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All sourcesNASA NTRSDOE OSTI
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

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 OSTI2026

Is the Matrix Completion of Reduced Density Matrices Unique?

Reduced density matrices are central to describing observables in many-body quantum systems. In electronic structure theory, the two-particle reduced density matrix (2-RDM) suffices to determine the energy and other key properties. Recent work has used matrix completion, leveraging the low-rank structure of RDMs and approximate theoretical models, to reconstruct the 2-RDM from partial data and thus reduce the computational cost. However, matrix completion is, in general, an under-determined problem. Revisiting Rosina’s theorem (Rosina, M. Queen’s Papers on Pure and Applied Mathematics , 1968, No. 11, 369), we here show that the matrix completion is unique under certain conditions, identifying the subset of 2-RDM elements that enables its exact reconstruction from incomplete information. Building on this, we introduce a hybrid quantum–stochastic algorithm that achieves exact matrix completion, demonstrated through applications to the Fermi–Hubbard model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Dynamic Matrix Completion Based State Estimation in Distribution Grids

The power distribution network is undergoing tremendous transformation due to an increase in the penetration of renewable energy resources and electric vehicles. These changes have resulted in greater uncertainty and dynamics in the distribution grid states. Therefore, the ability to track and monitor system states has become a critical need for accurate and timely control actions. In this paper, we propose two dynamic sparsity-based state estimation approaches for distribution systems: (1) locally weighted matrix completion (LW-MC) and (2) Bayesian matrix completion with Kalman filter prediction (BMC-KF). The performance of the proposed dynamic state estimation strategies is compared with the classic/static matrix completion (static-MC) approach using the IEEE 37 and IEEE 123 bus test systems. Finally, results indicate that BMC-KF approach outperforms both LW-MC as well as static-MC even when 30% of the measurement data is available. Computational complexity associated with both approaches is quantified.

42 ENGINEERING↗
DOE OSTI2021

Matrix Completion for Improved Observability in Low-Voltage Distribution Grids

This paper considers the problem of recovering missing entries in a partially observed matrix from relatively few measurements (i.e., the so-called matrix completion problem) with the aim of increasing the presently limited observability of low-voltage distribution grids. To this end, the partially observed matrix is formed using scarce voltage magnitude measurements while accounting for their spatial information. Voltage readings are assumed to be collected from distribution utility sensors and/or geographically-distributed cable television network sensors located in immediate proximity to distribution grid nodes. A matrix completion approach built on the parameter-less singular value shrinkage technique is used to estimate voltage magnitudes at otherwise non-observable low-voltage nodes using a small number of single- or multiple-snapshot data. The effectiveness of the proposed approach is demonstrated using a U.S.-style distribution test system from the synthetic SMART- DS data set under very low- to moderate-observability conditions.

low-rank matrix completion↗
DOE OSTI2023

Feeder Power Disaggregation: A Data-Efficient Matrix Completion Approach: Preprint

This paper presents a data-driven algorithm for the feeder power disaggregation problem in distribution systems. Leveraging spatio-temporal power patterns in residential homes, residential power is discomposed into three components: sparse-switching loads, periodic loads, and photovoltaic generation, using two sparse matrices and a rank-one matrix. The matrix completion process is data-efficient because of the matrix sparsity and low rankness, along with the use of power system models. The proposed approach is tested using real-world residential datasets on a 33-bus distribution system, demonstrating accurate power disaggregation with efficient matrix completion.

distribution system↗
DOE OSTI2023

Feeder Power Disaggregation: A Data-Efficient Matrix Completion Approach

This paper presents a data-driven algorithm for the feeder power disaggregation problem in distribution systems. Leveraging spatio-temporal power patterns in residential homes, residential power is discomposed into three components: sparse-switching loads, periodic loads, and photovoltaic (PV) generation, which are characterized through the design of two sparse matrices and a low-rank matrix. The matrix completion process is data-efficient because of the matrix sparsity and low rankness, along with the use of power system models. The proposed approach is tested using real-world residential data set on a 33-bus distribution system, demonstrating accurate power disaggregation with efficient matrix completion.

distribution system↗
DOE OSTI2022

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study (https://doi.org/10.1063/5.0018326), exploits the low-rank character of the polynomial expansion of potential energy to recover, using a small sample, vibrational frequencies (square roots of nuclear Hessian eigenvalues) constituting the reaction path. Furthermore, these frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Joint Matrix Completion and Compressed Sensing for State Estimation in Low-observable Distribution System

Limited measurement availability at the distribution grid presents challenges for state estimation and situational awareness. This paper combines the advantages of two sparsity-based state estimation approaches (matrix completion and compressive sensing) that have been proposed recently to address the challenge of unobservability. The proposed approach exploits both the low rank structure and a suitable transform domain representation to leverage the correlation structure of the spatio-temporal data matrix while incorporating the powerflow constraints of the distribution grid. Simulations are carried out on three phase unbalanced IEEE 37 test system to verify the effectiveness of the proposed approach. The performance results reveal - (1) the superiority over traditional matrix completion and (2) very low state estimation errors for high compression ratios representing very low observability.

