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clear9 R8 E! `% c$ y; m
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 W& d5 {; K5 W) B+ Er(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;
& n# y! o. u7 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;
* l3 |( W% e6 U# O& p$ Br(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;, ?+ T- ]: P+ X* E s. M% ~% 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;8 C$ @6 i3 v- _8 Y
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;
4 e4 b. U0 \1 zr(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;0 N2 U6 {5 i3 u! D
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;8 Y, j0 l$ M7 [' _8 j8 @# l
+ m6 o0 y3 ]) my(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;
. Y; u. ?% j% j: ^5 ]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;& O, e: @6 n8 Y V! }: f f2 T. L0 R
$ w( f; W( R8 ~( ifor m=1:14# v% O2 k/ V; f1 w3 |- ?* N
t(m)=0;5 f( T& u/ b" O+ d" r3 U
for n=1:14
* s- @2 A+ |; t0 ] t(m)=t(m)+y(m,n);) e( v ~+ ^0 O. l8 @6 J
end$ F8 v& M0 H5 Z1 v
if m==4( `; e/ o; T/ u( d" t+ o& S" X
t(m)=t(m)+0.190;
- F1 W: k( L( C. O' e end
7 |) q' P1 h$ P& Y8 b: Wend
X! ~ B4 k" {/ s8 j2 Q& [for m=1:14
5 a7 j* Q4 W+ b" g5 X3 j d(m)=0;
: p n) O& p- |6 R- {6 B for n=1:14* R' x. @, o [* H- k$ I: Y
if m==n
% t7 M6 F5 @4 B7 e9 G! h s* u6 X1 @. B+ B5 x2 r+ R
elseif (r(m,n)==0)&(x(m,n)==0) Y. X3 H2 `0 q# m5 A* S! E" |: k
d(m)=d(m)+0; : L# P9 l: d7 Y
else
% R. r+ W# u6 Q6 w/ O4 ? d(m)=d(m)+1/(r(m,n)+j*x(m,n));
4 g" X1 e; @) _4 d# D( F, p$ h/ N end, H5 P' x7 P4 L$ a
end7 z5 {2 G9 v A3 L. W+ \$ J
end
$ {4 _* H1 D$ K- W+ }for m=1:145 M3 }" h' `4 B4 V
for n=1:14; `% p3 o; a5 D7 [2 g* M
if m==n! ?- a6 R- B0 V, n2 S
Y(m,n)=j*t(m)+d(m); p- U* S# g( a6 X
elseif (r(m,n)==0)&(x(m,n)==0)
: d' F/ e7 R* ~$ U: H6 i* Q Y(m,n)=0;; n$ i8 h+ C- `6 c* x5 ^- H
else
7 M3 B4 V X/ Y+ p Y(m,n)=-1/(r(m,n)+j*x(m,n));( g! }/ L8 ~7 g/ u1 F) \9 _1 z
end
- S! j( ?1 O% Q* |% C. U8 p end+ ^$ o- v. k4 T7 e+ ~
end
; S: O5 {9 E: H4 B" @( `2 JY;9 N) s9 r+ v. a: o
G=real(Y);B=imag(Y);
4 \- `0 D" i9 c: x* x%给定节点电压初值和循环次数k=0
3 X" C' G! F) l0 r) mdelt(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;
/ Q. ?5 z' L& \p(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;
1 {' J T+ M# o: x5 _# g- G8 Dk=0;precision=1;N1=13;: F% l2 b6 p( A, V H
%求节点功率的不平衡量�6�2P和�6�2Q5 V; k. { I: Q+ c! A7 q. P0 U* c \
while precision>0.00001& @$ L& _& i8 z2 V/ x* I
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;! o0 Z! S1 W/ W4 Z; M! V) p
