  This two-part work puts forth the idea of engaging power electronics to probe
an electric grid to infer non-metered loads. Probing can be accomplished by
commanding inverters to perturb their power injections and record the induced
voltage response. Once a probing setup is deemed topologically observable by
the tests of Part I, Part II provides a methodology for designing probing
injections abiding by inverter and network constraints to improve load
estimates. The task is challenging since system estimates depend on both
probing injections and unknown loads in an implicit nonlinear fashion. The
methodology first constructs a library of candidate probing vectors by sampling
over the feasible set of inverter injections. Leveraging a linearized grid
model and a robust approach, the candidate probing vectors violating voltage
constraints for any anticipated load value are subsequently rejected. Among the
qualified candidates, the design finally identifies the probing vectors
yielding the most diverse system states. The probing task under noisy phasor
and non-phasor data is tackled using a semidefinite-program (SDP) relaxation.
Numerical tests using synthetic and real-world data on a benchmark feeder
validate the conditions of Part I; the SDP-based solver; the importance of
probing design; and the effects of probing duration and noise.

Optimization and Control;Machine Learning