One of the great benefits of an ungrounded delta is its ability to remain energized with a fault on any single line.
Unfortunately one of the great difficulties with an ungrounded delta is finding that fault.
A fault at any point in the system shows up exactly the same as another.
The only way that I have ever used successfully is to disconnect part of the system and see if the fault clears.
If not, reconnect that part and start again until you find what device clears the fault when it opens.
Now you know that the system is clear upstream of that point.
Now repeat that process further downstream of the source.
Keep repeating until you find the fault...it can take a while.
If you have more than 1 fault on the system...it can be a very long time since you only know that the phase is faulted or cleared; you'll never know if there is a single point of fault or more than one.
That's what doomed the ungrounded delta IMHO; it's very difficult to troubleshoot as the electrical system starts to grow.
I had a fault in a relatively simple system with 10 loads that was scheduled to be replaced as part of an upcoming renovation.
After trying to find the problem over the course of a week I finally gave up and replaced it in kind using EMT knowing that the whole thing would be in the dumpster in a few months.
In that particular case I not only got the process back online I saved a lot of troubleshooting time/expense.
The tough part was convincing the powers-that-be to spend some money on a temporary solution.
