Inertia Constant - Generator 1

[NateKling]

I am trying to calculate the Inertia constant of a generator for testing purposes using collected data. I also have software that will model transient stability studies. When I provide the model with the following information:

H=2
MW = 50
MVA = 156.25

I recieve the following data, simulating a load rejection of the generator.
Sec Freq
0.501 60.001
0.521 60.025
0.541 60.049
0.561 60.073
0.581 60.097
0.601 60.122
0.621 60.146
0.641 60.17
0.661 60.194
0.681 60.218
0.701 60.242
0.721 60.266
0.741 60.29
0.761 60.314
0.781 60.338
0.801 60.361
0.821 60.385
0.841 60.409
0.861 60.432
0.881 60.455
0.901 60.479
0.921 60.502
0.941 60.525

The trip occured at .5 seconds, and as expected, the freqency increased. However, as a verification of my methods, I attempted to calculate the Inertia constant from this data. The linear regression of the data had a slope of 1.193, which is df/dt.

Using the equation:

DP*fo
----------
(2*(df/dt)

I got

(50/156.25)*60
---------------- = 8.04305
(2*1.1936)

After trying to model this for four different inertia constant values, I noticed that each time, the calculated value was almost exactly 4 times what I had expected. ie...

H_real = 4.1 H_calc = 16.376
3 12.007
5 19.929

I have looked through many different calculations, and tried everything I could think of. Is my calculation wrong?

Thank you

Nate Klingerman

 

[ratz1]

What was used to calculate/estimate H. J or WK2? The ratio between J and WK2 is 4.

 

[NateKling]

Well, that is something I was struggling to understand. I tried to work out and derive this formula using J and angular velocity and wr^2 and was unsuccessful with everything I tried. I was looking for some guidance with where I was going wrong. I think it is with that part of the formula though.

 

[Marmite]

Number of poles?
Regards
Marmite

 

[ratz1]

Coefficient of inertia
The inertia constant H (in s) - is the ratio of energy stored in the rotor at nominal speed (E in Joules) over the nominal power (P in W) of the machine.

So: E= J*w^2/2 and H=E/P

where w=2*pi*rpm/60 (314 for 3000rpm, 157 for 1500rpm and so on..)

J= 4*WK2

 

[NateKling]

Here is some of the data from a test I simulated at four different hypothetical Inertia Constant values. Notice that the H_calc value is off by a factor of four each time. I still do not understand why this is happening.

How would you suggest finding a J or WK2 value from a freq vs. time chart?

I cannot figure out why my calculated value would be off by a factor of four. This is driving me insane.

Thank you!

 

[rbulsara]

NateKling:
Just curious, what is the purpose of your question/work? Is this an test of some kind for a research?

Rafiq Bulsara

http://www.srengineersct.com

 

[NateKling]

I am trying to simulate a test that would validate a generator's inertia. I just came up with some numbers for a large generator, and used standard parameters that I could find.

 

[ScottyUK]

Nate,

Have you considered the prime mover which is obviously coupled to the shaft, or are you just considering the generator in isolation? The generator OEMs usually publish data for the rotor, but there will be a separate set of data for the turbine.

If you're looking at real-world data from a trip event and this machine has a gas turbine prime mover then there is a trememdous braking action from the GT compressor immediately after the governors cut the fuel. A steam set with a condenser under vacuum will see a much gentler decelleration.


----------------------------------

If we learn from our mistakes I'm getting a great education!

 

[NateKling]

Yes, that has all been considered in the model. The only error that I am running into is when I try to work backwards from the model data, back to my initial H constant. No matter what other factors come into play, I should be able to work back to the initial inertia constant because the data is simulated, this should be possible. Like shown above, the calculation is almost working exactly like it should. I am off however by a factor of 4

 

[NateKling]

The last excel sheet I uploaded depended on a different file. I was not aware of this. Sorry for the mistake. This file should work.

 

[LionelHutz]

How would you suggest finding a J or WK2 value from a freq vs. time chart?

You know the angular acceleration. You could assume the output power of the prime mover at the time of the load rejection gets used to accelerate the inertia of the system instead. At the operating rpm this power corresponds to a certain torque. So, you could rearrange the formula T=Ia or torque = inertia x angular acceleration to calculate the inertia.

 

[NateKling]

Ok, I now think that this definately has to do with the number of poles in the generator. When I simulated the LR Test with the exact same generator running at 1800 RPM with 4 Poles, and plugged the data into my spreadsheet, I was off by a factor of 8 instead of a factor of 4. So my equation maybe needs a (2*Pf) in the denominator (where Pf is the number of pole fields). Can anyone mathematically confirm that this makes sense?

 

[NateKling]

Disregard the last post, I forgot to replace 3600 with 1800 in excel. I am just about to give up on this. I can't figure out what I am doing wrong.

 

[Marmite]

You can't relate system frequency to angular velocity without factoring in the number of poles, which is why I drew your attention to it in my earlier post.
Regards
Marmite

 

[NateKling]

@Marmite

I was incorrect by concluding poles was the issue.

By including the Initial and rate of change in the equation, the poles are accounted for.

For example:

dp * fo
H = ---------
2 * df/dt

To my understanding, the inertia constant is a perunitized resistance to change. The larger H is, the less the rate of frequency change. Therefore, because you are comparing two like values, the poles cancel out. Maybe?

 

[NateKling]

ratz1:

What was used to calculate/estimate H. J or WK2? The ratio between J and WK2 is 4.

I think this may be where my problem is, but I am having trouble working it out mathematically. Would you mind explaining a little deeper?

 

[Marmite]

You are right about the number of poles being cancelled out. Your formula is right, but I think the problem is you are comparing apples and pears.
The inertia coefficient of your machine is 2, so the ratio of rotational energy to generator rating at synchronous speed is 2. This is fixed by the mechanical inertia and electrical rating of the machine. H is in seconds. Another way of describing it would be that when rotating at synchronous speed the machine can deliver rated power for 2 seconds.
In your equation you have calculated the inertia coefficient H for a system comprising the generator plus a 50MW accelerating power input to the shaft to be 8 seconds. If you apply 50MW of input power to the shaft the generator will obviously be able to deliver rated power for more than the original 2 seconds because you have reduced the retarding power by 50MW.
Regards
Marmite

 

[wolf39]

Nate:

How sure are you that the inertia constant H = 2? Is this figure valid for the generator only or for the complete set (i.e. including turbine)? How has this H = 2 figure been calculated: With J or with WK2? Try to find out. Do you possibly mix up inertia constant H with starting time constant TA?

The active generator power of 50 MW doesn't match with the apparent power figure of 156.25 MVA.

To my knowledge the definition of starting time constant TA is as follows: TA is the time (in seconds) required to accelerate a machine from standstill to rated synchronous speed if a constant torque (equivalent to the rated torque) is present. The relation between TA and H is

H = TA/2.

Regards

Wolf

http://WWW.HYDROPOWER-CONSULT.COM

 

[NateKling]

The issue was in the power being rejected. it turns out the Auxiliary load and generator conditions were such that the rejected load was approximately 12.5 which just so happens to be 1/4 of 50. If it had been any other weird number, I probably would have figured that out right away but the exact factor of four blinded me to the equation.
Sorry for wasting ya'lls time on something so easy. Thank you for all of the suggestions.

Nate Klingerman