arXiv subjects

Sijia Geng

Publications and source records attributed to Sijia Geng.

16 recordsLinked to original sources

arXiv2026

Cluster-Based Distributed Small-Signal Stability Certificates for Grid-Forming Inverter Networks

Large-scale power networks are often organized by geography, ownership, or control authority, making stability certificates that require a fully assembled global model challenging. This paper develops a time-domain small-signal stability certification framework for grid-forming inverter networks with selectable clustering resolution. The objective is to certify stability at the same scale at which the network is organized and operated: each cluster verifies conditions using intra-cluster and limited boundary information, and these checks collectively yield a network-level stability certificate without requiring a global eigenvalue computation. After linearization about a phase-cohesive synchronized operating point, a small-angle approximation decomposes the model into a voltage subsystem and an angle-frequency subsystem, where the latter is certified by an energy argument using the symmetric weighted-Laplacian network structure. For the voltage subsystem, node-to-node gains are introduced and a cyclic small-gain argument yields a family of sufficient exponential stability certificates ranging from fully decentralized to cluster-based and centralized. For an arbitrary network partition, each cluster verifies intra-cluster directed-cycle conditions and inter-cluster path conditions. The singleton- and single-cluster limits recover the decentralized and centralized certificates, respectively. The resulting stability indices provide diagnostic information beyond a pass/fail verdict by localizing the limiting margin to individual nodes, internal feedback loops, and inter-cluster channels.

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arXiv2026

Decentralized Stability Certificates in IBR-Dominated Grids: The Role of the Network State

Small-signal instabilities, such as unforced sub-synchronous oscillations (SSOs), are increasingly observed in inverter-based resource (IBR) dominated grids. While decentralized stability certificates offer a scalable means to avoid instability onset, they are typically derived under restrictive network-state assumptions--such as small angle differences or negligible voltage drops--that cannot capture how departures from these conditions affect system stability. In this paper, we develop a network model and a decentralized analysis framework that explicitly characterizes how reactive power mismatches, line loading, and inverter control parameters jointly determine small-signal stability. We show that increased steady-state reactive power mismatches and line loading lead to more stringent conditions on admissible inverter droop gains. These results make decentralized stability certificates explicitly network-state dependent, showing how network stress shrinks the set of stabilizing local controller parameters.

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arXiv2026

Decentralized Stability-Constrained Optimal Power Flow for Inverter-Based Power Systems

Future inverter-dominated power systems feature higher variability and more stressed operating conditions, which motivates the consideration of stability in operational settings. Existing approaches to stability-constrained OPF often rely on eigenvalue calculation, global model information, or dynamic evaluation inside optimization formulation, which are computationally intensive and difficult to scale. This paper proposes the first decentralized stability-constrained OPF framework for inverter-based power systems. The key novelty lies in the incorporation of a class of algebraic decentralized small-signal stability criteria that admits tractable representations in steady-state variables and is therefore suitable for optimization. The decentralized stability condition is based on local voltage differences and enables clear theoretical and practical economic interpretation of the stability contribution from each inverter. We define a Nodal Stability Shadow Price (NSSP) for each inverter, and characterize the role of these stability constraints through their associated shadow prices, enabling a nodal interpretation of their economic impacts. It is proved that under active-power-only objectives in lossless networks, binding stability constraints may occur but will admit zero shadow prices if all other operational constraints are inactive. Most importantly, we reveal the importance of considering the opportunity cost of reactive power for inverter-based resources (IBRs) that have limited capacity. When reactive power costs are considered, stability constraints can carry strictly positive shadow prices and admit meaningful economic impacts.

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arXiv2026

Data-Driven Koopman Predictive Control for Frequency Regulation of Power Systems using Black-Box IBRs

Model uncertainty of inverter-based resources (IBRs) presents significant challenges for power system control and stability. This work studies secondary frequency regulation in inverter-based power systems using a Data-driven Koopman Predictive Control (DKPC) framework. The method employs Koopman theory to lift the nonlinear system dynamics into a higher-dimensional space where they can be approximated as linear. Based on Willems' fundamental lemma, a behavioral model is constructed directly from lifted input-output data. A receding-horizon predictive control formulation is then provided that operates entirely using observed data, without requiring a parametric model, while satisfying explicit constraints on the control input and system output. The proposed approach is particularly suited for IBRs with complex or uncertain dynamics. Numerical results demonstrate its effectiveness for frequency control as benchmarked against the Data-enabled Predictive Control (DeePC). The trade-off between tracking performance and control effort is illustrated through tuning of the weighting parameters.

