \6 }: V/ q3 \8 m1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000 * w4 Y) ^$ P* e, |. [! e
#########################初始电压向量输出完毕!#########################. m6 r/ ], p( S; ^" w; q
7 g: k1 a2 `' P6 e===================Iteration k = 0 Begin=========================! T8 Q) w' [ A2 b S2 S
P[0] = -0.14525
8 e4 o9 w% _- p+ s7 [Q[0] = 0.37497
6 W; N) V" c! i$ w/ D8 p2 TP[1] = 0.00000
& D8 V7 R" w- fQ[1] = -0.65434
$ ^& k. V3 G' j7 s0 H, BP[2] = 0.08715' L; @0 J% q6 M* g
Q[2] = 1.102507 n, V7 E* X- W3 z/ J9 E, \- n
误差向量 p、q:
" c v! @ f1 r# ~& \0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000,
2 H- H' H$ m e; P, _电流 aii、bii:
. O- l' \0 x+ A* oaii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
- m* D* D) m2 H3 j2 |2 E========================雅克比矩阵========================
- C; G% A0 D$ C) s1 G Z-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000 1 L# }# L+ L# P9 s! r
-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000
( C. K# ~9 o" \7 z9 c! A0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
3 R& w {2 o. I6 o8 G, w; C; M5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000 ' a7 j% J8 J# u6 b7 V% K
1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000
2 t; b1 ?$ a* m5 ?$ w& S0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000 + g w# s- W) \- D D, ]5 [
7 ^* I' u- w5 v Q2 D0 K( s: u所求矩阵的逆矩阵为：! o$ q( k5 G3 O. C7 t
-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618 3 h) S9 Y' m5 b! k
-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524
7 z B. g" P$ ^: d1 s4 c-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
4 E* w/ L8 p9 ?7 o9 l( b4 z-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524 & K0 y- P. K* d6 E( |8 H
0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619
) ~& k" z; ^- V; j4 c8 x. Z2 S6 T. {-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965
* ~, v5 D) s# Y$ c方程的解:; O# C9 V- G9 c6 W& C& z4 T; n
0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460
0 ?# ~2 j C% Q/ S新的电压值(e+jf):
% T3 M6 `5 C! \4 T/ {. y& _# m0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946, " T G3 V! X" {7 I2 o/ _1 g/ u
===================Iteration k = 0 End =========================
8 w, ~# J, D5 q- o( u===================Iteration k = 1 Begin=========================: F) v' n% |7 ]- h6 ?& ^8 ` ?$ J* I
P[0] = -0.02835. t) `( K0 s6 E
Q[0] = -0.00268, @9 q# }/ l; G0 o& n( w( O: J
P[1] = -0.46151
. Q N' C x8 P* r# \% _Q[1] = -0.20794
7 _7 c) o" z( [$ R- EP[2] = 0.20354
% f& x1 E5 a6 N' R% |- ^Q[2] = 1.10337- P O* g- c! j2 Q
误差向量 p、q:
; x* o9 x0 t/ A3 v& N1 }6 W) F9 s0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787, 8 _) J( ^& q. b$ z
电流 aii、bii:
6 G; R3 G" U1 f3 g1 [: faii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000
: Z! K8 |2 ?4 N% b6 D! g========================雅克比矩阵========================, E: S8 o) ]3 t) l1 P" Z/ C0 P
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000 # \( a* X, X8 B1 D |
-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000
8 U8 L" t: M2 m2 x0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
' {) @) C. m6 V" s/ E. z* [5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
6 V6 j9 o, V9 Z1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000
4 D& g7 l4 A' T0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000 ' t s& v' U4 K* i
) W) i4 m: K( m( R7 `所求矩阵的逆矩阵为：- ?( w- M9 o3 {' r% I4 b$ v- H* k
-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385 ! i( b0 p" k- t+ J
-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189 " h0 w& S5 t6 ^6 j5 ~
-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835