Dahale, Shweta↗
DOE OSTI2021

Low-observability matrix completion

An example device includes at least one processor configured to receive electrical parameter values corresponding to at least one first location within a power network. The at least one processor is further configured to determine, using matrix completion and based on the at least one electrical parameter value, an estimated value of at least one unknown electrical parameter. The at least one unknown electrical parameter corresponds to a second location within the power network. The at least one processor is also configured to cause at least one device within the power network to modify operation based on the estimated value of the at least one unknown electrical parameter.

Bernstein, Andrey↗
DOE OSTI2023

Bayesian High-Rank Hankel Matrix Completion for Nonlinear Synchrophasor Data Recovery

Phasor measurement units (PMUs) provide high temporal-resolution synchrophasor measurements for power system monitoring and control. The frequent data quality issues, such as missing and bad data, prevent the incorporation of synchrophasor data in real-time operations. Most existing data-driven data recovery methods assume the power system dynamics can be approximated by a linear dynamical system, and the recovery performance degrades significantly when the power system is experiencing nonlinear dynamics during significant events. Here, this paper proposes a data-driven Bayesian nonlinear synchrophasor data recovery method (Ba-NSDR) that can recover a consecutive time period of simultaneous data losses or errors across all channels, even when the underlying system is highly nonlinear. The idea is to lift the Hankel matrix of the spatial-temporal synchrophasor data to a higher dimension such that the lifted Hankel matrix is low-rank in that space and can be processed with the kernel trick. Our proposed Bayesian method then infers the probabilistic distributions of synchrophasor from the partial observations. Some distinctive features of Ba-NSDR include an uncertainty index to measure the accuracy of the recovery result and the robustness to parameter selections. Our method is verified on both synthetic and recorded event datasets.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2021

Decentralized Low-Rank State Estimation for Power Distribution Systems

This article considers the low-observability state estimation problem in power distribution networks and develops a decentralized state estimation algorithm leveraging the matrix completion methodology. Matrix completion has been shown to be an effective technique in state estimation that exploits the low dimensionality of the power system measurements to recover missing information. This technique can utilize an approximate (linear) load flow model, or it can be used with no physical models in a network where no information about the topology or line admittance is available. The direct application of matrix completion algorithms requires solving a semi-definite programming (SDP) problem, which becomes computationally challenging for large networks. We therefore develop a decentralized algorithm that capitalizes on the popular proximal alternating direction method of multipliers (proximal ADMM). The method allows us to distribute the computation among different areas of the network, leading to a scalable algorithm. By doing all computations at individual control areas and only communicating with neighboring areas, the algorithm eliminates the need for data to be sent to a central processing unit and thus increases efficiency and contributes to the goal of autonomous control of distribution networks. We illustrate the advantages of the proposed algorithm numerically using standard IEEE test cases.

41 EE - Solar Energy Technologies Office (EE-4S)↗
NASA NTRS1993

Axisymmetric micromechanics of elastic-perfectly plastic fibrous composites under uniaxial tension loading

The uniaxial response of a continuous fiber elastic-perfectly plastic composite is modeled herein as a two-element composite cylinder. An axisymmetric analytical micromechanics solution is obtained for the rate-independent elastic-plastic response of the two-element composite cylinder subjected to tensile loading in the fiber direction for the case wherein the core fiber is assumed to be a transversely isotropic elastic-plastic material obeying the Tsai-Hill yield criterion, with yielding simulating fiber failure. The matrix is assumed to be an isotropic elastic-plastic material obeying the Tresca yield criterion. It is found that there are three different circumstances that depend on the fiber and matrix properties: fiber yield, followed by matrix yielding; complete matrix yield, followed by fiber yielding; and partial matrix yield, followed by fiber yielding, followed by complete matrix yield. The order in which these phenomena occur is shown to have a pronounced effect on the predicted uniaxial effective composite response.

Lee, Jong-Won↗
DOE OSTI2022

Bayesian Framework for Multi-Timescale State Estimation in Low-Observable Distribution Systems

To support the smart grid paradigm, there has been a significant increase in sensor deployments and metering infrastructure in distribution systems. However, the measurements provided by these sensors and metering devices are typically sampled at different rates and could suffer from losses during the aggregation process. It is crucial to effectively reconcile the time-series measurements for a reliable state estimation. While weighted least squares has been the traditional approach for state estimation, sparsity-based approaches like matrix completion have become popular due to their superior performance in low-observability conditions. This paper proposes a Bayesian framework for both multi-timescale data aggregation and matrix completion based state estimation. Specifically, the multiscale time-series data aggregated from heterogenous sources are reconciled using a multitask Gaussian process that exploits the spatio-temporal correlations. Here, the resulting consistent timeseries alongwith the confidence bound on the imputations are fed into a Bayesian matrix completion method augmented with linearized power-flow constraints to accurately estimate the states in low-observability conditions. Results on three phase unbalanced IEEE 37 and IEEE 123 bus test systems reveal the superior performance of the proposed Bayesian framework. The computational complexity for the proposed Bayesian framework is also quantified.

42 ENGINEERING↗