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clear2 Y1 |9 @, E% F' n0 J5 X7 d) r! S
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;1 C g& e9 E( d; p% e+ _
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;
. b( }1 J+ p) J3 v% jr(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;5 h" C$ K/ J) y& \& d0 \. K0 H2 b
r(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;
" L! N& @( [8 |% a; R. ~- ur(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;
3 K) U: e% j& i% Q% f9 Hr(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;- r. y/ Z" K. S$ u1 N& M$ L
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;
5 g2 ^% P+ Y) ~& v6 Y5 [) Cr(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;
: ]6 D& w! y7 x9 a
2 i9 [8 c* o7 s4 g/ ?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;
& L: v7 l7 T/ m0 X. o4 ?3 ~' Zy(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;
" k, W M \+ |" n' m3 x
1 K, j* n% Z3 B& _! N( efor m=1:14# \9 ^, ?. M6 W4 d" f0 Q8 r
t(m)=0;& l3 S x- D* r; [
for n=1:14
5 |& c- T, Z& s9 \: g. }# f t(m)=t(m)+y(m,n);+ {% O: b3 J9 X& c% j2 `
end1 w5 @' \3 t; M$ @4 w( I3 M, ]1 I
if m==44 E, U W4 t3 Z) C% \
t(m)=t(m)+0.190;
) p" \' x' p6 s9 x9 ` end
1 f: p( T$ D# j+ Y2 X3 `% g- G( vend
G5 C$ p i1 b4 Qfor m=1:14: i# L M0 C1 @# `& s! ~, {, @( ~ f
d(m)=0;3 w# c3 F$ \: ]9 @! L+ g8 c3 _% ~
for n=1:14
3 B9 C5 G0 ~4 ^7 T, U0 M if m==n
: D1 Z- N3 @ R: D: x( X; e
3 x4 R$ B V* c elseif (r(m,n)==0)&(x(m,n)==0) z4 L6 L- f- _8 O. _
d(m)=d(m)+0;
% D$ J9 G5 ^ I# K: V |0 d else6 x0 n V" R O. {" J
d(m)=d(m)+1/(r(m,n)+j*x(m,n));
+ \* W9 y$ b4 G& G; Q/ Y8 U end
1 `, t3 g$ \9 l$ Q4 @3 b end( Y" o& V. _; S& s" T' h5 T* I: C" j
end! ]% w: {( r/ j2 j9 p7 ~
for m=1:14( i4 ?8 T2 z7 z
for n=1:14% p2 `. k: g* l5 ?; o+ l5 P, x
if m==n+ K2 {4 Y1 r: q9 A& c
Y(m,n)=j*t(m)+d(m);+ U% o0 k: @7 T8 O, H9 {. F
elseif (r(m,n)==0)&(x(m,n)==0)
9 U- P" I8 R7 J8 r Y(m,n)=0;
- v, g5 r2 {; \9 G2 ~# m5 F else% R# `" G4 {9 \% |4 m) U) {
Y(m,n)=-1/(r(m,n)+j*x(m,n));
- a$ @# s) f3 }3 G end }7 X* v, y" e v; {
end( |3 f W( L4 }6 r
end9 Q3 K3 |; E# y. Q4 X& T
Y;
. g' C, l8 T0 B$ i' d: }' vG=real(Y);B=imag(Y);
. q4 q I+ s h) y$ E: V3 o9 e1 O%给定节点电压初值和循环次数k=01 m) @$ N, a) q/ \; c
delt(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;
( z$ R+ ~/ j9 Sp(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;
' j a; s5 L4 ~# L0 Dk=0;precision=1;N1=13;
5 L$ ?; M/ T; H2 Q, x%求节点功率的不平衡量�6�2P和�6�2Q2 g" H! Q$ H# J# R' Z
while precision>0.00001; u" a. w# h' B5 k8 J4 n
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;( |$ H7 ]" M @9 y3 h
for m=1:N1 : [1 a9 ?9 W9 |, _' P3 A% p6 L( o$ Z
if m<=90 h! N1 p* G% d T6 }8 h' a
for n=1:N1+1 {1 D8 U" ?; H7 w! e; j
pt(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
