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.
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