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clear" i6 N6 U0 [ S- K/ v
r(14,10)=0.01938;x(14,10)=0.05917;r(10,11)=0.04699;x(10,11)=0.19797;r(10,1)=0.05811;x(10,1)=0.17632;r(14,2)=0.05403;x(14,2)=0.22304;r(10,2)=0.05695;x(10,2)=0.17388;9 Y& t' @% ^1 |; k) \, R$ Z
r(10,14)=0.01938;x(10,14)=0.05917;r(11,10)=0.04699;x(11,10)=0.19797;r(1,10)=0.05811;x(1,10)=0.17632;r(2,14)=0.05403;x(2,14)=0.22304;r(2,10)=0.05695;x(2,10)=0.17388;
8 P, l4 ~1 K& ]2 mr(11,1)=0.06701;x(11,1)=0.17103;r(1,2)=0.01335;x(1,2)=0.04211;r(2,12)=0.00000;x(2,12)=0.23488;r(1,3)=0.00000;x(1,3)=0.20452;r(3,13)=0.00000;x(3,13)=0.17615;
$ g! b9 J4 D4 ^- U# ^ Z* X7 mr(1,11)=0.06701;x(1,11)=0.17103;r(2,1)=0.01335;x(2,1)=0.04211;r(12,2)=0.00000;x(12,2)=0.23488;r(3,1)=0.00000;x(3,1)=0.20452;r(13,3)=0.00000;x(13,3)=0.17615;9 y) @+ x; a3 [* y+ R! v8 [
r(1,4)=0.00000;x(1,4)=0.53894;r(3,4)=0.00000;x(3,4)=0.11001;r(4,5)=0.03181;x(4,5)=0.08450;r(12,6)=0.09498;x(12,6)=0.19890;r(12,7)=0.12291;x(12,7)=0.25581;
1 y! o; S1 b: K& a6 pr(4,1)=0.00000;x(4,1)=0.53894;r(4,3)=0.00000;x(4,3)=0.11001;r(5,4)=0.03181;x(5,4)=0.08450;r(6,12)=0.09498;x(6,12)=0.19890;r(7,12)=0.12291;x(7,12)=0.25581;
8 J5 M' l O' e/ l8 D) k+ }r(12,8)=0.06615;x(12,8)=0.13027;r(4,9)=0.12711;x(4,9)=0.27038;r(5,6)=0.08205;x(5,6)=0.19207;r(7,8)=0.22092;x(7,8)=0.19988;r(8,9)=0.17093;x(8,9)=0.34802;
% X$ N- k P [* F8 ?r(8,12)=0.06615;x(8,12)=0.13027;r(9,4)=0.12711;x(9,4)=0.27038;r(6,5)=0.08205;x(6,5)=0.19207;r(8,7)=0.22092;x(8,7)=0.19988;r(9,8)=0.17093;x(9,8)=0.34802;, S' u- U1 l; e' A Q
# q: ^' {6 h3 m2 f+ B, K
y(14,10)=0.02640;y(10,11)=0.02190;y(10,1)=0.01870;y(14,2)=0.02460;y(10,2)=0.01700;y(11,1)=0.01730;y(1,2)=0.00640;y(2,12)=-0.31063;y(1,3)=-0.10999;y(1,4)=-0.05936;
3 ?$ }% p' q2 By(10,14)=0.02640;y(11,10)=0.02190;y(1,10)=0.01870;y(2,14)=0.02460;y(2,10)=0.01700;y(1,11)=0.01730;y(2,1)=0.00640;y(12,2)=0.28951;y(3,1)=0.10757;y(4,1)=0.05752;# j8 L3 R3 s1 M) _
( ]! [8 h: o4 {6 Y
for m=1:147 ]4 s1 B9 |- D7 E
t(m)=0;: l2 b# }3 m+ L+ r$ U
for n=1:145 ~9 [' g; \9 R9 ~' O2 `
t(m)=t(m)+y(m,n);
7 d T# A( J9 S' w/ q end
2 F6 {: i4 |) Q$ P8 N- o if m==4
' C4 l( ?3 Z( m8 |/ K t(m)=t(m)+0.190;
( F w4 ~- V4 q9 _9 D/ I) }7 K3 n( I end; {( H8 H% o, j. v8 p
end3 F! O. |- V+ |( Q. @( v
for m=1:14$ C; ?" ^; Z% ~7 W5 f
d(m)=0;
6 z L/ [$ b5 w0 h* S: g% E3 N for n=1:14# Y( W" d+ X( [: e! X" |( S
if m==n8 X7 w0 G8 i: R0 d4 I6 c( J
0 i4 P- Z# F% Z5 I# S
elseif (r(m,n)==0)&(x(m,n)==0)3 w! M/ O7 Q4 ~- v: n% B: u6 l
d(m)=d(m)+0; % G( a T6 F, ?7 L+ n! J' G
else
9 z, C1 k8 C2 n8 o6 ^4 ~7 _ a d(m)=d(m)+1/(r(m,n)+j*x(m,n)); . G0 m3 |: J( S6 m
end, n7 [) L/ ]4 z" e
