Publications

This manuscript presents a complete framework for the development and verification of physics-informed neural networks with application to the alternating-current power flow (ACPF) equations. Physics-informed neural networks (PINN)s have received considerable interest within power systems communities for their ability to harness underlying physical equations to produce simple neural network architectures that achieve high accuracy using limited training data. The methodology developed in this work builds on existing methods and explores new important aspects around the implementation of PINNs including: (i) obtaining operationally relevant training data, (ii) efficiently training PINNs and using pruning techniques to reduce their complexity, and (iii) globally verifying the worst-case predictions given known physical constraints. The methodology is applied to the IEEE-14 and 118 bus systems where PINNs show substantially improved accuracy in a data-limited setting and attain better guarantees with respect to worst-case predictions.

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The power grid, traditionally perceived as an independent physical network has undergone a significant transformation in recent years due to its integration with cyber communication networks and modern digital components. Cyber situations, including cyber-attacks and network anomalies, can directly affect the physical operation of the grid; therefore, studying this intricate relationship between the physical and cyber systems is pivotal for enhancing the resilience and security of modern power systems. In this digest, a novel Long Short-Term Memory (LSTM)-based Autoencoder (AE) model for cyber-physical data fusion and threat detection is proposed. The scenario under consideration includes the effective detection of a physical disturbance and a Denial-of-Service (DoS) attack, which obstructs control commands during the physical disturbance in the power grid. Detailed analysis and quantitative results regarding the LSTM-based AE model's training and evaluation phases is provided, which highlight its key operation features and benefits for guaranteeing security and resilience in the power grid.

Network Operation Centers (NOCs) and Security Operation Centers (SOCs) play a critical role in addressing a wide range of threats in critical infrastructure systems such as the electric grid. However, when considering the electric grid and related industrial control systems (ICSs), visibility into the information technology (IT), operational technology (OT), and underlying physical process systems are often disconnected and standalone. As the electric grid becomes increasingly cyber-physical and faces dynamic, cyber-physical threats, it is vital that cyber-physical situational awareness (CPSA) across the interconnected system is achieved. In this paper, we review existing NOC and SOC capabilities and visualizations, motivate the need for CPSA, and define design principles with example visualizations for a next-generation grid cyber-physical integrated SOC (CP-ISOC).

Accurate distribution system models are becoming increasingly critical for grid modernization tasks, and inaccurate phase labels are one type of modeling error that can have broad impacts on analyses using the distribution system models. This work demonstrates a phase identification methodology that leverages advanced metering infrastructure (AMI) data and additional data streams from sensors (relays in this case) placed throughout the medium-voltage sector of distribution system feeders. Intuitive confidence metrics are employed to increase the credibility of the algorithm predictions and reduce the incidence of false-positive predictions. The method is first demonstrated on a synthetic dataset under known conditions for robustness testing with measurement noise, meter bias, and missing data. Then, four utility feeders are tested, and the algorithm’s predictions are proven to be accurate through field validation by the utility. Lastly, the ability of the method to increase the accuracy of simulated voltages using the corrected model compared to actual measured voltages is demonstrated through quasi-static time-series (QSTS) simulations. The proposed methodology is a good candidate for widespread implementation because it is accurate on both the synthetic and utility test cases and is robust to measurement noise and other issues.

Distribution system model calibration is a key enabling task for incipient failure identification within the distribution system. This report summarizes the work and publications by Sandia National Laboratories on the GMLC project titled “Incipient Failure Identification for Common Grid Asset Classes”. This project was a joint effort between Sandia National Laboratories, Lawrence Livermore National Laboratory, National Energy Technology Laboratory, and Oak Ridge National Laboratory. The included work covers distribution system topology identification, transformer groupings, phase identification, regulator and tap position estimation, and the open-source release and implementation of the developed algorithms.

