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Simulation is vital for engineering disciplines, as it enables the prediction and design of physical systems. However, the computational challenges inherent to large-scale simulations often arise from complex device models featuring high degrees of nonlinearities or hidden physical behaviors not captured by first principles. Gray-box models combine deep neural networks (DNNs) with physics-based models to address the computational challenges in modeling physical systems. A well-crafted gray box model capitalizes on the interpretability and accuracy of a physical model while incorporating DNNs to capture hidden physical behaviors and mitigate computational load associated with highly nonlinear components. Previously, gray box models have been constructed by defining an explicit combination of physics-based and DNN models to represent the behavior of sub-systems; however this cannot represent the coupled interactions within physical systems. We explore an implicit gray box model, where both DNNs and physical equations share a common set of state-variables. While this approach captures coupled interactions at the boundary of DNN and physics-based models, simulating the implicit gray box model remains an open-ended problem. In this work, we introduce a new hybrid simulation that integrates DNNs into the numerical solvers of simulation engines to fully simulate implicit gray box models of large physical systems. This is accomplished by backpropagating through the DNN to calculate Jacobian values during each iteration of the numerical method. The hybrid simulation improves the accuracy and runtime compared to physics-based simulation and enables reusable DNN models with lower data requirements. We explore the advantages of this approach as compared to physics-based, black box, and other gray box methods for simulating the steady-state and transient behavior of power systems.

Federated learning harnesses the power of distributed optimization to train a unified machine learning model across separate clients. However, heterogeneous data distributions and computational workloads can lead to inconsistent updates and limit model performance. This work tackles these challenges by proposing FedECADO, a new algorithm inspired by a dynamical system representation of the federated learning process. FedECADO addresses non-IID data distribution through an aggregate sensitivity model that reflects the amount of data processed by each client. To tackle heterogeneous computing, we design a multi-rate integration method with adaptive step-size selections that synchronizes active client updates in continuous time. Compared to prominent techniques, including FedProx and FedNova, FedECADO achieves higher classification accuracies in numerous heterogeneous scenarios.

Second-order optimization methods exhibit fast convergence to critical points, however, in nonconvex optimization, these methods often require restrictive step-sizes to ensure a monotonically decreasing objective function. In the presence of highly nonlinear objective functions with large Lipschitz constants, increasingly small step-sizes become a bottleneck to fast convergence. We propose a second-order optimization method that utilizes a dynamic system model to represent the trajectory of optimization variables as an ODE. We then follow the quasi-steady state trajectory by forcing variables with the fastest rise time into a state known as quiescence. This optimization via quiescence allows us to adaptively select large step-sizes that sequentially follow each optimization variable to a quasi-steady state until all state variables reach the actual steady state, coinciding with the optimum. The result is a second-order method that utilizes large step-sizes and does not require a monotonically decreasing objective function to reach a critical point. Experimentally, we demonstrate the fast convergence of this approach for optimizing nonconvex problems in power systems and compare them to existing state-of-the-art second-order methods, including damped Newton-Raphson, BFGS, and SR1.

As the pace of progress that has followed Moore's law continues to diminish, it is critical that the US support Integrated Circuit (IC or chip) education and research to maintain technological innovation. Furthermore, US economic independence, security, and future international standing rely on having on-shore IC design capabilities. New devices with disparate technologies, improved design software toolchains and methodologies, and technologies to integrate heterogeneous systems will be needed to advance IC design capabilities. This will require rethinking both how we teach design to address the new complexity and how we inspire student interest in a hardware systems career path. The main recommendation of this workshop is that accessibility is the key issue. To this end, a National Chip Design Center (NCDC) should be established to further research and education by partnering academics and industry to train our future workforce. This should not be limited to R1 universities, but should also include R2, community college, minority serving institutions (MSI), and K-12 institutions to have the broadest effect. The NCDC should support the access, development, and maintenance of open design tools, tool flows, design kits, design components, and educational materials. Open-source options should be emphasized wherever possible to maximize accessibility. The NCDC should also provide access and support for chip fabrication, packaging and testing for both research and educational purposes., Comment: This material is based upon work supported by the NSF under Grant No. 2137629