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arXiv2026

Evaluating Power Flow Manifold from Local Data around a Single Operating Point via Geodesics

The widespread adoption of renewable energy poses a challenge in maintaining a feasible operating point in highly variable scenarios. This paper demonstrates that, within a feasible region of a power system that meets practical stability requirements, the power flow equations define a smooth bijection between nodal voltage phasors (angle and magnitude) and nodal active/reactive power injections. Based on this theoretical foundation, this paper proposes a data-based power flow evaluation method that can imply the associated power flow manifold from a limited number of data points around a single operating point. Using techniques from differential geometry and analytic functions, we represent geodesic curves in the associated power flow manifold as analytic functions at the initial point. Then, a special algebraic structure of the power flow problem is revealed and applied to reduce the computation of all higher-order partial derivatives to that of the first-order ones. Integrating these techniques yields the proposed data-based evaluation method, suggesting that a small number of local measurements around a single operating point is sufficient to imply the entire associated power flow manifold. Numerical cases with arbitrary directional variations are tested, certifying the efficacy of the proposed method.

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arXiv2026

Grid-Forming Control with Assignable Voltage Regulation Guarantees and Safety-Critical Current Limiting

This paper develops a nonlinear grid-forming (GFM) controller with provable voltage-formation guarantees, with over-current limiting enforced via a control-barrier-function (CBF)-based safety filter. The nominal controller follows a droop-based inner-outer architecture, in which voltage references and frequency are generated by droop laws, an outer-loop voltage controller produces current references using backstepping (BS), and an inner-loop current controller synthesizes the terminal voltage. The grid voltage is treated as an unknown bounded disturbance, without requiring knowledge of its bound, and the controller design does not rely on any network parameters beyond the point of common coupling (PCC). To robustify voltage formation against the grid voltage, a deadzone-adapted disturbance suppression (DADS) framework is incorporated, yielding practical voltage regulation characterized by asymptotic convergence of the PCC voltage errors to an assignably small and known residual set. Furthermore, the closed-loop system is proven to be globally well posed, with all physical and adaptive states bounded and voltage error transients (due to initial conditions) decaying exponentially at an assignable rate. On top of the nominal controller, hard over-current protection is achieved through a minimally invasive CBF-based safety filter that enforces strict current limits via a single-constraint quadratic program. The safety filter is compatible with any locally Lipschitz nominal controller. Rigorous analysis establishes forward invariance of the safe-current set and boundedness of all states under current limiting. Numerical results demonstrate improved transient performance and faster recovery during current-limiting events when the proposed DADS-BS controller is used as the nominal control law, compared with conventional PI-based GFM control.

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arXiv2025

Assessment of Power System Stability Considering Multiple Time-Scale Dynamics: Insights into Hopf Bifurcations in Presence of GFL and GFM IBRs

Real power systems exhibit dynamics that evolve across a wide range of time scales, from very fast to very slow phenomena. Historically, incorporating these wide-ranging dynamics into a single model has been impractical. As a result, power engineers rely on time-scale decomposition to simplify models. When fast phenomena are evaluated, slow dynamics are neglected (assumed stable), and vice versa. This paper challenges this paradigm by showing the importance of assessing power system stability while considering multiple time scales simultaneously. Using the concept of Hopf bifurcations, it exemplifies instability issues that would be missed if multi-time-scale dynamics are not considered. Although this work employs both grid-following and grid-forming inverter-based resource models, it is not a direct comparison. Instead, it presents a case study demonstrating how one technology can complement the other from a multi time-scale dynamics perspective.

