# Differential relay question



## joshtrevino (Mar 15, 2011)

I need help understanding this differential relay problem.

Problem Statement:

A three phase, delta-wye-connected, 30MVA, 33/11kv transformer is protected by a differential relay. Calculate the relay current setting for faults drawing up to 200 percent of the rated current. The CT ratio on the primary side is 500:5, and that on the secondary side is 2000:5.

Problem Solution:

Primary rated current = 30000/(1.73*33) = 524.88 amps; Secondary rated current = 3*(524.88) = 1574.64 amps

CT current on primary = 524.88*(5/500) = 5.249 amps; CT current on secondary = 1574.64*(5/2000)*(1.73) = 6.818 amps

Relay current at 200% of the rated current = 2*(6.818-5.249) = 3.3138 amps

My question: Why is the CT current from the wye connected secondary multiplied by 1.73 (the square root of 3)???

If anything, I would think that we would need to multiply the primary side by square root of 3 because it is a delta connection.

Please help.


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## cableguy (Mar 15, 2011)

In the old school scheme of things (which is the approach these problems take), when you have a delta-wye transformer, you hook your CT's in wye-delta configuration.

See the example that starts on page 329 of this book:

http://www.osinerg.gob.pe/newweb/uploads/G.../TEXTO%207A.pdf

Your sqrt(3) comes in to play because of that.

That's the old school way to do it though. With modern microprocessor relays, it's all Y connected.



> Secondary currents in phase on the differential relay could be provided byconnecting the abc set of CTs in wye or in delta with the ABC set of CTs in
> 
> delta or wye, respectively. However, connecting the abc CTs in wye would
> 
> ...


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## sd3232 (Mar 17, 2011)

cablguy, i looked at the ebook u provided, on pages 42,43,43, ANSI devices numbering, ur book says 87 is voltage and power directional relay, i believe whole table is wrong, its weird but the rest of info in the book is good?


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## cableguy (Mar 17, 2011)

Forgot to mention that. YES, there are errors in this book, and the ANSI table is one of them. It is bad. Don't use that part. That was the worst one I found. I found a few smaller formula errors, but they were pretty obvious. But that ANSI device number table is a huge, huge mistake.

Ironically, in the 2nd edition of this book (this is the 3rd), the table was correct.


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