Probability Distribution of Transformer Inrush

[HenryOhm]

Hi All,

I was just curious if anyone has any better or contradictory information on transformer inrush probability than this excerpt I found (out of a PhD thesis by Jinsheng Peng, "Assessment of Transformer Energisation; Transients and Their Impacts on Power Systems", Pg. 174):

"Furthermore, it was found that the probability of reaching the worst case dip magnitude (estimated by the commonly agreed worst case energisation condition) is lower than 0.5%, indicating that the worst case scenario is unlikely to occur in a system; in fact, about 80% of the dips are likely to be with magnitudes lower than 0.6 pu of the worst case."

https://pure.manchester.ac.uk/ws/portalfiles/portal/54533216/FULL_TEXT.PDF

I'm on a project involving an islanded power system. We have a couple of transformers that will be powered by either one or two generators. The transformers are fairly large relative to the size of generators so we are planning on some inrush testing before start-up.

The purpose of our testing is not to find the 0.5% worst case condition. If the above probabilities and my math is right, we'd have to energize one of these transformers 138 times to have a 50/50 chance of seeing that 0.5% level of inrush. However, if testing one of them 10 times has a really good chance of seeing the 0.7-0.9 pu type of inrush, that's what we really want to see. We want to measure voltage dip magnitude and duration during this testing and imagine some sort of distribution as indicated by the 5 x 4 grid of 20 inrush curves, Figure 6, about 2/3 down the page of this link:

https://www.altusdexter.com/the-true-risk-of-transformer-inrush-currents/

Thanks for any and all help!

 

[waross]

I would size the protection to withstand a very short transient of 25 times full load current and sleep well.
But, that is for a grid tied system.
For an islanded system you may wish to consider the following points:
Your energizations per week or year may be many times what a large grid experiences.
This will may your probability much higher than indicated in the study.
Consider the generator's ability to supply the peak calculated transient.

From personal experience with a small islanded, diesel supplied utility;
The last thing that we needed, coming online from an outage, was a transformer energization transient blowing a fue.

But, almost any short time setting on inverse time protection will ride through energization.
We used inverse time breakers on our generators for both overload and overcurrent protection and fuses on our transformers.
It was a long time ago and I don't remember the fuse ratings.
We did not have overload protection on the transformers.

I considered marking the transformers with heat sensitive paint or marker strips to identify overheating transformers but I was never able to implement that.

 

[dpc]

What is your concern with inrush current? If it is strictly voltage dip, then you have to define your acceptable criteria. The transformer manufacturer should be able to give you a reasonable estimate of maximum inrush current. Then you have to decide if this is acceptable. The probability distribution will depend on so many factors, I'm not sure benefit you will get from theoretical discussions. Also, the load being picked up on energization will impact the time constant and maximum current. I'd probably focus on being able to deal with the worst case inrush and sleep better at night, as waross says.