end
( P i6 }9 w' |4 J9 a9 x9 v! Nend' X: F0 j- `" d
for m=1:14
. F8 e) N7 Q, e3 Y& s1 z for n=1:14
8 @1 ]2 C+ P1 F- \0 h' M; L4 |( P if m==n
: H3 F: _$ R' {, P Y(m,n)=j*t(m)+d(m);) \5 e" |$ v0 E0 F$ O8 m- Y
elseif (r(m,n)==0)&(x(m,n)==0)6 m2 m0 s7 ]- C8 R i
Y(m,n)=0;& v9 U' q$ u, x* R; _. N& c5 N1 n: V8 o; X
else
8 T3 A8 Y5 G7 i+ a. j! l6 f Y(m,n)=-1/(r(m,n)+j*x(m,n));
) a4 U0 q, Y4 ~6 h& B4 u end
2 k# P! h$ Z. ] end
7 i& a0 U& u" z8 {2 _# uend0 B+ S2 F; W4 X! z: L
Y;
" M6 d8 g* I! a& W3 d# p5 O$ OG=real(Y);B=imag(Y);% |' B: \$ E/ c: y% s+ U0 Q
%给定节点电压初值和循环次数k=0
, B. A7 G- O$ v1 _* W0 Cdelt(10)=0;delt(11)=0;u(1)=1.0;delt(1)=0;u(2)=1.0;delt(2)=0;delt(12)=0;u(3)=1.0;delt(3)=0;delt(13)=0;u(4)=1.0;delt(4)=0;u(5)=1.0;delt(5)=0;u(6)=1.0;delt(6)=0;u(7)=1.0;delt(7)=0;u(8)=1.0;delt(8)=0;u(9)=1.0;delt(9)=0;
8 s" Y. H& s: W" J4 V/ d7 q% op(10)=0.183;p(11)=-0.942;p(1)=-0.478;q(1)=0.039;p(2)=-0.076;q(2)=-0.016;p(12)=-0.112;p(3)=0;q(3)=0;p(13)=0;p(4)=-0.295;p(5)=-0.09;q(5)=-0.058;p(6)=-0.035;q(6)=-0.018;p(7)=-0.061;q(7)=-0.016;p(8)=-0.135;q(8)=-0.058;p(9)=-0.149;q(9)=-0.05;
3 t; k# M6 q8 |* G2 Gk=0;precision=1;N1=13;
: v4 X: |1 A4 A0 T( D, ~/ Z%求节点功率的不平衡量�6�2P和�6�2Q) {2 A% g$ t; [& F, }* E' k
while precision>0.000016 D3 L( n4 ^/ E1 U
u(10)=1.0450;u(11)=1.01;u(12)=1.07;u(13)=1.09;u(14)=1.06;delt(14)=0;q(4)=-0.166+(u(4))^2*0.190;8 V2 x$ ^; [* F/ @8 H( V
for m=1:N1 * k2 N) T5 v6 D/ ^' L7 m
if m<=9% R! q* D' J$ j* q# Y$ H/ h; }
for n=1:N1+1/ F7 F6 l/ j# L' C$ H0 `7 |
pt(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
* C0 y: e0 Z/ x8 p& \3 gqt(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
) c+ w# B6 i0 Y6 J, E& o% y% _ end: W# J% {5 a% Z8 n
pp(m)=p(m)-sum(pt);qq(m)=q(m)-sum(qt);( g, D! P/ s8 }
else6 ^, `# \8 }/ V) q9 b' {
for n=1:N1+1
( F+ a4 ~ b8 [5 v, e$ kf(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
! x8 n, |- L* U9 s5 C: B4 U3 C end
2 ]0 S1 q6 E4 D4 C* F* N6 A2 k pp(m)=p(m)-sum(f);qq(m)=0;( x$ U; a" s; F; b, @
end ! r, I% ~+ d) g- S" P( f9 m
end; H: `8 b% A9 J/ y/ \9 \
%计算雅克比矩阵各元素8 H- \) ?" _; d! i/ i" }
for m=1:N1% h/ Z% N, J1 b( A5 n& i% E5 `
for n=1:N1+1" N, ^1 ~* W' Y
h0(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
8 B2 Q) i; B* W! {; b n0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
5 s' G7 B7 `9 O% D$ S j0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));% W7 \$ O5 H6 C* S3 K$ W) @
L0(n)=-u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
4 Z% }& n( J# ]6 B end! t1 N; M) X* @% e
if m<=9
& V f: ~/ _! G& ?9 RH(m,m)=sum(h0)- u(m)*u(m)*(G(m,m)*sin(delt(m)-delt(m))-B(m,m)*cos(delt(m)-delt(m)));* E5 D# m) W7 `' H1 k1 U! p9 w# |
