The performance of CTs when they are carrying the load current is not of concern as far as relaying needs are concerned.
The DC-component in fault-current causes the flux linkage to increase considerably above their steady-state peak, driving the CT into saturation. The secondary current of a CT may not represent the primary current faithfully if it goes into saturation, hence relays which depend upon the secondary current are likely to mis-operate during this period.
The ALF (Accuracy limit factor) specifies the maximum current at which the the CT must still conform to accuracy specifications. The ALC (Accuracy limit current) can be determined by multiplying the rated current (primary or secondary) with the ALF.
Therefore: ALC = I rated x ALF
Standard accuracy limit factors for protective transformers are 5, 10, 15, 20 and 30
The accuracy classes to which Protective CTs are manufactured is 5P and 10P. "P" indicates that it is a protective CT. Numbers 5 and 10 are the percentage composite error at rated primary ALC.
Thus a 10P15 CT have a 10% error at 15 times primary current.
For instantaneous overcurrent relays a Class 10P with a rated accuracy limit factor of 5 should be adequate.
For overcurrent relays with inverse-time characteristic, however, class 10P accuracy should be specified together witha rated ALF corresponding to the maximum overcurrent at which reasonable accuracy of the relay time caracteristic is required.
If you want to detect earth faults also(relay connected in the residual circuit of a three-phase set of CTs), a class 5P is required. (Essential to employ CTs with low exciting currents to secure reasonably low earth fault settings)
CT's for most forms of protection are covered by BS3938:1973 and guidance in the application of CTs is given in Appendix B of the British Standard.
Regards
Ralph