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From reading the original post and the responses I conclude there needs to be a more complete definition of terms, and some voltage measurements would help clarify what exists. What is the implication of the words "high leg service"? That needs to be understood.
In the meter panel I see three incoming hot wires. I can not see if there is a neutral. However, I do not believe it matters whether the source is Y or delta because you are connecting to one or more transformers (I assume these are isolation from input to output). From the standpoint of the transformer(s) it matters not how the 480 source is grounded because the transformers provide isolation. I can not read the data on your picture of the transformer tag.
What you are concerned with is the secondaries of the transformers.
There are various delta secondary possibilities. You can use two transformers to provide an open delta output. These secondaries could float (no ground), or any one and only one corner could be grounded, or a synthesized neutral could be generated.
This open delta can be modified further by center tapping one secondary, and using that center tapped winding for single phase 120-0-120 with the center tap being the single phase neutral and also grounded. This arrangement then labels the one leg not part of the 120-0-120 as a high leg. This is very common in our area where there is a large single phase load and a lesser 3 phase load. In this case the single phase transformer is larger than the transformer supplying the high leg.
The open delta can be modified by the addition of a third transformer to become a closed delta with a high leg. Not a big change other than an easy way to increase the 3 phase capability. So our power company puts up the big single phase transformer, and a smaller high leg transformer, then if power requirements increase add a third transformer.
A high leg system results from one secondary being center tapped, and this center tap being grounded. The the voltages from the center tapped secondary relative to ground (center tap) are 180 degrees out of phase with respect to each other. The high leg voltage is 90 degrees from either of these. In a balanced system the relation of the high leg voltage magnitude to the center tap to 1/2 of the center tapped secondary is Vhigh/Vhalf = sq-root of 3 or 1.732 .
The transformer that has been referenced in post 1 is stated as being a delta secondary, and is either two or three single phase transformers with one center tapped secondary, or a true three phase transformer with one secondary center tapped.
Voltage measurements should allow you to figure out what is the circuit. The load capability of the transformer(s) probably requires information from the vendor.
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