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This study presents an adaptive transmission line auto-reclosing scheme based on synchronised phasor measurement units. This scheme uses voltage and current phasors of different sequences at both ends of a transmission line to effectively classify transient and permanent faults occurring on transmission lines. In the case of a transient fault this scheme can provide a variable and adaptive dead time for reclosing circuit breakers via the detection of secondary arc extinction. System simulation studies show that the proposed scheme achieves excellent performance in classifying transient and permanent single-phase faults and estimating the secondary arc extinction time for correct auto-reclosing.