Probability Distribution of Transformer Inrush 4

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.

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.

The typical inrush curves for transformers assume an infinite bus approximation. For an islanded system with a transformer larger than the generator, that will be a rather poor assumption.

I am rather confused that the links suggest that 0.5% probability means something will never occur. If there is 0.5% chance to blow transformer fuses, and blow fuses then means you have to spend days without power while waiting for transformer testing equipment to arrive from the mainland, that may not be an acceptable consequence. However if the consequences of are less impactful (e.g. just redo the generator starting sequence) then aiming for a different acceptable probability may make sense for your situation.

First, I really appreciate the replies, and from some very knowledgeable posters that I've learned from just reading threads I'm not even in. FWIW, we have no fuses involved and the transformers will always be unloaded during transformer inrush. Yes, I don't discount the 0.5% probability case as never occurring. However, the transformers only see inrush during startup so during a less critical time. Agreeing with others here, it's the repetitive nature over time that worries me more. It's also with it happening to a crew that is not electrically-inclined than with engineers on hand.

So, the unknown for me is sort of wrapped up in this whitepaper from Cummins. I just have no idea what to expect based on this.
https://www.stamford-avk.com/sites/stamfordavk/files/AGN070_B.pdf

It starts right off by indicating 1X transformer inrush off a genset (+/- 25%), not 6X, 8X or 12X. That's why I am not even mentioning measuring current levels. The inrush current no longer seems like anything that would complicate a coordination curve as we usually tackle. I don't see how to link a grid-tied inrush multiple to a voltage dip range. I have some old GE databook curves that estimate voltage dip percentage but they are for a large motor line-starting on a generator. How much faith should I put in this Cummins whitepaper where it suggests the inrush would only be in the range from 0.75X to 1.25X?

My plan of attack was to lead a certain number of repeated closures of the transformer breakers. I wanted a pretty good chance of hitting the 60-100% of worst-case range of maximum inrush. If I can believe the 80%/0.6pu number, then 10 repeated tests would have an almost 90% chance of seeing something in that range, 14 tests about 95% and 20 tests almost 99%. I am thinking then that 20 would be the number of tests spaced with a few minutes between each closure and split up evenly between the two identical transformers.

The manufacturer of the generator breakers unfortunately only offers a broad range for where the voltage drop-out will trip them, somewhere from 40-65%. However, for other controls powering off this, I'd say if testing shows voltage dropping down to 80-85%, that would certainly be worrisome. A drop to 70-80% would probably all but require addition of premag circuits. I don't feel we need to see some 0.5% probability 50-60% voltage drop, for example. If we hit that 70-80% at any point in the testing, then the test is concluded at that point. I'm not sure I see the advantage in the above link's use of "excitation-build-up" vs premag.

Cummins:
AGN 070 ISSUE B/1/3
Application Guidance Notes: Technical Information from Cummins Generator Technologies
AGN 070 - Magnetizing Transformers
DESCRIPTION
Although very high inrush currents are quoted during transformer magnetisation, this situation
really only occurs when the transformer is being powered by the very low source impedance
of a Mains supply.
When a Generating Set magnetises a transformer, the inrush current becomes limited by the high source impedance of the alternator.
Test data and experience suggests when an alternator of the same rating as the transformer is being used to magnetise a transformer with an unloaded secondary, the typical level of inrush current (kVA) is generally in line with the transformers rated current (kVA).

Click to expand...

Note that this case applies when the transformer is the same capacity as the alternator.
For a transformer of 1/2 the capacity of the generator I suggest using rated current times two, plus or minus 25%.
For a transformer of 1/3 the capacity of the generator I suggest using rated current times three, plus or minus 25%.
For loaded transformers, which don't seem to be considered in the white paper, I would consider the alternators maximum short circuit current as determined by the sub transient reactance of the alternator. You may then scale this down by considering the air core reactance of the transformer.