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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Physics-informed graphical neural network for power system state estimation

State estimation is highly critical for accurately observing the dynamic behavior of the power grids and minimizing risks from cyber threats. However, existing state estimation methods encounter challenges in accurately capturing power system dynamics, primarily because of limitations in encoding the grid topology and sparse measurements. Here, this paper proposes a physics-informed graphical learning state estimation method to address these limitations by leveraging both domain physical knowledge and a graph neural network (GNN). We employ a GNN architecture that can handle the graph-structured data of power systems more effectively than traditional data-driven methods. The physics-based knowledge is constructed from the branch current formulation, making the approach adaptable to both transmission and distribution systems. The validation results of three IEEE test systems show that the proposed method can achieve lower mean square error more than 20% than the conventional methods.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

A Medium-/Low-Voltage Joint State Estimator Through Linear Uncertainty Propagation

Traditionally, distribution system state estimations (DSSE) are challenged by the lack of measurements at both primary and secondary sides of the system. The widely available cable television (CATV) voltage sensors installed in low-voltage (LV) networks bring opportunities to achieve higher quality DSSE covering a broader area of the distribution network. This study proposes a medium-/low-voltage (MV/LV) joint distribution system state estimation approach using the untapped CATV measurements. It aims at addressing the need for system situational awareness at the grid edge while improving the estimation accuracy at both the primary and secondary sides compared to its disjointed counterpart. Linearized measurement functions and boundary condition uncertainty propagation rules are derived to ensure the computational efficiency and accuracy of the joint state estimator. Numerical experiments are conducted on an IEEE test feeder to demonstrate the efficacy of the proposed method and the value of CATV measurements.

joint state estimation↗
DOE OSTI2021

Roles of Dynamic State Estimation in Power System Modeling, Monitoring and Operation

—Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, time synchronized measurements, and the advances in the capability, scalability, and affordability of computing and communications. This paper discusses the advantages of DSE as compared to static state estimation, and the implementation differences between the two, including the measurement configuration, modeling framework and support software features. The important roles of DSE are discussed from modeling, monitoring and operation aspects for today’s synchronous machine dominated systems and the future power electronics-interfaced generation systems. Several examples are presented to demonstrate the benefits of DSE on enhancing the operational robustness and resilience of 21st century power system through time critical applications. Future research directions are identified and discussed, paving the way for developing the next generation of energy management systems.

Zhao, Junbo↗
DOE OSTI2020

Real Time Effective Impedance Estimation for Power System State Estimation

Here, we introduce two tools-the Effective Impedance State Estimator (EISE), and the Real Time Effective Impedance Estimator (RTEIE). The EISE is novel in that it is an entirely data-driven state estimator, and does not require a network model. Thus, the EISE is well suited for applications in which an accurate network model is not available. Instead of using a network impedance model, the EISE uses an effective impedance network model that is learned online by the RTEIE. The RTEIE recursively estimates the effective impedance network model using phasor measurement unit (PMU) measurements. The mathematical reasoning for using an effective impedance model, rather than a full network impedance model, is given. The recursive estimation framework allows the RTEIE to take the entire history of phasor measurements into account to produce a model estimate, while still adjusting to changes in the network impedance due to external factors such as topology changes and temperature. The merits of the RTEIE and EISE are demonstrated by comparing the accuracy of the EISE with a conventional state estimator on a toy network.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Advanced Sensor Deployment for Distribution System State Estimation and Fault Identification

Distribution systems are currently facing steep operational challenges as a result of the rapidly increasing integration of renewables and other distributed energy resources (DERs) at both the primary and secondary circuit levels. Distribution utilities and system operators have traditionally had some visibility of their primary circuits using low-frequency supervisory control and data acquisition systems, and they have had very poor if not zero visibility of the secondary circuits where the presence of DERs is constantly increasing. Therefore, this paper presents simulation studies to demonstrate the benefits of an advanced, high-fidelity sensor technology, called as the Meta-Alert System (MAS), developed by Electrical Grid Monitoring, Ltd. (EGM), on the distribution grid. First, a reliable model of the EGM sensors is developed, and then two use cases, distribution system state estimation (DSSE) and fault identification are simulated to evaluate the performance of the MAS technology. Simulation results on the Electric Power Research Institute J1 feeder demonstrate that the MAS can effectively participate in system-level DSSE programs and can detect and locate faults faster than traditional distribution protection schemes.

