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Stability Analysis in IBR-Dominated Grids: Model-Based and Data-Driven Methodologies

Federico Cecati, Yang Wu, Florian Dörfler, Marco Liserre, Xiongfei Wang, Elisabetta Tedeschi

arXiv:2610.22227v1eess.SYcs.SY

TL;DR

IBR-grid stability involves interdependent static, small-signal, and large-signal phenomena, while IP protection limits access to detailed models. The paper reviews model-based and data-driven analysis tools and finds that the instability aspects are interdependent and warrant concurrent study. It also identifies remaining limitations in large-signal analysis and decentralized data-driven control.

  • Problem

    Static, small-signal, and large-signal stability aspects interact, while IP protection makes detailed converter and grid models unattainable and complicates analysis.

    Source: §I · p. 2

  • Method

    The paper discusses model-based and data-driven stability-analysis tools and assesses their capabilities across different instability scenarios.

    Source: §IV · p. 14

  • Results

    The paper demonstrates strict interdependence among static, small-signal, and large-signal instability, stressing the need to study them concurrently.

    Source: §IV · p. 14

  • Takeaways & Limitations

    Large-signal analysis in multi-IBR grids, including physical constraints such as current and energy-source limits, requires further investigation.

    Source: §IV · p. 14

    Large-signal analytical IBR models are often oversimplified relative to small-signal models, mainly because transient-stability methods scale poorly.

    Source: §IV · p. 14

Abstract

from arXiv · show

Stability issues in converter-dominated grids have a multifold nature, where static, small-signal and large-signal phenomena can influence each other. Capturing the interplay among these different stability aspects requires a rethinking of conventional modeling and analysis tools for power systems. As a further complication, Intellectual Property protection among manufacturers and system operators makes detailed converters and grid models unattainable. This motivates the use of data-driven approaches for stability analysis and control, nevertheless achieving an insightful representation of static, small-signal and large-signal phenomena from data still leaves many open questions. This paper discusses model-based and data-driven methodologies for stability analysis of converter-dominated grids. The instability mechanisms of static, small-signal and large-signal phenomena are conceptually explained, and the capability of different modeling and analysis tools to investigate them is examined. The effectiveness of data-driven methodologies to analyze instability phenomena in their multifold nature is debated, and the challenges on data completeness, model generalization under untrained conditions, physical interpretability, and uncertainty awareness are discussed.

I. INTRODUCTION

IBR-grid instability spans static, small-signal, and large-signal phenomena whose mechanisms and control trade-offs are interdependent. The paper reviews model-based and data-driven tools for analyzing that interplay, while highlighting unresolved data-driven challenges.

I. INTRODUCTION

  • IP protection limits access to detailed converter and grid models, while data-driven analysis of stability interplay remains difficult and leaves open questions.The paper reviews the theoretical foundations, developments, and research gaps in both methodological families.Source: §I · p. 2
  • Slow synchronization can improve small-signal stability while deteriorating large-signal stability, illustrating why IBR stability aspects must be studied together.The paper also notes that reactive-power regulation can alter both the grid equilibrium point and oscillation damping.Source: §I · p. 2
  • The paper reviews static, small-signal, and large-signal stability mechanisms and explains their interdependency in IBR-based grids.It also examines factors including control dynamics, physical constraints, and interactions with AC grids and other IBRs.Source: §I · p. 2
  • Nonlinear model-based tools for combined static and dynamic stability analysis are examined for their ability to capture interactions among stability aspects.The paper presents tools and analyzes their capabilities through simulations.Source: §I · p. 2
  • The paper discusses data-driven approaches and challenges involving data requirements, generalization under untrained conditions, physical interpretability, and uncertainty awareness.It also presents data-driven tools for capturing interactions between static operating points and dynamic stability, and discusses control applications.Source: §I · p. 2

II. MODEL-BASED METHODOLOGIES FOR STABILITY ANALYSIS OF IBR-DOMINATED GRIDS

IBR stability analysis distinguishes equilibrium existence, local behavior around an existing equilibrium, and nonlinear convergence within a limited region of attraction. These aspects can interact, so analysis tools should examine them together.

