01819229

clear
clc

% Fixed voltage magnitude at the slack bus
V1=1.01;

Pg=0;
PSOP=0;
% Load parameters of the two feeder system (p.u.)
ZL12=0.05+i*0.01;
ZL13=0.04;
ZL34=0.01;
Zload3=2.21;
Zload4=2.08+i*0.52;

% Admittance calculation
YL12=1/ZL12;
YL13=1/ZL13;
YL34=1/ZL34;
Yload3=1/Zload3;
Yload4=1/Zload4;

% Admittane matrix
Y=[YL12+YL13,-YL12,-YL13,0;
-YL12,YL12,0,0;
-YL13,0,YL13+YL34+Yload3,-YL34;
0,0,-YL34,YL34+Yload4];

% Obtaining real part of the complex number for Y matrix
G11=real(Y(1,1));
% Obtaining imaginary part of the complex number for Y matrix
B11=imag(Y(1,1));

G12=real(Y(1,2));
B12=imag(Y(1,2));

G13=real(Y(1,3));
B13=imag(Y(1,3));

G22=real(Y(2,2));
B22=imag(Y(2,2));

G33=real(Y(3,3));
B33=imag(Y(3,3));

G34=real(Y(3,4));
B34=imag(Y(3,4));

G44=real(Y(4,4));
B44=imag(Y(4,4));

PSOPArray = [];
for PSOP = 0:0.01:1

    % PSOP has been added for Q2a to extract 0.8 pu of active power from (2) to (4)
    % PSOP not added for Q1a
    % 6 unknowns variables - V2, V3, V4, theta2, theta3 and theta 4 are
    % calculated below by creating the function
f=@(V2,V3,V4,theta2,theta3,theta4) [V1*V2*(G12*cos(theta2)+B12*sin(theta2))+V2*V2*G22 + PSOP;
    V1*V3*(G13*cos(theta3)+B13*sin(theta3))+V3*V3*G33+V3*V4*(G34*cos(theta3-theta4)+B34*sin(theta3-theta4));
    % PSOP not added for Q1a
    % PSOP has been subtracted for Q2a to extract 0.8 pu of active power from (2) to (4)
    V4*V4*G44+V3*V4*(G34*cos(theta4-theta3)+B34*sin(theta4-theta3))- PSOP;
    V1*V2*(G12*sin(theta2)-B12*cos(theta2))-V2*V2*B22;
    V1*V3*(G13*sin(theta3)-B13*cos(theta3))-V3*V3*B33+V3*V4*(G34*sin(theta3-theta4)-B34*cos(theta3-theta4));
    -V4*V4*B44+V3*V4*(G34*sin(theta4-theta3)-B34*cos(theta4-theta3))];
    % derivative of the defined function to build Jacabian, J.

J=@(V2,V3,V4,theta2,theta3,theta4) [V1*(G12*cos(theta2)+B12*sin(theta2))+2*V2*G22, 0, 0, V1*V2*(-G12*sin(theta2)+B12*cos(theta2)), 0, 0;
    0, V1*(G13*cos(theta3)+B13*sin(theta3))+2*V3*G33+V4*(G34*cos(theta3-theta4)+B34*sin(theta3-theta4)), V3*(G34*cos(theta3-theta4)+B34*sin(theta3-theta4)), 0, V1*V3*(-G13*sin(theta3)+B13*cos(theta3))+V3*V4*(-G34*sin(theta3-theta4)+B34*cos(theta3-theta4)), V3*V4*(G34*sin(theta3-theta4)-B34*cos(theta3-theta4));
    0, V4*(G34*cos(theta4-theta3)+B34*sin(theta4-theta3)), V3*(G34*cos(theta4-theta3)+B34*sin(theta4-theta3))+2*V4*G44, 0, V3*V4*(G34*sin(theta4-theta3)-B34*cos(theta4-theta3)), V3*V4*(-G34*sin(theta4-theta3)+B34*cos(theta4-theta3));
    V1*(G12*sin(theta2)-B12*cos(theta2))-2*V2*B22, 0, 0, V1*V2*(G12*cos(theta2)+B12*sin(theta2)),0,0;
    0, V1*(G13*sin(theta3)-B13*cos(theta3))-2*V3*B33+V4*(G34*sin(theta3-theta4)-B34*cos(theta3-theta4)), V3*(G34*sin(theta3-theta4)-B34*cos(theta3-theta4)), 0, V1*V3*(G13*cos(theta3)+B13*sin(theta3))+V3*V4*(G34*cos(theta3-theta4)+B34*sin(theta3-theta4)), V3*V4*(-G34*cos(theta3-theta4)-B34*sin(theta3-theta4));
    0, V4*(G34*sin(theta4-theta3)-B34*cos(theta4-theta3)), -2*V4*B44+V3*(G34*sin(theta4-theta3)-B34*cos(theta4-theta3)), 0, V3*V4*(-G34*cos(theta4-theta3)-B34*sin(theta4-theta3)), V3*V4*(G34*cos(theta4-theta3)+B34*sin(theta4-theta3))];

fp=@(x) f(x(1),x(2),x(3),x(4),x(5),x(6));
Jp=@(x) J(x(1),x(2),x(3),x(4),x(5),x(6));
% Newton-Raphson
x=zeros(6,6);
x(1,:)=[1.01,1.01,1.01,0,0,0];
disp(norm(fp(x(1,:))));
for n=2:length(x)
    x(n,:)=x(n-1,:)-((Jp(x(n-1,:))^(-1))*fp(x(n-1,:)))';
    disp(norm(fp(x(n,:))));
end
disp('Solution:');
disp(x(n,:));

PSOPArray = [PSOPArray [x(n,1); x(n,2) ; x(n,3)]];

end
clf
hold on

plot(0:0.01:1,PSOPArray')

figure(1)
hold on
% plot graph of Voltages against PSOP for Q2d
disp('Intersection 1:');
P = InterX([0:0.01:1;PSOPArray(1,:)],[0:0.01:1;PSOPArray(2,:)])
plot(P(1),P(2),'ko');
disp('Intersection 2:');
P = InterX([0:0.01:1;PSOPArray(1,:)],[0:0.01:1;PSOPArray(3,:)])
plot(P(1),P(2),'bo');
disp('Intersection 3:');
P = InterX([0:0.01:1;PSOPArray(2,:)],[0:0.01:1;PSOPArray(3,:)])
plot(P(1),P(2),'ro');


hold off

xlabel ('PSOP (p.u.)')
ylabel ('Voltage (p.u.)')
title ('Voltages against PSOP range')
legend("V2","V3","V4")