武汉理工大学电力系统分析课程设计(直角坐标系下的牛顿法潮流计算

附录：直角坐标下牛顿法潮流计算Matlab程序及调试结果

Matlab程序：

clear

clc

N=4; %独立节点数

NPQ=2; %PQ节点数

NPV=1; %PV节点数

K=0; %迭代次数

%请输入最大迭代次数Kmax。可从0开始，以观察第Kmax次迭代的结果Kmax=input('\n\n 请输入最大迭代次数后回车Kmax=\n');

small=10^(-5); %ε不能太小

%节点导纳矩阵Y的实部

G=[1.042093 -0.588235 0 -0.453858;

-0.588235 1.069005 0 -0.480769;

0 0 0 0;

-0.453858 -0.480769 0 0.934627];

%节点导纳矩阵Y的虚部

B=[ -8.242876 2.352941 3.666667 1.891074;

2.352941 -4.727377 0 2.403846;

3.666667 0 -3.3333333 0;

1.891074

2.403846 0 -4.261590];

%Y矩阵

Y=complex(G,B);

%给定PQ节点的Pnode、Qnode，PV节点的Pnode、Vnode。

Pnode=[ -0.3 -0.55 0.5];%PQ、PV节点的初值P

Qnode=[ -0.18 -0.13 0];%PQ节点的初值Q

Vnode=[0 0 1.1 0];%PV节点的初值V

%迭代初值

e=[1.0 1.0 1.1 1.05];

f=[0 0 0 0];

%%-----------------------------------------------------------------------------------

%利用for循环来实现多次迭代。

for K=0:Kmax,

fprintf('\n 第%d次迭代(共%d个独立节点)',K,N);

%计算△W (平衡节点不参与迭代)

%计算NPQ个PQ节点的△P、△Q。算法：先初始化，再不断地累减

%初始化,得△P=【Pnode(1),Pnode(2),……，Pnode(NPQ)】

for i=1:NPQ,

dP(i)=Pnode(i);

dQ(i)=Qnode(i);

end

%不断地累减,得△P和△Q

for i=1:NPQ,

for j=1:N,

a(j)=G(i,j)*e(j)-f(j)*B(i,j);

b(j)=G(i,j)*f(j)+e(j)*B(i,j);

end

C(i)=sum(a);

D(i)=sum(b);

dP(i)=dP(i)-e(i)*C(i)-f(i)*D(i);%△P

dQ(i)=dQ(i)-f(i)*C(i)+e(i)*D(i);%△Q end

%计算NPV个PV节点的△P、（△V）^2

%初始化

for i=(NPQ+1):(N-1),

dP(i)=Pnode(i);

end

%不断地累减,得△P和（△V）^2

for i=(NPQ+1):(N-1),

for j=1:N,

c(j)=G(i,j)*e(j)-f(j)*B(i,j);

d(j)=G(i,j)*f(j)+e(j)*B(i,j);

end

E(i)=sum(c);

F(i)=sum(d);

dP(i)=dP(i)-e(i)*E(i)-f(i)*F(i);

dV2(i)=Vnode(i)^2-e(i)^2-f(i)^2;

end

%组合成△W=[△P1,△Q1,△P2,△Q2,……,△P,△V^2](平衡节点不参与%将△P间隔地赋入△W

a=1;

for i=1:(N-1),

dW(a)=dP(i);

a=a+2;

end

%将△Q间隔地赋入△W

a=2;

for i=1:NPQ,

dW(a)=dQ(i);

a=a+2;

end

%将△V^2间隔地赋入△W

a=NPQ*2+2;

for i=(NPQ+1):(NPQ+NPV),

dW(a)=dV2(i);

a=a+2;

end

dW

%%

%判断是否小于ε

if max(dW)

fprintf('\n 迭代是收敛的。第%d次迭代后终止迭代。\n',K-1);

break;

end

%计算雅克比矩阵各元素。算法：先初始化，再不断地累减

J=zeros(N-1);

%初始化

for i=1:N-1,

for j=1:N-1,

if i<=NPQ %求雅克比矩阵中PQ节点的元素

if i==j

for k=1:4

p1(k)=G(i,k)*e(k)-B(i,k)*f(k);

q1(k)=G(i,k)*f(k)+B(i,k)*e(k);

end

P1(i)=sum(p1);

Q1(i)=sum(q1);

J(2*i-1,2*j-1) =-P1(i)-G(i,i)*e(i)-B(i,i)*f(i);% P_e

J(2*i-1,2*j ) =-Q1(i)+ B(i,i)*e(i)-G(i,i)*f(i);%P_f

J(2*i ,2*j-1) =Q1(i)+ B(i,i)*e(i)-G(i,i)*f(i);%Q_e

J(2*i ,2*j ) =-P1(i)+G(i,i)*e(i)+B(i,i)*f(i);%Q_f

elseif i~=j

J(2*i-1,2*j-1) = -G(i,j)*e(i)-B(i,j)*f(i);% P_e

J(2*i-1,2*j ) = B(i,j)*e(i)-G(i,j)*f(i);%P_f

J(2*i ,2*j-1) = B(i,j)*e(i)-G(i,j)*f(i);%Q_e

J(2*i ,2*j ) = G(i,j)*e(i)+B(i,j)*f(i);%Q_f

end

end

if i>NPQ, %求雅克比矩阵中PV节点的元素

if i==j,

for k=1:N

p1(k)=G(i,k)*e(k)-B(i,k)*f(k);

P1(i)=sum(p1);

q1(k)=G(i,k)*f(k)+B(i,k)*e(k);