II. MODEL-BASED METHODOLOGIES FOR STABILITY ANALYSIS OF IBR-DOMINATED GRIDS

  • Static instability is the absence of a steady-state equilibrium for the IBR at a given operating point.It is linked to the inability to solve the IBR state-space equation under static conditions.Source: §II · p. 3
  • Small-signal analysis assesses local stability and dynamic properties around an existing equilibrium, which can vary across equilibrium points.It can investigate oscillatory phenomena in different frequency ranges.Source: §II · p. 3
  • Large-signal dynamic analysis examines nonlinear transients in which a state may leave the limited region of attraction of a stable equilibrium.Such events are often associated with physical constraints or sluggish control response.Source: §II · p. 3
  • IBR dynamics, physical constraints, and AC-grid interactions can affect multiple stability aspects, and tuning that improves one aspect may worsen another.The paper therefore calls for analysis of interactions across static, small-signal, and large-signal behavior.Source: §II · p. 3

A. Nonlinear Modeling of Grid-Forming IBR

The paper uses a nonlinear grid-forming IBR model to investigate interactions between small- and large-signal behavior. Its component blocks represent IBR dynamics and possible physical constraints.

A. Nonlinear Modeling of Grid-Forming IBR

  • The model represents IBR dynamics with differential and/or algebraic blocks, marking signals that may be affected by physical constraints such as current limiting.It targets stability phenomena below 1 kHz; electromagnetic transients above 1 kHz, such as semiconductor switching, are neglected.Source: A. Nonlinear Modeling of Grid-Forming… · p. 3
  • The synchronization block uses power synchronization for angle δ, while the active-power low-pass filter emulates inertia in a Virtual Synchronous Machine implementation.The active-power reference, filtered active power, filter time constant, and frequency droop gain define the described block.Source: A. Nonlinear Modeling of Grid-Forming… · p. 3
  • The model includes voltage and current loops, a reactive-power droop voltage set-point, coordinate transformations, inverter filtering, energy-source dynamics, and an AC-grid model.The AC grid is represented in its simplified form by a Thevenin equivalent with RL impedance.Source: A. Nonlinear Modeling of Grid-Forming… · pp. 3–4

B. Static large-signal stability analysis

Static large-signal analysis uses P-δ curves or numerical solutions of detailed IBR models to assess equilibrium existence under faults. Voltage sag and current limitation reshape power-transfer capability, while the simpler graphical method has restrictive assumptions and limited small-signal insight.

B. Static large-signal stability analysis

  • P-δ curve intersections with the active-power set-point define IBR equilibria, while voltage sags and current limitation reshape the curve and reduce maximum power transfer.The reduction is greater in Current Limitation Mode than in Normal Operating Mode.Source: B. Static large-signal stability… · p. 4
  • Conventional P-δ graphics assume an inductive grid, a single-machine-infinite-bus system, constant Vg = 1 p.u., and decoupled P-δ and Q-V relationships.They also provide limited small-signal information and can be inaccurate when details and interactions are neglected.Source: B. Static large-signal stability… · pp. 4, 6
  • Detailed dq-frame models with numerical static-equation solutions can capture interplay between static and small-signal phenomena by linearizing around the computed equilibrium.Numerical convergence can depend on initializing sufficiently near the solution.Source: B. Static large-signal stability… · pp. 5–6
  • Fault-related reductions in steady-state voltage magnitude depend on sag depth, SCR, and reactive-power-loop gain nq, and further shrink power-transfer capability.Current-limitation activation thresholds also depend on SCR; when triggered, current limitation can cause static instability by reducing P until the static equation is unsolvable.Source: B. Static large-signal stability… · pp. 5–6
  • At SCR = 1.5, static instability occurs for E < 0.8, independently of current limitation mode.The equilibrium is absent, making the static algebraic equation unsolvable and the post-fault numerical solution non-convergent.Source: B. Static large-signal stability… · pp. 5–6
  • Current-limitation-induced static instability occurs at higher post-fault voltage levels than the IBR static-instability limits.The numerical method’s flat-start initialization must be sufficiently close to the solution to avoid non-convergence from numerical issues.Source: B. Static large-signal stability… · p. 6

C. Small-signal stability analysis

Small-signal stability analysis addresses oscillatory phenomena across frequency ranges by examining an IBR model linearized around its computed equilibrium. The paper describes time-domain, frequency-domain, and other tools for assessing stability and margins.

