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.

Due to limited metering infrastructure, distribution grids are currently challenged by observability issues. On the other hand, smart meter data, including local voltage magnitudes and power injections, are communicated to the utility operator from grid buses with renewable generation and demand-response programs. This work employs grid data from metered buses towards inferring the underlying grid state. To this end, a coupled formulation of the power flow problem (CPF) is put forth. Exploiting the high variability of injections at metered buses, the controllability of solar inverters, and the relative time-invariance of conventional loads, the idea is to solve the non-linear power flow equations jointly over consecutive time instants. An intuitive and easily verifiable rule pertaining to the locations of metered and non-metered buses on the physical grid is shown to be a necessary and sufficient criterion for local observability in radial networks. To account for noisy smart meter readings, a coupled power system state estimation (CPSSE) problem is further developed. Both CPF and CPSSE tasks are tackled via augmented semi-definite program relaxations. The observability criterion along with the CPF and CPSSE solvers are numerically corroborated using synthetic and actual solar generation and load data on the IEEE 34-bus benchmark feeder.