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arXiv2025

Voltage Stability of Inverter-Based Systems: Impact of Parameters and Irrelevance of Line Dynamics

This paper investigates voltage stability in inverter-based power systems concerning fold and saddle-node bifurcations. An analytical expression is derived for the sensitivity of the stability margin using the normal vector to the bifurcation hypersurface. Such information enables efficient identification of effective control parameters in mitigating voltage instability. Comprehensive analysis reveals that reactive loading setpoint and current controller's feedforward gain are the most influential parameters for enhancing voltage stability in a grid-following (GFL) inverter system, while the voltage controller's feedforward gain plays a dominant role in a grid-forming (GFM) inverter. Notably, both theoretical and numerical results demonstrate that transmission line dynamics have no impact on fold/saddle-node bifurcations in these systems. Results in this paper provide insights for efficient analysis and control in future inverter-dominated power systems through reductions in parameter space and model complexity.

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arXiv2025

Integer-Clustering Optimization of Hydrogen and Battery EV Fleets Considering DERs

Electrified transportation leads to a tighter integration between transportation and energy distribution systems. In this work, we develop scalable optimization models to co-design hydrogen and battery electric vehicle (EV) fleets, distributed energy resources, and fast-charging and hydrogen-fueling infrastructure to efficiently meet transportation demands. A novel integer-clustering formulation is used for optimizing fleet-level EV operation while maintaining accurate individual vehicle dispatch, which significantly improves the computation efficiency with guaranteed performance. We apply the optimization model to Boston's public transit bus network using real geospatial data and cost parameters. Realistic insights are provided into the future evolution of coupled electricity-transportation-hydrogen systems, including the effects of electricity price structure, hydrogen fuel cost, carbon emission constraint, temperature effects on EV range, and distribution system upgrade cost.

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arXiv2025

Large-Signal Stability of Power Systems with Mixtures of GFL, GFM and GSP Inverters

Grid-following (GFL) inverters have very different large-signal stability characteristics to synchronous generators, and convenient concepts such as the equal-area criterion and global energy function do not apply in the same way. Existing studies mainly focus on the synchronization stability of an individual GFL inverter, while interactions between multiple inverters are less often addressed. This paper elucidates the interaction mechanisms between heterogeneous inverters, covering GFL, grid-forming (GFM), and grid-supporting (GSP) types, to determine the stability boundaries of systems with mixed inverter compositions. The generalized large-signal model for two-inverter systems is derived for various inverter combinations. This paper establishes that systems containing GFL inverters do not admit a global energy function, fundamentally limiting the applicability of traditional direct methods. To overcome this barrier, a manifold method is employed to accurately determine the region of attraction (ROA). To address the computational complexity of the manifold method, reduced-order models of inverter are used based on multiscale analysis. The large-signal stability margin is assessed by the shortest distance from a stable equilibrium point (SEP) to the boundary of the ROA, which is called the stability radius (SR). Using the proposed framework, the analysis reults of two-inverter system show that both GFM and GSP inverters significantly enhance the large-signal stability of a two-inverter system where the other inverter is GFL, with GFM providing slightly superior performance. This improvement is attributed to the voltage support effects and is maximized when the GFM or GSP inverter is located at the midpoint of the transmission line, where the voltage is lowest. All findings in this paper are validated through both EMT simulations and power hardware-in-the-loop (PHIL) experiments.

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arXiv2024

Unified Control Scheme for Optimal Allocation of GFM and GFL Inverters in Power Networks

With the rapid adoption of emerging inverter-based resources, it is crucial to understand their dynamic interactions across the network and ensure stability. This paper proposes a systematic and efficient method to determine the optimal allocation of grid-forming and grid-following inverters in power networks. The approach leverages a novel unified grid-forming/following inverter control and formulates an optimization problem to ensure stability and maximal energy dissipation during transient periods. An iterative algorithm is developed to solve the optimization problem. The resulting optimal droop gains for the unified inverters provide insights into the needs for grid-forming and grid-following resources in the network. A three-bus system is used to demonstrate the optimality and dynamic performance of the proposed method.