3 n* h2 P$ @: q0 q# K4 |0 Xqt(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n))); 9 r: m9 _2 k# P. r0 K
end' b& ] r$ i- l4 ^6 D
pp(m)=p(m)-sum(pt);qq(m)=q(m)-sum(qt);
" N( D7 V& _ v# s8 S. l) R$ j else. n8 ]% b2 Q% H/ I# x
for n=1:N1+1
3 \% ~# N5 w0 ~/ K* I, o' z' y) X4 Of(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));5 M/ ]! I0 B: i$ H2 K/ c
end) C! V- v' B6 T. {; g, h7 q, d
pp(m)=p(m)-sum(f);qq(m)=0;
2 ?0 Z8 m$ B; H- s9 b9 K end
3 V( l7 u6 q) q; p/ L9 H7 S& n. c end0 ~' j( A" v5 k n2 {) W7 }& a
%计算雅克比矩阵各元素
% y2 C8 K% \3 W0 q9 a. Cfor m=1:N1
+ L$ U2 k1 s6 H2 Q" y for n=1:N1+1
# Z8 | K6 n/ f0 {0 F h0(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));( G( I" [+ t" g$ S+ R% i& B
n0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));* i) C; @" K# w5 K. T g1 B! C \
j0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
+ O5 i, P% y9 b L0(n)=-u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
* ?- P/ b% F b O end7 Y8 p0 {' ^: ]" M
if m<=9) q/ ]5 x1 [9 f
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)));* k- G5 Y7 S6 `- N9 H/ A
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)));
' u/ L/ [* i9 e! @& T/ B* _J(m,m)=sum(j0)+u(m)*u(m)*(G(m,m)*cos(delt(m)-delt(m))+B(m,m)*sin(delt(m)-delt(m)));& C9 c3 x; G# U' _/ e8 ]
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)));
+ V8 Y, i/ Z/ l- Y2 u else# U! a# ^* _6 D& R, [
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)));# A# ]* b. U$ p1 ]1 F
N(m,m)=0;
/ ]- Z; Q% m+ B" V: xJ(m,m)=0;
" O1 }* V! [$ O0 X) DL(m,m)=0;. Y; z; z9 ~2 r; X4 v; I
end u; S$ z; Z N0 F9 P( V
end! N* h A- C c) W5 p2 O, S
for m=1:N1+ U+ E, r* }$ i+ Y
JJ(2*m-1,2*m-1)=H(m,m);JJ(2*m-1,2*m)=N(m,m);
" y; Z. @! R7 Z, ]: f0 G7 I JJ(2*m,2*m-1)=J(m,m);JJ(2*m,2*m)=L(m,m);
7 c' B: j9 q+ ]+ {* rend
8 h* ]+ B8 B- T' i8 ?
2 Y$ A0 k+ f& W$ B4 _# Z" I" q6 ]" Wfor m=1:N1. `& K5 A, Y3 w6 n
for n=1:N1 1 c0 B. M4 D3 W) [$ q4 u+ d$ O+ E
if (m<=9)&(n<=9)&(m~=n) ( d' ~1 f2 U7 }; N2 R5 o' u
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));2 [( Z' U: I6 t+ n+ {+ z2 t! ]! R
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
2 z5 Q5 y4 z( c2 _& P+ oN(m,n)=-J(m,n);L(m,n)=H(m,n);' Z5 t* k" l5 N' |& c
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);) m7 d: F1 g k
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=L(m,n);* Z: ]3 O2 Q" ~& P
elseif ((m==10)&(n<10))|((m==11)&(n<10))|((m==12)&(n<10))|((m==13)&(n<10))
+ }$ s" S1 n* w& i9 ~6 GH(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));! T5 q4 s; B4 I$ `
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
4 g' c. N! f1 q# z7 t: _N(m,n)=-J(m,n);
) l% I" S, g9 qJJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);% T2 o5 }( [+ g
JJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;
