A robust, versatile algorithm is proposed for quick detection and identification of transmission line faults. Our approach is based on time-domain simulations of power system transient dynamics using high-fidelity models. The proposed algorithm operates on real-time data from available PMU sensors, which can be sparsely placed and located far from the line fault. The algorithm successfully identifies faults during the transient regime, while avoiding false alarms. It is also shown to be robust against uncertainties in operational parameters, as well as adverse events such as sudden load changes. A case study is included to illustrate algorithm design, tuning, and performance.