Asked 17th Jul, 2022
  • Istanbul Medeniyet University

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.

Most recent answer

27th Jul, 2022
Veera Mani Kandan
Jaya Engineering College

All Answers (4)

18th Jul, 2022
Qamar Ul Islam
Universiti Sains Malaysia
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.
1 Recommendation
21st Jul, 2022
Subrata Mukhopadhyay
Netaji Subhas University of Technology (NSUT), New Delhi, India
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 =
>> [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.
21st Jul, 2022
Subrata Mukhopadhyay
Netaji Subhas University of Technology (NSUT), New Delhi, India
Mathematically it is the solution of det [sI-A] = 0, to say correctly, and also for linearized power system it is the characteristic equation.
27th Jul, 2022
Veera Mani Kandan
Jaya Engineering College

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