The controlled fault current of converter-interfaced renewable energy sources (CIRESs) may bring about lower sensitivity level or misoperation of fault component based directional relays (FCBDRs). In order to cope with this issue, a new control scheme is proposed to adjust sequence superimposed impedance angles of CIRESs by computing suitable current references of the CIRES controller. Meanwhile, these current references are maximized by an iterative algorithm to make full use of the short-circuit capacity of CIRESs. The proposed control scheme is applicable to various faulty conditions such as different fault types, power factors, weak grids and larger fault resistances. Compared with new directional relays that need to update protection devices, the proposed control strategy can make CIRESs compatible with commercially existing directional relays whilst the necessary fault ride through (FRT) requirements can still be satisfied. Furthermore, all the controller parameters are not required to be revised according to the detected fault type, even with only local measured data collected. The associated PSCAD simulations, real-time digital simulator (RTDS) experiment and downscale hardware experiment verify the proposed method.