We present a stochastic first-order optimization method specialized for deep neural networks (DNNs), ECCO-DNN. This method models the optimization variable trajectory as a dynamical system and develops a discretization algorithm that adaptively selects step sizes based on the trajectory's shape. This provides two key insights: designing the dynamical system for fast continuous-time convergence and developing a time-stepping algorithm to adaptively select step sizes based on principles of numerical integration and neural network structure. The result is an optimizer with performance that is insensitive to hyperparameter variations and that achieves comparable performance to state-of-the-art optimizers including ADAM, SGD, RMSProp, and AdaGrad. We demonstrate this in training DNN models and datasets, including CIFAR-10 and CIFAR-100 using ECCO-DNN and find that ECCO-DNN's single hyperparameter can be changed by three orders of magnitude without affecting the trained models' accuracies. ECCO-DNN's insensitivity reduces the data and computation needed for hyperparameter tuning, making it advantageous for rapid prototyping and for applications with new datasets. To validate the efficacy of our proposed optimizer, we train an LSTM architecture on a household power consumption dataset with ECCO-DNN and achieve an optimal mean-square-error without tuning hyperparameters., Comment: 25 pages, 11 figures

Data integration is considered a classic research field and a pressing need within the information science community. Ontologies play a critical role in such a process by providing well-consolidated support to link and semantically integrate datasets via interoperability. This paper approaches data integration from an application perspective, looking at techniques based on ontology matching. An ontology-based process may only be considered adequate by assuming manual matching of different sources of information. However, since the approach becomes unrealistic once the system scales up, automation of the matching process becomes a compelling need. Therefore, we have conducted experiments on actual data with the support of existing tools for automatic ontology matching from the scientific community. Even considering a relatively simple case study (i.e., the spatio-temporal alignment of global indicators), outcomes clearly show significant uncertainty resulting from errors and inaccuracies along the automated matching process. More concretely, this paper aims to test on real-world data a bottom-up knowledge-building approach, discuss the lessons learned from the experimental results of the case study, and draw conclusions about uncertainty and uncertainty management in an automated ontology matching process. While the most common evaluation metrics clearly demonstrate the unreliability of fully automated matching solutions, properly designed semi-supervised approaches seem to be mature for a more generalized application.

Beginning with the class of 2023, Pennsylvania high school students will need to demonstrate career or postsecondary preparedness to meet statewide graduation requirements and receive a high school diploma. The new graduation requirements were enacted in 2018 by Pennsylvania's Act 158. They are intended to codify high standards for all students and improve student achievement across Pennsylvania, while also taking into account student strengths, interests, and career goals. As profiled in PERC's recent related brief, Act 158 outlines five pathways to demonstrating career or postsecondary preparedness, two of which--the Keystone pathways-- require demonstrating proficiency on Pennsylvania's end-of-course subject exams for Literature, Algebra, and Biology. The remaining three pathways to graduation--the alternative pathways--require that a student (1) either earn a "Proficient" Keystone exam score or acceptable course grades in each Keystone subject area; and (2) demonstrate college or career readiness through one or multiple alternative metrics, such as through an industry-based competency certification, successful completion of a service-learning project, or an internship or cooperative education program, among other metrics. This report examines historical performance on Keystone exams to explore the potential impact of the policy on students in the School District of Philadelphia's high schools. While data to understand the impact on graduation outcomes through each of the five pathways are not yet available, existing data on Keystone proficiency can provide insights into the Keystone proficiency and composite pathways. Thus, in this report, pre-pandemic administrative data for students in the classes of 2018 and 2019 who took Keystone exams while enrolled in District middle or high schools was used to see how many and which students would have met or almost met Keystone-associated requirements for graduation as defined by Act 158, had the policy been in effect at that time. [For the related brief, "Changing Requirements in Pennsylvania for High School Graduation. A Policy Brief on Pennsylvania Act 158," see ED626029.]

