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This study proposes a novel fault feature extraction that could be used in fault detection and classification schemes for power system transmission lines, based on single-end measurements using time shift invariant property of a sinusoidal waveform. Various types of faults at different locations, fault resistance and fault inception angles on a 400 kV 361.65 km power system transmission line are investigated. The determinant function is used to extract distinctive fault features over various data window sizes namely, 1/4, 1/2 and a cycle of post-fault data. In addition, various delays were introduced before taking the post-fault measurements. The performance of the feature extraction scheme was tested on a machine intelligent platform WEKA by using three types of feature selection techniques: information gain, gain ratio and SVM. The result shows that, the determinant function defined over the phase current and neutral current is sufficient to classify ten types of short-circuit faults on doubly fed transmission lines; however, the scheme did not differentiate between 3 phase line faults (LLL) and 3 phase lines to ground faults (LLLG), the two types of faults are treated as the same type of fault, balanced fault. An accuracy between 95.95 and 100 is achieved.