: V0 e- J2 G/ k: F7 w# h/ n-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893 ' `( K/ V D6 l& b3 c' [& r
-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893
5 a' l3 i9 b4 e-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892 & T: t2 O$ |& A, o4 E
方程的解:
2 N; c% [9 u" w# j1 w" v0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815 9 G$ M3 X9 v8 s6 I- a4 D
新的电压值(e+jf):
" s9 M2 t% _$ ?+ l9 q0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328,
2 l; Q5 X9 g- A; K===================Iteration k = 1 End =========================" P1 G: c/ [8 @
===================Iteration k = 2 Begin=========================
+ X7 P0 n/ [" o8 P/ ~- qP[0] = -0.000504 B4 u$ v7 ]' g$ W8 B! t& [
Q[0] = 0.00005
' j" c9 ^/ J& S+ a5 XP[1] = -0.49877. F/ O( Y/ I' O* Z2 s7 F8 w% o
Q[1] = -0.295679 E: i% A7 L& |% R
P[2] = 0.20071- k U [' S" y3 U
Q[2] = 1.10251& f8 a% _) r& g# o3 P+ ^' W4 i/ A
误差向量 p、q:
% a4 d8 x1 N2 z3 M0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483,
+ Y' h1 P! p( f, S# ?电流 aii、bii:7 w2 A/ w- N9 U9 o. O
aii[0] = -0.0005202507 bii[0] = -0.0000131695 aii[1] = -0.4275816134 bii[1] = 0.3570182626 aii[2] = 0.1577813702 bii[2] = 0.0000000000
! f0 o/ u; v7 h7 X1 M* o========================雅克比矩阵========================
4 x/ {) {9 G9 K- o0 p-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000 ; }6 j/ A/ _& r% N: j
-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000
% }! S5 m# ?: G+ l& E9 D0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000 6 Q0 D h- U2 {& Q; t
5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000
7 w S& F, }) T: B8 l1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000
( X9 k, Y+ ~: {0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000 - \* [2 t* ?6 c2 i
$ d6 H8 W8 P4 R o所求矩阵的逆矩阵为：
$ s$ J% {) e( i-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342
2 t8 X7 M: ^6 [3 t& u-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058 2 M; L3 Q* m' @3 B1 j- E1 K
-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965 7 \: L, W' T1 [5 B
-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
* W) z, p7 M; h2 t( h* u; C# o% W i-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835
5 d) D: s* p" V/ a% d0 |-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478
: X; {3 b$ v9 n方程的解:
- c. o: i2 k& \$ c, Q1 t9 ^9 \7 t) R* B0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432 1 e" F9 B- x+ n$ T- y% V+ _
新的电压值(e+jf):/ d3 P0 r2 P8 l6 N: t
0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
7 |" r3 W) p) Y9 D" w- l===================Iteration k = 2 End =========================
* n& Y1 z- R; j* o# }6 S( d1 v7 {===================Iteration k = 3 Begin=========================* ^+ s7 A- o k8 O/ h8 \
P[0] = -0.00000
- _& R* J2 p. Y2 Y& E9 k0 H }; D6 j `, `# GQ[0] = 0.00000
% f& p5 G, N: u: l( |P[1] = -0.50000
' P1 a6 b" Z' \4 h+ B/ XQ[1] = -0.29999% t9 k$ \$ _ T! Q
P[2] = 0.20008
' L) g( ]6 v$ _7 ^1 o4 KQ[2] = 1.10250
% b" `. F$ T$ y3 b2 P2 ^误差向量 p、q:
. Z4 r$ E" D! M5 b. E. p0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, . ?& v' s- G1 C; [, c1 \0 f: _
电流 aii、bii:
/ U2 e2 B5 d, P* Zaii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 a. {3 U$ U2 C0 N
========================雅克比矩阵========================* q: X7 m# @* r5 P
-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000 l: c* ^( [: E
-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000
: Y2 B! T+ k5 s6 ?0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000 1 F$ H: W7 Y, P8 R3 z: n$ H
5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000 ; _8 D0 V( x) W2 j: Z
1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000 ' a' L6 O" ]7 ~/ p/ Z o9 M3 H
