Electromechanical oscillations

[521AB]

If one part of the network is weak, we can have electromechanical oscilaltion phenomena.
Is it really true that: one side of the circuitbreaker runs with 60 Hz and the other side "runs" at: (60 Hz - 20 mHz) + frequency oscillation with a period of 1 second of +/- 50 mHz?
Which means that the second side of the (open) circuit breaker shows a frequency modulated waveform (amplitude is constant) with carrier frequency of (60 mHz-20 mHz) and modulation period of one second.
I heard this from some colleagues... is that really true?

 

[dpc]

Maybe Google "subsynchronous oscillations" or "subsynchronous resonance" if you are asking what I think.

 

[521AB]

I think I have googled almost everything... never found ANY topic related to "frequency modulation of the voltage waveforms".

 

[alehman]

Periodically varying load? If the source impedance has non-zero X, then variation in current will result in variation in phase angle.

 

[Alex68]

What you described is a typical (stable or unstable) power swing, which is related to the frequency variation by the classical law of the P-f regulation.

Your CB (and its line) is the only link between two areas of a big grid. Each area can be substituted by an equivalent generator. A big gen with a big inertia for the strong area and a little gen for the weak area, plus an impedance connecting them.
Suppose that something like a load is switched on. The absorbed power is greater then the produced one and the generators slow down until their frequency regulators operate to obtain again the equilibrium. So you have a transient during which the frequency goes down and up again. The electrical frequency is always the same in the system and it is governed by the mechanical frequency biggest generator. But the two generators are not synchronous during the transient because the smallest one oscillates more than the other.
When you open the CB, the two separated grids are governed by two indipendent generators so the frequency can be different.

 

[521AB]

Alex68:
that is! The CB (the line) is the only LINK between the 2 grids. If there is just another link, this cannot happen. Is that what you mean?
Let's suppose than that there is only my line as link. Is it really true that I can model the voltage waveforms like a frequency modulation... i.e. the voltage amplitude remains constant? Is there any theoretical background on that or it is just a simplification?
In a "power swing" , stable r not stable, there is also a modulation in the voltage amplitude..
Just wondering....

 

[Alex68]

Yes, the bigger is the number of links, the lower is the possibility of oscillations, like in mechanical systems.

I'm just simulating an out of step condition and... Frequency is always the same in the whole system while voltage varies from point to point.
During a power swing you have an amplitude modulation of the voltage and not a frequency modulation.

Please refer to the impedance locus:
When your impedance point crosses the axis of your system, voltages and currents are exaclty the same as during a 3ph fault: low voltages (in phase opposition) and high currents.
When your point goes away from the axis, voltages increase and currents decrease.

So you have an "amplitude modulation" with constant frequency

 

[521AB]

Actually I am of the opinion that even if the system is well meshed, depending on the mechanical inertia of the generators, you can have electromechanical oscillations, I can agree that the frequency oscillates around the "steady state value", but what I also believe, is that if the CB is open, both voltages may oscillate in frequency, around the same value! And not around 2 different values, UNLESS the CB really devides the network in two separate parts.
I also believe that not only the frequency is modulated, but also the voltage amplitudes are modulated. So in my opinion, describing this phenomenon with a "pure frequency modulation" is wrong.
Is there any analitic (explicit) formula describing these oscillations?

 

[Alex68]

If you have only one link with the CB open, then you have two indipendent systems, whose frequency and voltages can vary.

The formula describing the phenomena are described in any book about the power system (electromechanical, transient, dynamic) stability.