Hi Jawwad,

Hope your research is going great !

What exactly do you imply by "damping frequency" ??

That natural frequency ? Or the actual frequency which is a function of natural frequency and damping ratio ??

-Sanjay

Dear Prof. Roy,

Thank you so much again for your response.

Sir, actually i am concerned about the actual frequency which is a function of natural frequency and damping ratio.

Best regards,

Jawwad,

I am trying a guess, but I don't think it is too far from the truth !

The actual frequency is w = sqrt( 1 - z2 ) * wn

where wn is the natural frequency and z is the damping ratio.

So isn't it obvious that if z drops, w should increase ? The wn remains roughly unchanged since it is largely dependent on the area inertia.

In fact, your observation about the frequency simply proves further that the damping ratio is undergoing a drop.

Hope that helped !!

(BTW, pl address me as "Sanjay". Why go for the formal "Prof. Roy" ??)

-Sanjay

Hello Sanjay,

Thank you so much again for your response.

I do apologize because i could not explain my question properly. Let me share the result with you.

Without wind power integration in stressed area (area 2):

Natural frequency= 2.893rad/sec

Actual Frequency = 0.46Hz

Damping ratio=0.301

After 80% wind power integration:

Natural frequency= 3.395rad/sec

Actual Frequency = 0.62Hz

Damping ratio=0.223

I am just trying to extract the reason from the above result. May be right or may be wrong but i need your expert opinion and guidance.

Actually frequency is increasing because it is the function of damping ratio and natural frequency. It is obvious from the relation that it will increase when damping ratio will decrease.

Natural frequency is also increased from 2.89 to 3.39 rad/s because it depends on area inertia and over all inertia of the system is decreased after 80% integration of wind power (560MW) which in result increases the natural frequency. Total generation in area 2  is 1414MW.

But my interpretation becomes wrong when i see the result in area 1 which export approx. 400MW to area 2 through tie-line.

Without wind power integration in area 1:

Natural frequency= 2.893rad/sec

Actual Frequency = 0.46Hz

Damping ratio=0.301

After 80% wind power integration:

Natural frequency= 2.712rad/sec

Actual Frequency = 0.43Hz

Damping ratio=0.321

I am getting more or less same result for both DFIG and Full-scale converter wind turbine.

Looking forward for your expert opinion and guidance.

Jawwad,

Sorry for the delay in reply. I was away from my Institute in Ropar for a while.

Frankly speaking, are we interpreting the figures correctly ? Or am I missing something ??

-Sanjay

Hi Sanjay,

Thank you again for your reply.

1. I am using exactly the same simple 2 area 4 machine network as depicted in Kunder's book, E12.8.

2. I am trying to see the response on both area as i connect on Bus 6 where G2 is connected and then on Bus 10 where G4 is connected. I am using each generator as 5 strongly coupled parallel machines, 5x180MW. parameters for generator have been taken from DigSilent Library. Reducing no of parallel machine from G2 and equivalent amount of power from wind turbine is integrated on Bus 6. I have chosen offshore wind turbine model which is located 25km away from the on-shore grid and is connected using sea cable.

3. Regarding   third point, i just apologize because i did some fundamental calculation mistakes and a typing error. Natural frequency can never be less than damping frequency. Simulation results are correct and it was my calculation mistake.

4. Again the same calculation mistake.

Now, i am just trying to co-relate the area inertia with natural frequency and actual frequency. what will be the response of increasing and decreasing of overall area inertia on natural and actual damping frequencies. And with the help of this i want to correlate it with damping ratio.

Because in all the literature i just read 2 reasons for positive and negative impact of wind turbine.

when damping ratio increased: Reason: because wind turbine is not synchronously connected with the power system and machine dynamics of wind turbine do not play any role in rotor angle oscillation.

When damping ratio is decreased in the area which import power: Reason: because the area is on stress and wind power negatively influenced the inter-area mode of stressed area.

This is what i learned in almost all the literature on this topic.

But i just want to dig out the reason in more detail and correlate it with some parameters like system inertia or other parameters.

Looking forward for your kind response

Best regards,

Jawwad

Hi Jawwad,

It is not the wind turbine per-se that improves damping by its inclusion - it is the induction generator, and some selected link controls in case of synchronous or PM generators. The second is difficult to explain in brief (the possibilities could be many !!) but the first is not. Remember that inclusion of an induction element always improves damping. (As an example, you improve damping in the basic synchronous machine by including dampers on the rotor - right ? And dampers are nothing but modified cage rotors of induction machine type !!)

In the end of your message you mention:

When damping ratio is decreased in the area which import power: Reason: because the area is on stress and wind power negatively influenced the inter-area mode of stressed area.

That is a highly subjective conclusion. According to me it is true sometimes, and not true in other cases - very system specific...

Hope all that helped. With best wishes.

-Sanjay

Hi Sanjoy,

First , thanks for the repl.

First i do apologiye for a very late response. Actually i was on site for last 2 month for some commissioning activities.

Now i will again continue with my research and will try to find out more in depth reasons as you mentioned in your last reply.

Thank you so much again for your continuous help.

Best wishes and regards,

Jawwad

Hi Jawwad,

I was in fact wondering as to where you have been :-) :-)

Welcome back on RG - do keep me posted about your developments.

-Sanjay