27th Jul, 2022

Jaya Engineering College

Question

Asked 17th Jul, 2022

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.

The following links and attachments are may be useful to your questions

- 3.61 MBeigen value of P.S.pdf
- 358.63 KBeigen value of P.S2.pdf
- 375.72 KBeigen value of P.S3.pdf
- 3.61 MBeigen value of P.S4.pdf
- 387.78 KBeigen value of P.S5.pdf

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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

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.

The following links and attachments are may be useful to your questions

- 3.61 MBeigen value of P.S.pdf
- 358.63 KBeigen value of P.S2.pdf
- 375.72 KBeigen value of P.S3.pdf
- 3.61 MBeigen value of P.S4.pdf
- 387.78 KBeigen value of P.S5.pdf

Article

- Jul 1973

A method for determining the Z//B//U//S and Y//B//U//S matrices of any power-system network, using structural numbers, is given. A brief account of the algebra of structural numbers is included and the method illustrated with a numerical example.

Article

- Oct 2020

Abstract: The requirements for high-current circuits, contact systems, switchboards, and electrical apparatuses differ from the typical requirements for devices with a low current load, not only because those are more complex, but also because new requirements arise due to the fact that the size of the designed devices and power systems is constant...

Article

- Jun 1994

The paper presents a new approach to the problem of large-scale power system stabilisation using the dominant subsystem principle. Sufficient conditions are derived for system stabilisation using local decentralised controllers, guaranteeing the dynamic stability of the power system. A new concept is used to design an adaptive controller based on a...

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