Precise fault location plays an important role in the reliability of modern power systems. With the increasing penetration of renewable energy sources, the power system experiences a decrease in system inertia and alterations in steady-state characteristics following a fault occurrence. Most existing single-ended phasor domain methods assume a certain impedance of the remote-end system or consistent current phases at both ends. These problems present challenges to the applicability of conventional phasor-domain location methods. This paper presents a novel single-ended time domain fault location method for single-phase-to-ground faults, one which fully considers the distributed parameters of the line model. The fitting of transient signals in the time domain is realized to extract the instantaneous amplitude and phase. Then, to eliminate the error caused by assumptions of lumped series resistance in the Bergeron model, an improved numerical derivation is presented for the distributed parameter line model. The instantaneous symmetrical components are extracted for decoupling and inverse transformation of three-phase recording data. Based on the above, the equation of instantaneous phase constraint is established to effectively identify the fault location. The proposed location method reduces the negative effects of fault resistance and the uncertainty of remote end parameters when relying on one-terminal data for localization. Additionally, the proposed fault analysis methods have the ability to adapt to transient processes in power systems. Through comparisons with existing methods in three different systems, the fault position is correctly identified within an error of 1%. Also, the results are not affected by sampling rates, data windows, fault inception angles, and load conditions.