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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:=========================/ v3 z0 u0 T: ^. Y" Y. o
2.9049 - j11.5030 0.0000 + j5.3182 -1.6600 + j3.1618 -1.2450 + j2.3714 9 t X5 y0 j4 t% H% `. C6 x
0.0000 + j5.3182 0.0000 - j4.6638 0.0000 + j0.0000 0.0000 + j0.0000 . a x& t4 |( w
-1.6600 + j3.1618 0.0000 + j0.0000 2.4900 - j4.7039 -0.8300 + j1.5809 3 g9 p# @, H. R0 T: w6 L- _
-1.2450 + j2.3714 0.0000 + j0.0000 -0.8300 + j1.5809 2.0750 - j3.9092 * d5 {. N5 t( {* [+ q0 d
#########################导纳矩阵输出完毕!#########################2 d4 B$ z8 t$ J& D! G; F9 a
2 U; H; |4 \: ]% L* u=========================初始功率向量输出开始:=========================
" S2 y- p3 F4 D& j0.0000 + j0.0000 -0.5000 + j-0.3000 0.2000 + j0.0000 0.0000 + j0.0000
: C3 s- T% V, V#########################初始功率向量输出完毕!#########################' ^$ t# ]* @0 I; T
/ I* X ~0 Y3 z/ z7 w' |) _
=========================初始电压向量输出开始:=========================4 h( x& a9 p' b2 L! P
1.0000 + j0.0000 1.0000 + j0.0000 1.0500 + j0.0000 1.0500 + j0.0000 3 g: o! K3 v4 O1 f7 J* S+ P4 M1 L
#########################初始电压向量输出完毕!#########################
% d8 X! M) g7 _8 L
6 w. x; s) q7 _2 v; |===================Iteration k = 0 Begin=========================6 M. e4 s `" ^7 J
P[0] = -0.14525+ Y4 f2 e6 g5 S0 }/ o
Q[0] = 0.37497
: s9 Z; ]$ `6 u" {P[1] = 0.00000& l. }# m$ p0 s+ ]$ A, c
Q[1] = -0.654348 W [% ]4 B, ]9 N Y0 n
P[2] = 0.08715- C6 e/ w" e) q
Q[2] = 1.10250
( x. L0 K9 n7 C9 a5 G误差向量 p、q:
* Y5 ?* p- {( K6 P0 G0.14524743, 0.14524743, -0.37496691, -0.50000000, 0.35433884, 0.11285154, 0.00000000, 9 o9 X- F* G: g7 h
电流 aii、bii:
# i& J2 ]! R. B: R% ]& Z, c( V& Gaii[0] = -0.1452474277 bii[0] = -0.3749669147 aii[1] = 0.0000000000 bii[1] = 0.6543388430 aii[2] = 0.0829985301 bii[2] = 0.0000000000
4 V/ B0 }& S* M+ i B========================雅克比矩阵========================8 T! A+ u' }1 Y; v6 X v' t
-2.7597000 -11.128100 0.00000000 5.31820000 1.66000000 3.16180000
3 ~ Z5 _$ v7 p' |8 W* q* z-11.878000 3.05020000 5.31820000 0.00000000 3.16180000 -1.6600000
3 D8 m1 M; E8 z9 [3 [- U0.00000000 5.31820000 0.00000000 -5.3182000 0.00000000 0.00000000
; @. v5 ~6 N7 U* H5.31820000 0.00000000 -4.0095000 0.00000000 0.00000000 0.00000000 9 M& `1 }$ S. A1 ^, D" t, \% S+ H
1.74300000 3.31990000 0.00000000 0.00000000 -2.6975000 -4.9391000 " u9 G9 T4 o- n, [* c$ S1 @& s
0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.00000000
9 U2 x9 R3 C T1 q& s$ u- {$ l
7 E( P7 C( y2 `. t所求矩阵的逆矩阵为：
# z' U N1 m% r1 I. k( [! t' o-0.08369 -0.15942 -0.08369 -0.21145 0.00000 -0.30618
, L7 n5 H. Q" e* x-0.23406 0.07113 -0.23406 0.09434 -0.17374 0.14524
$ D$ H+ Y% a% G' ]8 _-0.11101 -0.21145 -0.11101 -0.52987 0.00000 -0.40612
" N( F2 i: t) @0 [7 i* X" \5 q-0.23406 0.07113 -0.42209 0.09434 -0.17374 0.14524
4 G+ \- J( q- x0 P0.00000 -0.00000 0.00000 0.00000 0.00000 -0.47619 ' Z0 {8 l: R! \- L# }
-0.18686 -0.00845 -0.18686 -0.01121 -0.31925 0.24965 + ~2 s: n* f/ c3 ]
方程的解:5 \% T, C p! F3 r8 ?8 ?
