Re: Transformer troubleshooting
A shorted winding in an oil filled transformer is very hard to test for. After the fault occurs, the oil tends to reinsulates the windings. A TTR (transformer turns ratio) testor will not usually use high enough voltage output to jump between the shorted winding. Unless the winding are physically damaged by the fault to create an open circuit in the winding, resistance tests may not point to the problem either.
Depending on the winding voltage, a power factor test set or a dissapation test set can be use to energize the primary winding gradually up to 2.5 kV. The secondary voltage can then be measured to see where if the ratio deviates from nameplate. There are limitation as to how much energizing current the transformer utilizing and these test sets are very expensive.
You did the best thing you could do with the visual inspection of the transformer. Burned oil almost always equals a failed transformer.
There are tests you can perforom on the oil, both pre and post failure to predict and diagnose transformer problems.
Hope this is helpful. Contact a local NETA testing company in your area as they will have equipment and services availible to help in these situations.