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clear4 ~4 s' D( J! r( i: o
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;
& [4 ?1 x0 w1 r: Jr(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;. d! U; z3 V, @$ U- G
r(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;% M9 s) ?3 E( i( a8 K( `6 _
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;# M& f8 k4 f3 @+ N% w" F3 Q: |2 U
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;* H5 T4 [+ e% Y9 M+ D5 w4 K; c
r(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;9 i8 n; H8 G# Z, d( y- M
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;
; E! `% B$ A4 A$ l3 C& \+ or(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;
2 m7 A' j. [3 @, R" m8 I( Q$ d L% {9 k5 J0 ^# H) s2 p8 h
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;, z- i, C( }& L$ e/ S$ e7 q
y(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;$ T" U2 x) W) M7 n4 v
) S l; V9 N2 i8 Cfor m=1:148 i+ T% {5 c$ e+ s
t(m)=0;
5 |7 A4 A$ Q) ?1 \ for n=1:14
$ f: W0 c; y9 E t(m)=t(m)+y(m,n);
# r- W7 T# M) S" m/ D7 m% ^- I4 p end) Y9 }+ k& A- M7 X5 M5 A
if m==4
( v% p7 g+ g' [2 Y0 x5 y0 m0 J% o9 _ t(m)=t(m)+0.190;+ ? ?1 x; J6 ?/ R' y7 \" K! S
end% O/ I0 ~$ t, U0 `
end
1 b" M$ B) ? W) a% k1 D/ C% sfor m=1:149 ^) z1 v9 p9 L; F! D
d(m)=0;
+ y. M* _& n- t$ I) ^2 _# Q for n=1:14
- j k, A; C9 k8 u% P if m==n
# G9 x0 Y1 T0 p; ]" r - |+ z: D0 X* D# B1 W
elseif (r(m,n)==0)&(x(m,n)==0); }& _5 l1 B# `* X7 w4 R1 ^ m7 X
d(m)=d(m)+0; & ~, o8 M# z7 o I0 a8 [, Q7 c
else
+ `4 u# m" H( p6 [& f& S d(m)=d(m)+1/(r(m,n)+j*x(m,n)); " w9 Z! ~' J+ H5 v
end4 c/ D7 }7 i) W7 Z5 c2 x4 ]' d% `8 T
end
; }# O! J ^5 _ Qend# f$ b0 e3 h* F' h& f* q; S
for m=1:14! H' j' b2 S+ a* X5 H; b5 k
for n=1:14
5 b" [% N* y' ~& j- N! E2 B if m==n r) s- w; x j0 b0 l
Y(m,n)=j*t(m)+d(m);
2 s0 _! H; W% O. f( u9 n elseif (r(m,n)==0)&(x(m,n)==0)6 \0 r. h$ z) F( W, ^! Y
Y(m,n)=0;2 l0 c7 ]3 Q, t& \+ m! p' p7 i
else
0 b& ~# L2 D& h9 f+ P/ X Y(m,n)=-1/(r(m,n)+j*x(m,n));7 k2 _! X) F# r( M
end
7 R+ S9 P0 y# M7 z+ ^ end
" j [' I% G V/ _1 Hend
! B2 p h/ R* c/ YY;3 n& K% h g3 ^/ X; m2 {
G=real(Y);B=imag(Y);1 j6 j# S6 c3 D/ W0 O$ p( m% s: s
%给定节点电压初值和循环次数k=0
1 g3 a O5 Q4 |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;
0 D+ b* ?5 C% y! W0 ep(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;& X5 ~+ n) p' Z M
k=0;precision=1;N1=13;0 ~3 \& R8 V& b1 E. v
%求节点功率的不平衡量�6�2P和�6�2Q
! z8 z$ f* V8 _7 |! g# Kwhile precision>0.000011 Q- d9 ]! h( M. |7 J! l9 U0 ~
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;
( K) M# O# s/ X( t for m=1:N1
3 e8 d5 |* v; I/ O3 N if m<=92 S0 i+ D2 v; H2 s% E& j/ C6 O
for n=1:N1+1
