New investigations on the method of characteristics for the evaluation of line transients

The method of characteristics (MoC) transforms line equations into ordinary differential equations, and the numerical transient solution is typically performed through discretization in time and space. There exits also a version of MoC proposed in the literature, in which the discretization in space is eliminated for uniform lines. This has the potential to render the MoC faster than the traveling wave-based models. This paper examines in detail the possibility of removing spatial discretization and extends the application for the evaluation of transients on cables in addition to transients on lines. It has been demonstrated that, although removing spatial discretization is possible by introducing certain change of variables and approximations, the resulting model has limited numerical precision and may show numerically unstable behavior. This is principally due to the approximation error introduced by the linearization of differential equations, necessary to obtain a relationship between line ends. The paper discusses other sources of numerical errors and shows that the line needs to be subdivided to improve precision.