In many areas of constrained optimization, representing all possible constraints that give rise to an accurate feasible region can be difficult and computationally prohibitive for online use. Satisfying feasibility constraints becomes more challenging in high-dimensional, non-convex regimes which are common in engineering applications. A prominent example that is explored in the manuscript is the security-constrained optimal power flow (SCOPF) problem, which minimizes power generation costs, while enforcing system feasibility under contingency failures in the transmission network. In its full form, this problem has been modeled as a nonlinear two-stage stochastic programming problem. In this work, we propose a hybrid structure that incorporates and takes advantage of both a high-fidelity physical model and fast machine learning surrogates. Neural network (NN) models have been shown to classify highly non-linear functions and can be trained offline but require large training sets. In this work, we present how model-guided sampling can efficiently create datasets that are highly informative to a NN classifier for non-convex functions. We show how the resultant NN surrogates can be integrated into a non-linear program as smooth, continuous functions to simultaneously optimize the objective function and enforce feasibility using existing non-linear solvers. Overall, this allows us to optimize instances of the SCOPF problem with an order of magnitude CPU improvement over existing methods.

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Efficiently embedding and/or integrating mechanistic information with data-driven models is essential if it is desired to simultaneously take advantage of both engineering principles and data-science. The opportunity for hybridization occurs in many scenarios, such as the development of a faster model of an accurate high-fidelity computer model; the correction of a mechanistic model that does not fully-capture the physical phenomena of the system; or the integration of a data-driven component approximating an unknown correlation within a mechanistic model. At the same time, different techniques have been proposed and applied in different literatures to achieve this hybridization, such as hybrid modeling, physics-informed Machine Learning (ML) and model calibration. In this paper we review the methods, challenges, applications and algorithms of these three research areas and discuss them in the context of the different hybridization scenarios. Moreover, we provide a comprehensive comparison of the hybridization techniques with respect to their differences and similarities, as well as advantages and limitations and future perspectives. Finally, we apply and illustrate hybrid modeling, physics-informed ML and model calibration via a chemical reactor case study.

This report documents the Resilience Enhancements through Deep Learning Yields (REDLY) project, a three-year effort to improve electrical grid resilience by developing scalable methods for system operators to protect the grid against threats leading to interrupted service or physical damage. The computational complexity and uncertain nature of current real-world contingency analysis presents significant barriers to automated, real-time monitoring. While there has been a significant push to explore the use of accurate, high-performance machine learning (ML) model surrogates to address this gap, their reliability is unclear when deployed in high-consequence applications such as power grid systems. Contemporary optimization techniques used to validate surrogate performance can exploit ML model prediction errors, which necessitates the verification of worst-case performance for the models.

This report summarizes the work performed under a project funded by U.S. DOE Solar Energy Technologies Office (SETO), including some updates from the previous report SAND2022-0215, to use grid edge measurements to calibrate distribution system models for improved planning and grid integration of solar PV. Several physics-based data-driven algorithms are developed to identify inaccuracies in models and to bring increased visibility into distribution system planning. This includes phase identification, secondary system topology and parameter estimation, meter-to-transformer pairing, medium-voltage reconfiguration detection, determination of regulator and capacitor settings, PV system detection, PV parameter and setting estimation, PV dynamic models, and improved load modeling. Each of the algorithms is tested using simulation data and demonstrated on real feeders with our utility partners. The final algorithms demonstrate the potential for future planning and operations of the electric power grid to be more automated and data-driven, with more granularity, higher accuracy, and more comprehensive visibility into the system.

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The protection systems (circuit breakers, relays, reclosers, and fuses) of the electric grid are the primary component responding to resilience events, ranging from common storms to extreme events. The protective equipment must detect and operate very quickly, generally <0.25 seconds, to remove faults in the system before the system goes unstable or additional equipment is damaged. The burden on protection systems is increasing as the complexity of the grid increases; renewable energy resources, particularly inverter-based resources (IBR) and increasing electrification all contribute to a more complex grid landscape for protection devices. In addition, there are increasing threats from natural disasters, aging infrastructure, and manmade attacks that can cause faults and disturbances in the electric grid. The challenge for the application of AI into power system protection is that events are rare and unpredictable. In order to improve the resiliency of the electric grid, AI has to be able to learn from very little data. During an extreme disaster, it may not be important that the perfect, most optimal action is taken, but AI must be guaranteed to always respond by moving the grid toward a more stable state during unseen events.

