Faults considering them as discontinuities, could be located using discrete wavelet transform (DWT) specially with Har wavelet at higher detail (D) levels typically > 2. "Wavelets Theory and Applications for Manufacturing" is good book but I am not sure how exactly it could answer your question.

A comparison of different mother wavelets is used for fault detection and classification, but when it comes to fault location, wavelet coefficients are in most cases paired with artificial neural networks. I hope this can help you:

• Baqui, I., Zamora, I., Mazon, J., et al.: 'High impedance fault detection methodology using wavelet transform and artificial neural networks'. Electric Power Systems Research, 2011, 81, (7), pp. 1325-1333
• Michalik, M., Rebizant, W., Lukowicz, M., et al.: 'High-impedance fault detection in distribution networks with use of wavelet-based algorithm'. IEEE Transactions on Power Delivery, 2006, 21, (4), pp. 1793-1802
• Ngaopitakkul, A., Jettanasen, C.: ‘Combination of dicrete wavelet transform and probabilistic neural network algorithm for detecting fault location on transmission system’, Int. J. Innov. Comput. Inform. Control, 2011, 7, pp. 1861–1873
• K. Chen, C. Huang and J. He, "Fault detection, classification and location for transmission lines and distribution systems: a review on the methods," in High Voltage, vol. 1, no. 1, pp. 25-33, 4 2016.

An interesting q , Some suggestions :

1 I recall that the old method of fault discrimination was to use Impedance relays (Mason?) Maybe this can now be rehashed using transient measurements of voltage and current from base station over short time spans (less than 20 ms) with digital filtering and estimated speed of voltage/ current signals for higher frequency components.

2. Another possibility is to use traveling wave coupling into the power line and monitoring the reflections.

3. View the transmission line as an antenna and monitor frequencies which simulate say a "Taylor line source"

Cheers

Wavelet transform finds application in fault finding in power system as a classifier of different types of faults such as L-G, L-L-G faults. The classification is based on the features of transient fault current measured at the point where the occurred using phase measuring units(PMUs) and or PTs and CTs.The classification is made by inputting the measured fault currents into the WT and at its outputs you would obtained the classified features of the fault currents, which are separated as signals of different frequency bands and shapes. These output signals are then applied to artificial neural network, or a developed algorithm to identify the fault locations and distances.