0.014542 0.070185 -0.069086 0.164202 0.000000 0.029460 + T5 C$ ^3 `7 d8 I2 r& D6 y
新的电压值(e+jf):
3 f/ X( {3 `4 s6 \7 [0.98546 - j0.07019, 1.06909 - j0.16420, 1.05000 - j0.02946,
* m( D5 |7 K5 b; {& C===================Iteration k = 0 End =========================* m$ K; U- w3 L2 Z1 m+ j
===================Iteration k = 1 Begin=========================& L4 T2 e$ V0 v& ~
P[0] = -0.02835
' f, |, j5 L' T8 H9 P0 jQ[0] = -0.00268
. B+ [8 x( j2 fP[1] = -0.46151
- l( J6 }1 F4 t5 k5 V% rQ[1] = -0.207949 s/ N+ O! v* C, `1 t. X% A
P[2] = 0.203544 V3 d! J4 L+ S( ?; _! V+ B3 J
Q[2] = 1.10337
* g* t/ s- e6 n( w& ]" t$ j8 g误差向量 p、q:8 s) |2 m L& r7 h
0.02834863, 0.02834863, 0.00267722, -0.03848582, -0.09206171, -0.00353918, -0.00086787,
) z0 Y, s4 p: N8 ]电流 aii、bii:6 \/ v! `. i; b! O- r% X
aii[0] = -0.0284292626 bii[0] = 0.0047414768 aii[1] = -0.3925561267 bii[1] = 0.2547940506 aii[2] = 0.1642347318 bii[2] = 0.0000000000 o F2 o( V9 L$ S0 m. {
========================雅克比矩阵========================0 n9 K0 y0 b, E# \# @
-3.6416000 -11.136600 0.37330000 5.24080000 1.85770000 2.99940000
; G: D, k# d- X-11.127100 3.69850000 5.24080000 -0.3733000 2.99940000 -1.8577000 + R: }3 q z- l6 g2 c. H, G6 U% t
0.87330000 5.68560000 -0.3733000 -5.2408000 0.00000000 0.00000000
* n7 v, @: y+ [8 z# [5.68560000 -0.8733000 -4.7313000 1.15840000 0.00000000 0.00000000
+ E( V* G( h$ j$ C# R0 K, T' N5 y1.83610000 3.27100000 0.00000000 0.00000000 -2.9173000 -4.8658000
7 T4 Q8 s8 t- ~. {0.00000000 0.00000000 0.00000000 0.00000000 -2.1000000 0.05890000 " V$ A5 c" \1 w- b5 J
2 j2 U5 b) [: g, L: q% b
所求矩阵的逆矩阵为：4 U p4 c F! w. n) c0 X# o
-0.11168 -0.15094 -0.13743 -0.16516 -0.01477 -0.29385 # h% S- [9 Z) l+ u
-0.23803 0.07191 -0.22576 0.07869 -0.17259 0.13189
) \: U7 j+ v! \2 \' B2 o5 G+ k-0.15534 -0.17860 -0.23173 -0.40317 -0.03179 -0.34835
& E4 B; W- B8 S8 O-0.26578 0.06559 -0.44212 0.08656 -0.18743 0.11893
* k, ^" {4 W$ ?$ j- _ \) D( }' ?5 i-0.00558 -0.00024 -0.00562 -0.00026 -0.00903 -0.46893
. w; K- d5 ~: a; j0 O( c-0.19882 -0.00847 -0.20026 -0.00927 -0.32170 0.25892
6 I6 B: ^4 q4 S! R方程的解:
3 Y3 }3 I9 k6 _5 H/ {2 L# j0.017232 -0.004615 0.041568 0.002248 0.000520 0.003815 6 t7 h1 x* |1 r, e4 ~/ L2 j( Q; i
新的电压值(e+jf):
