As mentioned, Delta power systems were used, mostly in the past, as a form of fault tolerance, meaning the facility could withstand the FIRST ground fault and keep going. The NEC technically still allows for this, but the system must be EITHER: 1) Grounded, meaning "corner grounded delta"; or 2) Monitored, meaning a Ground Fault Monitoring system.
If it is a corner grounded delta, the grounded phase must be* grounded AT the transformer terminal, meaning you will be able to SEE the ground conductor in the termination box. If you don't see one, then it was an UNGROUNDED delta, and you have a ground fault somewhere else. if it is an UNgrounded delta system, you are supposed to have a ground monitoring system installed.
That said, Tony's comment is more true than ever now. Delta power systems are a bad thing for power electronics, like VFDs and UPS systems, requiring special attention and/or isolation of them.
*Actually, I guess not, but it USUALLY is...