How does current flow to the ground in Delta connection (Ungrounded) in an Earth Fault?

In normal configurations a single fault on a delta system will not cause any significant earth fault current. This is useful because the distribution system can tolerate a single fault without interruption to the consumers.

This benefit is of little use if the system does not detect the first fault and fix it. As a result, earth fault detection relays will monitor the phase-earth voltage on each line. (This will create a very weak star (wye) point on the system.) When an earth fault is detected on one phase then that phase is deliberately shorted to earth. This can help make fallen wires less likely to electrocute someone. A contact of the relay will signal the fault which can then be investigated, cleared and reset.

If the first fault is not cleared then a second fault will result in high earth current and trip out the system.

There is no such thing as an ungrounded system. The delta system is grounded through parasitic capacitance from each phase to ground. This parasitic capacitance appears in the zero sequence network as an impedance (XC) connected to the neutral bus. When you have a phase-earth fault the zero sequence current has to flow through this XC. As such, it is typically very very small.

In the picture i show below i have a one-line drawing showing a source at left (1.0 per unit = nominal voltage) connected to Bus H. The transformer between bus H & L is a wye-delta. So, bus L is an ungrounded delta bus like you are talking about. If we account for the parasitic phase-earth capacitance then we would connect the large XC from the bus to reference bus in each of the three sequence networks (positive, negative, and zero). In my figure i only show it in the zero sequence (bottom) because it is negligible in the positive (top) and negative (middle). Note that ZF = 0 for solid ground fault.

The lady's answer, "current flows from high potential to low potential (zero potential earth)" is just ignorant. Without an earthing source (zig-zag grounding bank etc.) there will be no significant fault current as i describe above. When you get to the point in your studies that you learn/practice symmetrical component analysis you will see this clearly.

I'd recommend Blackburn's book.

russ