+ J5 M4 D4 Q1 W( u% i4 z0.96823 - j0.06557, 1.02752 - j0.16645, 1.04948 - j0.03328, 1 \* ^$ F+ v. C M) W
===================Iteration k = 1 End =========================- m- [" _3 Z) b4 a" r4 Y
===================Iteration k = 2 Begin=========================
6 Q: @' L$ L/ c( H( eP[0] = -0.00050
; i& J$ d/ l9 Q8 D2 x8 s+ KQ[0] = 0.00005
1 g: K" w; Y2 u$ Q6 [P[1] = -0.498771 A& W E' q. q( C( F" J! c; m b
Q[1] = -0.29567
. Z( E- W" [, @; ]8 P. N" h9 n2 GP[2] = 0.20071
% `" z9 j" U8 nQ[2] = 1.10251, o/ Z4 [& W0 D: r/ S- l4 N' o" k
误差向量 p、q:. ~- T$ {1 d8 G) Q+ D% R, e
0.00050286, 0.00050286, -0.00004686, -0.00122615, -0.00432794, -0.00071146, -0.00001483,
) }/ A3 X- D/ O0 q4 z3 k电流 aii、bii:! _, v# ?% Z0 ~) f" G7 A( o6 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 g, x1 r9 x5 w
========================雅克比矩阵========================+ E9 C; ^. x9 K# x$ I
-3.5664000 -10.947100 0.34870000 5.14920000 1.81460000 2.95250000 5 D* C2 F% c2 m& }/ r; H
-10.947100 3.56740000 5.14920000 -0.3487000 2.95250000 -1.8146000 9 S/ j7 t; N) D ], `: U! r
0.88520000 5.46450000 -0.3487000 -5.1492000 0.00000000 0.00000000 4 J! K" k9 Q7 M2 Q; a1 X% i( |
5.46450000 -0.8852000 -4.4352000 1.20390000 0.00000000 0.00000000
^8 n. f9 b) h7 @7 p; x/ e1.84730000 3.26310000 0.00000000 0.00000000 -2.9275000 -4.8538000
# R( o l6 k! b L; b0 i# h- ?) P0.00000000 0.00000000 0.00000000 0.00000000 -2.0990000 0.06660000
/ W7 G W- R" k$ H& l2 o7 f4 I
% M( V v- s$ W) F: |3 t4 w2 v所求矩阵的逆矩阵为：& p% |! l1 z9 p2 }* V0 h& V
-0.11450 -0.15942 -0.14639 -0.18258 -0.01421 -0.30342
* d3 B8 l/ q) | g. O3 c-0.23498 0.07099 -0.22078 0.08130 -0.16768 0.13058 - E( l; \; u3 j, r8 y! ~3 M9 `& n
-0.16419 -0.19402 -0.25476 -0.44360 -0.03241 -0.36965
4 K) ~7 H/ ^$ n* B) M-0.25794 0.06106 -0.43642 0.08493 -0.17820 0.11145
+ h+ {2 z: M0 O. ~-0.00627 -0.00040 -0.00635 -0.00046 -0.01009 -0.46835 8 x2 b( O' m8 r2 p
-0.19777 -0.01271 -0.20031 -0.01456 -0.31808 0.25478
, n# t: d9 U: o* K方程的解:
* e. c5 f" A. k: H/ o' O0.000934 -0.000085 0.002187 0.000160 0.000021 0.000432
2 J L+ N; Y/ P2 o( ~新的电压值(e+jf):
$ `8 o% J- A9 K9 A0.96729 - j0.06549, 1.02533 - j0.16661, 1.04946 - j0.03371,
9 q% A& o/ o3 L===================Iteration k = 2 End =========================