C. Small-signal stability analysis

  • Small-signal instability in IBR grids includes oscillatory phenomena across diverse frequency ranges and has been among the causes of recent blackouts.The analysis linearizes the IBR model around the equilibrium computed through static analysis, if that equilibrium exists.Source: C. Small-signal stability analysis · p. 6
  • Eigenvalue analysis is a time-domain approach, while the Nyquist criterion is a frequency-domain approach to assessing small-signal stability.The analysis uses the IBR model linearized around its computed equilibrium, if one exists.Source: C. Small-signal stability analysis · p. 6
  • Robust stability tools, passivity, and small-gain or small-phase theorems are also used to assess small-signal stability and its margins.Source: C. Small-signal stability analysis · p. 6

1) Oscillation Damping Capability Evaluation:

Eigenvalue analysis characterizes oscillation damping and illustrates how grid conditions and operating-point changes affect small-signal properties. Impedance-based analysis complements it by applying generalized Nyquist methods to MIMO IBR models.

1) Oscillation Damping Capability Evaluation:

  • SCR and grid-voltage changes shift eigenvalues and alter IBR damping capability, while SCR also changes the equilibrium point and thereby affects small-signal properties indirectly.A real eigenvalue approaches the origin near the static limit as the model Jacobian becomes nearly singular at a saddle-node bifurcation.Source: 1) Oscillation Damping Capability… · p. 6
  • Transient CLM-related instability can escape static and small-signal detection, and high post-fault damping does not capture oscillation amplitude that may drive the state outside its region of attraction.Source: 1) Oscillation Damping Capability… · p. 6
  • For the phase-jump analysis, eigenvalue analysis with respect to frequency droop gain mp detects a small-signal instability at mp = 250 · 10−6; static analysis is omitted because mp does not affect the equilibrium point.Source: 1) Oscillation Damping Capability… · p. 6, Figure 5 · p. 6

2) Impedance-based small-signal stability analysis:

3) Decentralized small-signal stability criteria:

The section surveys decentralized small-signal criteria and large-signal stability methods, emphasizing that model assumptions, physical constraints, and the interplay of dynamics limit what each method can establish.

3) Decentralized small-signal stability criteria:

  • Conventional passivity criteria face low-frequency non-passive regions and can be conservative; extended MIMO conditions and phase-plus-gain approaches are among proposed refinements.Low-frequency synchronization and power-control dynamics can produce non-passive regions.Source: 3) Decentralized small-signal… · p. 7

D. Dynamic large-signal stability analysis

1) Analytical methodologies:

  • The Equal Area Criterion applies to IBRs represented by a P-δ relationship but is limited to single-machine-infinite-bus systems, while Lyapunov analyses face nonsmooth-control and scalability challenges.Numerical Sum-Of-Squares methods have been applied to small-scale grids and IBRs; neural-network Lyapunov functions show promise for scalability and generalizability.Source: 1) Analytical methodologies · p. 7

2) Time-domain simulation:

  • Time-domain simulations cover complex large-signal phenomena but assess limited initial conditions and settings, are hard to interpret, and provide no rigorous stability guarantees.Search and machine-learning approaches seek broader margin assessment, while EMT simulation's computational burden challenges large-grid use; physics-informed accelerators are under investigation.Source: 2) Time-domain simulation · pp. 7–8
  • At SCR=10, a 0.8 p.u. sag causes overcurrent followed by windup-induced instability; SCR=1.5 yields LOS, while SCR=5 is stable.The SCR=5 case has an equilibrium point and sufficient damping; anti-windup strategies can mitigate the post-fault instability at SCR=10.Source: 2) Time-domain simulation · p. 8
  • During phase jumps, large current-response amplitude can trigger CLM and dynamic large-signal instability even when post-fault damping is high.Damping ratio describes oscillation decay, not amplitude; no general analytical criterion or directly targeted grid requirement is established for this phenomenon.Source: 2) Time-domain simulation · pp. 8–9

E. Extension to multi-IBR systems

Analyzing multi-IBR stability requires nonlinear grid models to capture interactions among small- and large-signal dynamics, while available analytical warranties have restricted scope.

