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//Book - Power System: Analysis & Design 5th Edition
//Authors - J. Duncan Glover, Mulukutla S. Sarma, and Thomas J. Overbye
//Chapter - 6 ; Example 6.11
//Scilab Version - 6.0.0 ; OS - Windows
clear;
clc;
linedata=[2 4 0.0090 0.10 1.72 //Entering line data from table 6.2 & 6.3
2 5 0.0045 0.05 0.88
4 5 0.00225 0.025 0.44
1 5 0.00150 0.02 0.00
3 4 0.00075 0.01 0.00];
//enter busdata in the order type (1.slack,2.pv,3.pq),Pi,Qi,PL,QL,vmag,del,Qmin and Qmax.
//Data is taken from table 6.1
Busdata=[1 0 0 0 0 1 0 0 0
3 0 0 8 2.8 1 0 0 0
2 5.2 0 0.8 0.4 1.05 0 4 -2.8
3 0 0 0 0 1 0 0 0
3 0 0 0 0 1 0 0 0]
npv=1; //Number of generator or PV buses in the system
rem=Busdata(:,1);
Psp=Busdata(:,2)-Busdata(:,4);
Qsp=Busdata(:,3)-Busdata(:,5);
vsp=Busdata(:,6);
//Determination of bus admittance matrix:
sb=linedata(:,1) //Starting bus number of all the lines stored in variable sb
eb=linedata(:,2) //Ending bus number of all the lines stored in variable eb
lz=linedata(:,3)+linedata(:,4)*%i; //lineimpedance=R+jX
sa=linedata(:,5)*%i; //shunt admittance=jB since conductsnce G=0 for all lines
nb=max(max(sb,eb)); //Number of buses in the system
ybus=zeros(nb,nb);
for i=1:length(sb)
m=sb(i);
n=eb(i);
ybus(m,m)=ybus(m,m)+1/lz(i)+sa(i)/2;
ybus(n,n)=ybus(n,n)+1/lz(i)+sa(i)/2;
ybus(m,n)=-1/lz(i);
ybus(n,m)=ybus(m,n);
end
Y=ybus;
absY=abs(Y);
thetaY=atan(imag(Y),real(Y));
v=vsp';
iteration=0; //Initialization of iteration count
ang=zeros(1,nb);
mismatch=ones(2*nb-2-npv,1);
tol=1e-4; //Tolerance value for Newton Raphson Load Flow
while max(abs(mismatch))>tol & iteration<100 //Maximum iteration count is limited to 100
J1=zeros(nb-1,nb-1);
J2=zeros(nb-1,nb-npv-1);
J3=zeros(nb-npv-1,nb-1);
J4=zeros(nb-npv-1,nb-npv-1);
P=zeros(nb,1);
Q=P;
del_P=Q;
del_Q=Q;
del_del=zeros(nb-1,1);
del_v=zeros(nb-1-npv,1);
ang;
mag=abs(v);
for i=2:nb
for j=1:nb
P(i)=P(i)+mag(i)*mag(j)*absY(i,j)*cos(thetaY(i,j)-ang(i)+ang(j));
if rem(i)~=2
Q(i)=Q(i)+mag(i)*mag(j)*absY(i,j)*sin(thetaY(i,j)-ang(i)+ang(j));
end
end
end
//Q=-1*Q;
del_P=Psp-P;
del_Q=Qsp-Q;
for i=2:nb
for j=2:nb
if j~=i
J1(i-1,j-1)=-mag(i)*mag(j)*absY(i,j)*sin(thetaY(i,j)-ang(i)+ang(j));
J2(i-1,j-1)=mag(i)*absY(i,j)*cos(thetaY(i,j)-ang(i)+ang(j));
J3(i-1,j-1)=-mag(i)*mag(j)*absY(i,j)*cos(thetaY(i,j)-ang(i)+ang(j));
J4(i-1,j-1)=-mag(i)*absY(i,j)*sin(thetaY(i,j)-ang(i)+ang(j));
end
end
end
for i=2:nb
for j=1:nb
if j~=i
J1(i-1,i-1)=J1(i-1,i-1)+mag(i)*mag(j)*absY(i,j)*sin(thetaY(i,j)-ang(i)+ang(j));
J2(i-1,i-1)=J2(i-1,i-1)+mag(j)*absY(i,j)*cos(thetaY(i,j)-ang(i)+ang(j));
J3(i-1,i-1)=J3(i-1,i-1)+mag(i)*mag(j)*absY(i,j)*cos(thetaY(i,j)-ang(i)+ang(j));
J4(i-1,i-1)=J4(i-1,i-1)+mag(j)*absY(i,j)*sin(thetaY(i,j)-ang(i)+ang(j));
end
end
J2(i-1,i-1)=2*mag(i)*absY(i,i)*cos(thetaY(i,i))+J2(i-1,i-1);
J4(i-1,i-1)=-2*mag(i)*absY(i,i)*sin(thetaY(i,i))-J4(i-1,i-1);
end
J=[J1 J2;J3 J4] //Entire Jacobian matrix of the system
lenJ=length(J1);
i=2;
j=1;
while j<=lenJ
if rem(i)==2
j=j+1;
else
J(:,length(J1)+j)=[];
lenJ=lenJ-1;
end
end
i=i+1;
lenJ=length(J1);
i=1;
j=2;
while i<=lenJ
if rem(j)==3
i=i+1;
else
J(length(J1)+i,:)=[];
lenJ=lenJ-1;
Q(i+1)=[]
del_Q(i+1,:)=[]
end
end
P(1,:)=[] //Removing slack bus entries
Q(1,:)=[]
del_P(1,:)=[];
del_Q(1,:)=[];
mismatch=[del_P;del_Q];
del=J\mismatch;
del_del=del(1:nb-1);
del_v=del(nb:length(del));
ang=ang(2:nb)+del_del'; //Updating voltage angle for PV and PQ buses
j=1;
for i=2:nb //Step to update voltage magnitude for all PQ buses
if rem(i)==3
v(i)=v(i)+del_v(j);
j=j+1;
end
end
mag=abs(v);
ang=[0 ang];
nbr=1:nb;
iteration=iteration+1;
if iteration==1
[r c]=size(J);
printf('The size of the Jacobian matrix is %d X %d\n',r,c)
printf('The change in power at the end of first iteration is DelP2=%.4f pu\n',del_P(1))
printf('The Jacobian matrix element J1(2,4) after first iteration is: %.4f pu\n',J(1,3))
disp(J,'The Jacobian Matrix of the system at the end of first iteration is given by:')
end
end
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