arXiv subjects

Shimiao Li

Publications and source records attributed to Shimiao Li.

18 recordsLinked to original sources

arXiv2025

Homotopy-Guided Self-Supervised Learning of Parametric Solutions for AC Optimal Power Flow

Learning to optimize (L2O) parametric approximations of AC optimal power flow (AC-OPF) solutions offers the potential for fast, reusable decision-making in real-time power system operations. However, the inherent nonconvexity of AC-OPF results in challenging optimization landscapes, and standard learning approaches often fail to converge to feasible, high-quality solutions. This work introduces a \textit{homotopy-guided self-supervised L2O method} for parametric AC-OPF problems. The key idea is to construct a continuous deformation of the objective and constraints during training, beginning from a relaxed problem with a broad basin of attraction and gradually transforming it toward the original problem. The resulting learning process improves convergence stability and promotes feasibility without requiring labeled optimal solutions or external solvers. We evaluate the proposed method on standard IEEE AC-OPF benchmarks and show that homotopy-guided L2O significantly increases feasibility rates compared to non-homotopy baselines, while achieving objective values comparable to full OPF solvers. These findings demonstrate the promise of homotopy-based heuristics for scalable, constraint-aware L2O in power system optimization.

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arXiv2025

Frequency-Aware Sparse Optimization for Diagnosing Grid Instabilities and Collapses

This paper aims to proactively diagnose and manage frequency instability risks from a steady-state perspective, without the need for derivative-dependent transient modeling. Specifically, we jointly address two questions (Q1) Survivability: following a disturbance and the subsequent primary frequency response, can the system settle into a healthy steady state (feasible with an acceptable frequency deviation $\Delta f$)? (Q2) Dominant Vulnerability: if found unstable, what critical vulnerabilities create instability and/or full collapse? To address these questions, we first augment steady-state power flow states to include frequency-dependent governor relationships (i.e., governor power flow). Afterwards, we propose a frequency-aware sparse optimization that finds the minimal set of bus locations with measurable compensations (corrective actions) to enforce power balance and maintain frequency within predefined/acceptable bounds. We evaluate our method on standard transmission systems to empirically validate its ability to localize dominant sources of vulnerabilities. For a 1354-bus large system, our method detects compensations to only four buses under N-1 generation outage (3424.8 MW) while enforcing a maximum allowable steady-state frequency drop of 0.06 Hz (otherwise, frequency drops by nearly 0.08 Hz). We further validate the scalability of our method, requiring less than four minutes to obtain sparse solutions for the 1354-bus system.

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arXiv2025

Voltage-Regulated Sparse Optimization for Proactive Diagnosis of Voltage Collapses

This paper aims to proactively diagnose and manage the voltage collapse risks, i.e., the risk of bus voltages violating the safe operational bounds, which can be caused by extreme events and contingencies. We jointly answer two resilience-related research questions: (Q1) Survivability: Upon having an extreme event/contingency, will the system remain feasible with voltage staying within a (preferred) safe range? (Q2) Dominant Vulnerability: If voltage collapses, what are the dominant sources of system vulnerabilities responsible for the failure? This highlights some key locations worth paying attention to in the planning or decision-making process. To address these questions, we propose a voltage-regulated sparse optimization that finds a minimal set of bus locations along with quantified compensations (corrective actions) that can simultaneously enforce AC network balance and voltage bounds. Results on transmission systems of varying sizes (30-bus to 2383-bus) demonstrate that the proposed method effectively mitigates voltage collapses by compensating at only a few strategically identified nodes, while scaling efficiently to large systems, taking on average less than 4 min for 2000+ bus cases. This work can further serve as a backbone for more comprehensive and actionable decision-making, such as reactive power planning to fix voltage issues.

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arXiv2025

Sparsity-exploiting Gaussian Process for Robust Transient Learning of Power System Dynamics

Advances in leveraging Gaussian processes (GP) have enabled learning and inferring dynamic grid behavior from scarce PMU measurements. However, real measurements can be corrupted by various random and targeted threats, leading to inaccurate and meaningless results. This paper develops robust transient learning to overcome this challenge by exploiting the sparse corruption patterns in the data flow. Specifically, we integrate sparse optimization with method of moments (MoM) to make learning robust to a sparse distribution of data corruptions; then, we optimize sparse weights to identify corrupted meter locations. To improve inference speed on large-scale systems, we further adopt K-medoid clustering of locations to develop dimension reduction (DR) and aggregate representation (AR) heuristics. Experimental results demonstrate robustness against random large errors, targeted false data injections, and local PMU clock drifts. On a 1354-bus system, inference turns out to be 18x faster using DR and 400x faster when further combined with AR heuristics.