% d; G; T3 V* ]" E& J: t0 [. ~; I elseif ((n==10)&(m<10))|((n==11)&(m<10))|((n==12)&(m<10))|((n==13)&(m<10))# j) C8 W2 y, R! A
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));& E; m f, g; B8 [/ M1 N
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));2 q* X% p K# j2 l# b, O
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;$ k8 W3 d$ E. [+ |/ P
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=0;! E6 x: S/ H+ o: C4 t' F- H w/ m: q
elseif (m>=10)&(n>=10)&(m~=n)- |9 V( ^: g ~0 _6 T6 h
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
- z2 V* r3 |5 w. F9 G7 H; XJJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;9 r) n3 U4 V8 {1 e$ b/ ?5 }6 x
JJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;7 @( G$ }8 z2 \' n4 T2 E
end( @' e6 R3 y7 H- U$ {- K: p
end0 H2 c, p. n/ S9 s: \$ ]' m, W6 w& i
end
- I( `) x. t* Q* t( d: o* J% 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
+ h. z/ u* ~5 n0 @5 sb=0;
( T% r* ~# A8 ?9 [; `* {for m=1:22
; [$ Y! ^+ H" P( u for n=1:22
3 c6 _- m- _, x. ~/ |. X2 P3 G if (m<=18)&(n<=18)
5 I' z0 }1 ^8 c7 [" i A(m,n)=JJ(m,n);( z/ }$ F- Y; l/ R
elseif (m>18)&(n<=18)+ h9 U7 e( C9 o2 `- M* x
A(m,n)=JJ(m+b,n);# R$ o! K7 `7 c, V, S2 b1 i
end , Z _: R; i8 A. ~
end5 W* W" @* a0 T5 [0 ~; s+ K0 I
if m>18) M2 Q% |+ Y" V; c2 `' K7 ]: L
b=b+1;% V/ q" A, z: O- r/ X
end
+ `# H- N9 v' O% G. |end
: e- u3 W$ T7 `3 M
; {4 k. X" G9 j$ i# i+ Jb=0;& ^% i8 O _4 z9 @' g" r8 V
for n=1:22
6 h; q2 v: I5 G* [* a% f for m=1:22
( X6 c9 o/ [: M if n<=18
2 `9 B/ y+ v4 V% S8 D A(m,n)=A(m,n);. W3 I$ H, W4 c$ `. h( y& h
elseif (m<=18)&(n>18)' k5 G$ O: f) [% ^% [
A(m,n)=JJ(m,n+b);
1 l; I9 `0 x5 n; K& G; f! q: h0 j, g end
9 t# F' } T% l% V- }" ` end4 k% \* S/ ^' l, A0 n
if n>180 c( G% Y* X8 y F8 M
b=b+1;
! B' K# C: {/ [ end' C# y4 \" m3 P. z8 N
end
. b. v" Z0 o0 F3 y 1 Z/ R5 }6 A" i- E- T) B1 k- T
b=0;
: j7 y3 ~1 {7 o* ?8 E& P5 nfor m=1:22% j0 N$ s- W$ w& {* o6 w
for n=1:266 E' d' {; H- i& e
if (m>=19)&(n>=19): _* |1 ?+ n- y& X7 T3 ?
D(m,n)=JJ(m+b,n); H0 q$ g! ~3 V& D4 Z9 O1 q% ?9 c3 F$ M; e
end
$ a% W- ?2 o3 Y- d end
0 d" N. T6 ^2 G$ u if m>18" X$ ]0 d7 o" t! x: J: j4 N
b=b+1;) i2 ]1 M+ S! s# J5 s5 [- T
end
. ]8 v: g5 r* ^% `! e) N" V# Qend
( g, m/ _! }+ |" p1 {$ Q " U: n% ]- k7 o6 G _: W! F
b=0;
5 y+ T" Q4 ?! {for n=1:22+ D; F" h9 ]* V J- H$ m' ]2 E: D
for m=1:226 f4 q' e7 d. J, z# d% g
if (m>=19)&(n>=19) ) ?; P6 B: M3 R( @ \; D4 b
D(m,n)=D(m,n+b);% ?& V+ w% P5 O/ {) i2 d8 U
end1 {+ @1 ^6 t/ L5 r4 l8 ]$ `
end" Q% a9 S8 k/ Y* `# i, L
if n>18
$ _" g4 C& t% S/ n9 I b=b+1;
( L9 V9 T) }& G# m0 l7 [ end7 L: I2 W; } r$ n
end- Y" a3 N0 P. L; g- s5 F @2 U1 }
9 ~6 M8 o1 B% z4 O3 T% t% P# `
for m=1:22
( G/ `; a# ~8 ^6 l* I for n=1:22
s- j/ o3 E+ L7 F7 e" i& |$ \ if (m>=19)&(n>=19)
# Q. @$ A. d& A0 U( M/ g A(m,n)=D(m,n);2 h3 S; u, O' P8 L8 X2 n* @
else! r3 d! a4 o; u3 u- ?