E. Extension to multi-IBR systems

  • A nonlinear state-space model is needed to analyze the interplay of small- and large-signal stability in multi-IBR grids; generalized CCM provides a way to build such models.The original Component Connection Method interconnects linear IBR models for small-signal analysis only.Source: E. Extension to multi-IBR systems · p. 9
  • Multi-IBR static analysis uses generalized power flow to detect voltage violations and missing equilibria, while small-signal tools identify IBRs contributing to undamped oscillations.Large-signal decentralized stability warranties apply only under specific assumptions and do not scale to arbitrary grids with heterogeneous IBRs; simulation remains a computationally heavy option.Source: E. Extension to multi-IBR systems · p. 9

III. DATA-DRIVEN METHODOLOGIES FOR STABILITY ANALYSIS OF IBR-DOMINATED GRIDS

Data-driven methods address information barriers that impede model-based analysis, but representing the interplay of small- and large-signal dynamics remains challenging. The section reviews measurement-based and gray-box models, including their accuracy, interpretability, and operating-point constraints.

III. DATA-DRIVEN METHODOLOGIES FOR STABILITY ANALYSIS OF IBR-DOMINATED GRIDS

  • IP-protected data silos leave operators without IBR models and manufacturers with limited grid knowledge, motivating data-driven use of measurements and operational data.Analyzing small- and large-signal interplay remains more challenging with data-driven than with model-based methods.Source: §III · pp. 9–10

A. Measurement and gray-box modeling for IBRs

  • Encrypted EMT models can accurately simulate IBR-grid interactions but are time-consuming across operating points; encrypted diagonal-form state-space surrogates retain eigenvalue information but hide state-variable meaning.The surrogate models remain operating-point dependent and add complexity.Source: A. Measurement and gray-box modeling… · p. 10
  • Hammerstein-Wiener gray-box models separate nonlinear phase and voltage-magnitude transformations from a linear core, offering efficient large-scale stability emulation.They are presented as an alternative to black-box EMT simulation models.Source: A. Measurement and gray-box modeling… · p. 10
  • Measurement-based impedance models preserve vendor IP while capturing small-signal behavior, but require broad-frequency measurements at multiple operating points and two independent d- and q-axis perturbations.The dq-frame model includes cross-couplings between axes.Source: A. Measurement and gray-box modeling… · p. 10
  • PRBS and Gaussian Pulse multi-frequency injections can make impedance measurement faster and more reliable when operating-point changes would otherwise impair accuracy.The measured perturbations identify entries of the MIMO impedance matrix.Source: A. Measurement and gray-box modeling… · p. 10
  • Vector fitting embeds assumed control structure for interpretable impedance models, but structural mismatch can cause modeling error; neural-network residual correction adds complexity and may still lose accuracy.The cascade first fits an impedance model to measurements, then learns its residual errors.Source: A. Measurement and gray-box modeling… · pp. 10–11

B. Black-box impedance models of IBRs for small-signal analysis

Data-driven impedance models learn operating-condition-to-impedance mappings or use compact features to represent impedance profiles. Feature-driven models can predict unstable operating points from stable-point measurements, while training-data coverage, model design, and aggregation remain challenges.

OP-driven neural-network-based model

  • Training on stable operating points assumes an existing equilibrium, while surrogate models learn input-output mappings from collected data,.Pretraining on high-fidelity simulations followed by limited experimental fine-tuning can reduce measurement burden; transfer learning can reuse pretrained weights.Source: B. Black-box impedance models of IBRs… · p. 11
  • OP-driven neural networks map operating points and inspected frequency to impedance, with training data spanning operating conditions,.Inputs can include active power, reactive power, and PCC voltage; outputs are the real and imaginary impedance components across channels.Source: B. Black-box impedance models of IBRs… · p. 11
  • Neural-network design and sampling affect accuracy: hidden-layer size depends on transfer-function poles and zeros, and active and reactive power may need denser sampling.For some GFL-IBR control and grid configurations, PCC-voltage variation has a weaker impedance effect than active- and reactive-power variation.Source: B. Black-box impedance models of IBRs… · p. 11
  • Assigning physical meaning to network layers can simplify the architecture and improve modeling accuracy, but requires partial control-system knowledge,.That knowledge compromises the surrogate's strictly black-box character.Source: B. Black-box impedance models of IBRs… · p. 11

