A time-domain fault location technique for HVDC transmission lines based on numerical solution of differential equation

This paper introduces an accurate fault location method for high-voltage direct current (HVDC) transmission lines based on time-domain data. The proposed method employs the distributed parameter model of transmission lines and applies the Variational Iteration Method (VIM) from the field of mathematics to solve the partial differential form of the transmission line equations. By deriving the expressions for current and voltage following a fault and substituting the instantaneous values of current and voltage at both ends at the fault moment, a distribution matrix of current and voltage along the line over time can be obtained. The fault location is identified by comparing the similarity of voltage waveforms at the same position on the line, derived separately from data at the beginning and end of the line after the fault. The point of highest similarity indicates the fault location. The accuracy of the result is further refined using the bisection method. Simulation results demonstrate that this method is unaffected by fault location, fault type, or the magnitude of transition resistance at the fault moment, and it exhibits high accuracy and stability.