for j = 1:nb
Pi(i,1)=Pi(i,1)+bus(i,2)*bus(j,2)*(real(Y(i,j))*cos(bus(i,3)-bus(j,3))+imag(Y(i,j))*sin(bus(i,3)-bus(j,3)));
Qi(i,1)=Qi(i,1)+bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3))); end
end % 初始化并计算Qi和Pi for i = 1:nb-1
for j = 1:nb-1 if i~=j
H(i,j)=-bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3))); else
H(i,j)=Qi(i,1)+imag(Y(i,j))*((bus(i,2))^2);
end % 分别计算H矩阵的对角及非对角元素 if j < nPQ+1 if i~=j
N(i,j)=-bus(i,2)*bus(j,2)*(real(Y(i,j))*cos(bus(i,3)-bus(j,3))+imag(Y(i,j))*sin(bus(i,3)-bus(j,3))); else
N(i,j)=-Pi(i,1)-real(Y(i,j))*((bus(i,2))^2); end
end % 分别计算N矩阵的对角及非对角元素 if i < nPQ+1 if i~=j
K(i,j)=bus(i,2)*bus(j,2)*(real(Y(i,j))*cos(bus(i,3)-bus(j,3))+imag(Y(i,j))*sin(bus(i,3)-bus(j,3))); else
K(i,j)=-Pi(i,1)+real(Y(i,j))*((bus(i,2))^2);
end % 分别计算K矩阵的对角及非对角元素 if j < nPQ+1 if i~=j
L(i,j)=-bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3))); else
L(i,j)=-Qi(i,1)+imag(Y(i,j))*((bus(i,2))^2); end
end % 分别计算L矩阵的对角及非对角元素
end end end
J = [H N; K L]; % 生成雅克比矩阵
\作用为计算每个节点的功率注入
function bus = PQ(bus,Y,nPQ,nPV)
n = nPQ+nPV+1; % n为总节点数 for i = nPQ+1:n-1 for j = 1:n
bus(i,5)=bus(i,5)+bus(i,2)*bus(j,2)*(real(Y(i,j))*sin(bus(i,3)-bus(j,3))-imag(Y(i,j))*cos(bus(i,3)-bus(j,3))); end
end % 利用公式计算PV节点的无功注入 for j =1:n
bus(n,4)=bus(n,4)+bus(n,2)*bus(j,2)*(real(Y(n,j))*cos(bus(n,3)-bus(j,3))+imag(Y(n,j))*sin(bus(n,3)-bus(j,3)));
bus(n,5)=bus(n,5)+bus(n,2)*bus(j,2)*(real(Y(n,j))*sin(bus(n,3)-bus(j,3))-imag(Y(n,j))*cos(bus(n,3)-bus(j,3)));
end % 计算平衡节点的无功及有功注入
\作用为对节点和线路数据恢复编号
function [bus,line] = ReNum(bus,line,nodenum) [nb,mb]=size(bus); [nl,ml]=size(line);
bus_temp = zeros(nb,mb); % bus_temp矩阵用于临时存放bus矩阵的数据 k = 1;
for i = 1 :nb
for j = 1 : nb
if bus(j,1) == k
bus_temp(k,:) = bus(j,:); k = k + 1; end end
end % 利用bus矩阵的首列编号重新对bus矩阵排序并存入bus_temp矩阵中
bus = bus_temp; % 重新赋值回bus，完成bus矩阵的重新编号 for i=1:nl
for j=1:2
for k=1:nb
if line(i,j)==nodenum(k,1)
line(i,j)=nodenum(k,2); break end end end
end % 恢复line的编号
\作用为计算线路的等效Yt和Ym，以计算线路潮流
function YtYm = YtYm(line) [nl,ml]=size(line);
YtYm = zeros(nl,5); % 对YtYm矩阵赋初值0
YtYm(:,1:2) = line(:,1:2); % 矩阵前两列为线路两段节点编号，后三列分别为线路等效Yt，i侧的等效Ym，j侧的等效Ym j = sqrt(-1); for k=1:nl
I=line(k,1); J=line(k,2);
Zt=line(k,3)+j*line(k,4); if Zt~=0 Yt=1/Zt; end
Ym=line(k,5)+j*line(k,6); K=line(k,7);
if (K==0)&(J~=0) % 普通线路: K=0 YtYm(k,3) = Yt; YtYm(k,4) = Ym; YtYm(k,5) = Ym; end
if (K==0)&(J==0) % 对地支路: K=0,J=0,R=X=0 YtYm(k,4) = Ym; end
if K>0 % 变压器线路: Zt和Ym为折算到i侧的值,K在j侧 YtYm(k,3) = Yt/K;
YtYm(k,4) = Ym+Yt*(K-1)/K; YtYm(k,5) = Yt*(1-K)/K/K; end
if K<0 % 变压器线路: Zt和Ym为折算到K侧的值,K在i侧 YtYm(k,3) = -Yt*K;
YtYm(k,4) = Ym+Yt*(1+K); YtYm(k,5) = Yt*(K^2+K); end end
\计算并返回节点数据结果
function bus_res = bus_res(bus) [nb,mb]=size(bus);
bus_res = zeros(nb,4); % bus_res矩阵储存着节点计算结果 bus_res(:,1:2) = bus(:,1:2);
bus_res(:,3) = bus(:,3) *180 / pi; % 相角采用角度制 bus_res(:,4) = bus(:,4) + (sqrt(-1))*bus(:,5); % 注入功率 end
\计算并返回线路潮流
function S_res = S_res(bus,line,YtYm) [nl,ml]=size(line);
S_res = zeros(nl,5); % S_res矩阵储存着线路潮流计算结果 S_res(:,1:2) = line(:,1:2); % 前两列为节点编号 for k=1:nl
I = S_res(k,1); J = S_res(k,2);
if (J~=0)&(I~=0)
S_res(k,3)=bus(I,2)^2*(conj(YtYm(k,3))+conj(YtYm(k,4)))-bus(I,2)*bus(J,2)*(cos(bus(I,3))+j*sin(bus(I,3)))*(conj(cos(bus(J,3))+j*sin(bus(J,3))))*conj(YtYm(k,3));
S_res(k,4)=bus(J,2)^2*(conj(YtYm(k,3))+conj(YtYm(k,5)))-bus(I,2)*bus(J,2)*(conj(cos(bus(I,3))+j*sin(bus(I,3))))*(cos(bus(J,3))+j*sin(bus(J,3)))*conj(YtYm(k,3));
S_res(k,5)=S_res(k,3) + S_res(k,4); % 利用公式计算非接地支路的潮流 else if(J==0 )
S_res(k,3)=bus(I,2)^2*conj(YtYm(k,4)); S_res(k,5)=S_res(k,3)+S_res(k,4); else
S_res(k,4)=bus(J,2)^2*conj(YtYm(k,5));
S_res(k,5)=S_res(k,3)+S_res(k,4); % 利用公式计算接地支路的潮流 end end end end
作业
y=pifun(10000)
y =
3.1415
>> clear all >> tic;
>> y=pifun(100000); >> toc;
Elapsed time is 0.014727 seconds.
function y= pifun(n) y=0;
for i=1:n
y=y+(-1)^(i-1)*1/(2*i-1); end
y=y*4; end
>> a=0:pi/12:2*pi; >> x=5*cos(a); >> y=3*sin(a); >> plot(x,y) 3210-1-2-3-5-4-3-2-1012345
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