The compensated-current-differential relay uses the same restraining current as a conventional relay, but the differential current is modified to compensate for the effects of the exciting current. Delta winding current is necessary to obtain the modified differential current for a $Y-Delta$ transformer. This paper describes an estimation algorithm of the delta winding current and its application to a compensated-current-differential relay for a $Y-Delta$ transformer. Prior to saturation, the core-loss current is calculated and used to modify the differential current. When the core first enters saturation, the initial value of the core flux is obtained by inserting the modified differential current into the magnetization curve. This flux value is used to derive the magnetizing current and consequently the modified differential current. The operating performance of the proposed relay was compared against a conventional current differential relay with harmonic blocking. Test results indicate that the proposed relay remained stable during severe magnetic inrush and over-excitation, and its operating time is significantly faster than a conventional relay. The relay is unaffected by the level of remanent flux and does not require an additional restraining or blocking signal to maintain stability. This paper concludes by implementing the proposed algorithm into a prototype relay based on a digital signal processor.