DC grids of system voltages above 20V demand different safety concepts compared to conventional AC grids. More elaborate protection devices have to be developed to detect not only high-power, but also low-power faults. The discrimination between faults and load variations can be supported by model-based machine learning methods. For this purpose, this contribution developes time-invariant and linearized system-models with chains of two-ports including possible faults. To consider faults in transmission lines occuring after steady-state system conditions, the initial distribution of voltages and currents is modeled by spatially concentrated equivalent sources. This approach leads to an analytic frequency domain solution without spatial discretization. Measurements on a two-core cable compare favourably with this closed form model.