Digital Twins (DT) facilitate monitoring and reasoning processes in cyber-physical systems. They have progressively gained popularity over the past years because of intense research activity and industrial advancements. Cognitive Twins is a novel concept, recently coined to refer to the involvement of Semantic Web technology in DTs. Recent studies address the relevance of ontologies and knowledge graphs in the context of DTs, in terms of knowledge representation, interoperability and automatic reasoning. However, there is no comprehensive analysis of how semantic technologies, and specifically ontologies, are utilized within DTs. This Systematic Literature Review (SLR) is based on the analysis of 82 research articles, that either propose or benefit from ontologies with respect to DT. The paper uses different analysis perspectives, including a structural analysis based on a reference DT architecture, and an application-specific analysis to specifically address the different domains, such as Manufacturing and Infrastructure. The review also identifies open issues and possible research directions on the usage of ontologies and knowledge graphs in DTs., Comment: The Systematic Literature Review (SLR) is submitted to Future Generation Computer System journal's Special Issue on Digital Twin for Future Networks and Emerging IoT Applications (2023)

Distributed optimization is an essential paradigm to solve large-scale optimization problems in modern applications where big-data and high-dimensionality creates a computational bottleneck. Distributed optimization algorithms that exhibit fast convergence allow us to fully utilize computing resources and effectively scale to larger optimization problems in a myriad of areas ranging from machine learning to power systems. In this work, we introduce a new centralized distributed optimization algorithm (ECADO) inspired by an equivalent circuit model of the distributed problem. The equivalent circuit (EC) model provides a physical analogy to derive new insights to develop a fast-convergent algorithm. The main contributions of this approach are: 1) a weighting scheme based on a circuit-inspired aggregate sensitivity analysis, and 2) an adaptive step-sizing derived from a stable, Backward-Euler numerical integration. We demonstrate that ECADO exhibits faster convergence compared to state-of-the art distributed optimization methods and provably converges for nonconvex problems. We leverage the ECADO features to solve convex and nonconvex optimization problems with large datasets such as: distributing data for logistic regression, training a deep neural network model for classification, and solving a high-dimensional problem security-constrained optimal power flow problem. Compared to state-of-the-art centralized methods, including ADMM, centralized gradient descent, and DANE, this new ECADO approach is shown to converge in fewer iterations.

We introduce a new workflow for unconstrained optimization whereby objective functions are mapped onto a physical domain to more easily design algorithms that are robust to hyperparameters and achieve fast convergence rates. Specifically, we represent optimization problems as an equivalent circuit that are then solved solely as nonlinear circuits using robust solution methods. The equivalent circuit models the trajectory of component-wise scaled gradient flow problem as the transient response of the circuit for which the steady-state coincides with a critical point of the objective function. The equivalent circuit model leverages circuit domain knowledge to methodically design new optimization algorithms that would likely not be developed without a physical model. We incorporate circuit knowledge into optimization methods by 1) enhancing the underlying circuit model for fast numerical analysis, 2) controlling the optimization trajectory by designing the nonlinear circuit components, and 3) solving for step sizes using well-known methods from the circuit simulation. We first establish the necessary conditions that the controls must fulfill for convergence. We show that existing descent algorithms can be re-derived as special cases of this approach and derive new optimization algorithms that are developed with insights from a circuit-based model. The new algorithms can be designed to be robust to hyperparameters, achieve convergence rates comparable or faster than state of the art methods, and are applicable to optimizing a variety of both convex and nonconvex problems.

Recent years have seen a rich literature of data-driven approaches designed for power grid applications. However, insufficient consideration of domain knowledge can impose a high risk to the practicality of the methods. Specifically, ignoring the grid-specific spatiotemporal patterns (in load, generation, and topology, etc.) can lead to outputting infeasible, unrealizable, or completely meaningless predictions on new inputs. To address this concern, this paper investigates real-world operational data to provide insights into power grid behavioral patterns, including the time-varying topology, load, and generation, as well as the spatial differences (in peak hours, diverse styles) between individual loads and generations. Then based on these observations, we evaluate the generalization risks in some existing ML works causedby ignoring these grid-specific patterns in model design and training.

