5. Modify the Ybus from the previous problem directly if mutual couplings exist

Question

5. Modify the Ybus from the previous problem directly if mutual couplings exist in the system as shown below. Specifically, there is a mutual coupling between branch 1-3 and 2-3 with mutual impedance j0.15 p.u. Also there is a mutual coupling between branch 2-3 and 2-5 of value 30.125 ?.u. Verify your result by modifying the primitive admittance and recalculating the Ybus using the incidence matrix approach in MATLAB. You must submit your script to receive credit for this problem. ,0.4 j0.5 j0.5 jl 0.125 j1.25 10° pu + 0.9

Explanation / Answer

clc;

clear all;

elements=input('Enter number of elements=');

zdata=zeros(elements,6);

fprintf('enter data in this format: 1. Element no 2. Frombus no 3.To bus no 4.Self impedance 5. Mutually coupled element no 6. Mutual impedance value ');

fprintf('If element has no mutual coupling enter item 6 as zero If program ask for "zdata",Enter like the following example ');

fprintf('zdata=[1 0 2 0.25j 2 0.01j;2 0 1 0.2j 1 0.01j;etc] ');

yprimitive=zeros(elements,elements);

zprimitive=zeros(elements,elements);

zdata=input('Enter zdata=');

x=zdata(:,5);

for i=1:elements

zprimitive(i,i)=zdata(i,4);

if x(i)~=0

zprimitive(x(i),i)=zdata(i,6);

end

end

nb=max(max(zdata(:,2)),max(zdata(:,3)));

nbuses=nb-1;

A=zeros(elements,nbuses);

for i=1:elements

if zdata(i,2)~=0

A(i,zdata(i,2))=1;

end

if zdata(i,3)~=0

A(i,zdata(i,3))=-1;

end

end

A

yprimitive=inv(zprimitive)

Ybus=A'*yprimitive*A

RESULTS:

Enter number of elements= 9 (press enter)

enter data in this format:
1. Element no 2. Frombus no 3.To bus no 4.Self impedance
5. Mutually coupled element no 6. Mutual impedance value

If element has no mutual coupling enter item 6 as zero

If program ask for "zdata",Enter like the following example

zdata=[1 0 2 0.25j 2 0.01j;2 0 1 0.2j 1 0.01j;etc]
Enter zdata=

[1 0 1 1i 0 0; 2 1 2 0.4i 0 0; 3 1 3 0.5i 4 0.15i; 4 2 3 0.25i 3 0.15i; 4 2 3 0.25i 5 0.125i; 5 2 5 0.2i 4 0.125i; 6 3 4 0.125i 0 0; 7 4 5 0.5i 0 0; 8 4 0 2 0 0; 9 0 5 1.25i 0 0]

A =
-1 0 0 0 0
1 -1 0 0 0
1 0 -1 0 0
0 1 -1 0 0
0 1 -1 0 0
0 1 0 0 -1
0 0 1 -1 0
0 0 0 1 -1
0 0 0 1 0


yprimitive =

0.0000 - 1.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 - 2.5000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 2.4390i 0.0000 + 1.4634i 0.0000 + 0.0000i 0.0000 - 0.9146i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 1.4634i 0.0000 - 4.8780i 0.0000 + 0.0000i 0.0000 + 3.0488i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 8.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 5.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 8.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 - 2.0000i 0.0000 + 0.0000i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 0.0000i 0.5000 + 0.0000i


Ybus =

0.0000 - 5.9390i 0.0000 + 3.0488i 0.0000 + 0.9756i 0.0000 + 0.0000i 0.0000 + 0.9146i
0.0000 + 3.9634i 0.0000 -17.3293i 0.0000 +11.4146i 0.0000 + 0.0000i 0.0000 + 1.9512i
0.0000 + 0.9756i 0.0000 + 9.2805i 0.0000 -20.3902i 0.0000 + 8.0000i 0.0000 + 2.1341i
0.0000 + 0.0000i 0.0000 + 0.0000i 0.0000 + 8.0000i 0.5000 -10.0000i 0.0000 + 2.0000i
0.0000 + 0.0000i 0.0000 + 5.0000i 0.0000 + 0.0000i 0.0000 + 2.0000i 0.0000 - 7.0000i

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