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Traditional smart meters, which measure energy usage every 15 minutes or more and report it at least a few hours later, lack the granularity needed for real-time decision-making. To address this practical problem, we introduce a new method using generative adversarial networks (GAN) that enforces temporal consistency on its high-resolution outputs via hard inequality constraints using convex optimization. A unique feature of our GAN model is that it is trained solely on slow timescale aggregated historical energy data obtained from smart meters. The results demonstrate that the model can successfully create minute-by-minute temporally correlated profiles of power usage from 15-minute interval average power consumption information. This innovative approach, emphasizing inter-neuron constraints, offers a promising avenue for improved high-speed state estimation in distribution systems and enhances the applicability of data-driven solutions for monitoring and subsequently controlling such systems. 

Recently, we demonstrated the success of a time-synchronized state estimator using deep neural networks (DNNs) for real-time unobservable distribution systems. In this paper, we provide analytical bounds on the performance of the state estimator as a function of perturbations in the input measurements. It has already been shown that evaluating performance based only on the test dataset might not effectively indicate the ability of a trained DNN to handle input perturbations. As such, we analytically verify the robustness and trustworthiness of DNNs to input perturbations by treating them as mixed-integer linear programming (MILP) problems. The ability of batch normalization in addressing the scalability limitations of the MILP formulation is also highlighted. The framework is validated by performing time-synchronized distribution system state estimation for a modified IEEE 34-node system and a real-world large distribution system, both of which are incompletely observed by micro-phasor measurement units. 

As the phasor measurement unit (PMU) placement problem involves a cost-benefit trade-off, more PMUs get placed on higher-voltage buses. However, this leads to the fact that many lower-voltage levels of the bulk power system cannot be observed by PMUs. This lack of visibility then makes time-synchronized state estimation of the full system a challenging problem. In this paper, a deep neural network-based state estimator (DeNSE) is proposed to solve this problem. The DeNSE employs a Bayesian framework to indirectly combine the inferences drawn from slow-timescale but widespread supervisory control and data acquisition (SCADA) data with fast-timescale but selected PMU data, to attain sub-second situational awareness of the full system. The practical utility of the DeNSE is demonstrated by considering topology change, non-Gaussian measurement noise, and detection and correction of bad data. The results obtained using the IEEE 118-bus system demonstrate the superiority of the DeNSE over a purely SCADA state estimator and a PMU-only linear state estimator from a techno-economic viability perspective. Lastly, the scalability of the DeNSE is proven by estimating the states of a large and realistic 2000-bus synthetic Texas system. 

Recently, there has been a major emphasis on developing data-driven approaches involving machine learning (ML) for high-speed static state estimation (SE) in power systems. The emphasis stems from the ability of ML to overcome difficulties associated with model-based approaches, such as handling of non-Gaussian measurement noise. However, topology changes pose a stiff challenge for performing ML-based SE because the training and test environments become different when such changes occur. This paper circumvents this challenge by formulating a graph neural network (GNN)-based time-synchronized state estimator that considers the physical connections of the power system during the training itself. The results obtained using the IEEE 118-bus system indicate that the GNN-based state estimator outperforms both the model-based linear state estimator and a data-driven deep neural network-based state estimator in the presence of non-Gaussian measurement noise and topology changes, respectively.