% d; `& t6 o" J5 Z" a6 f===================Iteration k = 3 Begin=========================% B: {. Y" F- w' ^5 M
P[0] = -0.00000* O8 Q0 e- x: B4 T% b, y1 }
Q[0] = 0.00000
/ A6 y: @, n# P7 AP[1] = -0.50000; z* T: V4 M" q2 T+ b4 y
Q[1] = -0.29999
1 K0 m7 c3 I; \5 H) IP[2] = 0.20008
3 O' h# F9 o! P$ QQ[2] = 1.10250
) K7 v( b$ O, S& m5 y# q" n P误差向量 p、q:
; _2 N4 I8 R1 f% D4 h6 }. m! v4 m0.00000048, 0.00000048, -0.00000006, -0.00000179, -0.00001164, -0.00008305, -0.00000019, ( O0 F5 z; s! J4 [. d; }' c; s
电流 aii、bii:
7 B# J% F, C0 j1 C' x$ Maii[0] = -0.0000005025 bii[0] = -0.0000000245 aii[1] = -0.4287817842 bii[1] = 0.3622513393 aii[2] = 0.1567496678 bii[2] = 0.0000000000 ^, s+ c* L( c, Q
========================雅克比矩阵========================7 M1 t1 q' a, N. J W* l, A8 V
-3.5632000 -10.936600 0.34830000 5.14420000 1.81270000 2.94970000
2 t7 _8 P; J( L& s7 Z A) y! O-10.936600 3.56320000 5.14420000 -0.3483000 2.94970000 -1.8127000 / M$ i5 n9 P f
0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
/ G6 `- U: B/ w; r) K7 `* y0 L5.45290000 -0.8861000 -4.4197000 1.20580000 0.00000000 0.00000000
2 H0 b4 Q) b+ C7 t1.84860000 3.26230000 0.00000000 0.00000000 -2.9284000 -4.8527000
* b, a' E: h2 F0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06740000
' ~' }" |' ^" |6 R
0 R: b4 W8 g: b+ s所求矩阵的逆矩阵为：, a9 {" Q/ G! H( J% a1 R4 a7 D
-0.11472 -0.15989 -0.14693 -0.18356 -0.01423 -0.30393 ! |6 } x. o- H" m. c) B
-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050
9 {6 ]5 f% ?# e- I* [# K9 J+ y-0.16472 -0.19489 -0.25605 -0.44590 -0.03248 -0.37084
4 u1 @: Y6 C5 `. o+ Y-0.25751 0.06086 -0.43612 0.08491 -0.17772 0.11109
J. L. e E% E( f9 }9 R-0.00635 -0.00042 -0.00643 -0.00048 -0.01021 -0.46826 & o$ L$ {! d3 ^
-0.19773 -0.01296 -0.20034 -0.01488 -0.31788 0.25453 ' }- j' ?# ~+ C6 }) v/ `' D
方程的解:
- ]" @+ v+ p& B0 j0 q ]/ s( }0.000004 0.000013 0.000008 0.000014 0.000001 0.000027 & W. ]1 e2 p' T: I Y! d
新的电压值(e+jf):& t* ~8 }: y6 V+ p. @+ U
0.96729 - j0.06550, 1.02532 - j0.16662, 1.04946 - j0.03373,
, X( F# ^* w+ n. g0 H===================Iteration k = 3 End =========================
+ X9 Q2 L4 k9 g* r% r7 q===================Iteration k = 4 Begin=========================, L' s: Z' i9 F& ?
