Modernizing traditional systems (such as power, water, and gas distribution systems) with sensing, computation, control, and communication infrastructure has led to the development of smart systems. This modernization has been motivated by the need for improved reliability, resiliency, operational efficiency, and safety. However, various challenges, such as limited measurements, low observability, and bidirectional power flow due to renewables, introduce challenges in the control and operation of these systems. To ensure the safe operation of distribution systems, grid operators require knowledge of the system states obtained using state estimators to take corrective actions. However, the low-observability conditions result in the poor performance of current state-of-the-art techniques. Therefore, in this dissertation, we develop novel state estimators that utilize spatiotemporal correlations, network topology, and power flow constraints to improve state estimation performance under low-observability conditions. We also tackle problems such as topology identification, meter placement, and error analysis to aid the developed state estimators.

Firstly, we formulate the state estimation problem as a low-rank tensor completion problem with power flow equations as constraints. The formulation introduces feature scaling and weighted tensor nuclear norm to improve the sensitivity of the estimates to all physical quantities in the tensor. We demonstrate the superiority of this approach over existing sparsity-aware techniques. Secondly, we address the challenges of reducing computational time and eliminating the need for complete knowledge of network parameters. We achieve this objective by converting the tensor completion-based state estimators into their graph neural network (GNN) equivalents. These estimators perform comparably to the tensor completion-based approaches while requiring several orders of magnitude lower computational time. Further, these estimators learn the interdependencies in the data without prior knowledge of the network parameters.

In this work, we also derive error bounds for state estimates of the model-based state estimators and introduce a technique to optimize hyperparameters. We then exploit the interdependencies among the data to develop meter placement strategies for determining metering locations. These techniques maximize the information available to the developed state estimators and thus aim to reduce state estimation errors. Next, we address the data channel congestion issues associated with increasing metering deployments by developing data-driven dictionaries. We then utilize these dictionaries with compressive sensing-based frameworks. We demonstrate the need to use dictionaries tailored to the data to obtain superior data compression and reconstruction performance over deterministic dictionaries. Finally, we study problems in other cyber-physical systems, such as leak detection in water distribution networks, and develop meter placement strategies.