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000
" T0 G7 H" E6 L& D1 n' w. ^
7 w6 E$ r" \$ Z" h- C( X1 {0 T所求矩阵的逆矩阵为：! |* W5 ?9 V! q. {; b- B+ m: P
-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 $ E% _5 p8 j0 Z2 F$ b% ?' b' w' y
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 9 J' U# w, G! Y/ R# O2 T) F
-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
/ D; a: [3 @) E-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109
0 L7 U: S6 o- P. _" Q3 @. R2 w* l-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826
& g1 i2 k* h' W0 l" ^2 {4 v-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453
# L" G0 N6 L+ R/ {6 A方程的解:6 E* t- D# q& r
0.000004 0.000013 0.000008 0.000014 0.000001 0.000027
# U/ |. d0 l5 g' ?新的电压值(e+jf):
- Y0 F, G8 |/ s7 q! V0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373,
0 b+ T; ] P1 N) y. r- M===================Iteration k = 3 End =========================% P& B# w) }5 \' r
===================Iteration k = 4 Begin=========================
% J3 h1 \- ?1 K2 H7 n! mP[0] = -0.00000) t$ ]) r9 J+ V9 m: O1 T/ E% D) G
Q[0] = -0.00000! R; Y5 A; w5 c8 Z/ e
P[1] = -0.500005 ^# D& N+ K; C* s4 c9 Y2 `- I
Q[1] = -0.30000
$ p9 H- A/ e( w$ A4 N. T3 mP[2] = 0.20001. s4 t8 @9 P k! I1 O' M6 }: C+ t% t
Q[2] = 1.10250
$ }1 ]: F% u+ l; d1 Q2 n) P误差向量 p、q:
+ n* `& c' C' I1 ?: b( B5 `0 @0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000, 9 J4 n8 x" y6 B R" ]2 ]( D
电流 aii、bii:
" p7 R% O/ ~$ W1 n' o# Y1 G9 _- |" taii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000
7 k2 ~9 A) n; @/ i+ b8 c; E========================雅克比矩阵========================1 Q5 M$ E7 a6 K1 o; P
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000
$ V7 E4 ?1 a; h W-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000 6 W2 W- o) ~" q1 n2 s
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
0 G e0 G7 I7 _) A4 M, ]5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000
! L& G- M9 e$ q8 r' T1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000
8 l* J u6 B. S& Z) `9 j" c0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 ! _- [1 U" |; c4 p! Y( M7 G( Y. g
; j% l; \" O" l: n5 ]; Z3 ?. V( S3 i所求矩阵的逆矩阵为：
s/ B/ W" } ?4 F. `-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393 g! N% n7 o4 J6 Y
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 : e7 p) c. M' h: [
-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084
- Z) T8 t$ _$ ]5 I) Z6 J-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108
1 H: I- b* f4 D' c, {-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825 5 k3 X2 K- q. W9 {/ Q% `
-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452 7 H5 U2 G: M9 A+ `& d" d
方程的解:
( j2 D7 ~" c3 y0.000000 0.000001 0.000000 0.000001 0.000000 0.000002 , E R' L+ f) O
新的电压值(e+jf):
$ [: S% W2 S: @) l0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374, 6 l. M/ a3 {. Z) m
===================Iteration k = 4 End =========================; s2 l1 t1 D$ W/ [' V/ }, O! |
===================Iteration k = 5 Begin=========================
$ F% u8 Q0 S1 N: d; g& z! [* WP[0] = 0.00000& b" S& _7 t5 u5 h
Q[0] = -0.00000
& u2 r* h3 A- v% g5 u. `2 AP[1] = -0.50000
( q- z o. u1 RQ[1] = -0.30000
; h) v( A0 a% y+ c# O6 ~P[2] = 0.200003 ~- J. F4 O- x; X, X8 B' n
Q[2] = 1.102504 ]4 D$ W$ v7 i; Q- {) p3 a
误差向量 p、q:) C9 Q$ J" b9 C9 Q, l/ d
-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
- A. ^* H: e% g. D- x' Z=================k=5时，结果收敛=======================
8 h$ d% J7 R& l Y. c( R% _+ T================牛顿法计算共耗时:0秒:609毫秒========= |
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