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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 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 OSTI2022

Multiarea Distribution System State Estimation via Distributed Tensor Completion

Here, this paper proposes a model-free distribution system state estimation method based on tensor completion using canonical polyadic decomposition. In particular, we consider a setting where the network is divided into multiple areas. The measured physical quantities at buses located in the same area are processed by an area controller. A three-way tensor is constructed to collect these measured quantities. The measurements are analyzed locally to recover the full state information of the network. A distributed closed-form iterative algorithm based on the alternating direction method of multipliers is developed to obtain the low-rank factors of the whole network state tensor where information exchange happens only between neighboring areas. The convergence properties of the distributed algorithm and the sufficient conditions on the number of samples for each smaller network that guarantee the identifiability of the factors of the state tensor are presented. To demonstrate the efficacy of the proposed algorithm and to check the identifiability conditions, numerical simulations are carried out using the IEEE 123-bus system and a large-scale real utility feeder.

24 POWER TRANSMISSION AND DISTRIBUTION↗

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 OSTI2020

Gradient-Based Multi-Area Distribution System State Estimation

The increasing distributed and renewable energy resources and controllable devices in distribution systems make fast distribution system state estimation (DSSE) crucial in system monitoring and control. We consider a large multi-phase distribution system and formulate DSSE as a weighted least squares (WLS) problem. We divide the large distribution system into smaller areas of subtree structure, and by jointly exploring the linearized power flow model and the network topology, we propose a gradient-based multi-area algorithm to exactly and efficiently solve the WLS problem. The proposed algorithm enables distributed and parallel computation of the state estimation problem without compromising any performance. Numerical results on a 4,521-node test feeder show that the designed algorithm features fast convergence and accurate estimation results. Comparison with traditional Gauss-Newton method shows that the proposed method has much better performance in distribution systems with a limited amount of reliable measurement. The real-time implementation of the algorithm tracks time-varying system states with high accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2019

Distribution System State Estimation: A Semidefinite Programming Approach

Distribution system state estimation (DSSE) is one of the vital components in the next-generation distribution management system which allows operators to monitor the entire system's operating conditions. Due to the lack of real-time measurements, DSSE has to process measurements whose quality varies significantly across different sources, which causes a convergence issue to the Gauss-Newton solver. In this paper, a semidefinite programming (SDP) framework is proposed to reformulate the DSSE problem into a rank- constrained SDP problem. One challenge of this technique is the nonconvex rank-one constraint, which is generally relaxed. However, the relaxed SDP-DSSE problem cannot guarantee a rank-one solution and hence loses optimality. Therefore, we propose two solution approaches to obtain rank-one solutions for the SDPDSSE problem: the rank reduction approach and the convex iteration approach. The model and the effectiveness of the proposed solution approaches are numerically demonstrated on the IEEE 13-bus, 34-bus, and 123-bus distribution systems.

convex iteration↗

DOE OSTI2022

Advanced Sensor Deployment for Distribution System State Estimation and Fault Identification: Preprint

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 J1feeder 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 monitoring↗

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 OSTI2019

Distribution System State Estimation in the Presence of High Solar Penetration

In recent years, the low-to-medium voltage distribution networks are experiencing rising levels of distributed energy resources, including renewable generation, along with improved sensing, communication and automation infrastructure. As such, state estimation methods for distribution systems are becoming increasingly relevant as a means to enable better control strategies that can both leverage the benefits and mitigate the risks associated with high penetration of variable and uncertain distributed generation resources. Primary challenges of this problem include modeling complexities (nonlinear non-convex power-flow equations), limited availability of sensor measurements, and high penetration of uncertain renewable generation. This paper formulates the distribution system state estimation as a nonlinear weighted least squares problem, based on sensor measurements as well as forecasts data (both load and generation). We investigate the sensitivity of state estimator accuracy to (load/generation) forecast uncertainties, sensor accuracy, and sensor coverage levels.

Distribution system state estimation, nonlinear op↗

DOE OSTI2021

A Scalable Meter Placement Method for Distribution System State Estimation

This paper studies the optimal meter placement problem for distribution system state estimation given limited measurement resources. We formulate the problem as a mixed integer semi-definite programming that minimizes the worst case estimation errors over a set of operating points. To solve the problem, we first relax the problem as a convex optimization problem. Motivated by the lack of scalability of existing solvers, we next leverage the special structure of the cost function and propose an algorithm based on barrier method that solves the problem with significantly better numerical performance. The proposed method has been validated on the IEEE 13-bus, IEEE 123-bus, and IEEE 8,500-bus feeders.

barrier method↗

DOE OSTI2022

Online Distribution System State Estimation via Stochastic Gradient Algorithm

Distribution network operation is becoming more challenging because of the growing integration of intermittent and volatile distributed energy resources (DERs). This motivates the development of new distribution system state estimation (DSSE) paradigms that can operate at fast timescale based on real-time data stream of asynchronous measurements enabled by modern information and communications technology. To solve the real-time DSSE with asynchronous measurements effectively and accurately, this paper formulates a weighted least squares DSSE problem and proposes an online stochastic gradient algorithm to solve it. The performance of the proposed scheme is analytically guaranteed and is numerically corroborated with realistic data on IEEE 123-bus feeder.

distribution system state estimation↗

DOE OSTI2021

Multi-Area Distribution System State Estimation Using Decentralized Physics-Aware Neural Networks