Q1(i)=sum(q1);

end

J(2*i-1,2*j-1) =-P1(i)-G(i,i)*e(i)-B(i,i)*f(i);% P_e

J(2*i-1,2*j ) =-Q1(i)+ B(i,i)*e(i)-G(i,i)*f(i);%P_f

J(2*i ,2*j-1) = -2*e(i);

J(2*i ,2*j ) = -2*f(i);

elseif i~=j

J(2*i-1,2*j-1) = -G(i,j)*e(i)-B(i,j)*f(i);% P_e

J(2*i-1,2*j ) = B(i,j)*e(i)-G(i,j)*f(i);%P_f

J(2*i ,2*j-1) = 0;

J(2*i ,2*j ) = 0;

end

end

end

end

H=J;

J=[H(2,:);H(1,:);H(4,:);H(3,:);H(6,:);H(5,:)]

dH=dW';

dW2=[dH(2,1);dH(1,1);dH(4,1);dH(3,1);dH(6,1);dH(5,1)];

%不断地累减

%for i=1:NPQ,

% for k=1:N,

% J(2*i-1,2*i-1) = J(2*i-1,2*i-1)-G(i,k)*e(k)+B(i,k)*f(k);

% J(2*i-1,2*i) = J(2*i-1,2*i)-G(i,k)*f(k)-B(i,k)*e(k);

% J(2*i,2*i-1) = J(2*i,2*i-1)+G(i,k)*f(k)+B(i,k)*e(k);

% J(2*i,2*i) = J(2*i,2*i)-G(i,k)*e(k)+B(i,k)*f(k);

% end

% end

%根据△W=-J*△V, 得△V

dV=(-J)\dW2;

%用dV对e、f进行修正,并得到复数表示的V

for i=1:(N-1),

e(i)=e(i)+dV(2*i-1);

f(i)=f(i)+dV(2*i );

V(i)=complex(e(i),f(i));

end

V(N)=complex(e(N),f(N));

format long g;

V

end

调试结果：

请输入最大迭代次数后回车Kmax=

4

第1次迭代(共4个独立节点)

dW =

Columns 1 through 3

-0.2773071 -0.0509736000000012 -0.52596255 Columns 4 through 6

0.0196023000000006 0.5 0 J =

Columns 1 through 3

-8.1138496 1.0647859 2.352941

-1.0194001 -8.3719024 0.588235

2.352941 -0.588235 -4.5777747

0.588235 2.352941 -1.04496755

0 0 0

0 4.0333337 0 Columns 4 through 6

-0.588235 3.666667 0

2.352941 0

3.666667

1.09304245 0 0

-4.8769793 0 0

0 -2.2 0

0 0 -3.666667 V =

Column 1

0.993514216814943 - 0.00882844639325064i

Column 2

0.976339009868481 - 0.107817878429079i

Column 3

1.1 + 0.126652332934368i

Column 4

1.05

第2次迭代(共4个独立节点)

dW =

Columns 1 through 3

-0.00133294595315922 -0.00277676438603064 -0.0135290080657808 Columns 4 through 6

-0.0547116718789582 0.00301194536855756 -0.0160408134377179

J =

Columns 1 through 3

-7.9991772509487 1.40711407820907 2.33248713366264

-0.809097921062021 -8.36125161156212 0.60519264881312

2.23384583650122 -0.828005884158782 -4.36413332291915

0.828005884158782 2.23384583650122 -1.01896809464575

0 0 0

-0.464391929643459 4.0333337 0 Columns 4 through 6

-0.60519264881312 3.6428857928262 -0.0323709730514011

2.33248713366264 0.0323709730514011

3.6428857928262

2.08784598919201 0 0

-4.63639613373075 0 0

0 -2.2 -0.253304665868735

0 -0.0323709730514011 -3.6428857928262 V =

Column 1

0.984747556450846 - 0.00858486289103907i

Column 2

0.959002712892889 - 0.108374041635935i

Column 3

1.09244606907871 + 0.128933517085255i

Column 4

1.05

第3次迭代(共4个独立节点)

dW =

Columns 1 through 3

-3.60024206952716e-005 -3.72031420662056e-005 -0.000253704312255576 Columns 4 through 6

-0.00105962549946942 6.65806363944008e-005 -6.22656734941308e-005

J =

Columns 1 through 3

-7.92281414082541 1.39995632778377 2.3120029834003

-0.79396866348097 -8.29359740637982 0.599462654744568

2.19272739789519 -0.819116686719446 -4.22099361868917

0.819116686719446 2.19272739789519 -0.986486637198967

0 0

-0.472756272290441 4.00563595077062 0 Columns 4 through 6

-0.599462654744568 3.61074136856895 -0.0314778334620975

2.3120029834003 0.0314778334620975

3.61074136856895

2.08852065664668 0 0

-4.61443633228768 0 0

0 -2.18489213815742 -0.25786703417051

0 -0.0314778334620975 -3.61074136856895 V =

Column 1

0.984636349501068 - 0.00859560046446195i

Column 2

0.958689612744677 - 0.108386929719187i

Column 3

1.09241505000661 + 0.128954875586076i

Column 4

1.05

第4次迭代(共4个独立节点)

dW =

Columns 1 through 3

-6.91306070331119e-008 -7.69551480872543e-008 -5.98727410704358e-008 Columns 4 through 6

-3.83100107859136e-007 2.93037294668569e-008 -3.17684608744595e-008

迭代是收敛的。第3次迭代后终止迭代。