distribution system↗
DOE OSTI2020

Robust Medium-Voltage Distribution System State Estimation using Multi-Source Data

Due to the lack of sufficient online measurements for distribution system observability, pseudo-measurements from short-term load or distributed renewable energy resources (DERs) forecasting are used. However, the accuracy of them is low and thus significantly limits the performance of distribution system state estimation (DSSE). In this paper, a robust DSSE that integrates multi-source measurement data is proposed. Specifically, the historical low-voltage (LV) side smart meters are used to forecast load and DERs injections via the support vector machine (SVM) with optimally tuned parameters. By contrast, the online smart meters at LV side are utilized to derive equivalent power injections at the MV/LV transformers, yielding more accurate pseudo-measurements compared to the forecasted injections. Furthermore, to deal with bad data caused by communication loss, instrumental errors and cyber attacks, robust DSSE that relies on generalized maximum-likelihood (GM)-estimation criterion is developed. The projection statistics are developed to adjust the weights of each measurement, leading to better balance between pseudo- and real-time measurements. Numerical results conducted on modified IEEE 33-bus system with DG integration demonstrate the effectiveness and robustness of the proposed method.

distribution system state estimation↗
DOE OSTI2025

Unorthodox parallelization for Bayesian quantum state estimation

Quantum state tomography (QST) allows for the reconstruction of quantum states through measurements and some inference technique under the assumption of repeated state preparations. Bayesian inference provides a promising platform to achieve both efficient QST and accurate uncertainty quantification, yet is generally plagued by the computational limitations associated with long Markov chains. In this work, we present a novel Bayesian QST approach that leverages modern distributed parallel computer architectures to efficiently sample a D-dimensional Hilbert space. Using a parallelized preconditioned Crank–Nicholson Metropolis–Hastings algorithm, we demonstrate our approach on simulated data and experimental results from IBM Quantum systems up to four qubits, showing significant speedups through parallelization. Although highly unorthodox in pooling independent Markov chains, our method proves remarkably practical, with validation ex post facto via diagnostics like the intrachain autocorrelation time. We conclude by discussing scalability to higher-dimensional systems, offering a path toward efficient and accurate Bayesian characterization of large quantum systems.

Bayesian inference↗
DOE OSTI2020

Estimation Matrix Calibration of PMU Data-driven State Estimation Using Neural Network

Linear state estimation (LSE) is a phasor measurement unit (PMU) data-based power system state estimation that incorporates a linear measurement model in rectangular coordinates. Due to the high computational efficiency and high observational time-resolution, LSE can act as a supplementary state estimation in a wide-area monitoring system (WAMS). The performance of LSE is relatively sensitive to noises in measurements. Therefore, the estimation accuracy relies heavily on the accuracy of the estimation matrix, which is directly influenced by the measurement weight matrix. This paper proposes two novel calibration method of the estimation matrix using neural networks. One is based on the minimum absolute network loss (ANL), and the other is based on the minimum average squared network loss (ASNL). Both methods are tested and compared with LSE algorithms on the IEEE 14-bus system

neural network↗
DOE OSTI2023

System state estimation with asynchronous measurements

The present disclosure provides techniques for estimating network states using asynchronous measurements by leveraging network inertia. For example, a device configured in accordance with the techniques of the present disclosure may receive electrical parameter values corresponding to at least one first location within a power network and determine, based on the electrical parameter values and a previous estimated state of the power network, an estimated value of unknown electrical parameters that correspond to a second location within the power network. The device may further cause at least one device within the power network to modify operation based on the estimated value of the unknown electrical parameters. The leveraging of network inertia may obviate the need for probabilistic models or pseudo-measurements.

