Small-Signal Stability of a Unified Single-Unit Infinite-Bus Swing-Equation Model for Generators and Inverters

Jul 16, 2026

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A unified swing-equation model is developed for energy-conversion interfaces connected to an infinite bus, using generalized, equilibria-dependent inertia, damping, and synchronization constants. The formulation combines second-order active-power versus voltage-phasor-angle dynamics with network interconnection through power-flow equations. Unified parameterization links reduced-order models for synchronous generators, grid-following inverters with fast frequency response, and droop and virtual synchronous generator grid-forming inverters. Necessary and sufficient small-signal stability conditions for angle equilibria are derived.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages7

Reading Time18 min

Introduction

Small-signal stability background

Unified swing-equation model

Dynamics and assumptions

Generalized equilibria-dependent parameters

Stability analysis

Routh–Hurwitz conditions

Equilibrium stability insights

Validation and results

Phase-portrait plots

Eigenvalue plots

Small-signal Stability of a Unified Single-unit Infinite-bus Swing-equation Model for Generators and Inverters Debjyoti Chatterjee, Nathan Baeckeland, Bala Kameshwar Poolla, Gab-Su Seo, Brian Johnson, and Sairaj Dhople arXiv :2607 .00161v1 [ ee ss . SY] 30 Jun 2026 Abstract—We present a swing-equation model with generalized and equilibria-dependent inertia, damping, and synchronization constants for energy conversion interfaces with second-order active-power versus voltage-phasor-angle dynamics connected to an infinite bus. The model is unified in that prudent parameterization of the second-order angle-to-power transfer function aligns with reduced-order models for synchronous generators, grid-following inverters with fast frequency-response capability, and droop- and virtual synchronous generator-based gridforming inverters. Parametric necessary and sufficient conditions to examine small-signal stability of angle equilibria are derived from the unified swing-equation model. Index Terms—Grid-following inverter, grid-forming inverter, small-signal stability, swing equation, synchronous generator. I. INTRODUCTION SMALL-SIGNAL stability of angle equilibria single-machine infinite-bus (SMIB) model is a for the founda- tional tenet of power systems dynamics. While the setup is not remotely representative of complexity encountered in practice, the treatment sheds light on the interplay of power-flow equations and machine dynamics as they relate to an elementary notion of stability. Stability assessment has assumed increased importance with the changing resource mix on grids worldwide that now feature increasing numbers of grid-following (GFL) and grid-forming (GFM) inverterbased resources (IBRs) alongside synchronous generators (SGs) [1] . Networks with varying complexity—including elemental single-unit models—have been in focus; however, much of the recent work on swing-equation-type models and stability of the SMIB setup in the context of IBRs is unitspecific. The main contribution of this effort is to update the ubiquitous SMIB model to one that can acknowledge the dynamics of contemporary frequency-responsive power electronics alongside SGs while preserving a pathway to analytically examine small-signal stability. We study the quasi-steady-state dynamics of a controlledvoltage-source model for an energy-conversion interface connected to an infinite bus through an RL line. It is assumed This work was authored by the National Laboratory of the Rockies (NLR) for the U.S. Department of Energy (DOE), operated under Contract No. DE-AC36-08GO28308 . Funding provided in part by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy under the Solar Energy Technologies Office Award Number 38637 (UNIFI Consortium) and by the Laboratory Directed Research and Development (LDRD) Program at NLR. The views expressed do not necessarily represent those of the DOE or the U.S. Government. The U.S. Government retains, and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce this work for Government purposes. D. Chatterjee and B. Johnson are with the University of Texas at Austin; N. Baeckeland, B.K. Poolla, and G.-S. Seo are with the Power Systems Engineering Center of NLR; and S. Dhople is with the University of Minnesota. to inject a nominal amount of (commanded) active power modulated by a linear frequency-versus-power relationship. A second-order transfer function is presumed for the active power versus voltage-phasor angle, and the network interconnection is modeled via power-flow equations. A second-orderswing-equation model that captures the small-signal angle dynamics emerges upon linearization about an equilibrium point. Unlike the classical swing equation for SGs, this version is generalized and sports equilibria-dependent inertia, damping, and synchronization co

FAQs

What unified swing-equation model is proposed in the document?

The document proposes a swing-equation model with generalized and equilibria-dependent inertia, damping, and synchronization constants for interfaces connected to an infinite bus, capturing second-order active-power versus voltage-phasor-angle dynamics.

Which energy-conversion interfaces does the unified model encompass?

It unifies reduced-order models for synchronous generators, grid-following inverters with fast frequency response, and grid-forming inverters based on droop and virtual synchronous generator concepts.

How are small-signal stability conditions for angle equilibria obtained?

By applying the Routh–Hurwitz criterion to the unified swing-equation model, the document derives necessary and sufficient conditions on unit and network parameters to assess small-signal stability of angle equilibria.

Jul 16, 2026

Upload by Jiven