To accurately locate stator ground faults in synchronous generators, a fault location method based on third harmonics and the mesh current method is proposed. A third-harmonic equivalent circuit model incorporating distributed capacitance and grounding transformer impedance is established, the mathematical relationships between the third-harmonic voltages at the neutral point and generator terminals and the fault location as well as the transition resistance are derived, and the fault characteristic equations are constructed using the mesh current method. Considering the nonlinear variation of voltage phase with fault location, a fault location objective function is constructed by minimizing the deviation between the measured and calculated voltages while incorporating precise model coefficients. The particle swarm optimization algorithm is employed for global optimization and determines the fault location. The proposed model is verified by PSCAD simulations, demonstrating high accuracy. The proposed method maintains high fault location precision under various fault scenarios, different load conditions, and unbalanced operating conditions, and is applicable to different generator parameters. Without requiring additional sensors, the method achieves precise fault location across the entire winding using only conventional third-harmonic voltage measurements, providing an effective technical means for rapid diagnosis and maintenance of generator stator ground faults.