27th Jul, 2022
Jaya Engineering College
Question
Asked 17th Jul, 2022
How to calculate the eigenvalues of a power system?
I am researching the analysis of power systems in the Matlab simulink environment. I'm studying power systems with various numbers of busbars, such as 5,9,14.
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All Answers (4)
Hakan Öztürk Solve for using the equation det(A-I) = 0. Calculate all of the possible values of, which are the matrix A's needed eigenvalues.
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It is in fact solution of det [sI-A], where 's' is the scalar Laplace Operator corresponding to d/dt, I is the identity or Unity Matrix with Diagonal elements as 1, while all off-diagonal elements are zero, A is the System Matrix of order n. Thus matrix [sI-A] is also of the order of n. There will be n roots or eigen values.
Once you form A, then under MATLAB, command is as follows:
B=eig(A). where through a column vector of n rows B will provide eigen values, real or complex conjugate.
If you wish to know about eigen vectors in addition, then command is as given below:
[V,D] = eig(A), where matrix V gives corresponding eigen vectors and matrix D is a Diagonal Matrix with eigen values as its diagonal elements.
It will be clear from the following example of third order system:
A = [4 3 -1;-2 0 2;3 3 0];
>> B = eig(A)
B =
0.0000
1.0000
3.0000
>> [V,D] = eig(A)
V =
-0.5774 0.7071 0.7071
0.5774 -0.5657 0.0000
-0.5774 0.4243 0.7071
D =
0.0000 0 0
0 1.0000 0
0 0 3.0000
Hope it clarifies and satisfies the need.
Mathematically it is the solution of det [sI-A] = 0, to say correctly, and also for linearized power system it is the characteristic equation.
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