for m=1:N1 ! o; G! j( J/ p! H7 @% u6 f
if m<=9
3 C. _. }( }3 S9 Y$ h for n=1:N1+1
. R5 c1 C8 l# E- [pt(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));# o. e+ R% @* T% ?9 Z% z
qt(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
/ q/ t% I, A) j- O/ t9 s$ ]' x end* h' }0 w7 ]& ]4 B) g
pp(m)=p(m)-sum(pt);qq(m)=q(m)-sum(qt);
" j" u# E2 \' d0 W, H9 Q* [! x9 i else* f. t" E. x# L- H$ F8 h* B! C- `
for n=1:N1+1
+ ~4 K$ Z) c- [9 b5 T7 o& m+ K1 {f(n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
0 z, v+ q& k& a5 Q* @+ w end
* P9 ^7 f0 `- b B' X9 K" e pp(m)=p(m)-sum(f);qq(m)=0;3 |8 @0 z: O" x: [
end ; ~; Z7 w: X2 n$ T/ c. k
end+ D1 k5 k9 q# U
%计算雅克比矩阵各元素5 Y- o. b1 x& u( X2 S8 {
for m=1:N17 X! z1 |0 s( n! I; w! V W8 ]
for n=1:N1+18 t6 Z p! i, w, o
h0(n)=u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));' @0 w' ~! `- D
n0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));! s3 I, D4 h. ^ W; D0 F
j0(n)=-u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));6 X+ \% M5 j% n* _- T
L0(n)=-u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
7 a( r6 A2 {% G& o end
0 T+ |2 r3 n- x$ y# `: L if m<=9
. y. L! G; [, N+ }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)));1 T) E+ T8 p$ h3 I( Q' m/ `
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)));) I- z+ I0 [, V4 T
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)));. w6 t1 z4 E" @% r5 a1 O# _5 l
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)));
) u! {3 V7 E2 Z! W6 H0 L$ o' L e else
% ^/ E3 X8 `9 oH(m,m)=sum(h0)- u(m)*u(m)*(G(m,m)*sin(delt(m)-delt(m))-B(m,m)*cos(delt(m)-delt(m)));
& c9 Q, G2 [6 W) c4 L) k; y) \N(m,m)=0;. V$ Q j L6 s1 Y
J(m,m)=0;: Z; k" C# }+ S
L(m,m)=0;+ z) \! b* d1 m- v; }" L
end
, ^9 {( g4 q% F. wend! W6 }0 g" n2 p* b, R
for m=1:N1
" J: G: E6 b) a' ]7 A JJ(2*m-1,2*m-1)=H(m,m);JJ(2*m-1,2*m)=N(m,m);2 m# T4 {0 j/ v) V% ^8 a
JJ(2*m,2*m-1)=J(m,m);JJ(2*m,2*m)=L(m,m);
* |2 `, C3 j: _2 @% x) x5 [ Xend
0 e/ }& l! p; ?0 j4 f8 d5 @ j" |& [6 [% P( \7 f* [+ N
for m=1:N1
, E- N" ~! Z9 o/ B' Y for n=1:N1
g6 P; w- z- W; c! F/ b* F if (m<=9)&(n<=9)&(m~=n)
! u) ?4 n$ `+ q8 I- R# |% hH(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
7 W4 k6 V6 d# m' r8 t/ K; }6 D, gJ(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));
0 r1 W4 |% [# q4 ^2 oN(m,n)=-J(m,n);L(m,n)=H(m,n);8 _4 k/ g6 ?- x c6 B1 e
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);0 F3 h" B! P; u. n# [1 V
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=L(m,n);. n5 i- ] m0 K u1 h- F7 K) q4 w% F) w
