  In order to maintain stable grid operations, system monitoring and control
processes require the computation of grid states (e.g. voltage magnitude and
angles) at high granularity. It is necessary to infer these grid states from
measurements generated by a limited number of sensors like phasor measurement
units (PMUs) that can be subjected to delays and losses due to channel
artefacts, and/or adversarial attacks (e.g. denial of service, jamming, etc.).
We propose a novel graph signal processing (GSP) based algorithm to interpolate
states of the entire grid from observations of a small number of grid
measurements. It is a two-stage process, where first an underlying Hermitian
graph is learnt empirically from existing grid datasets. Then, the graph is
used to interpolate missing grid signal samples in linear time. With our
proposal, we can effectively reconstruct grid signals with significantly
smaller number of observations when compared to existing traditional approaches
(e.g. state estimation). In contrast to existing GSP approaches, we do not
require knowledge of the underlying grid structure and parameters and are able
to guarantee fast spectral optimization. We demonstrate the computational
efficacy and accuracy of our proposal via practical studies conducted on the
IEEE 118 bus system.