Neural networks (NN)s have been increasingly proposed as surrogates for approximation of systems with computationally expensive physics for rapid online evaluation or exploration. As these surrogate models are integrated into larger optimization problems used for decision making, there is a need to verify their behavior to ensure adequate performance over the desired parameter space. We extend the ideas of optimization-based neural network verification to provide guarantees of surrogate performance over the feasible optimization space. In doing so, we present formulations to represent neural networks within decision-making problems, and we develop verification approaches that use model constraints to provide increasingly tight error estimates. We demonstrate the capabilities on a simple steady-state reactor design problem.

Frequent changes in penetration levels of distributed energy resources (DERs) and grid control objectives have caused the maintenance of accurate and reliable grid models for behind-the-meter (BTM) photovoltaic (PV) system impact studies to become an increasingly challenging task. At the same time, high adoption rates of advanced metering infrastructure (AMI) devices have improved load modeling techniques and have enabled the application of machine learning algorithms to a wide variety of model calibration tasks. Therefore, we propose that these algorithms can be applied to improve the quality of the input data and grid models used for PV impact studies. In this paper, these potential improvements were assessed for their ability to improve the accuracy of locational BTM PV hosting capacity analysis (HCA). Specifically, the voltage- and thermal-constrained hosting capacities of every customer location on a distribution feeder (1,379 in total) were calculated every 15 minutes for an entire year before and after each calibration algorithm or load modeling technique was applied. Overall, the HCA results were found to be highly sensitive to the various modeling deficiencies under investigation, illustrating the opportunity for more data-centric/model-free approaches to PV impact studies.

The installation of digital sensors, such as advanced meter infrastructure (AMI) meters, has provided the means to implement a wide variety of techniques to increase visibility into the distribution system, including the ability to calibrate the utility models using data-driven algorithms. One challenge in maintaining accurate and up-to-date distribution system models is identifying changes and event occurrences that happen during the year, such as customers who have changed phases due to maintenance or other events. This work proposes a method for the detection of phase change events that utilizes techniques from an existing phase identification algorithm. This work utilizes an ensemble step to obtain predicted phases for windows of data, therefore allowing the predicted phase of customers to be observed over time. The proposed algorithm was tested on four utility datasets as well as a synthetic dataset. The synthetic tests showed the algorithm was capable of accurately detecting true phase change events while limiting the number of false-positive events flagged. In addition, the algorithm was able to identify possible phase change events on two real datasets.

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This report summarizes the work performed under a project funded by U.S. DOE Solar Energy Technologies Office (SETO) to use grid edge measurements to calibrate distribution system models for improved planning and grid integration of solar PV. Several physics-based data-driven algorithms are developed to identify inaccuracies in models and to bring increased visibility into distribution system planning. This includes phase identification, secondary system topology and parameter estimation, meter-to-transformer pairing, medium-voltage reconfiguration detection, determination of regulator and capacitor settings, PV system detection, PV parameter and setting estimation, PV dynamic models, and improved load modeling. Each of the algorithms is tested using simulation data and demonstrated on real feeders with our utility partners. The final algorithms demonstrate the potential for future planning and operations of the electric power grid to be more automated and data-driven, with more granularity, higher accuracy, and more comprehensive visibility into the system.

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High penetration of solar photovoltaics can have a significant impact on the power flows and voltages in distribution systems. In order to support distribution grid planning, control and optimization, it is imperative for utilities to maintain an accurate database of the locations and sizes of PV systems. This paper extends previous work on methods to estimate the location of PV systems based on knowledge of the distribution network model and availability of voltage magnitude measurement streams. The proposed method leverages the expected impact of solar injection variations on the circuit voltage and takes into account the operation and impact of changes in voltage due to discrete voltage regulation equipment (VRE). The estimation model enables determining the most likely location of PV systems, as well as voltage regulator tap and switching capacitors state changes. The method has been tested for individual and multiple PV system, using the Chi-Square test as a metric to evaluate the goodness of fit. Simulations on the IEEE 13-bus and IEEE 123-bus distribution feeders demonstrate the ability of the method to provide consistent estimations of PV locations as well as VRE actions.

