Time-Variant Current w/ 51 Element

[ZeroSeq]

Hello, I have a question regarding a typical 51 element's response to a decaying AC current.

If I were to have a decaying AC (no DC or asymmetrical component) current and a standard ANSI inverse overcurrent element, would you assume the best way to calculate the time to trip is using an iterative approach in excel? Is anyone aware of any formulas or rules-of-thumb for time-overcurrent element response to time-variant current?

For example, if I had a linearly decaying fault current, I would calculate it by using very small time intervals and iterating as follows:

1. Using small time intervals such as 4.1667ms (1/4 cycle), calculate the time to trip at that current value (lets say 1.5s at this current)
2. Divide the time interval (4.1667ms) by the time to trip (1.5s) to get the percentage of total time to trip for this interval.
3. Doing the same calculation in the next row, add the previous row to this row to acquire the cumulative % of time to trip.
4. Continue the iteration until the cumulative percentage reaches 100%. At this point, if you were using a time-invariant (constant) current value, the cumulative time to trip (total sum of time intervals) would equal the time to trip as calculated by the ANSI 51 element formula.




Thanks

 

[davidbeach]

You've listed what I understand happens in the relays. At each time increment you're adding that increment's "disk travel" to the preceding "disk position" and waiting for the contact to close when the "disk" makes it to the end.

That works until the current falls below pick up. If it stays below pickup from then on out no issue. But if the current bounces around pickup you have to look at the reset characteristic. Most modern relays default to an instantaneous reset, the "disk" snaps back to zero on the first time increment below pickup. Many can be set to have an electromechanical type reset in which the "disk" slowly unwinds back toward zero. If the current rises above pickup again the "disk" starts moving toward trip. In that case you have to keep track of the position until you get back to zero if a trip doesn't happen.

 

[dpc]

Agree that's how the relay should respond. How it is actually going to work is another question, since it basically a digital device - it all depends on the algorithm.

David is correct on the reset behavior if the current falls below the pickup value. I'm old enough to have done reset calculations for reclosing breakers protected by induction disk relays. That was a PITA.

And no overtravel to worry about with digital relays!