  Distribution grids currently lack comprehensive real-time metering.
Nevertheless, grid operators require precise knowledge of loads and renewable
generation to accomplish any feeder optimization task. At the same time, new
grid technologies, such as solar photovoltaics and energy storage units are
interfaced via inverters with advanced sensing and actuation capabilities. In
this context, this two-part work puts forth the idea of engaging power
electronics to probe an electric grid and record its voltage response at
actuated and metered buses, to infer non-metered loads. Probing can be
accomplished by commanding inverters to momentarily perturb their power
injections. Multiple probing actions can be induced within a few tens of
seconds. In Part I, load inference via grid probing is formulated as an
implicit nonlinear system identification task, which is shown to be
topologically observable under certain conditions. The conditions can be
readily checked upon solving a max-flow problem on a bipartite graph derived
from the feeder topology and the placement of actuated and non-metered buses.
The analysis holds for single- and multi-phase grids, radial or meshed, and
applies to phasor or magnitude-only voltage data. The topological observability
of distribution systems using smart meter or phasor data is cast and analyzed a
special case.