N(m,m)=sum(n0)-2*u(m)^2*G(m,m)+u(m)*u(m)*(G(m,m)*cos(delt(m)-delt(m))+B(m,m)*sin(delt(m)-delt(m)));
" P% Y- e9 C+ @/ `- A v tJ(m,m)=sum(j0)+u(m)*u(m)*(G(m,m)*cos(delt(m)-delt(m))+B(m,m)*sin(delt(m)-delt(m)));+ P" h8 ~8 ~9 N; Y$ j+ q( I
L(m,m)=sum(L0)+2*u(m)^2*B(m,m)+u(m)*u(m)*(G(m,m)*sin(delt(m)-delt(m))-B(m,m)*cos(delt(m)-delt(m)));2 [" {, K# K# D6 s$ P' ~5 [
else- x0 H$ }; [) O! {
H(m,m)=sum(h0)- u(m)*u(m)*(G(m,m)*sin(delt(m)-delt(m))-B(m,m)*cos(delt(m)-delt(m)));
( E- k4 Y4 Y" }( DN(m,m)=0;+ i! P1 e' |$ l; @' R
J(m,m)=0;
% y# v* C( Y1 AL(m,m)=0;
8 X* u# ~' ]( ` end+ @( M, L" e# T& G
end
6 B$ j) o0 r. \4 l5 h; b% v8 |; Kfor m=1:N18 d& C$ r" C# b! N
JJ(2*m-1,2*m-1)=H(m,m);JJ(2*m-1,2*m)=N(m,m);
9 X9 S2 n* V4 c! Z/ w JJ(2*m,2*m-1)=J(m,m);JJ(2*m,2*m)=L(m,m);* u; D x( m, `* t
end
2 N0 Q- F7 Z+ F1 Z7 C7 D0 I/ @( S A0 O * H" \9 R$ }7 {: O) }9 a5 M2 L1 e. c
for m=1:N17 ?! [, t$ u6 k- o0 M4 [6 Z
for n=1:N1
2 | Q$ {0 s. S; C. [0 f8 H if (m<=9)&(n<=9)&(m~=n) $ @6 j8 C. D: _4 I5 y4 q) `
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));6 V( e0 }/ b: A/ d" k
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));+ B) D7 I/ ]; p0 E. A+ P
N(m,n)=-J(m,n);L(m,n)=H(m,n);
! \- _4 u/ [; a" L7 W1 U1 Y: eJJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);" p* [3 G8 ~: u! G
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=L(m,n);
. t/ H0 a/ L, r: z elseif ((m==10)&(n<10))|((m==11)&(n<10))|((m==12)&(n<10))|((m==13)&(n<10))
2 W2 U0 P! Q1 \( e- B) hH(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
0 a, m. g5 U7 D! Z1 g G; ?' pJ(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));2 b# i/ x' l+ X9 s3 E
N(m,n)=-J(m,n);- x, a, p$ s+ c$ @. U
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);; Y9 @4 a" N6 q, \$ ]- x* e
JJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;
2 j: l& t2 C* `9 m' e9 r |6 f elseif ((n==10)&(m<10))|((n==11)&(m<10))|((n==12)&(m<10))|((n==13)&(m<10))
{" V6 N6 B9 c. v: ?+ y2 RH(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));- b, r. @3 B$ O/ P% C* y( m
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));. L( D) [. N/ v4 X8 @- a. j9 z
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;( R4 P$ | G, W7 Q
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=0;! a0 l- [- ?3 g: Q8 c5 \8 m% [
elseif (m>=10)&(n>=10)&(m~=n); N" X7 j. L+ q$ {. t
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
; U) V4 [; R, {JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;$ A- Q" e7 j5 J
JJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;
5 r/ j E9 `0 x( w6 _ end# ]7 O, H. b/ h) ~) I! D% w: i" ~1 i" ?
