The injection or absorption of reactive power by the static synchronous compensator (STATCOM) may lead to the misoperation of protective relays and single-phase-tripping systems that operate based on impedance measurement. Also, high-frequency harmonic components caused by switching the internal circuitry of a STATCOM lead to unintended tripping of relays that work based on traveling waves. This paper proposes a single-terminal approach to detect, locate, and identify the faulty line(s) and phase(s) in parallel transmission lines equipped with STATCOMs using traveling waves. To that end, these processes were designed so that adding a STATCOM or different operating modes does not degrade their efficiency and accuracy. The faults and faulty phases were simultaneously detected using the first set of traveling waves received at the sending end of the parallel lines at a sampling frequency of 200 kHz. Furthermore, a sampling frequency of 1 MHz was used briefly to improve the fault location accuracy. The discrete wavelet transform (with BD4 mother wavelet) was adopted to extract the traveling waves. All simulations and analyses were conducted in the PSCAD environment. The results obtained from numerous simulations at different places and states of the networks verified the high accuracy and validity of the proposed methods.