Properties of Direct-Time and Reversed-Time Transfer Functions to Locate Disturbances along Power Transmission Lines

The paper discusses specific frequency-domain properties of the electromagnetic time reversal (EMTR) method applied to locate faults and, more in general, disturbances in power networks. Specifically, we investigate the properties of two transfer functions: (i) the direct-time transfer function relating the source of disturbance and the induced transients at the observation point, and (ii) the reversed-time transfer function relating the time-reversed back-injected transients and the characterization variables at a guessed location along the line. We show that, at the exact location of the disturbance, the two transfer functions are identical. This property can potentially be used as an efficient means to locate sources of disturbances in EMTR-based systems. Making reference to typical power lines and underground cables, the developed transfer function property is numerically illustrated.