elseif ((m==10)&(n<10))|((m==11)&(n<10))|((m==12)&(n<10))|((m==13)&(n<10))
* [& ^# P6 z# iH(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));6 T. s, e' }7 {, W! e3 B
J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));. o( B& ]' w3 g# b/ d
N(m,n)=-J(m,n); ?0 C( k$ s z# n$ |
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=N(m,n);
7 W/ Z" O1 {% U4 N$ ?3 zJJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;
# u& U1 r+ P8 ]4 b7 a7 ? elseif ((n==10)&(m<10))|((n==11)&(m<10))|((n==12)&(m<10))|((n==13)&(m<10))& P% N0 q( \& g+ U
H(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));
4 L; [% J, L! n. ^J(m,n)=u(m)*u(n)*(G(m,n)*cos(delt(m)-delt(n))+B(m,n)*sin(delt(m)-delt(n)));) a. ~, l" ]+ Q5 t2 M$ M
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;$ L- m p6 W& W6 X. z* D
JJ(2*m,2*n-1)=J(m,n);JJ(2*m,2*n)=0;
7 G& @* `; F7 a, q+ t2 i elseif (m>=10)&(n>=10)&(m~=n)
$ e2 n. Y& E; a* RH(m,n)= -u(m)*u(n)*(G(m,n)*sin(delt(m)-delt(n))-B(m,n)*cos(delt(m)-delt(n)));8 g. g1 m* L( _
JJ(2*m-1,2*n-1)=H(m,n);JJ(2*m-1,2*n)=0;
' y' `6 r* q( a0 e! gJJ(2*m,2*n-1)=0;JJ(2*m,2*n)=0;
3 L% T, O$ V4 A7 j7 M9 k& u end
& l7 s" } C$ |" T# @5 ?2 \ end
! e6 Q! I& Q6 W. r7 |; M1 e% yend7 ^4 J) ?7 ]5 P8 T$ x2 _2 m
% 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2 y- d7 ^. b9 i, w8 Z6 I7 `
b=0;% D6 p P- K9 p% Y9 r
for m=1:22
/ O6 Z9 Q; d" ?4 C for n=1:229 R9 v7 g. w: A: I5 {! G/ g7 _
if (m<=18)&(n<=18)
0 z2 K& Y6 y7 ]9 I1 V. m: T A(m,n)=JJ(m,n);
, @0 P% ^2 V. \4 { elseif (m>18)&(n<=18)
4 ?# x/ u% s1 K& L A(m,n)=JJ(m+b,n);
( F9 `* v w6 Q" X, I3 N% n! K, U end $ G4 }0 s# l% L( P$ [4 V3 {
end# [8 R R* S. w/ B) [- `
if m>18
; p/ d% Z. {- i b=b+1;
6 h& R8 R- r$ }- \2 [ end
3 \/ H- o. ?7 f9 x% L( tend) U1 E+ v# ^+ j6 h# g2 M
9 x5 L, l4 h5 K- Cb=0;, y$ g$ }* s' J7 C$ k0 W2 I! V
for n=1:22
' _0 ?2 u: u$ c5 F# q# [ for m=1:22
& c8 P( @% N1 y5 F3 t! T# H7 I if n<=18
0 b9 U5 J5 P( f$ B) s7 m3 e A(m,n)=A(m,n);, n$ |& v' {9 f3 G7 s
elseif (m<=18)&(n>18)
( e R7 y! d& y/ F- |% O# L A(m,n)=JJ(m,n+b);1 p1 l! e2 a, z1 l6 y$ c
end
- `0 a7 ^) `5 x+ |$ D- B8 ]) m end, h# [# Y; Z% Z5 a. S
if n>188 H8 T$ j# P7 m7 `; q
b=b+1;/ i" t# J4 s- H& C& o3 a' H! z
end
@; h0 _& V% a$ {% Yend5 `5 z9 J0 O. ^3 [
7 t+ W0 q* c% ?b=0;7 H8 E+ ^. _5 W& d5 }* L
for m=1:225 I1 L( h. r/ w9 l. J/ z
for n=1:26* N$ u6 v: h. _* M
if (m>=19)&(n>=19)
' X" s" C' |: `" O X D(m,n)=JJ(m+b,n);
! z1 d8 O; d* }* j1 @% @5 A end
( \! z- c# o1 T& E, x; D8 ^+ C end' a# v! x1 K) \5 f
if m>18+ P) n& m2 S& f1 @, [' Q
b=b+1;: k' Y& p7 F8 W, W1 ^! e
end. T' s" i* |. }: U