Feature-driven neural-network-based model

  • Feature-driven models compress impedance profiles into latent features and decode full profiles from feature combinations, avoiding direct dependence on operating-point-to-impedance mappings.This approach addresses limitations of OP-driven models for aggregated IBRs, where PCC impedance may not map one-to-one to operating points and computation grows with IBR count.Source: B. Black-box impedance models of IBRs… · pp. 11–12
  • Enlarging feature space permits prediction of unstable operating points from stable-point impedance measurements and stability-boundary assessment from single-frequency measurements.Searching the enlarged space yields probable impedance profiles, each evaluated with the generalized Nyquist criterion; compact features also support multi-IBR prediction and scalability without detailed controller knowledge.Source: B. Black-box impedance models of IBRs… · pp. 12–13

C. Black-box nonlinear model of IBRs for large-signal analyses

Data-driven large-signal analysis includes neural models that approximate nonlinear IBR dynamics and methods that infer stability from trajectories or measurements. These approaches face demanding data and generalization requirements, while data-driven control trades model interpretability against design flexibility and real-time constraints.

C. Black-box nonlinear model of IBRs for large-signal analyses

  • A feedforward neural network can approximate a GFM-IBR's full nonlinear dynamics from measurements and support region-of-attraction estimation through a neural-approximated Lyapunov function.The approach treats the inverter as a fixed-order unknown nonlinear system; another method couples networks trained separately on large- and small-signal dynamics [130].Source: C. Black-box nonlinear model of IBRs… · p. 13
  • Large-signal identification remains harder than small-signal modeling because it spans nonlinear operating ranges, current limitation, grid interactions, physical constraints, and multiple time scales.These demands increase dataset size and computational cost and make models less generalizable; capturing interplay among static, small-, and large-signal phenomena remains open.Source: C. Black-box nonlinear model of IBRs… · p. 13

D. Data-driven stability analysis and data-driven control

  • Neural networks can rapidly map operating points to stability labels, but conventional networks may not reliably warn of prediction failures,.The direct mapping supports large-scale operating-condition screening.Source: D. Data-driven stability analysis and… · p. 13
  • Control-theoretic data-driven alternatives include trajectory-based linear analysis, PINN Lyapunov functions, and Koopman representations of nonlinear dynamics,,,.These approaches are presented as data-based counterparts for small- and large-signal stability analysis.Source: D. Data-driven stability analysis and… · p. 13
  • Time-domain measurements can support early detection of large- and small-signal instability, while dynamic mode decomposition extracts modal frequency and damping for online monitoring –.These methods use locally measurable terminal voltages and currents and avoid time-consuming frequency scanning.Source: D. Data-driven stability analysis and… · p. 13
  • Direct model-free control can outperform indirect model-based design, but predictive-control methods face real-time computation limits and implementations remain restricted to linear world models, –.Model-based design offers interpretability, while uncertainty in data and model selection is difficult to propagate through identification and control; data-driven models also face untrained-condition generalization, multi-inverter, data-sharing, physical-consistency, and interpretability challenges.Source: D. Data-driven stability analysis and… · pp. 13–14

IV. CONCLUSIONS AND FUTURE TRENDS

The paper reviews coupled static, small-signal, and large-signal instability, assesses model-based and data-driven analysis tools, and identifies research gaps in analysis, data-driven modeling, and control.

IV. CONCLUSIONS AND FUTURE TRENDS

  • Static, small-signal, and large-signal instability are interdependent, motivating concurrent analysis with tools suited to different scenarios.The paper assesses model-based tools and discusses data-driven analysis and control motivated by unavailable detailed models under IP protection.Source: §IV · p. 14
  • Large-signal analysis in multi-IBR grids needs further work on scalable methods and physical constraints, including current and energy-source limitations.Analytical models for large-signal analysis are often more simplified than their small-signal counterparts.Source: §IV · p. 14
  • Decentralized small-signal stability criteria and multi-vendor interoperability remain under investigation, while large-signal IBR functional specifications have received insufficient research.Source: §IV · p. 14
  • Data-driven small-signal analysis is maturing, but large-signal models leave key aspects unresolved and prior-knowledge integration still raises generalizability concerns.Source: §IV · p. 14
  • Interactions among multiple IBRs using decentralized data-driven control strategies are poorly understood, with limited stability-guarantee results.Source: §IV · p. 14
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