I was not trying to answer any technical question, I was trying to answer an English one. The word "open" can get confusing for some people at times when dealing in electrical.It is not the same setup.
A broken delta is used to measure 3Vo (the sum of the delta voltages) for a ground relay.
Once you have the zig-zag, you can use it to measure ground currents. The broken delta just for protection schemes.The use of a zig-zag transformer is discussed as a means of low reactance grounding, not protection. A delta-wye transformer is shown as a form of low resistance grounding.
Yes, the broken delta is for ungrounded systems.The broken delta is used on ungrounded systems.
Using the zig-zag would ground the system, so other types of protection schemes would be used.