Recursive functional expansion technique for computer-based impedance and differential protection

The development of a recursive functional expansion algorithm for extracting the desired frequency components from transient power system relaying signals is presented. The applications of this algorithm to impedance detection in transmission line protection and to harmonic restraint in transformer differential protection are discussed. The recursive algorithm generates fast fault detection timings for transmission lines and does not have restrictions on sample rate, data window or spacing of samples with respect to time. For power transformer differential protection, the combined second- and fifth-harmonic amplitude of the differential current is compared with the fundamental amplitude to arrive at a trip decision.