The protection of meshed HVDC grids requires the fast identification of faults affecting the transmission lines. Communication-based methods are thus not suited due to the transmission delays. Many approaches involving a model of the transient behavior of the faulty line have recently been proposed. Nevertheless, an accurate description of the traveling wave phenomenon in multi-conductor lines such as overhead lines requires complex computations ill-suited for fast fault identification. This paper presents a single-ended fault identification algorithm using a closed-form parametric model of the fault transient behavior. The model combines physical and behavioral parts and depends explicitly on the parameters that characterize the fault, namely the fault distance and impedance. When a fault is suspected, the fault parameters are estimated so that the model fits best the received measurements. The confidence region of the estimated fault parameters is used to decide whether the protected line is actually faulty or not. The proposed algorithm is tested on a 4 station grid simulated with EMTP-RV software. The method is able to identify the faulty line using a measurement window of less than 0.5 ms. This allows ultra-fast fault clearing and can hence improve the overall reliability of future HVDC grids.