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In this paper, a new noncommunication-based scheme is presented for the protection of three-terminal transmission lines. Using this scheme, simultaneous operation of circuit breakers (CBs) at all terminals is provided for all internal faults. This scheme can discriminate between external and internal faults based on initiated transients by faults, considering the high-stop filtering property of busbars through modeling their stray capacitances and employing a newly defined mathematical morphology (MM) filter to analyze the captured transients. Moreover, the transients generated by lightning or switching are identified and prohibited to enter the algorithm. The presented scheme has been applied on one of three-terminal lines in Iran's Transmission Grid. The effects of fault resistance, fault inception angle, (internal) fault location, and fault type on the performance of the proposed scheme are evaluated, where the high dependability, accuracy, and speed are verified.