end+ q, x S2 j, D: B: D& I
end3 Z2 z: u8 F8 c6 P+ N6 z9 C8 R) q
% 对雅克比矩阵进行修正,使之变成非奇异阵,以便后续求逆计算# }; V7 ?6 V B8 D& `3 u
b=0;
- o4 g/ n! u% r' V: K( Ffor m=1:22% S( }2 A6 U; X
for n=1:22
+ v: X0 B0 [1 F$ |7 _: E if (m<=18)&(n<=18)
/ X$ U. X: Z, [# w8 B% \ A(m,n)=JJ(m,n);8 s( Y; E3 ~ n4 A
elseif (m>18)&(n<=18)1 E. T. k4 b# Z& n1 h% v) [
A(m,n)=JJ(m+b,n);
5 v0 h/ H$ E8 _6 B# o* G5 { end ' |. g8 S0 Q* y% |. O
end1 G7 k) O% o! E L1 }; s
if m>18
( e; C3 d W( v7 q) t b=b+1;
: n8 j* R/ r5 m1 D% v end
- e9 `6 `# A/ n. Y8 S; e: mend6 C7 p* z! O2 t" C. ?1 ^
+ F% y7 f' J/ h5 W9 Zb=0;
5 ^0 Y& U) I, R- i: o/ s" K+ Z; U' Tfor n=1:22
: P$ {" ]7 |- y$ U. e for m=1:228 [4 I( J+ }4 y( E
if n<=18
! w, O; Q( G" D5 r) q2 X A(m,n)=A(m,n);
" } V5 A9 g) C& n3 U3 x5 l elseif (m<=18)&(n>18)( h9 u5 [$ j8 H V3 O& m5 ~
A(m,n)=JJ(m,n+b);, ?6 ?; q1 G, Z
end4 z* i) E; S- v/ h
end* u. [/ e# O3 B7 U* H
if n>18
; `! J) \' J1 h) j6 h& q. @ b=b+1;
m) U3 W; l- s' b+ k6 P. s& R, I end
. [! T, s, z/ yend0 [4 G8 E- _0 W- ~3 \
, h; Q' N. G5 |; ?. Z$ L( W* U& x/ Rb=0;& L0 h4 n. B& G! r, k$ q2 m7 B0 g- X
for m=1:22
: a0 M( I- ]! V5 c$ {0 b# @! K for n=1:26
+ Q/ |2 U% \5 Y j0 M' }1 ? if (m>=19)&(n>=19)
/ r, B" ?$ \* Y6 f, M: c3 w D(m,n)=JJ(m+b,n);
$ h+ T5 M' N! f9 G/ [# A- C( u end# S1 K0 J$ D4 u# p. u8 V n/ O1 v
end
2 N3 n& |) o2 O if m>180 m/ A5 z2 g0 D, ]8 U* C
b=b+1;
: [4 G- Q- k4 Z. h end
* f( z7 j/ Q1 q, dend( z# d# |3 q6 B$ H# X3 T( {! J
" j' M2 ^. B* S8 s G7 @7 j ^b=0;0 [' W& k0 I7 d% J( B& k: y, X
for n=1:22& y# X1 d4 A* G( {
for m=1:22 n% M$ _$ a, u8 t8 [/ D V1 i
if (m>=19)&(n>=19)
; \9 s$ X2 N6 [( U) W. V7 d& C# k. b D(m,n)=D(m,n+b);. Q0 ^% M2 k" K" G* g5 J+ W
end1 [. P/ F" k6 U, ?9 Y8 Q G$ o
end6 b5 K' S5 G: O. h; q8 h3 k
if n>18
! ]1 r' V5 { s" t9 r$ N b=b+1;% o' \; C8 Y4 J9 d4 ^) H5 e& J( u2 v
end q* t T y: c# x9 G
end
/ L1 y/ t* E3 N, d. I8 ~7 `( x# Q& K: M. T : V9 @3 u7 F+ C4 }- Q, E
for m=1:22
( }4 g1 ?- F) a2 J5 C for n=1:22! j1 {! |$ V/ P* _+ ?! U2 o, U2 h) z
if (m>=19)&(n>=19)