Cyberthreats are an increasingly common risk to the power grid and can thwart secure grid operations. We propose to extend contingency analysis to include cyberthreat evaluations. However, unlike the traditional N-1 or N-2 contingencies, cyberthreats (e.g., MadIoT) require simulating hard-to-solve N-k (with k >> 2) contingencies in a practical amount of time. Purely physics-based power flow solvers, while being accurate, are slow and may not solve N-k contingencies in a timely manner, whereas the emerging data-driven alternatives are fast but not sufficiently generalizable, interpretable, and scalable. To address these challenges, we propose a novel conditional Gaussian Random Field-based data-driven method that performs fast and accurate evaluation of cyberthreats. It achieves speedup of contingency analysis by warm-starting simulations, i.e., improving starting points, for the physical solvers. To improve the physical interpretability and generalizability, the proposed method incorporates domain knowledge by considering the graphical nature of the grid topology. To improve scalability, the method applies physics-informed regularization that reduces model complexity. Experiments validate that simulating MadIoT-induced attacks with our warm starter becomes approximately 5x faster on a realistic 2000-bus system., Comment: arXiv admin note: substantial text overlap with arXiv:2205.03673

In a context of constant evolution and proliferation of AI technology,Hybrid Intelligence is gaining popularity to refer a balanced coexistence between human and artificial intelligence. The term has been extensively used in the past two decades to define models of intelligence involving more than one technology. This paper aims to provide (i) a concise and focused overview of the adoption of Ontology in the broad context of Hybrid Intelligence regardless of its definition and (ii) a critical discussion on the possible role of Ontology to reduce the gap between human and artificial intelligence within hybrid intelligent systems. Beside the typical benefits provided by an effective use of ontologies, at a conceptual level, the conducted analysis has pointed out a significant contribution of Ontology to improve quality and accuracy, as well as a more specific role to enable extended interoperability, system engineering and explainable/transparent systems. Additionally, an application-oriented analysis has shown a significant role in present systems (70+% of the cases) and, potentially, in future systems. However, despite the relatively consistent number of papers on the topic, a proper holistic discussion on the establishment of the next generation of hybrid-intelligent environments with a balanced co-existence of human and artificial intelligence is fundamentally missed in literature. Last but not the least, there is currently a relatively low explicit focus on automatic reasoning and inference in hybrid intelligent systems.

Modern distribution grids that include numerous distributed energy resources (DERs) and battery electric vehicles (BEVs) will require simulation and optimization methods that can capture behavior under infeasible operating scenarios to assess reliability. A three-phase infeasibility analysis (TPIA) localizes and identifies power deficient areas in distribution feeders via a non-convex optimization that injects and subsequently minimizes slack sources, subject to AC network constraints. In this paper, we extend the TPIA framework by introducing operational bounds to ensure realistic, actionable solutions. We incorporate current, reactive power, and susceptance slack sources to model real-world assets, and discuss their potential use cases. We show that the voltage-bounded TPIA formulations provide actionable solutions for realistic networks of up to 5360 nodes where power flow simulations either fail or return low-voltage solutions. We demonstrate reactive power compensation using the slack susceptance formulation on an infeasible test case.

We propose an adaptive optimization algorithm for solving unconstrained scaled gradient flow problems that achieves fast convergence by controlling the optimization trajectory shape and the discretization step sizes. Under a broad class of scaling functions, we establish convergence of the proposed approach to critical points of smooth objective functions, while demonstrating its flexibility and robustness with respect to hyperparameter tuning. First, we prove convergence of component-wise scaled gradient flow to a critical point under regularity conditions. We show that this controlled gradient flow dynamics is equivalent to the transient response of an electrical circuit, allowing for circuit theory concepts to solve the problem. Based on this equivalence, we develop two optimization trajectory control schemes based on minimizing the charge stored in the circuit: a second order method that uses the true Hessian and an alternate first order method that approximates the optimization trajectory with only gradient information. While the control schemes are derived from circuit concepts, no circuit knowledge is needed to implement the algorithms. To find the value of the critical point, we propose a time step search routine for Forward Euler discretization that controls the local truncation error, a method adapted from circuit simulation ideas. In simulation we find that the trajectory control outperforms uncontrolled gradient flow, and the error-aware discretization out-performs line search with the Armijo condition. Our algorithms are evaluated on convex and non-convex test functions, including neural networks, with convergence speeds comparable to or exceeding Adam., Comment: 16 pages

