×
INTELLIGENT WORK FORUMS
FOR ENGINEERING PROFESSIONALS

Log In

Come Join Us!

Are you an
Engineering professional?
Join Eng-Tips Forums!
  • Talk With Other Members
  • Be Notified Of Responses
    To Your Posts
  • Keyword Search
  • One-Click Access To Your
    Favorite Forums
  • Automated Signatures
    On Your Posts
  • Best Of All, It's Free!
  • Students Click Here

*Eng-Tips's functionality depends on members receiving e-mail. By joining you are opting in to receive e-mail.

Posting Guidelines

Promoting, selling, recruiting, coursework and thesis posting is forbidden.

Students Click Here

Jobs

Moment of Inertia?

Moment of Inertia?

Moment of Inertia?

(OP)
Hi

I have an 11kV, 50Hz, 4.818MVA, 16-pole hydro generator. Shaft height = 1m, width = 1.95m. Any idea what the moment of inertia in J in kg.m2 is please? or what is a typical value for this type of machine. Have tried the manufacturer but it's like trying to pull chicken teeth!

Thanks in advance.

RE: Moment of Inertia?

in the vicinity of 5000-7000 kg-M^2, but the OEM should have this information.

RE: Moment of Inertia?

(OP)
Thanks Fred.

RE: Moment of Inertia?

In my opinion, if the rotor weight is known and rotor diameter also then
J=GD^2=1/8*W*D^2 W=weight in kg ; D=rotor diameter [m]; J [kg.m^2]
If it is not known ,we may use the H constant formula:
J=2*H*Srated/(2*π*Frated/N)^2[kg.m^2]
Where H constant [2-4 Ws/VA]; Srated [4818000 VA]; Frated =50 Hz N=number of pole pairs[8]
In your case it could be 12500 to 25000 kg.m^2.
The above formula it is the same as per IEEE Std 399/1997 Brown Book 4.9.3.3.2 The H constant.
See[for instance]:
http://www.mathworks.com/help/physmod/sps/ref/mach...
file:///D:/D_My%20Documents/Engineering/Generators/Synchronous%20generator%20dynamics%20Lund%20Un.pdf

RE: Moment of Inertia?

(OP)
7anoter4

Still working through your equations. First one no problem. Busy with 2nd one.

I did finally manage to get the rotor data from the OEM. The stated J = 2723 kg·m2 is substantially lower than the predictions in this post and I'm wandering why?

However, if I use the equation for J = m·r2/2 (identical to your first equation) = 3080kg·m2 as follows:

Add up the weights of the fan + shaft + magnetic wheel + rectifiers + exciter = 14582kg

Assume radius, r = 0.65m (approximately) to get

J = 14582*0.652/2 = 3080kg·m2 which is in the ballpark of 2723kg.m2

RE: Moment of Inertia?

(OP)
What I also find intriguing is the following:

H = K/Sr = (5.48e-6·J·N2)/Sr =(5.48e-6·2723·3752)/4818000 = 0.436 J/VA.

where K = kinetic energy at rated frequency in Joules
Sr = rated power in VA
N = speed in rpm

Also a bit outside the range of 2-4 Ws/VA.

RE: Moment of Inertia?

(OP)
7anoter4,

Your 2nd formula, J = 2*H*Sr/(2*Π*f/N)2 is the same as mine. I used rpm instead of frequency and pole pairs. If H = 0.436, I get J = 2723 again using your formula.

Still a bit perturbed by the substantial discrepancy between the OEM values for J and the values suggested in this post.

RE: Moment of Inertia?

Have you left out the hydraulic end of the shaft? All of that rotating mass counts too.

RE: Moment of Inertia?

It does not help here, I was about to say what you need is Fred, but we have already a post from a Fred, so you need a joe. He's the little old guy in maintenance who jealously guards all the original plant data. This is because he knows how difficult it is going to be to replace it - from manufacturers who merged or went out of business.

Joe retires and the new guy, usually with an MBA or what ever throws "all that old junk" out.

I have seen this time and time again!

I have seen the inertia checked from a free run down. It was done graphically, but was 40 years ago, so sorry cannot remember the details. It was done at low speed, to minimize windage. I don't know the practicalities of doing it in your case.

RE: Moment of Inertia?