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Distribution system model accuracy is increasingly important and using advanced metering infrastructure (AMI) data to algorithmically identify and correct errors can dramatically reduce the time required to correct errors in the models. This work proposes a data-driven, physics-based approach for grouping residential meters downstream of the same service transformer. The proposed method involves a two-stage approach that first uses correlation coefficient analysis to identify transformers with errors in their customer grouping then applies a second stage, using a linear regression formulation, to correct the errors. This method achieved >99% accuracy in transformer groupings, demonstrated using EPRI's Ckt 5 model containing 1379 customers and 591 transformers.

The use of grid-edge sensing in distribution model calibration is a significant aid in reducing the time and cost associated with finding and correcting errors in the models. This work proposes a novel method for the phase identification task employing correlation coefficients on residential advanced metering infrastructure (AMI) combined with additional sensors on the medium-voltage distribution system to enable utilities to effectively calibrate the phase classification in distribution system models algorithmically. The proposed method was tested on a real utility feeder of ∼800 customers that includes 15-min voltage measurements on each phase from IntelliRupters® and 15-min AMI voltage measurements from all customers. The proposed method is compared with a standard phase identification method using voltage correlations with the substation and shows significantly improved results. The final phase predictions were verified to be correct in the field by the utility company.

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The rapid increase in penetration of distributed energy resources on the electric power distribution system has created a need for more comprehensive interconnection modeling and impact analysis. Unlike conventional scenario-based studies, quasi-static time-series (QSTS) simulations can realistically model time-dependent voltage controllers and the diversity of potential impacts that can occur at different times of year. However, to accurately model a distribution system with all its controllable devices, a yearlong simulation at 1-second resolution is often required, which could take conventional computers a computational time of 10 to 120 hours when an actual unbalanced distribution feeder is modeled. This computational burden is a clear limitation to the adoption of QSTS simulations in interconnection studies and for determining optimal control solutions for utility operations. The solutions we developed include accurate and computationally efficient QSTS methods that could be implemented in existing open-source and commercial software used by utilities and the development of methods to create high-resolution proxy data sets. This project demonstrated multiple pathways for speeding up the QSTS computation using new and innovative methods for advanced time-series analysis, faster power flow solvers, parallel processing of power flow solutions and circuit reduction. The target performance level for this project was achieved with year-long high-resolution time series solutions run in less than 5 minutes within an acceptable error.

In power grid operation, optimal power flow (OPF) problems are solved several times per day to find economically optimal generator setpoints that balance given load demands. Ideally, we seek an optimal solution that is also “N-1 secure”, meaning the system can absorb contingency events such as transmission line or generator failure without loss of service. Current practice is to solve the OPF problem and then check a subset of contingencies against heuristic values, resulting in, at best, suboptimal solutions. Unfortunately, online solution of the OPF problem including the full N-1 contingencies (i.e., two-stage stochastic programming formulation) is intractable for even modest sized electrical grids. To address this challenge, this work presents an efficient method to embed N-1 security constraints into the solution of the OPF by using Neural Network (NN) models to represent the security boundary. Our approach introduces a novel sampling technique, as well as a tuneable parameter to allow operators to balance the conservativeness of the security model within the OPF problem. Our results show that we are able to solve contingency formulations of larger size grids than reported in literature using non-linear programming (NLP) formulations with embedded NN models to local optimality. Solutions found with the NN constraint have marginally increased computational time but are more secure to contingency events.

