The aim of this paper is to provide the theoretical fundamentals needed to monitor power grids using high-frequency sensors. In our context, network monitoring refers to the harvesting of different kinds of information: topology of the grid, load changes, presence of faults, and cable degradation. We rely on the transmission line theory to carry out a thorough analysis of how high-frequency signals, such those produced by power line communication modems, propagate through multi-conductor power networks. We also consider the presence of electrical anomalies on the network and analyze how they affect the signal propagation. In this context, we propose two models that rely on reflectometric and end-to-end measurements to extrapolate information about possible anomalies. An in-depth discussion is carried out to explain the properties of each model and measurement method, in order to enable the development of appropriate anomaly detection and location algorithms.