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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. 

The increasing penetration of renewable energy resources in distribution systems necessitates high-speed monitoring and control of voltage for ensuring reliable system operation. However, existing voltage control algorithms often make simplifying assumptions in their formulation, such as real-time availability of smart meter measurements (for monitoring), or real-time knowledge of every power injection information (for control). This paper leverages the recent advances made in high-speed state estimation for real-time unobservable distribution systems to formulate a deep reinforcement learning (DRL)-based control algorithm that utilizes the state estimates alone to control the voltage of the entire system. The results obtained for a modified (renewable-rich) IEEE 34-node distribution feeder indicate that the proposed approach excels in monitoring and controlling voltage of active distribution systems. 

Recent studies indicate that the noise characteristics of phasor measurement units (PMUs) can be more accurately described by non-Gaussian distributions. Consequently, estimation techniques based on Gaussian noise assumptions may produce poor results with PMU data. This paper considers the PMU based line parameter estimation (LPE) problem, and investigates the performance of four state-of-the-art techniques in solving this problem in presence of non-Gaussian measurement noise. The rigorous comparative analysis highlights the merits and demerits of each technique w.r.t. the LPE problem, and identifies conditions under which they are expected to give good results. 

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. 

Fast and accurate knowledge of power flows and power injections is needed for a variety of applications in the electric grid. Phasor measurement units (PMUs) can be used to directly compute them at high speeds; however, a large number of PMUs will be needed for computing all the flows and injections. Similarly, if they are calculated from the outputs of a linear state estimator, then their accuracy will deteriorate due to the quadratic relationship between voltage and power. This paper employs machine learning to perform fast and accurate flow and injection estimation in power systems that are sparsely observed by PMUs. We train a deep neural network (DNN) to learn the mapping function between PMU measurements and power flows/injections. The relation between power flows and injections is incorporated into the DNN by adding a linear constraint to its loss function. The results obtained using the IEEE 118-bus system indicate that the proposed approach performs more accurate flow/injection estimation in severely unobservable power systems compared to other data-driven methods. 

Accurate knowledge of transmission line parameters is essential for a variety of power system monitoring, protection, and control applications. The use of phasor measurement unit (PMU) data for transmission line parameter estimation (TLPE) is well-documented. However, existing literature on PMU-based TLPE implicitly assumes the measurement noise to be Gaussian. Recently, it has been shown that the noise in PMU measurements (especially in the current phasors) is better represented by Gaussian mixture models (GMMs), i.e., the noises are non-Gaussian. We present a novel approach for TLPE that can handle non-Gaussian noise in the PMU measurements. The measurement noise is expressed as a GMM, whose components are identified using the expectation-maximization (EM) algorithm. Subsequently, noise and parameter estimation is carried out by solving a maximum likelihood estimation problem iteratively until convergence. The superior performance of the proposed approach over traditional approaches such as least squares and total least squares as well as the more recently proposed minimum total error entropy approach is demonstrated by performing simulations using the IEEE 118-bus system as well as proprietary PMU data obtained from a U.S. power utility.