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.

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.

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 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.

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.

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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.

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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.

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.

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.

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.

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.

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.

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