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arXiv2024

Effects of Line Dynamics on Stability Margin to Hopf Bifurcation in Grid-Forming Inverters

This paper studies the parameter sensitivity of grid-forming inverters to Hopf bifurcations to address oscillatory instability. An analytical expression for the sensitivity of the stability margin is derived based on the normal vector to the bifurcation hypersurface. We identify the most effective control parameters through comprehensive analysis. In particular, the impacts of line dynamics on the stability margin to Hopf bifurcation are investigated. The results indicate that the feedforward gain in the voltage control loop is the most effective parameter for enhancing the stability margin. Furthermore, it is observed that line dynamics introduce a uniform reduction in the stability margin across all parameters. However, the reduction is generally small for most parameters except for the voltage-reactive power droop gain, which shows a more pronounced effect.

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arXiv2023

An Integer Clustering Approach for Modeling Large-Scale EV Fleets with Guaranteed Performance

Large-scale integration of electric vehicles (EVs) leads to a tighter integration between transportation and electric energy systems. In this paper, we develop a novel integer-clustering approach to model a large number of EVs that manages vehicle charging and energy at the fleet level yet maintain individual trip dispatch. The model is then used to develop a spatially and temporally-resolved decision-making tool for optimally planning and/or operating EV fleets and charging infrastructure. The tool comprises a two-stage framework where a tractable disaggregation step follows the integer-clustering problem to recover an individually feasible solution. Mathematical relationships between the integer clustering, disaggregation, and individual formulations are analyzed. We establish theoretical lower and upper bounds on the true individual formulation which underpins a guaranteed performance of the proposed method. The optimality accuracy and computational efficiency of the integer-clustering formulation are also numerically validated on a real-world case study of Boston's public transit network under extensive test instances. Substantial speedups with minimal loss in solution quality are demonstrated.

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arXiv2023

Approximating Voltage Stability Boundary Under High Variability of Renewables Using Differential Geometry

This paper proposes a novel method rooted in differential geometry to approximate the voltage stability boundary of power systems under high variability of renewable generation. We extract intrinsic geometric information of the power flow solution manifold at a given operating point. Specifically, coefficients of the Levi-Civita connection are constructed to approximate the geodesics of the manifold starting at an operating point along any interested directions that represent possible fluctuations in generation and load. Then, based on the geodesic approximation, we further predict the voltage collapse point by solving a few univariate quadratic equations. Conventional methods mostly rely on either expensive numerical continuation at specified directions or numerical optimization. Instead, the proposed approach constructs the Christoffel symbols of the second kind from the Riemannian metric tensors to characterize the complete local geometry which is then extended to the proximity of the stability boundary with efficient computations. As a result, this approach is suitable to handle high-dimensional variability in operating points due to the large-scale integration of renewable resources. Using various case studies, we demonstrate the advantages of the proposed method and provide additional insights and discussions on voltage stability in renewable-rich power systems.

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arXiv2020

An Empirical Study on Benchmarks of Artificial Software Vulnerabilities

Recently, various techniques (e.g., fuzzing) have been developed for vulnerability detection. To evaluate those techniques, the community has been developing benchmarks of artificial vulnerabilities because of a shortage of ground-truth. However, people have concerns that such vulnerabilities cannot represent reality and may lead to unreliable and misleading results. Unfortunately, there lacks research on handling such concerns. In this work, to understand how close these benchmarks mirror reality, we perform an empirical study on three artificial vulnerability benchmarks - LAVA-M, Rode0day and CGC (2669 bugs) and various real-world memory-corruption vulnerabilities (80 CVEs). Furthermore, we propose a model to depict the properties of memory-corruption vulnerabilities. Following this model, we conduct intensive experiments and data analyses. Our analytic results reveal that while artificial benchmarks attempt to approach the real world, they still significantly differ from reality. Based on the findings, we propose a set of strategies to improve the quality of artificial benchmarks.

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arXiv2019

Distributed Barrier Certificates for Safe Operation of Inverter-Based Microgrids

Inverter-interfaced microgrids differ from the traditional power systems due to their lack of inertia. Vanishing timescale separation between voltage and frequency dynamics makes it critical that faster-timescale stabilizing control laws also guarantee by-construction the satisfaction of voltage limits during transients. In this article, we apply a barrier functions method to compute distributed active and reactive power setpoint control laws that certify satisfaction of voltage limits during transients. Using sum-of-squares optimization tools, we propose an algorithmic construction of these control laws. Numerical simulations are provided to illustrate the proposed method.

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