Teacher mobility, or teacher turnover, has long garnered attention as a critical educational equity gap. This attention is warranted as, within schools, teachers have the single greatest impact on student achievement. The unprecedented interruptions to school-based learning and the trials of navigating remote and hybrid instruction due to the COVID-19 pandemic heightened concerns about the stability of the teacher workforce and the potential of a pending teacher shortage across the U.S., state of Pennsylvania, and locally in Allegheny County. This study takes a closer look at teacher mobility in the region by examining six years of data leading up to the pandemic. Specifically, this study: (1) Identifies teacher mobility trends in Allegheny County public schools from 2014-2015 to 2019-2020; (2) Describes the destinations of mobile teachers; and (3) Identifies key characteristics of mobile teachers and the schools they exited and entered within the county to determine if potential equity gaps exist. This report concludes with implications for policy and practice including a list of suggestions for educational leaders to reduce mobility and eliminate consequential disparities for students.

When applied to a real-world safety critical system like the power grid, general machine learning methods suffer from expensive training, non-physical solutions, and limited interpretability. To address these challenges for power grids, many recent works have explored the inclusion of grid physics (i.e., domain expertise) into their method design, primarily through including system constraints and technical limits, reducing search space and defining meaningful features in latent space. Yet, there is no general methodology to evaluate the practicality of these approaches in power grid tasks, and limitations exist regarding scalability, generalization, interpretability, etc. This work formalizes a new concept of physical interpretability which assesses how a ML model makes predictions in a physically meaningful way and introduces an evaluation methodology that identifies a set of attributes that a practical method should satisfy. Inspired by the evaluation attributes, the paper further develops a novel contingency analysis warm starter for MadIoT cyberattack, based on a conditional Gaussian random field. This method serves as an instance of an ML model that can incorporate diverse domain knowledge and improve on these identified attributes. Experiments validate that the warm starter significantly boosts the efficiency of contingency analysis for MadIoT attack even with shallow NN architectures.

This work presents the design of AC line outage distribution factor created from the circuit-theoretic power flow models. Experiment results are shown to demonstrate its efficacy in quantifying the impact of line outages on the grid, and its resulting potential for fast contingency screening.

"Where Do We Go Next?" explores three interconnected areas of young people's lives that have been particularly salient over the past year and are fundamental to supporting their learning and growth in the future. Those three areas are young people's sense of wellbeing, including their mental health and relationships; their opportunities to learn about race and racism in school and how that affects the ways they understand and engage with the world around them; and their plans for after high school and sense of readiness for pursuing those plans.

Nationally, credit recovery has been used as a strategy to encourage and enable students to re-take previously failed courses needed to graduate. The School District of Philadelphia (SDP) offers both in-person and online options for recovering failed or missing credits required for graduation. This study provides a snapshot of the district's school-year credit recovery utilization--including eligibility, enrollment, and completion--using newly available data for high school students who entered the 2018-19 school year with a record of one or more failed courses. The authors first examine credit recovery eligibility in traditional high schools at the end of the 2017-18 school year. Then, the authors examine school-year credit recovery enrollment the following school year in 2018-19, among those eligible. They then examine course completion and pass rates among students who enrolled in credit recovery in 2018-19. The authors also follow students through 2019-20 to examine subsequent course-taking among those who successfully recovered credits the previous year. District stakeholders can use these findings to inform district and school credit recovery policies. In addition, the descriptive data presented here can be used to generate more specific research questions about which credit recovery options work best and for whom, and what supports are needed to ensure equity in course completion and pass rates for all students and all schools across the district.

In Philadelphia, if a student chooses not to attend their neighborhood school, other options include schools with specialized programming in the arts, sciences, or business fields, schools with career and technical education options, and competitive magnet schools. But choosing an out-of-catchment school rather than a neighborhood school may require a longer or more complicated commute, particularly for students relying on public transit to get to school. Research has shown that commute time and complexity can influence attendance, academic achievement, engagement in school, and health factors associated with sleep. This report uses School District of Philadelphia high school student enrollment and residence data to estimate student commutes to all 52 traditional district high schools via public transit. Transit data from the 2017-18 school year was estimated how long it would take for high schoolers to get to school using public transit based on where they live and under optimal conditions (i.e., no delays and use of all available routes). Also analyzed was how estimated commutes vary by type of school admission (i.e., Neighborhood, Citywide, or Special Admission) and student residential neighborhood (defined as the City Council District in which they live). The findings of this study, can help guide families and students to consider commute time and complexity when selecting schools. The authors also anticipate that the analysis of variation in commutes may be useful for policy makers at the School District of Philadelphia (SDP) and its School Board, City Council, and Southeastern Pennsylvania Transportation Authority (SEPTA) (Philadelphia's transit authority) as they make ongoing decisions about system-wide school offerings, start times and scheduling options, and transit networks. Four appendices are included in this report. [This is Brief 2 of the Back to School series. For Brief 1, "Strategies for Reducing Student Absenteeism in Philadelphia," see ED608079.]