end
. @. X3 V9 g+ j6 o/ s* Z! T7 Q
# S4 Q' W; d3 o2 L$ hb=0;7 |7 a& ]+ f6 M6 X
for n=1:22
( \+ }( f- W% ?# w9 X5 C# \! U for m=1:22
6 |! \% A$ {7 B s) E' k3 x# L if (m>=19)&(n>=19) 0 g0 V: t2 s) o3 H6 H4 [1 l
D(m,n)=D(m,n+b); E; r4 K- B6 c' B# @* M- S
end0 m |! P! z5 U. T6 ~. Z* `
end
4 N, F2 ^/ C- b, f% B if n>187 t9 l+ S! Y6 F; r
b=b+1;
0 \/ F5 |+ V; i+ D- C, M% I end* n" X$ p) c) e6 E( S6 Q% G6 v3 I
end1 C* P( w+ A' b' V; X' E% t
, V, n! x4 D- Q# \! zfor m=1:22
0 W0 D! K. d$ X3 W0 k for n=1:22* j$ ]% Y) h& e6 H O* l, a2 @
if (m>=19)&(n>=19) 7 p. c5 o$ i( |5 N! B
A(m,n)=D(m,n);
. [5 u" |6 o9 r, U else
9 L) A- I$ [, E1 y$ m; e* \ A(m,n)=A(m,n);; p2 J5 i$ Y2 f3 m
end$ ~& [ r: D; f
end: U3 `$ I0 R" L) H
end
& ^4 l3 g6 |- O6 c% 形成不平衡量的列矩阵* }* J2 N1 s u. @; W- X7 l: N* n6 A+ h
for m=1:N1
" k! m4 s' W( x9 y2 {8 B8 B PP(2*m-1)=pp(m);PP(2*m)=qq(m);
. b9 K" @/ x# b; Eend
9 `# F$ H5 V+ o* ` UC=PP(1:1:18);3 G) v; X1 n$ U& f# I2 }# t
b=0;
# o; A4 {; }. n( Qfor m=1:22
3 t1 l# N" U, ?, O* M# ? if m<=18
: X! n, Q1 K" W* V C=C;. `9 A* E p, @) L, }( S
else
7 x# R% |) X, ^ C(m)=PP(m+b);
- x7 h6 R3 c0 h3 a) }' H b=b+1;
' g/ @! H- S: E+ k0 V end8 o) K- Y4 |% k
end6 |* H3 k, T( l2 c) D
% 解修正方程式,得到修正量" ?) N% S. B. G, Q$ h/ _
uu=-inv(A)*C';9 c( ~9 W3 F- ]3 d
precision=max(abs(uu));& e$ h1 c& ?* g+ v0 W0 b6 y. n
% 计算个节点电压新值,即修正后值
# r ~* {- c' F) a! Pfor n=1:N1
7 s' K$ B! L; D* G5 w8 ^ if n<=9
; {6 u% J+ W0 W7 Q delt(n)=delt(n)+uu(2*n-1);
( W0 I& I1 p3 T! C0 N6 W u(n)=u(n)+uu(2*n);
' }9 k+ z- N+ l3 o7 r* x* {4 M else
: m$ k5 A: f( |" a% h* @' a. l delt(n)=delt(n)+uu(n+9);" q* i4 c* v3 p/ I
u(n)=u(n);; q2 s, t, [. y) m& r
end
6 v$ B! U: C5 N4 |end
1 Y) A2 _' b2 U1 r$ ~% 循环次数k加一,带入新值进入下一次迭代) G* _9 g8 I9 y! s" S# y9 G
k=k+1;
6 l" w* ` F' U+ I1 M1 Rend( }) C9 I+ B! ?* r. q5 r0 S
% 迭代完成后,求迭代次数、节点母线电压幅值与相角, B& l) E( e6 U( |
k-1,(delt*180/pi)',u'
" |! Y$ l0 A& z% V* T. g% d8 T& S% B% 计算各节点的功率和线路功率% P% i% K2 d6 F; a3 H0 U/ R
for n=1:N1+1
& q m8 Y4 @& t- k9 t! m$ E U(n)=u(n)*(cos(delt(n))+j*sin(delt(n))); G% K- s* `1 t! V: V
end+ [* A* B" ?7 m, m9 s: `
for m=1:N1+1
8 a' s1 s8 }4 Q, o5 T, o for n=1:N1+1
& b' L+ J" }5 i; t+ B% V9 q I(n)=Y(m,n)*U(n);" t: q: x2 Q% z
end
$ N7 a7 v3 w1 ?, i4 {" Q" r S(m)=U(m)*sum(conj(I));
/ l* B% c) w( `8 \' R Z" P9 z3 Zend) x* n4 L; S1 _
S1 Y/ X8 z( @8 ]' \
for m=1:N1+1
! M d; E' u. S' T" B9 O for n=1:N1+1 o5 H3 u2 D5 l* k' m
T(m,n)=U(m)*conj((U(m)-U(n))*(-Y(m,n)))+U(m)*conj(U(m)*j*y(m,n));* G- J/ H P Y/ B9 g2 y/ Q f
end* W; @ g! J. M
end
0 i5 O% `6 u% Q9 iT |