UETian Blogger: December 2015

Kron Reduction

In power system anylasis, kron reduction is a way of reducing buses in Y bus matrix of the power system. It usually used for two reasons

To remove a bus where current injection is zero to reduce size of matrix thereby effectively making computation easy. Buses with no load or source don't inject currents.
To use only some buses specific buses instead of whole system to know required voltages only. This way we can get voltages of our interest with less computational power of our computer.

If Y j ,k is our matrix to be kron reduced and p is number of row and coloum to be reduced then this formula is used to find kron reduced elements.

Matlab Code:

%Author: Muhammad Awais fb/awais12506

%Kron Reduction

%p is row and colum to be removed

%Y is array to be kron reduced

clear all

clc

p=2;

Y=[-16.75i 11.75i 2.5i 2.5i

11.75i -19.25i 2.5i 5i

2.5i 2.5i -5.8i 0

2.5i 5i 0 8.3i];

[row,col]=size(Y);

Y_new=zeros(row,col); %Produces 4 by 4 matrixes of zeros

%In this loop all p colum and row is replaced by 0 and other by respective

%value

for k=1 :row

for l=1 : col

if k==p || l==p

Y_new(k,l)=0;

else

Y_new(k,l)=Y(k,l)-((Y(k,p)*Y(p,l))/(Y(p,p)));

end

% To remove p row and colum

Y_new(:, p) = [];

Y_new(p, :) = [];

Y_new

Example:

Kron Reduction by calculation

Kron Reduction by our Program:

Y_new =

0 - 9.5779i 0 + 4.0260i 0 + 5.5519i

0 + 4.0260i 0 - 5.4753i 0 + 0.6494i

0 + 5.5519i 0 + 0.6494i 0 + 9.5987i

There was a mistake while entering data so answer was a bit wrong. Mistake is corrected and now also I have written the code in function form ....

MATLAB Code:

%Author: Muhammad Awais fb/awais12506
%Descrption: Function uses Kron Reduction to reomove a column
%Input:Y==> Matrix to be reduced, p==> Row and Colum to be removed
%OutPut: Reduced Matrix
function Y_Reduced=KronReduction(Y,p)
[row,col]=size(Y);
Y_new=zeros(row,col);  %Produces 4 by 4 matrixes of zeros

%In this loop all p colum and row is replaced by 0 and other by respective
%value
for k=1 :row
    for l=1 : col
        if k==p || l==p
            Y_new(k,l)=0;
        else
           Y_new(k,l)=Y(k,l)-((Y(k,p)*Y(p,l))/(Y(p,p)));

        end
    end
end
% To remove p row and colum
Y_new(:, p) = [];
Y_new(p, :) = [];
Y_Reduced=Y_new;
end

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Kron Reduction using Matlab Code

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