In 2018, the School District of Philadelphia (SDP) developed an indicator for being "on track" at the end of a high school student's freshman year. As part of the district's overall strategy for improving graduation rates, school administrators currently use the Ninth Grade On-Track indicator as an early marker of progress towards graduation and to identify students in need of intervention. Using four cohorts of SDP data prior to its development and implementation, Philadelphia Education Research Consortium (PERC) found that one-third of first-time freshman in 2013-2017 would have been flagged by On-Track indicator as "off-track" after their first year of high school. Although the On-Track indicator was not yet in place, the reports serve as a benchmark against which progress can be measured. Building upon this prior work, this report examines two of those same cohorts of off-track freshman in the expected graduating classes of 2017 and 2018, following them over time to understand which students were able to graduate and when they got back on track. Similar to the prior work, these findings describe student experiences that pre-date the establishment of SDP's On-Track indicator. Thus, this report serves as baseline for the district to assess progress toward efforts to improve graduation rates through schools' use of the On-Track indicator to identify and connect students to supports. The goal of examining these patterns is to understand which off-track students and which schools might need the most support. This report offers a first-time look at graduation rates for off-track students in SDP. The findings will be informative to school and district administrators working to support high school students who fall off-track in ninth grade. These findings raise questions about whether some students and schools may benefit from more resources and/or different systems or approaches than others. The findings also point to the need for more research to examine why some students in some schools recover at higher rates than others and build evidence for effective interventions for getting students back on track. Four appendices are included in this report. [This is Brief 3 of the Back to School series. For Brief 2, "How Long Will It Take Me to Get to School? Transit Times to School District of Philadelphia High Schools," see ED608080.]

The utility of domain-specific knowledge for modeling, simulation, and optimization has been demonstrated for various research problem domains, including power systems. The concept of Equivalent Circuit Programming was previously developed and facilitated for robust, efficient, and scalable solution of network simulation and optimization problems. This paper extends the theoretical foundation of Equivalent Circuit Programming to enable the fusion of optimization theory and algorithms with the numerical methods that utilize the domain-specific knowledge of power flow models. The generality, scalability, and numerical robustness of the resulting framework are demonstrated on realistic AC power flow (ACPF) models of up to 70k buses with proper enforcement of industry-required operational and security constraints., Comment: Under review: submitted for consideration for IEEE Transactions on Power Systems

Electricity systems are experiencing increased effects of randomness and variability due to emerging stochastic assets. The increased effects introduce new uncertainties into power systems that can impact system operability and reliability. Existing steady-state methods for assessing system-level operability and reliability are primarily deterministic, therefore, ill-suited to capture randomness and variability. This work introduces a probabilistic steady-state analysis inspired by statistical worst-case circuit analysis to evaluate the risk of operational violations due to stochastic resources. Compared to parallelized Monte Carlo analyses (MCS), we have seen up to 24x improvement in runtime speed using our approach without significant loss of probabilistic accuracy for a Texas7k low-wind day test system., Comment: Submitted for publication to IEEE Transactions in Power Systems and pending review

In recent years, the ML community has seen surges of interest in both adversarially robust learning and implicit layers, but connections between these two areas have seldom been explored. In this work, we combine innovations from these areas to tackle the problem of N-k security-constrained optimal power flow (SCOPF). N-k SCOPF is a core problem for the operation of electrical grids, and aims to schedule power generation in a manner that is robust to potentially k simultaneous equipment outages. Inspired by methods in adversarially robust training, we frame N-k SCOPF as a minimax optimization problem - viewing power generation settings as adjustable parameters and equipment outages as (adversarial) attacks - and solve this problem via gradient-based techniques. The loss function of this minimax problem involves resolving implicit equations representing grid physics and operational decisions, which we differentiate through via the implicit function theorem. We demonstrate the efficacy of our framework in solving N-3 SCOPF, which has traditionally been considered as prohibitively expensive to solve given that the problem size depends combinatorially on the number of potential outages., Comment: Accepted at Neural Information Processing Systems (NeurIPS) 2021