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Distribution system models play a critical role in the modern grid, driving distributed energy resource integration through hosting capacity analysis and providing insight into critical areas of interest such as grid resilience and stability. Thus, the ability to validate and improve existing distribution system models is also critical. This work presents a method for identifying service transformers which contain errors in specifying the customers connected to the low-voltage side of that transformer. Pairwise correlation coefficients of the smart meter voltage time series are used to detect when a customer is not in the transformer grouping that is specified in the model. The proposed method is demonstrated both on synthetic data as well as a real utility feeder, and it successfully identifies errors in the transformer labeling in both datasets.

Calibrating distribution system models to aid in the accuracy of simulations such as hosting capacity analysis is increasingly important in the pursuit of the goal of integrating more distributed energy resources. The recent availability of smart meter data is enabling the use of machine learning tools to automatically achieve model calibration tasks. This research focuses on applying machine learning to the phase identification task, using a co-association matrix-based, ensemble spectral clustering approach. The proposed method leverages voltage time series from smart meters and does not require existing or accurate phase labels. This work demonstrates the success of the proposed method on both synthetic and real data, surpassing the accuracy of other phase identification research.

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Timeseries power and voltage data recorded by electricity smart meters in the US have been shown to provide immense value to utilities when coupled with advanced analytics. However, Advanced Metering Infrastructure (AMI) has diverse characteristics depending on the utility implementing the meters. Currently, there are no specific guidelines for the parameters of data collection, such as measurement interval, that are considered optimal, and this continues to be an active area of research. This paper aims to review different grid edge, delay tolerant algorithms using AMI data and to identify the minimum granularity and type of data required to apply these algorithms to improve distribution system models. The primary focus of this report is on distribution system secondary circuit topology and parameter estimation (DSPE).

This paper discusses common types of errors that are frequently present in utility distribution system models and which can significantly influence distribution planning and operational assessments that rely on the model accuracy. Based on Google Earth imagery and analysis of correlation coefficients, this paper also illustrates some common error types and demonstrates methods to correct the errors. Error types include misla-beled interconnections between customers and service transformers, three-phase customers labeled as single-phase, unmarked transformers, and customers lacking coordinates. Identifying and correcting for these errors is critical for accurate distribution planning and operational assessments, such as load flow and hosting capacity analysis.

Spectral clustering is applied to the problem of phase identification of electric customers to investigate the data needs (resolution and accuracy) of advanced metering infrastructure (AMI). More accurate models are required to accurately interconnect high penetrations of PV/DER and for optimal electric grid operations. This paper demonstrates the effects of different data collection implementations and common errors in AMI datasets on the phase identification task. This includes measurement intervals, data resolution, collection periods, time synchronization issues, noisy measurements, biased meters, and mislabeled phases. High quality AMI data is a critical consideration to model correction and accurate hosting capacity analyses.

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Smart grid technologies and wide-spread installation of advanced metering infrastructure (AMI) equipment present new opportunities for the use of machine learning algorithms paired with big data to improve distribution system models. Accurate models are critical in the continuing integration of distributed energy resources (DER) into the power grid, however the low-voltage models often contain significant errors. This paper proposes a novel spectral clustering approach for validating and correcting customer electrical phase labels in existing utility models using the voltage timeseries produced by AMI equipment. Spectral clustering is used in conjunction with a sliding window ensemble to improve the accuracy and scalability of the algorithm for large datasets. The proposed algorithm is tested using real data to validate or correct over 99% of customer phase labels within the primary feeder under consideration. This is over a 94% reduction in error given the 9% of customers predicted to have incorrect phase labels.

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High-resolution, quasi-static time series (QSTS) simulations are essential for modeling modern distribution systems with high-penetration of distributed energy resources (DER) in order to accurately simulate the time-dependent aspects of the system. Presently, QSTS simulations are too computationally intensive for widespread industry adoption. This paper proposes to simulate a portion of the year with QSTS and to use decision tree machine learning methods, random forests and boosting ensembles, to predict the voltage regulator tap changes for the remainder of the year, accurately reproducing the results of the time-consuming, brute-force, yearlong QSTS simulation. This research uses decision tree ensemble machine learning, applied for the first time to QSTS simulations, to produce high-accuracy QSTS results, up to 4x times faster than traditional methods.