CT sizing formulae

[Power0020]

I was reviewing an ABB document sizing CTs and VTs for a 230 kV GIS and noticed that the designer had used variation for maximum external circuit e.m.f. based on type of relaying.

The basic secondary emf formula is : Ikmax*(Isn/Ipn)*(Rct+RL+Sr/Ir^2).

For Breaker failure protection the following formula is provided:

5*Ioperate*(Isn/Ipn)*(Rct+RL+Sr/Ir^2) considering the Ioperate=10Iprimary_nominal

for differential protection, two cases are considered. the formulae for Ikamx are as follows:

30*Ipower_trasformer_primary_nominal for internal fault and 2*I_through_fault for through fault.

ABB relays application guides have quotes these formulae however I couldn't locate any derivation and got the feeling of something "empirical" here!.

Any clue about the basis of these equations?

 

[bwen08]

Well since I just reviewed CT sizing recently I can point you to reference documents. I'm not sure where the differential equations you quote come from but the basic CT sizing equations and derivations are referenced in the following documents:

"Selection of Current Transformers & Wire Sizing in Substations" Sethuraman Ganesan (ABB Inc.) -- Google this and you can find a non IEEE download.

"Sizing Current Transformers for Line Protection Applications" SEL Document has all the same equations and derivations as the ABB document.

https://www.selinc.com/workarea/downloadasset.aspx?id=101009

"Relaying Current Transformer Application" WECC

https://www.wecc.biz/Reliability/White Paper on Relaying Current Transformer Application.pdf