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Today high speed protection of power system elements is necessary and realizable. This paper introduces time-domain protection techniques for transmission lines using voltage and current signals in Cartesian coordinates. Three techniques are proposed using this approach for line protection. Direction of fault is obtained using change in angle between Cartesian planes of voltage and current. In the second application on unit protection scheme, internal and external faults in transmission lines are discriminated using dot product of the normals to both end current planes. Fault type identification is obtained using the angle between incremental changes in currents in Cartesian coordinates. The output of each protection function using the new concept is derived in a quarter-cycle. The performance of each of the proposed techniques is tested for load variation, high resistance fault, different fault types, power swing, fault inception angles and signal with noise. Further, the proposed techniques are evaluated using field data from a 400 kV double circuit line. [ABSTRACT FROM AUTHOR]