Estimating cable temperature in mixed circuits with time-domain reflectometry

We present a real-world application of time-domain reflectometry as a tool to estimate the average temperature of individual cable sections in a mixed-cable circuit. Short-duration pulses are injected into the cable circuit, and reflections coming from impedance discontinuities such as cable transition joints are measured. We developed a model that can reliably detect the arrival times of these reflections in the data, and thus derive the shifts in the propagation speed caused by cable heating for individual cable segments. The model relies on precise knowledge of the lengths of the cable sections, which introduces some uncertainty in the values. A regression-enhanced Random Forest model was used to learn the relationship between wave propagation speed and cable heating from field temperature measurements for different cable types. We demonstrate that for a circuit consisting of two different cable types with an approximate 3:2 ratio, changes in the arrival time of reflections due to thermal variations can be determined within a temporal accuracy of ±0.04µs. When combined with our predictive model, we are sensitive to relative changes of ±4 °C. This approach enables temperature estimates for underground power cables using existing sensors and does not require detailed knowledge of soil conditions typically needed for thermal modelling.