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arXiv2025

Cyber-Resilient System Identification for Power Grid through Bayesian Integration

Power grids increasingly need real-time situational awareness under the ever-evolving cyberthreat landscape. Advances in snapshot-based system identification approaches have enabled accurately estimating states and topology from a snapshot of measurement data, under random bad data and topology errors. However, modern interactive, targeted false data can stay undetectable to these methods, and significantly compromise estimation accuracy. This work advances system identification that combines snapshot-based method with time-series model via Bayesian Integration, to advance cyber resiliency against both random and targeted false data. Using a distance-based time-series model, this work can leverage historical data of different distributions induced by changes in grid topology and other settings. The normal system behavior captured from historical data is integrated into system identification through a Bayesian treatment, to make solutions robust to targeted false data. We experiment on mixed random anomalies (bad data, topology error) and targeted false data injection attack (FDIA) to demonstrate our method's 1) cyber resilience: achieving over 70% reduction in estimation error under FDIA; 2) anomalous data identification: being able to alarm and locate anomalous data; 3) almost linear scalability: achieving comparable speed with the snapshot-based baseline, both taking <1min per time tick on the large 2,383-bus system using a laptop CPU.

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arXiv2025

Multi-Period Sparse Optimization for Proactive Grid Blackout Diagnosis

Existing or planned power grids need to evaluate survivability under extreme events, like a number of peak load overloading conditions, which could possibly cause system collapses (i.e. blackouts). For realistic extreme events that are correlated or share similar patterns, it is reasonable to expect that the dominant vulnerability or failure sources behind them share the same locations but with different severity. Early warning diagnosis that proactively identifies the key vulnerabilities responsible for a number of system collapses of interest can significantly enhance resilience. This paper proposes a multi-period sparse optimization method, enabling the discovery of persistent failure sources across a sequence of collapsed systems with increasing system stress, such as rising demand or worsening contingencies. This work defines persistency and efficiently integrates persistency constraints to capture the ``hidden'' evolving vulnerabilities. Circuit-theory based power flow formulations and circuit-inspired optimization heuristics are used to facilitate the scalability of the method. Experiments on benchmark systems show that the method reliably tracks persistent vulnerability locations under increasing load stress, and solves with scalability to large systems (on average taking around 200 s per scenario on 2000+ bus systems).

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arXiv2025

Synergies between Federated Foundation Models and Smart Power Grids

The recent emergence of large language models (LLMs) such as GPT-3 has marked a significant paradigm shift in machine learning. Trained on massive corpora of data, these models demonstrate remarkable capabilities in language understanding, generation, summarization, and reasoning, transforming how intelligent systems process and interact with human language. Although LLMs may still seem like a recent breakthrough, the field is already witnessing the rise of a new and more general category: multi-modal, multi-task foundation models (M3T FMs). These models go beyond language and can process heterogeneous data types/modalities, such as time-series measurements, audio, imagery, tabular records, and unstructured logs, while supporting a broad range of downstream tasks spanning forecasting, classification, control, and retrieval. When combined with federated learning (FL), they give rise to M3T Federated Foundation Models (FedFMs): a highly recent and largely unexplored class of models that enable scalable, privacy-preserving model training/fine-tuning across distributed data sources. In this paper, we take one of the first steps toward introducing these models to the power systems research community by offering a bidirectional perspective: (i) M3T FedFMs for smart grids and (ii) smart grids for FedFMs. In the former, we explore how M3T FedFMs can enhance key grid functions, such as load/demand forecasting and fault detection, by learning from distributed, heterogeneous data available at the grid edge in a privacy-preserving manner. In the latter, we investigate how the constraints and structure of smart grids, spanning energy, communication, and regulatory dimensions, shape the design, training, and deployment of M3T FedFMs.

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arXiv2024

Exploiting sparse structures and synergy designs to advance situational awareness of electrical power grid

The growing threats of uncertainties, anomalies, and cyberattacks on power grids are driving a critical need to advance situational awareness which allows system operators to form a complete and accurate picture of the present and future state. Simulation and estimation are foundational tools in this process. However, existing tools lack the robustness and efficiency required to achieve the level of situational awareness needed for the ever-evolving threat landscape. Industry-standard (steady-state) simulators are not robust to blackouts, often leading to non-converging or non-actionable results. Estimation tools lack robustness to anomalous data, returning erroneous system states. Efficiency is the other major concern as nonlinearities and scalability issues make large systems slow to converge. This thesis addresses robustness and efficiency gaps through a dual-fold contribution. We first address the inherent limitations in the existing physics-based and data-driven worlds; and then transcend the boundaries of conventional algorithmic design in the direction of a new paradigm -- Physics-ML Synergy -- which integrates the strengths of the two worlds. Our approaches are built on circuit formulation which provides a unified framework that applies to both transmission and distribution. Sparse optimization acts as the key enabler to make these tools intrinsically robust and immune to random threats, pinpointing dominant sources of (random) blackouts and data errors. Further, we explore sparsity-exploiting optimizations to develop lightweight ML models whose prediction and detection capabilities are a complement to physics-based tools; and whose lightweight designs advance generalization and scalability. Finally, Physics-ML Synergy brings robustness and efficiency further against targeted cyberthreats, by interconnecting our physics-based tools with lightweight ML.

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arXiv2023

Power Grid Behavioral Patterns and Risks of Generalization in Applied Machine Learning

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.

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arXiv2023

Contingency Analyses with Warm Starter using Probabilistic Graphical Model

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.

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arXiv2022

Towards Practical Physics-Informed ML Design and Evaluation for Power Grid

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.

