This paper proposes a one-terminal traveling wave (TW)-based transmission line protection for line commutated converter (LCC) of high-voltage direct current (HVDC) systems. The method requires the first and second wavefronts to reach the local bus and considers the boundary conditions of the system. A detailed mathematical analysis of the sampling frequency effects, as the basis for a number of innovations of practical interest, is presented here. Firstly, a definition of a minimum sampling frequency is formulated. This is crucial when dealing with the high sampling frequencies traditionally needed by TW-based methods. Secondly, mathematical expressions of protected, unprotected, and uncertainty zones on the transmission line are defined. Thanks to these calculations, the method is also capable of distinguishing faults at the line terminals from faults on the protected transmission line. Thirdly, the non-requirement for the TW propagation speed estimation is proven. Some TW-based protection elements require knowledge of the TW propagation speed, which is a source of errors. The proposed function presented good dependability and was able to operate below 15 ms for a transmission line of 2900 km in length.