# Single machine-Infinite bar (SMIB)

1. Sep 21, 2011

### DianeS

Well I'm trying to do some small-signal studies, and i'm familiar with the deMello-Concordia linearized model. As far as i know all the constants used in that model (K1-K6) depend on the system, and so they change as the system changes too. I have a large system with several synchronous machines and i want to obtain the SMIB model for one of those machines. So how do i obtain the external reactance connected to the infinite bar, representing the transmission line? I know this reactance corresponds to the Thevenin equivalent, but is there a way to obtain this value by using a power flow simulation software?

Or is it a good approach to assume this value to be zero?
Thanks a bunch

2. Sep 22, 2011

### jim hardy

""So how do i obtain the external reactance connected to the infinite bar, representing the transmission line? I know this reactance corresponds to the Thevenin equivalent, but is there a way to obtain this value by using a power flow simulation software?""

what an interesting question.

In the utility where i worked we had a whole department dedicated to calculating just such things, and we just asked them. But the number depends on how many lines are in operation and how many units are connected.

I seem to recall they gave us per-unit numbers like 0.013 so i wouldn't use zero. It was however a lot less than the stepup transformer impedance.

Here's a link i found with some formulas, perhas you could approximate a reasonable line to get your simulation running then tweak it with real numbers from your utility's system people.

www.powerworld.com/Document%20Library/version.../TransCalcHelp.pdf[/URL]

"Power System Analysis" by Charles M Gross is a practical textbook.
Dr Gross was my instructor for some undergrad courses and he has a God-given talent for clear explanations. I saw his book in the bookcases of many engineers in that department i mentioned, they all spoke highly of it -- so ask among your colleagues, if you find a copy i think it'll have some practical examples worked out that are quite similar to your question.

Sorry i'm not an expert.

old jim

Last edited by a moderator: Apr 26, 2017
3. Sep 23, 2011

### DianeS

Well thank you Jim! I've been using DigSilent for this purpose, and i guess i'll just have to trust in it. By simulating a three phase short circuit, i can obtain the values for R and X, which i asume are Thevenin equivalent for positive sequence.

4. Sep 23, 2011

### jim hardy

for what little this is worth --

our big steam turbine plant had natural frequency against system of ~ 1 hz
largely due to 17% main tansformer
i think that is typical

it also had main shaft resonance of 7 hz
so that was a frequency to avoid like the plague in anything connected to it.

we overdamped voltage regulator to calm system troubles (2/3 hz divergent oscillations) that were solved initially by power system stabilizers , finally by stouter transmission lines.

wish i could be more help.

good luck with your studies -
that is a field i watched "through the fence" like Charly in 'Flowers for Algernon'.

old jim

5. Oct 5, 2011

### DianeS

Well thanks Jim, i appreciate your help.
I'm now trying to find out which type of short circuit i should use to find the thevenin equivalent, because I've found that you can find a 3-phase or1-phase Thevenin equivalent and i'm not so sure if this is true.

By running a 1-phase short circuit i would find impedances in all 3 sequences. Is it enough to find only the positive sequence impedance by running a 3-phase short circuit in my software for the SMIB equivalent??

I'm also aware that for big systems Rthev is negligible so i can only consider Xthev in y analysis, and that this value is the inverse of the imaginary part of the short circuit current. But again which short circuit current? 1-phase or 3-phase?

Thanks again. Would like to get more people involved too. Don't be shy :P

6. Oct 5, 2011

### jim hardy

""Is it enough to find only the positive sequence impedance by running a 3-phase short circuit in my software for the SMIB equivalent??
""

I wish i could answer that question.
My intuition says use the three phase
the power system guys i used to observe in 1980's were excited about new relay schemes that could interrupt one phase at a time for single line faults

so i would think your small signal studies would be focused on balanced three phase.
but that is a guess.

our power system oscillations were during steady state operation not fault induced.
came from interactions of rotating inertia, system impedance and voltage regulators.

Is there a genuine power system engineer in the house ?

Dr Gross - are you out there?
old jim hardy - UMR '69, your student for AC machinery