Decomposition of Post-Fault Transients on Power Lines and Analytical Solution of Its Stationary Component

Based on the background of power lines with fault, the sinusoidal steady-state response can be easily analytically solved. However, the transient response cannot be solved for a complex network due to non-determinacy of network topology. The problem of the analytical solution of post-fault transients on faulted power lines was studied by decomposing post-fault transients into transient non-stationary component (TNC) and transient stationary component (TSC). TNC reflects mutational changes or wave-fronts in post-fault transients, whereas TSC is a uniformly continuous and low-frequency signal because it is the rest of post-fault transients whose mutational changes are ‘removed’. Then, the approximate analytical solution of TSC was deduced by building an equivalent circuit model based on its physical interpretation. At last, the accurate numerical solution of TSC was obtained by EMTP simulation and compared with its analytical solution. The errors are extremely small.