P[0] = -0.00000
- Y8 M% T5 i# S1 h! \ T" qQ[0] = -0.00000
, I' G/ b& e3 e }1 `4 ]4 XP[1] = -0.50000# u4 F+ n. j+ N
Q[1] = -0.30000
) \; \9 Z" |% m$ _6 Z, s4 _P[2] = 0.20001" v5 F: w$ I! C7 S$ Y
Q[2] = 1.10250; ]0 t5 c- F0 [6 t$ S
误差向量 p、q:
8 U9 C4 ] X5 h9 P6 B0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000000, -0.00000516, -0.00000000,
& q4 G! K7 _& `8 s- O/ Z电流 aii、bii:
5 R7 d( y- Q$ s1 F Jaii[0] = -0.0000000000 bii[0] = 0.0000000000 aii[1] = -0.4287787078 bii[1] = 0.3622711617 aii[2] = 0.1566485901 bii[2] = 0.0000000000
. B# w, R& s6 K========================雅克比矩阵========================% [" x9 X: @( T
-3.5634000 -10.936500 0.34830000 5.14420000 1.81280000 2.94970000
7 M8 r) E4 w5 m! O N+ m7 K' N% [9 o-10.936500 3.56340000 5.14420000 -0.3483000 2.94970000 -1.8128000
3 U1 P& Q+ K7 A0.88610000 5.45290000 -0.3483000 -5.1442000 0.00000000 0.00000000
c* C& o" i; X5 o" A5.45290000 -0.8861000 -4.4197000 1.20590000 0.00000000 0.00000000
6 B6 j. Y6 H' [1 h1.84870000 3.26220000 0.00000000 0.00000000 -2.9284000 -4.8526000 % V( u. H% X4 D h+ F3 b
0.00000000 0.00000000 0.00000000 0.00000000 -2.0989000 0.06750000 2 D P- I8 ~6 Y6 w) o
9 j2 ^ |* s+ ~3 Y
所求矩阵的逆矩阵为：7 t4 A. g3 |- O2 x
-0.11473 -0.15989 -0.14693 -0.18357 -0.01423 -0.30393
% I! w& T1 t8 S4 e) t- ~% w-0.23481 0.07095 -0.22052 0.08145 -0.16742 0.13050 5 X- ^; \' ` O( x% P
-0.16473 -0.19489 -0.25606 -0.44590 -0.03248 -0.37084
: ^2 b/ ~- n% i-0.25751 0.06086 -0.43611 0.08491 -0.17772 0.11108 - y7 m9 W2 @1 m- P2 z1 k, ]: o
-0.00636 -0.00042 -0.00644 -0.00048 -0.01022 -0.46825
: n# P- h) J' v1 h: b4 T# R-0.19773 -0.01297 -0.20034 -0.01489 -0.31788 0.25452 3 J+ |6 I$ i' q I; N; | I' ?! `
方程的解:! U/ Q4 w; u/ u9 w+ i; V G
0.000000 0.000001 0.000000 0.000001 0.000000 0.000002
5 V" U2 ]. X; b, _$ U1 A新的电压值(e+jf):3 K5 Z# p. ]2 h: e$ I
0.96729 - j0.06550, 1.02532 - j0.16663, 1.04946 - j0.03374,
; R' X0 C( n, ~1 \. B===================Iteration k = 4 End =========================
9 [) I; {$ ^9 ^* a# y& G2 J' j* e===================Iteration k = 5 Begin=========================. O( y8 _5 C/ v2 ~2 b3 p% M
P[0] = 0.00000+ n% k) m) }% C
Q[0] = -0.00000
& ]1 t; D+ K; X- q* Z! ?P[1] = -0.50000% R% c3 M. B) Y
Q[1] = -0.30000
3 l6 m* m4 T: A& J8 \* `* ? p% [" M: MP[2] = 0.20000
' w4 @$ [; i/ Z' j3 ]Q[2] = 1.102503 ~) E, _9 B! z& m& s# ?
误差向量 p、q:
' g2 y7 v# R% ^-0.00000000, -0.00000000, 0.00000000, 0.00000000, 0.00000000, -0.00000032, -0.00000000,
0 I- S C# h" P; j=================k=5时，结果收敛=======================
# E1 ^0 V' s; e: b8 e4 I* l================牛顿法计算共耗时:0秒:609毫秒========= |
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