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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 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 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 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 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 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↗
DOE OSTI2024

Ensuring Solution Uniqueness in Three-Phase Power System State Estimation

This paper is concerned with the issue of potential non-unique solutions in three-phase state estimation. Theory of observability analysis for positive sequence power system state estimation is based on certain assumptions that avoid possibility of multiple solutions. Also, it is shown that observability of a positive sequence network remains independent of the network parameters or the operating state. When extending single-phase observability analysis directly to the three-phase case, this paper considers the possibility of converging to multiple solutions, i.e. solution non-uniqueness, even for cases where state estimator successfully converges. The study illustrates via numerical examples the likelihood of converging to entirely different solutions for certain network parameters. It also examines how the operating state, particularly under unbalanced loading, leads to solution non-uniqueness. The paper then describes an alternative approach to ensure a unique solution in three-phase state estimation. This method aims to accurately and uniquely estimate the state of any unbalanced three-phase system, irrespective of load imbalance, network configuration, existence of synchronous generators or transformers.

Power System State Estimation, Three-Phase, Distri↗
DOE OSTI2023

Anomaly Detection in Power System State Estimation: Review and New Directions

Foundational and state-of-the-art anomaly-detection methods through power system state estimation are reviewed. Traditional components for bad data detection, such as chi-square testing, residual-based methods, and hypothesis testing, are discussed to explain the motivations for recent anomaly-detection methods given the increasing complexity of power grids, energy management systems, and cyber-threats. In particular, state estimation anomaly detection based on data-driven quickest-change detection and artificial intelligence are discussed, and directions for research are suggested with particular emphasis on considerations of the future smart grid.

42 ENGINEERING↗
DOE OSTI2025

Adaptive Linear State Estimation for Unbalanced Distribution System

The inclusion of PMU functionality in distribution relays enables the implementation of a linear state estimator (LSE) in Distribution Systems (DS). However, the unbalanced topology and phase coupling in distribution lines necessitate modifications to the LSE formulation. Additionally, the higher fault frequency in distribution systems requires a state estimation approach that is resilient to contingencies. This work proposes an adaptive linear state estimation algorithm tailored for unbalanced distribution systems with single-phase and two-phase laterals. Furthermore, a modified Optimal PMU Placement (OPP) strategy is introduced to ensure full observability in distribution systems with single-phase and two-phase buses. To maintain adaptability to topology changes, the state estimator incorporates circuit breaker status data provided by PMUs, ensuring robust performance during topology changes triggered by faults. The performance of the algorithm is verified on the IEEE 13-bus, 34-bus, and 123-bus systems.

PMUs↗
DOE OSTI2024

Specifying angular reference for robust three-phase state estimation

While the phase angle of any of the bus voltages can be chosen as the angular reference in the state estimation formulation of positive sequence networks, the same approach does not readily extend to three-phase network state estimation problem. It is commonly assumed that there is at least one bus where the bus voltages are perfectly balanced with phase angles displaced ±120° and these balanced three phase voltages are used as the three-phase reference in solving the three-phase state estimation problem. This assumption may be quite realistic in transmission networks, and for distribution networks with a strong transmission system connection. However, it might not be realistic to assume existence of a perfectly balanced reference bus in today’s distribution systems with ever increasing penetration of renewable sources or for isolated operation of microgrids. In this paper, a novel state estimation formulation will be presented which facilitates correct solution irrespective of the existence of buses with perfectly balanced voltages. The new formulation is general, and lends itself to bad data processing. It yields accurate results in any three-phase power system irrespective of its operating conditions (balanced or highly unbalanced), configuration (isolated microgrid, connected to transmission system, etc.) and whether or not it contains any synchronous generators. The performance of the method is validated using the IEEE 123 bus three-phase system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Efficient Network Partitioning: Application for Decentralized State Estimation in Power Distribution Grids

Increase in the proliferation of distributed energy resources require real-time situational awareness for efficient grid operations. State estimation plays an important role for the real-time control and management of the power grid. As the sensing infrastructure grows, aggregating and handling high volumes of data at a centralized location is extremely difficult. To address this challenge, this paper first proposes a novel and efficient hier-archical spectral clustering-based network partitioning algorithm followed by a decentralized compressive sensing (DCS)-based state estimation. The applicability of the proposed network partitioning algorithm is tested on an IEEE 123-bus network, an IEEE 8,500-node system, and a 6,000+ node distribution network. The results shows that the proposed approach efficiently divides the network into multiple sub-networks with the minimum number of edge connections among the neighbors. Then, we perform DCS-based state estimation on the 6,000+ node distribution network after dividing the network into 18 optimal partitions. Simulation results show that the DCS-based state estimation recovers the system states with high accuracy and low complexity.

alternating direction method of multipliers↗
DOE OSTI2023

A Robust Parallel Distributed State Estimation for Large Scale Distribution Systems

The growing need and interest in real-time monitoring of large distribution networks motivated by the rapid population of renewable sources, EVs and etc. demand a computationally efficient state estimation framework. Furthermore, this paper presents an improved computational framework for implementing a robust state estimator using a multi-core processor. The main contribution of the paper is the proposed computational framework along with two partitioning strategies which enable fast and robust state estimation for large scale radial and/or meshed distribution systems. Formulation of the proposed method and its implementation are described in detail. Performance of the estimator is tested by simulations first using a small 84-bus radial distribution system. Then the method’s scalability is demonstrated by simulations on two very large scale distribution networks one configured radially and the other meshed each containing over 12,500 buses.