With the increase of distributed energy resources in the distribution grid, planning to ensure sufficient infrastructure and resources becomes critical. Planning at the distribution level is limited by the complexities of optimizing unbalanced systems. In this paper we develop a three-phase infeasibility analysis that identifies weak locations in a distribution network. This optimization is formulated by adding slack current sources at nodes in the system and minimizing their norm subject to distribution power flow constraints. Through this analysis we solve instances of power flow that would otherwise be infeasible and diverge. Under conditions when power flow is feasible, our approach is equivalent to standard three-phase power flow; however, for cases where power flow fails, the nonzero slack injection currents compensate for missing power to make the grid feasible. Since an uncountable number of injected currents can provide feasibility, we further explore the optimization formulation that best fits the solution objective through use of both a least squares and an L1 norm objective. Our L1 norm formulation localizes power deficient locations through its inherent sparsity. We show the efficacy of this approach on realistic unbalanced testcases up to 8500 nodes and for a scenario with a high penetration of electric vehicles.

Alternating-Current Optimal Power Flow (AC-OPF) is an optimization problem critical for planning and operating the power grid. The problem is traditionally formulated using only continuous variables. Typically, control devices with discrete-valued settings, which provide valuable flexibility to the network and improve resilience, are omitted from AC-OPF formulations due to the difficulty of integrality constraints. We propose a two-stage homotopy algorithm to solve the AC-OPF problem with discrete-valued control settings. This method does not rely on prior knowledge of control settings or other initial conditions. The first stage relaxes the discrete settings to continuous variables and solves the optimization using a robust homotopy technique. Once the solution has been obtained using relaxed models, second homotopy problem gradually transforms the relaxed settings to their nearest feasible discrete values. We test the proposed algorithm on several large networks with switched shunts and adjustable transformers and show it can outperform a similar state-of-the-art solver., Comment: Under review: submitted for consideration for 22nd Power Systems Computation Conference

An accurate and up-to-date topology is critical for situational awareness of a power grid; however, wrong switch statuses due to physical damage, communication error, or cyber-attack, can often result in topology errors. To maintain situation awareness under the possible topology errors and bad data, this paper develops ckt-GSE, a circuit-theoretic generalized state estimation method using node-breaker (NB) model. Ckt- GSE is a convex and scalable model that jointly estimates AC state variables and network topology, with robustness against different data errors. The method first constructs an equivalent circuit representation of the AC power grid by developing and aggregating linear circuit models of SCADA meters, phasor measurement units(PMUs), and switching devices. Then based on this circuit, ckt-GSE defines a constrained optimization problem using weighted least absolute value (WLAV) objective to form a robust estimator. The problem is a Linear Programming (LP) problem whose solution includes accurate AC states and a sparse vector of noise terms to identify topology errors and bad data.This paper is the first to explore a circuit-theoretic approach for an AC-network constrained GSE algorithm that is: 1) applicable to the real-world data setting, 2) convex without relaxation, scalable with our circuit-based solver; and 3) robust with the ability to identify and reject different data errors

Quantifying the impact of inverter-based distributed generation (DG) sources on power-flow distribution system cases is arduous. Existing distribution system tools predominately model distributed generation sources as either negative PQ loads or as a PV generator and then employed a PV-PQ switching algorithm to mimic Volt/VAR support. These models neglect the unique characteristics of inverter-based distributed generation sources, have scalability and convergence issues, and are ill-suited for increasing solar penetration scenarios. This work proposes an inverter-based DG model accounting for the inverter's topology, sensing position, and control strategies. The model extends recently introduced analytical positive sequence generator models for three-phase studies. The use of circuit-simulation based heuristics help achieve robust convergence. Simulation of the PG&E prototypical feeders using a prototype solver demonstrate the model's accuracy and efficacy., Comment: \copyright 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works