Coursework Task 2

%===========================================%
%Power Electronics in Distribution Networks %
%Coursework Task 2                          %
%===========================================%
%Clear Data
clear
clc
%System Parameters
V1=1.01;
ZL12=0.05+1i*0.01;
ZL13=0.04;
ZL34=0.01;
Zload3=2.21;
Zload4=2.08+1i*0.52;
%SOP Parameters
%PG=0.6;
PG=0;
PSOP=0;
QSOP2=0;
QSOP4=0;
%Admittance Matrix
YL12=1/ZL12;
YL13=1/ZL13;
YL34=1/ZL34;
Yload3=1/Zload3;
Yload4=1/Zload4;

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

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

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

G14=real(Y(1,4));
B14=imag(Y(1,4));

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

G23=real(Y(2,3));
B23=imag(Y(2,3));

G24=real(Y(2,4));
B24=imag(Y(2,4));

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));

%Define a vector voltage_at_2 to store the calculated V2 at each loop
voltage_at_2=[];

%Loop for plotting the figure when PG=0
for n= 1:30000
%resolution defined as 0.0001
PSOP=-1.0001+0.0001*n;
f=@(V2,V3,V4,theta2,theta3,theta4) [
    V1*V2*(G12*cos(theta2)+B12*sin(theta2))+V2*V2*G22+V2*V3*(G23*cos(theta2-theta3)+B23*sin(theta2-theta3))+V4*V2*(G24*cos(theta2-theta4)+B24*sin(theta2-theta4))-PG+PSOP;
    V1*V3*(G13*cos(theta3)+B13*sin(theta3))+V2*V3*(G23*cos(theta3-theta2)+B23*sin(theta3-theta2))+V3*V3*G33+V4*V3*(G34*cos(theta3-theta4)+B34*sin(theta3-theta4));
    V1*V4*(G14*cos(theta4)+B14*sin(theta4))+V2*V4*(G24*cos(theta4-theta2)+B24*sin(theta4-theta2))+V4*V3*(G34*cos(theta4-theta3)+B34*sin(theta4-theta3))+V4*V4*G44-PSOP;
    V1*V2*(G12*sin(theta2)-B12*cos(theta2))-V2*V2*B22+V2*V3*(G23*sin(theta2-theta3)-B23*cos(theta2-theta3))+V2*V4*(G24*sin(theta2-theta4)-B24*cos(theta2-theta4))+QSOP2;
    V1*V3*(G13*sin(theta3)-B13*cos(theta3))+V2*V3*(G23*sin(theta3-theta2)-B23*cos(theta3-theta2))-V3*V3*B33+V3*V4*(G34*sin(theta3-theta4)-B34*cos(theta3-theta4));
    V1*V4*(G14*sin(theta4)-B14*cos(theta4))+V2*V4*(G24*sin(theta4-theta2)-B24*cos(theta4-theta2))+V3*V4*(G34*sin(theta4-theta3)-B34*cos(theta4-theta3))-V4*V4*B44+QSOP4;];

fp=@(x) f(x(1),x(2),x(3),x(4),x(5),x(6));
disp(x);
theta2=x(4);
theta3=x(5);
theta4=x(6);
%Define vectors to  to store the calculated V2, V3, V4 at each loop
voltage_at_2(n)=x(1);
voltage_at_3(n)=x(2);
voltage_at_4(n)=x(3);
end


%Loop for plotting the figure when PG=0.6
for n= 1:30000
PG=0.6;
PSOP=-1.0001+0.0001*n;
f=@(V2,V3,V4,theta2,theta3,theta4) [
    V1*V2*(G12*cos(theta2)+B12*sin(theta2))+V2*V2*G22+V2*V3*(G23*cos(theta2-theta3)+B23*sin(theta2-theta3))+V4*V2*(G24*cos(theta2-theta4)+B24*sin(theta2-theta4))-PG+PSOP;
    V1*V3*(G13*cos(theta3)+B13*sin(theta3))+V2*V3*(G23*cos(theta3-theta2)+B23*sin(theta3-theta2))+V3*V3*G33+V4*V3*(G34*cos(theta3-theta4)+B34*sin(theta3-theta4));
    V1*V4*(G14*cos(theta4)+B14*sin(theta4))+V2*V4*(G24*cos(theta4-theta2)+B24*sin(theta4-theta2))+V4*V3*(G34*cos(theta4-theta3)+B34*sin(theta4-theta3))+V4*V4*G44-PSOP;
    V1*V2*(G12*sin(theta2)-B12*cos(theta2))-V2*V2*B22+V2*V3*(G23*sin(theta2-theta3)-B23*cos(theta2-theta3))+V2*V4*(G24*sin(theta2-theta4)-B24*cos(theta2-theta4))+QSOP2;
    V1*V3*(G13*sin(theta3)-B13*cos(theta3))+V2*V3*(G23*sin(theta3-theta2)-B23*cos(theta3-theta2))-V3*V3*B33+V3*V4*(G34*sin(theta3-theta4)-B34*cos(theta3-theta4));
    V1*V4*(G14*sin(theta4)-B14*cos(theta4))+V2*V4*(G24*sin(theta4-theta2)-B24*cos(theta4-theta2))+V3*V4*(G34*sin(theta4-theta3)-B34*cos(theta4-theta3))-V4*V4*B44+QSOP4;];

fp=@(x) f(x(1),x(2),x(3),x(4),x(5),x(6));
[x, fval, info] = fsolve (fp, [1.01;1.01;1.01;0;0;0]);
disp(x);
theta2=x(4);
theta3=x(5);
theta4=x(6);
voltage_at_22(n)=x(1);
voltage_at_33(n)=x(2);
voltage_at_44(n)=x(3);
end


%Loop for plotting the upper and lower boundary
for n=1:30000
ub(n)=1.02;
lb(n)=0.98;
end

figure(1)
index=-1.0000:0.0001:1.9999;
plot(index,voltage_at_2)
hold on
plot(index,ub)
hold on
plot(index,lb)
hold on
plot(index,voltage_at_3)
hold on
plot(index,voltage_at_4)
hold on
plot(index,voltage_at_22)

hold off