A(m,n)=A(m,n);
; C, o t- c5 l9 w5 y S end
5 Z" l6 k v1 m& a* E end
/ G' e' u1 Q; b9 s3 N, vend
+ o: U; u, m) ?! P% 形成不平衡量的列矩阵
% y; n, E! D$ C" O9 S( Hfor m=1:N1" T* F) F" C/ i3 {4 K! Q
PP(2*m-1)=pp(m);PP(2*m)=qq(m);
) F0 D% Y6 l6 a1 ^% y0 w6 I8 ^1 @end
$ Y6 [7 q+ _( P( }* Q1 q; vC=PP(1:1:18);
9 M4 y* |" u' f; Zb=0;
) @! }$ B! M! [: [7 `for m=1:22$ ]8 o8 I9 Q1 M, _
if m<=18; h5 I4 [' E5 e$ ]9 w
C=C;/ ` ^' H( }7 r5 y
else: \: U; S' A2 {- c3 _; x/ ~
C(m)=PP(m+b);
9 u. E; c: G W& m' z& V b=b+1;2 g7 i3 h6 ^2 y% A2 Z8 G. L8 [
end$ @ s2 r. ?- J
end
* `( D9 q) ]$ O/ J) V7 n% 解修正方程式,得到修正量
9 A1 @/ A* T! f( K3 quu=-inv(A)*C';
7 z1 U; t+ n& ^: c5 [$ Zprecision=max(abs(uu));& J) U2 i& z+ Z4 [8 n' E* m
% 计算个节点电压新值,即修正后值
0 d0 R& C$ F5 v3 v, s3 O- Sfor n=1:N11 C2 K+ r* x5 ^0 g3 g% W; @$ a
if n<=9
, z5 I0 K6 T0 ?4 [ delt(n)=delt(n)+uu(2*n-1);& ^. r+ z. n+ g, d7 B
u(n)=u(n)+uu(2*n);; K3 m% X9 ]2 `& C
else
+ E. t! j9 h i% Q% N delt(n)=delt(n)+uu(n+9);- A% C& B9 T( ]$ M; p* C( q5 t
u(n)=u(n);. a5 @! T. k4 Y3 @
end
4 C7 X: K. s3 k0 h% W: I8 `end% ?4 O9 v6 ]6 T% ?0 S: P/ R* _" v
% 循环次数k加一,带入新值进入下一次迭代, u( D! z. v- Q! R* b
k=k+1;
9 w1 z1 M* u7 ]. V K7 Yend+ K8 s9 [6 A* f: R
% 迭代完成后,求迭代次数、节点母线电压幅值与相角; k" ^& S& J# J% ]1 y- l
k-1,(delt*180/pi)',u') ]/ o3 J" X$ H3 g- ^& |) U" N
% 计算各节点的功率和线路功率
1 X& w, K8 A0 U4 e: mfor n=1:N1+1
& Z( K' b2 u# e1 G U(n)=u(n)*(cos(delt(n))+j*sin(delt(n)));
$ J5 C+ C: e8 j5 [' S9 k; yend
+ B4 T( v( Y) B7 `' y8 sfor m=1:N1+1) p- g& Y, d) I8 v7 s$ j' S0 t
for n=1:N1+1- C8 h$ o/ o/ u8 s; R3 d6 P v/ _
I(n)=Y(m,n)*U(n);& |" g' x# C# S0 O
end6 M8 ]6 K/ {3 m0 n+ {7 F. a
S(m)=U(m)*sum(conj(I));% A- ?2 f& T" Z- x
end
8 i; `- q7 o. S$ U4 O- q* pS
" B$ w5 \7 M, f" `for m=1:N1+13 N3 D4 I1 u% B8 j
for n=1:N1+1
3 A7 ~0 i7 r& R$ W$ k0 \# R T(m,n)=U(m)*conj((U(m)-U(n))*(-Y(m,n)))+U(m)*conj(U(m)*j*y(m,n));
1 F$ h4 C$ F! _( _2 D end
- i! e0 m+ d2 u* ^6 N/ Wend
7 _& ?8 Q! ?5 D" F; H. M4 XT |