2 b/ P0 G& _! C7 @$ B1 `" S/ w9 Gpt(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
3 s* t! C) j. r- b, A1 Yqt(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n))); - j5 }1 w- f* d' Z: @; o
end5 v7 K9 P" X& S. Z+ t. x
pp(m)=p(m)-sum(pt);qq(m)=q(m)-sum(qt);- I3 J: {8 p, s
else6 X- a3 F! m0 p7 H
for n=1:N1+1
! v0 D5 s% c/ Q& pf(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
' F1 U# g) O* A# [! G" y4 V end. t" [, m) F2 A9 a4 ~
pp(m)=p(m)-sum(f);qq(m)=0;7 s; C3 W1 J3 v9 ^0 V
end o f$ n3 F0 w4 b+ `- z
end; g# ^) Q+ F' \" J6 v
%计算雅克比矩阵各元素
+ i. g" n3 k4 j% T& l5 ufor m=1:N13 W) E4 n2 a- V0 Y
for n=1:N1+12 o1 [/ Y5 o4 H8 r, B/ s( P
h0(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
- P2 r3 g# Z7 E/ u, p# b: y7 _. J n0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
3 V o1 r. F, H j0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
" Z% _' `5 Q, w L0(n)=-u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));: }6 v* R( H$ y; S$ X
end; z9 t" i3 [( k, \6 n3 z3 d' u" H
if m<=9
7 p$ G2 x1 F! e7 h* ?" TH(m,m)=sum(h0)- u(m)*u(m)*(G(m,m)*sin(delt(m)-delt(m))-B(m,m)*cos(delt(m)-delt(m)));
# s2 p7 F0 h3 ?+ Y4 j2 M! c+ 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)));
5 V/ `) f3 d4 X5 @* bJ(m,m)=sum(j0)+u(m)*u(m)*(G(m,m)*cos(delt(m)-delt(m))+B(m,m)*sin(delt(m)-delt(m)));
0 i8 H' G4 A% h& d* j- a" M% RL(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)));1 f, x9 K$ N/ A% L" ?' G- I5 g" B
else
7 B k) {9 x" q& N! f$ p6 j4 q! mH(m,m)=sum(h0)- u(m)*u(m)*(G(m,m)*sin(delt(m)-delt(m))-B(m,m)*cos(delt(m)-delt(m)));- t# E4 V1 k' M% h0 G; c. [! D: v
N(m,m)=0;9 f. s0 U( C8 ]0 b
J(m,m)=0;
5 w; z, H4 T0 h' m% rL(m,m)=0;
2 l4 _- o4 G+ N1 I* g0 m4 O8 Q end/ ]! D) f4 F0 u1 h# T
end6 S$ q, ^% W( \% \! S
for m=1:N19 J0 S- U ^. U8 c& w s( i+ {
JJ(2*m-1,2*m-1)=H(m,m);JJ(2*m-1,2*m)=N(m,m);
1 o3 E# L& ~1 d! }) u6 o# D- Y: E JJ(2*m,2*m-1)=J(m,m);JJ(2*m,2*m)=L(m,m);
( h' y& `+ z. `7 Fend
1 l1 k" U O3 F ?7 p1 j ' l! @6 @5 w6 d9 L! l( J
for m=1:N1
. s5 b/ F+ `' `9 z& M% P& ^3 Z5 S for n=1:N1
9 f( p4 o0 H% ]: j if (m<=9)&(n<=9)&(m~=n)
- ?" d. ]! l- Y! V5 RH(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
) o/ _; B$ R8 A3 F0 ^* Y0 P, ]3 _J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
' W# G3 v. O& x/ BN(m,n)=-J(m,n);L(m,n)=H(m,n);
1 w0 ~/ X) y: R% N$ D1 }# M! fJJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);/ \; [9 N) m" b% b5 O
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=L(m,n);
: E3 O, j$ B) d S elseif ((m==10)&(n<10))|((m==11)&(n<10))|((m==12)&(n<10))|((m==13)&(n<10))5 [( }5 P5 \$ `( G0 w, g) G
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));# x9 p. G6 m& T6 E' ^
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));0 \; a; q5 V, Z! n/ [+ P- p# Z0 c% L* x