Cavraro, Guido↗
DOE OSTI2025

Explainable multi-fidelity Bayesian neural network for distribution system state estimation

Distribution System State Estimation (DSSE) is frequently constrained by limited real-time measurements, the uncertainties introduced by distributed energy resources, and the presence of bad data. To address them, this paper proposes an enhanced Multi-Fidelity Bayesian Neural Network (MFBNN) DSSE approach. A low-fidelity layer based on a Deep Neural Network (DNN) is first pre-trained on pseudo-measurement data to learn fundamental state features. Subsequently, a high-fidelity Bayesian Neural Network (BNN) layer leverages limited but high-quality real-time measurements to refine these features, thereby achieving accurate DSSE. Additionally, the deep SHapley Additive exPlanation (SHAP) is developed to quantify the influence of measurement data on DSSE through dual perspectives of global feature importance and local nodal contributions, establishing a hierarchical explainability framework for machine learning-based DSSE. Comparative studies conducted on the IEEE 13-bus system and a real-world 2135-node system from Dominion Energy demonstrate that the proposed method excels in estimation accuracy, even under situations of high noise levels, bad data, and missing data. Further comparisons with Weighted Least Squares (WLS) and other machine learning-based DSSE approaches verify that the proposed framework offers higher accuracy, improved interpretability, and enhanced robustness.

Bad data↗
DOE OSTI2020

Enhanced Tensor Completion Based Approaches for State Estimation in Distribution Systems

Grid state estimation is essential for effective control and management of distribution systems. While weighted least squares has been the conventional method for state estimation, sparsity-aware methods have become popular due to their superior performance with limited data. Matrix completion and compressed sensing-based state estimation approaches exploit the underlying smoothness in the state variables. However, classic matrix completion methods do not take into account the temporal correlation of system states. Compressed sensing methods, on the other hand, require an appropriate choice of sparsifying basis that may not be easy to identify. This paper proposes a blocktensor completion based framework which uses an alternative approach to estimate voltage phasor, power injections and branch currents. This approach utilizes the temporal correlation of the system states in a tensor trace-norm minimization formulation with power flow equations as constraints. Herein, feature scaling is introduced in the problem formulation to benefit from the improved sensitivity of the tensor trace norm to the matrix columns in the scaled unfoldings of the tensor. Weighted tensor norm is utilized to exploit the structures of the different unfoldings of the state measurement tensor to improve the voltage estimation. The estimation accuracy is further improved by alternatively estimating the tensor columns and increasing the available data at each stage in the tensor completion process. The proposed methods are evaluated on the IEEE-33, 37 test systems and a 100- node test system. The proposed methods are shown to provide significant performance gains relative to the classic matrix and tensor completion based approaches.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Real-Time Distribution System State Estimation with Asynchronous Measurements

We report state estimation is a fundamental task in power systems. Although distribution systems are increasingly equipped with sensing devices and smart meters, measurements are typically reported at different rates and asynchronously; these aspects pose severe strains on workhorse state estimation algorithms, which are designed to process batches of data collected in a synchronous manner from all the measurement units. In this paper, we develop a novel state estimation algorithm to continuously update the estimate of the state based on measurements received in an asynchronous manner from measurement units. The synthesis of the algorithm hinges on a proximal-point type method, implemented in an online fashion, and capable of processing measurements received sequentially from sensors. A performance analysis is presented by providing bounds on the estimation error in terms of the mean and variance that hold at each iteration and asymptotically. The scheme is also compared with a more traditional Weighted Least Squares estimator that compensates for the lack of measurement data by using, as pseudo measurements, the measurement retrieved during a certain time window. Numerical simulations on the IEEE 37-bus feeder corroborate the analytical findings.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Formulation of Three-Phase State Estimation Problem Using a Virtual Reference

