Regarding How to calculate the participation factors based on the eigenvalues ?

Hi all

Can you please suggest me How to calculate participation factors based on the eigenvalues real and complex.

1. Eigenvalues

1.0e+03 *
[-0.034236848980183 + 6.751951884207693i
-0.034236848980183 - 6.751951884207693i
-0.034236848980183 + 6.123633353489733i
-0.034236848980183 - 6.123633353489733i
-0.055866396510321 + 0.314159265358979i
-0.055866396510321 - 0.314159265358979i]

How to find the participation factors using matlab script ?

Can you please suggest me or any references.

Answer 1

[Manish]

Hi,

I understand that you want to find participation factor based on eigen values using MATLAB 

Generally,participation factor is calculated with the help of left and right eigen vectors.

Eigenvalues can be real or complex conjugate pair. Real eigenvalues correspond to non-oscillatory modes whereas, complex conjugate pair corresponds to oscillatory modes.

Refer to the following sample MATLAB code for better understanding:

% Define the matrix A
A = [0 -1;-1  0];

% Calculate the eigenvalues and right eigenvectors 
[V, D] = eig(A); 

% Calculate the left eigenvectors 
W = inv(V); 

% Initialize the participation factor matrix 
P = zeros(size(A)); 

% Calculate participation factors 
for i = 1:size(A, 1) 
    for j = 1:size(A, 2) 
        % Participation factor P(i, j) 
        P(i, j) = abs(V(i, j) * W(j, i)); 
    end 
end 

Refer to MathWorks documentation below to know more about “eig” function:

https://www.mathworks.com/help/matlab/ref/eig.html

Additionally, you can refer to the following MATLAB answer related to similar query:

https://www.mathworks.com/matlabcentral/answers/403279

Hope it helps!

[Jiaxing Lei]

Thanks for your code.

For some matrics, the sum of each column of P could be higher than 1. What does this mean? Should the each column of P be normalized?

Best regards.