N(m,n)=-J(m,n);
2 t7 Y/ |& N6 D1 m6 F/ Q& bJJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);
- {0 M" P- d% \; XJJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;: ]4 W8 j5 b+ Z) l( M& q! K2 K
elseif ((n==10)&(m<10))|((n==11)&(m<10))|((n==12)&(m<10))|((n==13)&(m<10))0 _" K: b4 H' L' i
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));# R5 k$ J- y+ D
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
) `, ?, y5 h2 z9 WJJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;: F* b: r7 P, ?6 k; J4 _
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=0;+ m, e+ h- O K6 i
elseif (m>=10)&(n>=10)&(m~=n). s7 j C; c$ G' k
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
i: t. O6 m: E( L- Q( FJJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;0 H9 U; Z. {1 \$ H0 j; p
JJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;$ \4 Z8 }* A0 L r: r1 `
end# u) s) z+ D1 N( j4 `
end
5 z3 x# r' Q6 l2 L' ]end( s M+ B# S" v/ a
% 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1 r7 b8 J; h7 e4 L7 x5 t& R
b=0;. E5 F+ t) o2 L( l- P
for m=1:22
5 }' x( f9 X4 e! B3 o o for n=1:22
7 d8 U& M {) g( F5 e if (m<=18)&(n<=18)
& l# B5 t$ u+ d3 k/ D A(m,n)=JJ(m,n);
`& w9 J9 a& U% a, X7 w* |; q$ f elseif (m>18)&(n<=18)) X% @5 n4 ]& n- ?1 B6 N
A(m,n)=JJ(m+b,n);
0 B+ X/ p+ }3 e) Y& E: m end 8 G2 Q) u8 Y: Y) r3 q/ t
end% \! ]/ D6 R+ |: z7 ?/ Y
if m>18
2 x3 T' n C- T6 a3 u' \! c, V, y b=b+1;( H/ ]( y! y" u" b
end
, V; r; o) B, F$ G9 _% J6 ?end
- ]; p: ~; F; T% {4 e
/ `0 T7 L1 `. b X$ H" B0 p8 C' ~b=0;' w; C3 H+ V- {0 ~4 D' W
for n=1:222 D+ n" P2 E) Y( i" |" W' G
for m=1:22
, z1 P1 ~) S3 p$ U if n<=18* ?; \' `# s3 b* T7 J9 w
A(m,n)=A(m,n);
' ]# n+ k2 V6 a, O elseif (m<=18)&(n>18)( b- h: b/ i3 i6 e# G/ m
A(m,n)=JJ(m,n+b);
3 o0 S+ `- P; n end
6 q0 Y4 G' S. Z$ c8 p$ h: v end
! S. Q) h& z' K# o if n>187 E! b0 s. i/ Q' B) a! ?4 e
b=b+1;0 O9 r7 ^- e- z5 q1 u) ^
end
, r# Y: j3 ~% d/ ~end
2 ` |) I. D, ]4 B9 ^' }% q0 c% n $ P, w* B- V1 G1 l
b=0;( L* o* B9 O- _3 ?3 s+ l& ?" F3 T& i
for m=1:22
3 Z- G" G4 _/ ? for n=1:26; f2 P' d }+ I# ^/ l) [4 e
if (m>=19)&(n>=19)
1 u. i Y5 v( ^+ N D(m,n)=JJ(m+b,n);
5 y- B, b" n! h | end0 p) J) |$ F, t$ F; }7 m
end* B: A9 R$ u/ w1 ~8 ~
if m>18% j C9 O% ^# t
b=b+1;
) H4 \( i6 j' p0 [( x8 p8 A end' C3 e% b* C1 Y+ [1 R9 d' X: H
end2 U! X4 q. q6 r7 m1 E8 ~
. Y& _1 D6 G8 X6 R& V: Lb=0;
* M# h9 P8 f' r5 ~! b4 `0 S* ^/ Bfor n=1:22
1 c9 t9 d3 [6 |" _: M* [+ o for m=1:229 d' H0 Z, i% b/ `9 ~( G2 [7 R7 z' O
if (m>=19)&(n>=19) , q7 i+ K1 T1 X$ Y2 P
D(m,n)=D(m,n+b);
) \& b y/ ^ ^; B1 e end
- M1 I/ Q: y# J8 I end* A! B. P* I9 L( N
if n>18, S ?* Z( u9 E
b=b+1;) R/ Y- @& U% y% T6 ?