State Estimation (SE) is the backbone of modern Energy Management System (EMS) due its capability of processing real time measurements and provide reliable information to system operators. Since its introduction to power systems in the 70’s, SE has been widely used in transmission networks. Distribution grids on the other hand lack sufficient number of real time measurements, and for that reason SE has not been widely implemented on these systems. The recent increase in the number of renewable energy sources connected to the grid at lower voltage levels, the advent of Distribution Automation (DA) and Smart Grids necessitate closer monitoring of distribution networks and thus forcing utilities to upgrade their operations and deploy Advanced Distribution Management Sytems (ADMS). Therefore, Distribution System State Estimation (DSE) is paramount to provide real time monitoring of active distribution grids. This papers investigates the formulation of the three-phase distribution state estimation where in the most general case, none of the system buses may have balanced three phase voltages. In such a case, the choice and definition of the slack bus need to be revisited. Most of the existing work arbitrarily assign the root bus of the distribution feeder as the balanced three-phase reference which may not be realistic for today’s active distribution systems. This paper addresses this shortcoming of the existing SE formulations by introducing a virtual reference bus. Here, the proposed approach is effectively validated by simulations carried out on distribution test systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Two-Stage Optimization Framework for Detecting and Correcting Parameter Cyber-Attacks in Power System State Estimation

One major tool of Energy Management Systems for monitoring the status of the power grid is State Estimation. Since the results of state estimation are used within the energy management system, the security of the state estimation process is most important. The focus research in this area is on detecting False Data Injection attacks on measurements. While this is important, State Estimation also rely on database that are used to describe the relationship between measurements and systems' states. This paper presents a two-stage programming framework to detect and correct attacks in the parameters of the measurement model used by the state estimation process in the Energy Management System. In the first stage, an estimate of the line parameters ratios are obtained. In the second stage, the estimated ratios from stage I are used in a Bi-Level model for obtaining a final estimate of the measurements' model parameters. Hence, the presented framework does not only unify the detection and correction in a single optimization run, but also provide a monitoring scheme for the SE database that is typically considered static. In addition, in the two stages, linear programming framework is preserved. For validation, the IEEE 118 bus system is used for implementation. The results of this paper illustrate the effectiveness of the proposed model for detecting attacks in the database used in the state estimation process.

state estimation, two-stage optimization, cyber-ph↗
DOE OSTI2025

Meta-Learning Enhanced Physics-Informed Graph Attention Convolutional Network for Distribution Power System State Estimation

Promptly perceiving distribution system states is challenged by frequent topology changes and uncertain power injections. To address these issues, a Meta-learning enhanced physics-informed graph attention convolutional network (Meta-PIGACN) model is proposed to handle topological variability in distribution system state estimation (DSSE). Specifically, physics information is integrated into the graph convolutional network, enabling a physics-informed edge-weighting process that incorporates physical information to control the aggregation of neighboring nodes. Besides, the graph attention mechanism automatically adjusts the importance of different neighboring nodes, allowing the capture and preservation of inherent system features across varying topologies, thereby improving state estimation accuracy. Furthermore, meta-learning is proposed to acquire empirical knowledge across multiple topologies so that the model can rapidly adapt to new configurations through iterative gradient descent updates even in large-scale systems. In conclusion, the simulation results based on the 33/118/1746-node distribution systems show the high accuracy and efficiency of the proposed model.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Physics-Informed Deep Neural Network Method for Limited Observability State Estimation

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, due to for example cyber attacks, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Towards Smart Grids Enhanced Situation Awareness: A Bi-Level Quasi-Static State Estimation Model

Smart Grid situational awareness is provided by Energy Management Systems. A core process of these systems is State Estimation. The great majority of state estimators model the Smart Grid through a set of nonlinear algebraic equations, named the measurement model. Problem formulation considers the Gauss solution. Several model improvements have been presented regarding the Gauss solution, aiming between others to provide measurement noise robustness to the state estimation process. While considerable effort has been focused on such developments, state estimation is still constrained by the implicit modelling error, and thus inevitably vulnerable to cyber-threats. In this work, a state estimation bi-level formal model is presented towards Smart Grids enhanced situational awareness considering the concepts of synthetic measurements and innovation. Comparative test results with the state-of-the-art on the IEEE 14-bus system are presented highlighting improved situational awareness to bad data. Easy-to-implement model, without hard-to-derive parameters, built-on the classic weighted least squares solution, highlight potential aspects for real-life implementation.

cyber security↗