Electrical Machines and Power Flow

[lcr_melo]

TL;DR Summary

What is the impact of increasing power system loading on generator reactance? Should we consider synchronous generator reactance constant for each loading solved by power flow?

I have been studying the representation of generators in power flow studies and I would appreciate your comments in this thread.

From the book Fitzgerald & Kingsley's Electric Machinery, I understand that there are unsaturated and saturated reactances.
In section 5.3.2 of the book it is said: "For operation at or near rated terminal voltage, it is common to assume that the machine is equivalent to an unsaturated one with a linear magnetizing characteristic which starts at the origin and which passes through the rated-voltage point on the open-circuit characteristic ".
By this statement, I can assume that near the terminal voltage the reactance of the generator with the unsaturated value, which is approximately constant.

Here starts my question, as I am willing to perform power flow studies under different operating conditions.
My question is this: can I assume that under conditions other than terminal voltage, the generator has a variable reactance, such as the saturated reactance?
This will be important in the solutions of power flow study when I consider the reactive limit of the generators, as the terminal voltage will be allowed to vary. By varying the terminal voltage, I understand that the reactance will no longer be constant.

Is this reasoning correct?

Also, I would like to add information obtained from the article "BAN, D .; ŽARKO, D.; MALJKOVIC, Z. The analysis of saturated reactances of the 247 MVA turbogenerator by using the finite element method": The saturation of the machines is different for each operative point. The values of the synchronous reactances in steady-state are to armature current, terminal voltage and power factor. In the figures below are shown the direct and quadrature reactances in function of armature current (I), power factor (cos phi) and terminal voltage (u).

Thank you very much for you help!

 

[anorlunda]

Summary:: What is the impact of increasing power system loading on generator reactance? Should we consider synchronous generator reactance constant for each loading solved by power flow?

By this statement, I can assume that near the terminal voltage the reactance of the generator with the unsaturated value, which is approximately constant.

Yes that's right. We typically do not change the reactances dynamically in a simulation. The entire synchronous generator model is linear except for saturation dependent on field current.

As you said, terminal voltage is approximately constant. Also frequency is approximately constant.

The only exception is when we study loss of synchronism which leads to extremes in voltage and frequency.

 

[lcr_melo]

Thank you for your answer, anorlunda.

In the case where the terminal voltage is constant I agree we have constant reactance.

Now I am considering two cases:
i) In a heavily loaded system where terminal voltage is approximately constant but the armature current increases. Can I assume that the reactance decreases? (I'm saying it based on the article I mentioned, but I don't have any book with this information)
ii) When generators' reactive power limit is reached the terminal voltage isn't constant. In this case, the armature current is increasing and the terminal voltage is decreasing. Can I assume that the reactancead a decreases?

I would like to read a book talking specifically about this topic, but I'm not finding one.

 

[anorlunda]

I prefer to say impedance rather than resistance or reactance.

Impedance tells us the ratio of current and voltage. It is frequently constant over a reasonable range of V and I.

I can tell you that in system studies, load flow plus transient simulation, we do not vary the impedances with operating point. The one exception I mentioned is in the field current. Extreme, overvoltage, overcurrent, and overfrequency conditions excepted.

In a model as below. All those X and T values are considered to be constants.

 

[dlgoff]

I prefer to say impedance rather than resistance or reactance.

Impedance tells us the ratio of current and voltage. It is frequently constant over a reasonable range of V and I.

I can tell you that in system studies, load flow plus transient simulation, we do not vary the impedances with operating point. The one exception I mentioned is in the field current. Extreme, overvoltage, overcurrent, and overfrequency conditions excepted.

In a model as below. All those X and T values are considered to be constants.
View attachment 279867

I've always liked this animation:
http://people.ece.umn.edu/users/riaz/animations/sqmovies.html

 

[anorlunda]

I've always liked this animation:

That video is about induction machines. This whole thread is about synchronous machines, right?

 

[dlgoff]

That video is about induction machines. This whole thread is about synchronous machines, right?

Right.