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

Luis David Pabon Ospina, Martin Braun, Sushobhan Chatterjee, Sijia Geng

TL;DR

The paper addresses the risk of oscillatory instability arising from interactions between slow (LTC/OEL) and fast (inverter) dynamics in power systems with IBRs. It adopts a multi-timescale framework based on singular perturbation and time-domain simulations to reveal Hopf bifurcations (S-LT3) that are missed by single-timescale analyses. Through a Nordic test-system case study with GFL and GFM IBRs, it demonstrates how slow dynamics can drive fast PLLs into limit cycles and how GFM (or CVR and slower PLL) can mitigate these risks. The findings underscore the practical need for multi-timescale modeling to ensure stable, reliable operation of modern grids with high IBR penetration and guide deployment strategies for CVR and energy storage.

Abstract

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.

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

TL;DR

The paper addresses the risk of oscillatory instability arising from interactions between slow (LTC/OEL) and fast (inverter) dynamics in power systems with IBRs. It adopts a multi-timescale framework based on singular perturbation and time-domain simulations to reveal Hopf bifurcations (S-LT3) that are missed by single-timescale analyses. Through a Nordic test-system case study with GFL and GFM IBRs, it demonstrates how slow dynamics can drive fast PLLs into limit cycles and how GFM (or CVR and slower PLL) can mitigate these risks. The findings underscore the practical need for multi-timescale modeling to ensure stable, reliable operation of modern grids with high IBR penetration and guide deployment strategies for CVR and energy storage.

Abstract

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.

Paper Structure

This paper contains 12 sections, 1 equation, 16 figures, 1 table.

Table of Contents

  1. Introduction
  2. Preliminaries on Nonlinear Dynamics
  3. Test System and Dynamic Models
  4. Test System
  5. GFL IBR Model
  6. GFM IBR Model
  7. Numerical Studies and Main Results
  8. Case 1 - GFL (Fast PLL) Without Voltage Emergency Control
  9. Case 2 - GFL (Fast PLL) With Voltage Emergency Control
  10. Case 3 - GFL (Slow PLL) With Voltage Emergency Control
  11. Case 4 - GFL (Fast PLL) Plus GFM Battery
  12. Conclusions and Future Work

Figures (16)

  • Figure 1: Equilibrium manifolds that intercept pes_tr9.
  • Figure 2: Equilibrium manifolds that do not intercept pes_tr9.
  • Figure 3: Evolution of voltage magnitudes in Case 1.
  • Figure 4: Phase-space trajectory in Case 1.
  • Figure 5: Eigenvalues (a) and participation factors (b).
  • ...and 11 more figures