) N, ^7 w) Q) d A(m,n)=D(m,n);; e$ W& v O' n- ~) b# C
else
* ^* S5 i. h; \2 r2 c A(m,n)=A(m,n);
) j: `, a$ I: x+ b% c5 s9 y end" G M" N% k, x5 Q. U* R# t! l2 z
end3 Z& O4 O" S7 |7 [/ u; V
end8 h7 O2 k N" L( g
% 形成不平衡量的列矩阵
* N; @) l' Z: D) c6 \( M) Vfor m=1:N1* ?+ w) G) h& I
PP(2*m-1)=pp(m);PP(2*m)=qq(m);: f$ U* R# A+ F {& @
end$ O' B8 ?, f0 a: Q# {, Y
C=PP(1:1:18);
5 \4 {- l, ?% d: [; q+ p8 db=0;
! z, x" H6 G( D; t. zfor m=1:22. @" m2 w. v) r5 @# I
if m<=18. W; U2 y+ I& v3 T2 {. ~2 t; {
C=C;/ e& A! D" ^" n: `. D. h. |0 X
else
, P- b8 f+ Y+ P; r C(m)=PP(m+b);
/ ~, o( E' U$ D5 H" Z4 _+ @ b=b+1;8 w+ M, H( T i2 E y( w5 y1 s3 t
end
1 J. \; A6 E- {% wend9 V/ D7 m* Q' c9 ^5 r
% 解修正方程式,得到修正量7 J. s* n, ]) o$ }
uu=-inv(A)*C';: k3 T' }; ^0 [: { U; t# b& m& W. K
precision=max(abs(uu));" ?1 j. j! I n" I# E7 @
% 计算个节点电压新值,即修正后值0 k' D! u# U8 ?; X
for n=1:N1& i/ w$ N- q& g9 F6 L# m4 j
if n<=9
) F& A1 }2 f; v; t7 P* E u delt(n)=delt(n)+uu(2*n-1);
~: j: P$ L- H" l u(n)=u(n)+uu(2*n);+ a' p& r' M2 z/ u* i/ N+ A
else" M) |4 O" _2 C& L, z* s
delt(n)=delt(n)+uu(n+9);& p+ X. Z. |$ C' ]4 w; j6 S7 _
u(n)=u(n);
0 n1 L2 I' v/ A0 n! S end
2 d) Q* @& Q; o4 U# @" hend0 G* a t4 F* O5 X
% 循环次数k加一,带入新值进入下一次迭代0 v9 T7 `3 l( u t9 X" A2 `9 W
k=k+1;. v$ G! b5 u2 B& ~+ _6 X
end
6 ^. N+ n3 A" h0 r! h. Z0 Y% 迭代完成后,求迭代次数、节点母线电压幅值与相角
7 T; m$ p. S1 d6 H' B6 pk-1,(delt*180/pi)',u'/ N$ Y: `/ y" i' }/ \# L$ B
% 计算各节点的功率和线路功率8 X9 r% b$ f5 S9 }
for n=1:N1+1" b+ ?% l9 r7 F! w5 i
U(n)=u(n)*(cos(delt(n))+j*sin(delt(n)));8 o0 r9 N/ Q% s0 _0 X0 L0 Q5 W
end- Q {3 @! d, P: _6 I$ ?& H
for m=1:N1+1
6 K* ^9 W+ ~, @7 j% s" N( z4 T. T3 } for n=1:N1+1
/ U* e0 I; T8 e; {$ [6 Z I(n)=Y(m,n)*U(n);0 B7 }& I r& _
end6 I. z6 P- i7 j1 n: i* m5 j+ O8 Y
S(m)=U(m)*sum(conj(I));
8 e0 e3 p3 [# e Oend! h: i- Z% z" I6 z H* c
S5 Z/ J1 m% ]3 o/ z6 W( r6 Y
for m=1:N1+1
# y( G# a6 X# [1 _% h+ f3 E7 L for n=1:N1+1
* S2 G Y2 F/ C, V1 D T(m,n)=U(m)*conj((U(m)-U(n))*(-Y(m,n)))+U(m)*conj(U(m)*j*y(m,n));/ E, O- p3 r8 _" u# ~
end0 i6 `6 g' J2 I7 X
end
3 b2 O% f5 d/ F: IT |