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arXiv2022

Circuit-theoretic Line Outage Distribution Factor

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.

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arXiv2021

Dynamic Graph-Based Anomaly Detection in the Electrical Grid

Given sensor readings over time from a power grid, how can we accurately detect when an anomaly occurs? A key part of achieving this goal is to use the network of power grid sensors to quickly detect, in real-time, when any unusual events, whether natural faults or malicious, occur on the power grid. Existing bad-data detectors in the industry lack the sophistication to robustly detect broad types of anomalies, especially those due to emerging cyber-attacks, since they operate on a single measurement snapshot of the grid at a time. New ML methods are more widely applicable, but generally do not consider the impact of topology change on sensor measurements and thus cannot accommodate regular topology adjustments in historical data. Hence, we propose DYNWATCH, a domain knowledge based and topology-aware algorithm for anomaly detection using sensors placed on a dynamic grid. Our approach is accurate, outperforming existing approaches by 20% or more (F-measure) in experiments; and fast, running in less than 1.7ms on average per time tick per sensor on a 60K+ branch case using a laptop computer, and scaling linearly in the size of the graph.

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arXiv2021

A Convex Method of Generalized State Estimation using Circuit-theoretic Node-breaker Model

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

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arXiv2021

Combined Transmission and Distribution State-Estimation for Future Electric Grids

Proliferation of grid resources on the distribution network along with the inability to forecast them accurately will render the existing methodology of grid operation and control untenable in the future. Instead, a more distributed yet coordinated approach for grid operation and control will emerge that models and analyzes the grid with a larger footprint and deeper hierarchy to unify control of disparate T&D grid resources under a common framework. Such approach will require AC state-estimation (ACSE) of joint T&D networks. Today, no practical method for realizing combined T&D ACSE exists. This paper addresses that gap from circuit-theoretic perspective through realizing a combined T&D ACSE solution methodology that is fast, convex and robust against bad-data. To address daunting challenges of problem size (million+ variables) and data-privacy, the approach is distributed both in memory and computing resources. To ensure timely convergence, the approach constructs a distributed circuit model for combined T&D networks and utilizes node-tearing techniques for efficient parallelism. To demonstrate the efficacy of the approach, combined T&D ACSE algorithm is run on large test networks that comprise of multiple T&D feeders. The results reflect the accuracy of the estimates in terms of root mean-square error and algorithm scalability in terms of wall-clock time.

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arXiv2021

A WLAV-based Robust Hybrid State Estimation using Circuit-theoretic Approach

For reliable and secure power grid operation, AC state-estimation (ACSE) must provide certain guarantees of convergence while being resilient against bad-data. This paper develops a circuit-theoretic weighted least absolute value (WLAV) based hybrid ACSE that satisfies these needs to overcome some of the limitations of existing ACSE methods. Hybrid refers to the inclusion of RTU and PMU measurement data, and the use of the LAV objective function enables automatic rejection of bad data while providing clear identification of suspicious measurements from the sparse residual vector. Taking advantage of linear construction of the measurement models in circuit-theoretic approach, the proposed hybrid SE is formulated as a LP problem with guaranteed convergence. To address efficiency, we further develop problem-specific heuristics for fast convergence. To validate the efficacy of the proposed approach, we run ACSE on large cases and compare the results against WLS-based algorithms. We further demonstrate the advantages of our solution methodology over standard commercial LP solvers through comparison of runtime and convergence performance.

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arXiv2020

A Circuit-Theoretic Approach to State Estimation

Traditional state estimation (SE) methods that are based on nonlinear minimization of the sum of localized measurement error functionals are known to suffer from non-convergence and large residual errors. In this paper we propose an equivalent circuit formulation (ECF)-based SE approach that inherently considers the complete network topology and associated physical constraints. We analyze the mathematical differences between the two approaches and show that our approach produces a linear state-estimator that is mathematically a quadratic programming (QP) problem with closed-form solution. Furthermore, this formulation imposes additional topology-based constraints that provably shrink the feasible region and promote convergence to a more physically meaningful solution. From a probabilistic viewpoint, we show that our method applies prior knowledge into the estimate, thus converging to a more physics-based estimate than the traditional observation-driven maximum likelihood estimator (MLE). Importantly, incorporation of the entire system topology and underlying physics, while being linear, makes ECF-based SE advantageous for large-scale systems.

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arXiv2019

A LASSO-Inspired Approach for Localizing Power System Infeasibility

A method is proposed to identify and localize the cause of network collapse with augmented power flow analysis for a grid model with insufficient resources. Owing to heavy network loading, insufficient generation, component failures and unavoidable disturbances, power grid models can sometimes fail to converge to a feasible solution for a steady-state power flow study. For applications such as system expansion planning, it is desirable to locate the system buses that are contributing to network infeasibilities to facilitate corrective actions. This paper proposes a novel LASSO-inspired regularization of the power flow matrix that enforces sparsity to localize and quantify infeasibilities in the network. One of the examples demonstrates how the proposed method is capable of localizing a source of blackout to a single dominant bus on an 80k+ bus eastern interconnection model.

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