end
+ ~( B! ?% ]6 Q4 m! v d9 hend( ~- n+ a% q$ ]6 \
9 c( }5 ?# W2 b. D. `3 e
for m=1:22
6 p. A& {& E2 N% B$ I9 ] for n=1:22
l8 z9 b! t" I! X; a6 K% X if (m>=19)&(n>=19) ' {! g+ T Z! |2 \# }9 f' G
A(m,n)=D(m,n);
. J9 t5 N9 R, I$ ]( m else( b" E ~4 G/ g6 h3 E
A(m,n)=A(m,n);7 N( i) E4 A- ]" L
end( t" m l3 A) U2 p3 U/ D: G
end* `: B% X, g2 P5 F* i9 k
end* e3 }$ M5 @0 K" A. [3 I. P9 N
% 形成不平衡量的列矩阵
: e% r3 ]- Q5 q4 |for m=1:N1. V; l- j$ \6 s7 `! B9 o, W6 {
PP(2*m-1)=pp(m);PP(2*m)=qq(m);. u- f1 i6 T. Z' Q' P+ f
end
. A$ P+ o8 h9 `9 H. Z' H: _; d% k, MC=PP(1:1:18);
9 J/ q0 l. i6 W& f1 s3 y- p% a) [b=0;. U# \0 u* S% a% @% `( e; X9 b
for m=1:22% I; R. q2 ~ R$ x; G, i3 d+ \$ @
if m<=18; O; C# r* r1 }. q. }2 J' f
C=C;' F4 G( \' d. ^9 e' G# e! t
else
* a1 g: g& f ^% X/ v7 Q C(m)=PP(m+b);& g: Y: Y2 b. L7 y# |5 |
b=b+1;# F9 T/ m* T% E- n9 S6 d* p, g
end
* \' L. _, j. r% ^7 r2 cend/ s0 j+ z+ K" e$ g- x8 s
% 解修正方程式,得到修正量
) k+ y! W) Z, U8 c+ | auu=-inv(A)*C';
+ J- O8 f, e3 a" H/ x! zprecision=max(abs(uu));
8 m8 E8 W/ @+ v% 计算个节点电压新值,即修正后值
0 S+ S1 u$ B9 H4 {for n=1:N1
' r: \7 ~9 k! a# B5 M( a if n<=9% n/ X! G8 f! A5 C
delt(n)=delt(n)+uu(2*n-1);
* l& t. ~1 @$ h+ [1 y) w! v8 j u(n)=u(n)+uu(2*n);1 L6 L: O6 C- }6 c
else
3 [8 G4 b( l. m+ m delt(n)=delt(n)+uu(n+9);
! R. y% r' G4 H) A. Z8 v5 ~ u(n)=u(n);
. H) x% O/ n9 Z0 e. E end. C! O) R" k; H x# E
end0 _2 _; y! X2 y7 Y
% 循环次数k加一,带入新值进入下一次迭代0 g0 R4 A1 o, Z9 m
k=k+1;' m) F" l! S" E# G# U, r( x
end# x) p+ q7 M! H( P9 R; L% B
% 迭代完成后,求迭代次数、节点母线电压幅值与相角; v o* ]) E1 d
k-1,(delt*180/pi)',u'
' }) I! `7 W6 |9 ?2 O. \6 `6 e% 计算各节点的功率和线路功率
% t, H# ]+ E3 e9 f2 U4 Gfor n=1:N1+1
! Y) r. m: w0 ^4 p* W U(n)=u(n)*(cos(delt(n))+j*sin(delt(n)));
1 ~$ c. q! r& a1 t) m( [2 [end
) U. J- ` Q, ~$ k; Ifor m=1:N1+1
# r3 w) n& E& \ for n=1:N1+1
( y1 e( u! M5 R- Y+ j$ [ I(n)=Y(m,n)*U(n);/ t4 `# M1 v/ o
end% B- [( J, ?) g7 q
S(m)=U(m)*sum(conj(I));. b4 V; @& Y" R* a
end& g, Q( t1 j! Q7 T( K* E9 G2 o5 V
S
% L; B! z: _, [& k# ]7 ?' Mfor m=1:N1+1
9 P* M+ u* i. L0 G$ g2 x( n" W for n=1:N1+12 g/ \( b1 s J) S6 C5 s
T(m,n)=U(m)*conj((U(m)-U(n))*(-Y(m,n)))+U(m)*conj(U(m)*j*y(m,n));
0 O& Y. N: ^( ^$ S+ W. g0 m end% i# @7 G9 h6 j8 @$ Q
end
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