Setting of earth fault relay

[riddle]

A 20 KV switchgear have equipped with one zig-zag earthing transformer. As you know,
A grounding transformer must handle the unbalanced load on the circuit as well as the duty during line-to-ground faults. If the circuit has a lot of unbalance load, then we must concern the continuous rating of transformer in addition of its short time withstand currents. The continuous rating power of mentioned grounding transformer is 100 KVA.
The primary current setting of related earth fault relay that installed in neutral point of E.T. is 8 Amp.
This set point current is chosen in base of E.T. continuous rating current and following calculations:

It =100/ (20x1.73) = 2.89 A

In= 3x It = 8.67 A

But the earth fault current calculation and analyses dictate other primary current setting (12.5 A).

Which one current setting is correct? Which one do you choose?



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[riddle]

پاسخ : Setting of earth fault relay

Unfortunately, nowadays with our world information transmission system (internet), we usually neglect the basic conceptions and deep thinking about new problems.
With more deep thinking, we can find that the mentioned evident equation (S = 1.73 VI) is not correct for zig-zag earthing transformers.
Indeed, each leg of a grounding transformer carries one-third of the neutral current and has line-to-neutral voltage. So in a grounded wye - delta transformer, the total power rating including all three phases is the neutral current times
The line-to-ground voltage:
S= 1.73 VI
But a zig-zag transformer is more efficient than a grounded wye - delta transformer.
In a zig-zag, each winding has less than the line-to-ground voltage,
by a factor of 1.73, so the bank may be rated lower:
S = 1.73/1.7.3 VI = VI
Therefore, the continuous rating current of E/T is 5 A and rating neutral current is 15A, and we can choose 12.5A as correct earth fault primary current setting.

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