  Motivated by the need to localise faults along electrical power lines, this
paper adopts a frequency-domain approach to parameter estimation for an
infinite-dimensional linear dynamical system with one spatial variable. Since
the time of the fault is unknown, and voltages and currents are measured at
only one end of the line, distance information must be extracted from the
post-fault transients. To properly account for high-frequency transient
behaviour, the line dynamics is modelled directly by the Telegrapher's
equation, rather than the more commonly used lumped-parameter approximations.
First, the governing equations are non-dimensionalised to avoid
ill-conditioning. A closed-form expression for the transfer function is then
derived. Finally, nonlinear least-squares optimisation is employed to search
for the fault location. Requirements on fault bandwidth, sensor bandwidth and
simulation time-step are also presented. The result is a novel end-to-end
algorithm for data generation and fault localisation, the effectiveness of
which is demonstrated via simulation.