42 ENGINEERING↗
DOE OSTI2023

Modified Eigen-Decomposition-based Interval Analysis (MEDIA) for Power System Dynamic State Estimation

The Bayesian approach has been used for the dynamic state estimation (DSE) of a power system. However, due to the complexity of noise resources, it is difficult to quantify measurement and process noise using probability density functions (PDFs). To overcome the difficulty, the authors of this paper propose a modified eigen-decomposition-based interval analysis (MEDIA) method, which employs bounds instead of PDFs to quantify the noise, and uses the eigen decomposition method to reduce the negative impact of the overestimation problem. Using the simulation data generated from IEEE 16-machine and IEEE 10-machine systems, it is shown that the proposed MEDIA method can estimate the hard boundaries of dynamic states in real time. Furthermore, comparison with the forward-backward propagation method and the extended set-membership filter also shows that the proposed MEDIA method performs better by providing narrower boundaries in the DSE.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Artificial Neural Network-based State Estimation for Low Observable, Unbalanced Microgrids for Microgrid Building Blocks

The microgrid building blocks (MBB) were proposed as microgrid components with combined sub-components with power conversion, communication, and microgrid control capability, or a subset of such sub-components. This work addresses the microgrid controller, present in an MBB, which requires accurate state estimation to perform its tasks, including for monitoring, power flow (dispatch), fault detection, etc. In this paper, an artificial neural network (ANN)-based framework for state estimation is proposed for an MBB, especially for unbalanced and low observable microgrids. To overcome the challenge of low observability in unbalanced systems, a concept of extended adjacent matrix is introduced to reduce the required number of measurements for state estimation. Addressing the challenges, a feed forward neural network (FNN) is utilized to enhance estimation accuracy and reliability with the reduced number of measurements. The proposed state estimation is validated through extensive simulations on a microgrid, which was achieved from the modified IEEE 34-bus distribution test feeder with multiple distributed energy resources (DERs) and demonstrated superior performance in estimation accuracy and low observability.

Choi, Jongchan↗
DOE OSTI2023

Uncertainty Error Modeling for Non-Linear State Estimation With Unsynchronized SCADA and µPMU Measurements

Distribution systems of the future smart grid require enhancements to the reliability of distribution system state estimation (DSSE) in the face of low measurement redundancy, unsynchronized measurements, and dynamic load profiles. Micro phasor measurement units (µPMUs) facilitate co-synchronized measurements with high granularity, albeit at an often prohibitively expensive installation cost. Supervisory control and data acquisition (SCADA) measurements can supplement µPMU data, although they are received at a slower sampling rate. Further complicating matters is the uncertainty associated with load dynamics and unsynchronized measurements–not only are the SCADA and µPMU measurements not synchronized with each other, but the SCADA measurements themselves are received at different time intervals with respect to one another. This paper proposes a non-linear state estimation framework which models dynamic load uncertainty error by updating the variances of the unsynchronized measurements, leading to a time-varying system of weights in the weighted least squares state estimator. Case studies are performed on the 33-Bus Distribution System in MATPOWER, using Ornstein–Uhlenbeck stochastic processes to simulate dynamic load conditions.

Cooper, Austin↗
DOE OSTI2024

Distribution System State Estimation Using a Multiple Iteration Extended Kalman Filter Approach

To support the operation of modern distribution systems, operators require real-time visibility into system states. Due to a lack of measurements and unbalanced operation, the state estimation in distribution systems is challenging as compared to transmission systems. This paper proposes the utilization of a Multiple Iteration - Extended Kalman Filter based approach for the distribution system state estimation. This modified version of the baseline extended Kalman filter iterates over the update step multiple times thereby reducing the estimation error. The proposed algorithm along with the auxiliary algorithms such as bad data detection is integrated into a co-simulation environment. Case studies show that the proposed state estimation method can result in a lesser estimation error as compared to the baseline approach.

Bhatti, Bilal Ahmad↗
DOE OSTI2025

Unorthodox Parallelization for Bayesian Quantum State Estimation

Bayesian inference enables informationally efficient quantum state tomography (QST) yet is challenging to scale computationally. We demonstrate a parallelizable Bayesian QST method that, although unorthodox, proves remarkably practical, attaining significant speedups in multiqubit state estimation.

Nguyen, Hanson H. [Arizona State University] (ORCI↗
DOE OSTI2024

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. Furthermore, the comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

97 MATHEMATICS AND COMPUTING↗