I think the error stays in the moment of inertia units. If 2-4 refers to gravimetric units then H has to be divided by 9.8 then 2 to 4 correspond to 2/9.8=0.204 to 4/9.8=0.408
J=GD^2/4/g g=9.81 m/s^2
See[for instance]:
http://www.nissei-gtr.co.jp/english/gtr/pdf/mini_e...

RE: Moment of Inertia?

(OP)
Ok, will check it out, thank you. The rather low J for the machine is in itself good and bad. Bad because the machine will "react" relatively more to system disturbances than a higher J machine which of course is not desired. Good in that it is easier detectable with something like ROCOF which I am setting up for Loss of Mains. Wonder where's the ugly...

RE: Moment of Inertia?

(OP)
7anoter4,

Sorry, could not open the attachment. Needs some Adobe Acrobat Extended Asian Language font pack which I unsuccessfully tried to install. Maybe an alternative way to resend?

RE: Moment of Inertia?

(OP)
Many thanks dArsonval, got it.

7anoter4 - makes sense now.

Hoxton - I know what you mean. Thankfully, this is a new generator and the OEM is still around. Just not very good at communicating.

Regards.

RE: Moment of Inertia?

Quote:

However, if I use the equation for J = m·r2/2 (identical to your first equation)
I don't know if that was a typo, but there is no /2 involved here.

=====================================
(2B)+(2B)' ?

RE: Moment of Inertia?

A decade ago, I wrote an application note on calculating moments of inertia starting from the most basic concepts. Partly I was working through things myself to make sure I understood every step, but also I was seeing people make mistakes by plugging into formulas they didn't fully understand. Using weight values instead of mass and then forgetting to use "g" is a common mistake.

Anyway, I offer the app note here. Comments (even corrections!) welcome.

Curt Wilson
Omron Delta Tau

RE: Moment of Inertia?

(OP)
electricpete,

J = m·r2/2 is the formula for the inertia of a solid cylinder of mass m and radius r rotating on its axis. Units are kg·m2 (SI). I have seen this in more than one reputable text on the subject. However, I will also be first to admit that I have taken it on face value as I have never delved into deriving it from first principles.

Reading through the excellent text of Curt, also verifies this formula.

So I am still interested to know why you say there is no /2?

RE: Moment of Inertia?

My formula would apply for thin-walled hollow cylinder of radius R.
Yours would apply for solid cylinder of radius R.
I don't know which context you were working with.

=====================================
(2B)+(2B)' ?

RE: Moment of Inertia?

(OP)
Yeah, the rotor of a generator is approximated by a solid cylinder, hence the formula I used.

RE: Moment of Inertia?

One of the more intriguing threads for me in a while here. For I have great respect for those who speak via higher mathematics.
Are you able to share any “hint” as to what you’re actually attempting to solve?

Your original post was worded, “…Any idea what the moment of inertia in J in kg.m2 is please? or what is a typical value for this type of machine.”

For proprietary reasons, it may be out of place to ask what you are going to do with the answer when you finally narrow it down.

Yet, I’ll throw the above sentence in the recycle bin and ask, what are you going to do with the answer?

John

RE: Moment of Inertia?

(OP)
You're welcome to ask. And I do agree regarding the maths bit. I'm doing the generator protection for the hydro-generator as introduced in my first post. The trickiest part is the loss of mains (LoM) protection which is critical to ensure that the machine is tripped off when the network supply is lost. What makes it even more dangerous is the fact that there is autoreclosing used on the network side. It is thus imperative that the LoM trips off the machine during the ARC deadtime (10s).

LoM = ROCOF and vector shift. Client cannot afford any transient studies and has requested I "see what I can do". I have found some guidance regarding this from ENA Engineering Recommendation G59, Aug 2014. In particular section 13.7.2 shows how the df/dt can be calculated manually.

Hence my request for the J value. If you are interested I'm willing to share my findings.

RE: Moment of Inertia?

Is the hydro generator in the UK?

RE: Moment of Inertia?

(OP)
No, Australia.

Red Flag This Post

Please let us know here why this post is inappropriate. Reasons such as off-topic, duplicates, flames, illegal, vulgar, or students posting their homework.

Red Flag Submitted

Thank you for helping keep Eng-Tips Forums free from inappropriate posts.
The Eng-Tips staff will check this out and take appropriate action.

Reply To This Thread

Posting in the Eng-Tips forums is a member-only feature.

Click Here to join Eng-Tips and talk with other members!


Resources