The development of active distribution grids requires more accurate and lower computational cost state estimation. In this paper, the authors investigate a decentralized learning-based distribution system state estimation (DSSE) approach for large distribution grids. The proposed approach decomposes the feeder-level DSSE into subarea-level estimation problems that can be solved independently. The proposed method is decentralized pruned physics-aware neural network (D-P2N2). The physical grid topology is used to parsimoniously design the connections between different hidden layers of the D-P2N2. Monte Carlo simulations based on one-year of load consumption data collected from smart meters for a three-phase distribution system power flow are developed to generate the measurement and voltage state data. The IEEE 123-node system is selected as the test network to benchmark the proposed algorithm against the classic weighted least squares and state-of-the-art learning-based DSSE approaches. Numerical results show that the D-P2N2 outperforms the state-of-the-art methods in terms of estimation accuracy and computational efficiency.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Matrix Completion Using Alternating Minimization for Distribution System State Estimation

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power flow constraints has been shown to be effective in estimating voltage phasors under low-observability conditions using single-snapshot information. However, the method requires solving a semidefinite programming (SDP) problem, which becomes computationally infeasible for large systems and if multiple-snapshot (time-series) information is used. This paper proposes an efficient algorithm to solve the constrained matrix completion problem with time-series data. This algorithm is based on reformulating the matrix completion problem as a bilinear (non-convex) optimization problem, and applying the alternating minimization algorithm to solve this problem. This paper proves the summable convergence of the proposed algorithm, and demonstrates its efficacy and scalability via IEEE 123-bus system and a real utility feeder system. This paper also explores the value of adding more data from the history in terms of computation time and estimation accuracy.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2020

Matrix Completion Using Alternating Minimization for Distribution System State Estimation: Preprint

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2019

Linear Distribution System State Estimation Using Synchrophasor Data and Pseudo-Measurement

State estimation is often a challenging task in distribution systems due to deploying a limited number of measurement devices. Moreover, the integration of precise distributionlevel phasor measurement unites, a.k.a micro-PMUs, along with inaccurate pseudo-measurements in state estimation introduces another challenge. These issues might decrease the efficiency of traditional standard weighted least squares (WLS) for distribution system state estimation. This paper proposes a novel linear distribution system state estimation with taken different types of measurements, including micro-PMU measurements and line current measurements, into account. To involve pseudomeasurements into the linear state estimation, a linearization method based on the Taylor’s approximation is adopted to reformulate pseudo-measurement functions in a linear form. The results obtained via numerical simulations show that the proposed linear state estimation method performs similarly to the standard nonlinear WLS estimator. In addition, the sensitivity analyses results show that our method has a better performance compared to WLS once a limited number of highly precise micro-PMUs are accompanied with inaccurate pseudo-measurements in state estimation.

State estimation Distribution system Micro-PMU Lin↗

DOE OSTI2019

A Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in Distribution System State Estimation

In this paper, we present an efficient computational framework with the purpose of generating weighted pseudo-measurements to improve the quality of distribution system state estimation (DSSE) and provide observability with advanced metering infrastructure (AMI) against unobservable customers and missing data. The proposed technique is based on a game-theoretic expansion of relevance vector machines (RVMs). This platform is able to estimate the nodal power consumption and quantify its uncertainty while reducing the prohibitive computational burden of model training for large AMI datasets. To achieve this objective, the large training set is decomposed and distributed among multiple parallel learning entities. The resulting estimations from the parallel RVMs are then combined using a game-theoretic model based on the idea of repeated games with vector payoff. It is observed that through this approach and by exploiting the seasonal changes in customers’ behavior the accuracy of pseudo-measurements can be considerably improved, while introducing robustness against bad training data samples. The proposed pseudo-measurement generation model is integrated into a DSSE using a closed-loop information system, which takes advantage of a branch current state estimator (BCSE) to further improve the performance of the designed machine learning framework. This method has been tested on a practical distribution feeder model with smart meter data for verification.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Enhancement of Distribution System State Estimation Using Pruned Physics-Aware Neural Networks

Realizing complete observability in the three-phase distribution system remains a challenge that hinders the implementation of classic state estimation algorithms. In this paper, a new method, called the pruned physics-aware neural network (P2N2), is developed to improve the voltage estimation accuracy in the distribution system. The method relies on the physical grid topology, which is used to design the connections between different hidden layers of a neural network model. To verify the proposed method, a numerical simulation based on one- year smart meter data of load consumptions for three-phase power flow is developed to generate the measurement and voltage state data. The IEEE 123-node system is selected as the test network to benchmark the proposed algorithm against the classic weighted least squares (WLS). Numerical results show that P2N2 outperforms WLS in terms of data redundancy and estimation accuracy.

distribution system state estimation↗

DOE OSTI2021

Analyzing the Effects of Cyberattacks on Distribution System State Estimation

Key components of power systems—such as energy management systems, automatic generation control, and state estimation—are under serious vulnerability from cyberattacks. Cyber threats in electric grids have increased significantly because of the increased interconnectivity of supervisory control and data acquisition systems and public network infrastructure. As the penetration level of distributed energy resources increases, it is imperative to employ system-monitoring techniques such as state estimation for the reliable operation of distribution systems. Recently, multiple methods have been developed that exploit the low rank property of distribution system state matrix and are robust to bad data, such as matrix completion. This paper analyzes the impact of various realistic cyberattack scenarios on matrix completion. Realistic cyberattack scenarios are converted into data corruption models that are used in an extensive simulation of a custom IEEE 123-bus system.

41 EE - Solar Energy Technologies Office (EE-4S)↗