I am working on power system stability. I would like to ask how can calculate Eigenvalue analysis and damping ratio for multi-machine power system by using MATLAB/Simulink.
I am not sure about MATLAB, but software called "PSAT" can be run inside MATLAB/Simulink to calculate the eigenvalue results.
http://faraday1.ucd.ie/psat.html
Dear Dr Samundra Gurung ,
Many thanks for your contribution. Previously, I checked PSAT, although it is run inside MATLAB, but we have to re-build the our system in PSAT.
if you model your system in MATLAB as a state-space model, then you can find the eigen values using the function eig(A), where A is the state-vector coefficent matrix in your state-space modelling
Dear Dr Neelotpal Majumdar
I appreciate your feedback.
Any method can be used for Simulink (SimPowerSystems) model?
The model is given by electrical elements, includes generators, excitation systems, PSSs, transformers, lines, and loads. Therefore, we are looking for a method to calculate Eigenvalue for this system.
you can use this fun (linmod) if your system is linear or (dlinmod) if your system is discrete, after that you will get four matrices (A,B, C,D), you can get the eigenvalues from A using (e=eig(A)), the real and imag part in this form λ=𝜎+jw? you can get it easily from (e)
Dear Dr Hasan Abumeteir
Thanks for your answer,
Are the functions used in Simulink model? or only used in m. file?
Ahmad Adel Alsakati if your system has name "sys", you can write in the command window in matlab [A B C D]=linmod("sys")
then you will get the matrix A
Hi Ahmad, once you have buit up the state matrix of the power system under analysis, use the "eig(X)" function in matlab, wher X is the state matrix, it is " z=eig(X)" in "z" you'll have the eigenvalues of the state matrix in the form "a+i*b". Then you may determine the damping ratio of each eigenvalue as
"dr=-b/sqrt(a*a+b*b)"
Dear Dr Jorge Calderon
Many thanks for your contribution. I attached an example of a network which we are working on using Matlab/Simulink. Is it possible to extract the state matrix of power system from Matlab?
If you are working in state-space model with system matrix A (a square matrix) known then there are two types of commands in MATLAB, namely,
B = eig(A) will give in a column all the eigenvalues in B, and
[V,D] = eig(A) will give eigenvectors through V while D will be a diagonal matrix with the eigenvalues in the diagonal of the matrix.
Further with λ=𝜎+jw, damping ratio will be 𝜎/sqrt(𝜎*𝜎+w*w).
Dear prof. Subrata Mukhopadhyay
Thanks for your interest. Could you advise me how to extract the state-space model from MATLAB/Simulink model?
Immediately I am not in a position to check out due to restriction in movement vis-a-vis access. I have sought help from students. But definitely it should be possible after MATLAB/SIMULINK (s-domain) representation to find out overall transfer function (considering of course linearity maintained). From the same then one can progress for finding eigenvalues and damping that they provide.
Hope to come back.
I am still waiting for the feedback from my students. In the meantime on a search I could locate the following which may be useful.
Build a model at Simulink then to get the Transfer Function of that model, put a step response to see the output. Then make a controller on the TF with SisoTool. So this way one can get the TF of the model. It is some sort of equivalent construction.
Dear Prof. Subrata Mukhopadhyay
Your contribution is highly appreciated. I will check the explained method while we are waiting other views.
Thanks in advance,
Ahmad
Further I could locate the following, which may be looked into:
How to get a transfer function from a Simulink model into Matlab?
Link: https://stackoverflow.com/questions/20588200/how-to-get-a-transfer-function-from-a-simulink-model-into-matlab
Unfortunately I am not in a position to check.
Dear Ahmad Adel Alsakati
Please extract the transfer function of the total system.
You can still represent your system using a single machine connected with an infinite bus. Extracting state-space equations for the multi-machine model is a bit complicated because you need to find the synchronisation torque for each interconnection. Without this sync torque, you can still be able to connect them, but it will be more simplified as you lose some of the dynamics from the network.
You can have a look at any textbook, e.g. Power System Stability by kundur, for the answer, how to get simplified transfer function of the multi-area system. I forgot the exact chapter name though.
once you get state-space, Matlab will let you know how to get eignen values, even more methods to do your stability analysis.
Please let us or me know your update.
Good luck
Ahmad Adel Alsakati Have you found the solution? Please let me know too, I have also the exact Problem with Simulink Model for DFIG Wind farm working in a Weak Grid.
Dear Syed Zia ul Hussnain
Unfortunately, not.
Currently, I am working on transient stability analysis, I use the relative power angle and speed deviation of generators to evaluate the stability.
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