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

Sushobhan Chatterjee, Sijia Geng

TL;DR

This paper addresses voltage stability in inverter-based power systems by analyzing fold and saddle-node bifurcations and deriving a closed-form sensitivity of the stability margin using the normal vector to the bifurcation surface, enabling efficient parameter tuning. It proves that transmission line dynamics do not affect these bifurcations for both grid-following and grid-forming inverters, allowing accurate margin estimation with static-line models. The authors identify the most effective control channels: for GFL inverters, the reactive-load setpoint and current-control feedforward gain, and for GFM inverters, the voltage-control feedforward gain, supported by a practical normal-vector based sensitivity formula. Collectively, these results reduce model and parameter complexity and provide a scalable framework for voltage-stability analysis in future inverter-dominated grids.

Abstract

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.

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

TL;DR

This paper addresses voltage stability in inverter-based power systems by analyzing fold and saddle-node bifurcations and deriving a closed-form sensitivity of the stability margin using the normal vector to the bifurcation surface, enabling efficient parameter tuning. It proves that transmission line dynamics do not affect these bifurcations for both grid-following and grid-forming inverters, allowing accurate margin estimation with static-line models. The authors identify the most effective control channels: for GFL inverters, the reactive-load setpoint and current-control feedforward gain, and for GFM inverters, the voltage-control feedforward gain, supported by a practical normal-vector based sensitivity formula. Collectively, these results reduce model and parameter complexity and provide a scalable framework for voltage-stability analysis in future inverter-dominated grids.

Abstract

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.

Paper Structure

This paper contains 21 sections, 1 theorem, 22 equations, 6 figures, 12 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Fold and Saddle-Node Bifurcations
  5. Irrelevance of Line Dynamics
  6. Stability Margin to Bifurcations
  7. Normal Vectors to Bifurcation Hypersurfaces
  8. Parameter Sensitivity of Stability Margin
  9. Numerical Results
  10. GFL Inverters
  11. System Setup and Ground Truth
  12. Sensitivity Analysis of Control Parameters Using Normal Vectors
  13. Example on Stability Margin Estimation
  14. GFM Inverters
  15. System Setup and Ground Truth
  16. ...and 6 more sections

Key Result

Proposition 1

dobson2011irrelevance Let $f(x,\lambda) = $ be a smooth function with component functions $f^1 : \mathbb{R}^{\tilde{n}} \times \mathbb{R}^{n-\tilde{n}} \times \mathbb{R}^m \rightarrow \mathbb{R}^{\tilde{n}}$ and $f^2 : \mathbb{R}^{\tilde{n}} \times \mathbb{R}^{n-\tilde{n}} \times \mathbb{R}^m \right

Figures (6)

  • Figure 1: General architecture of a single-inverter-infinite-bus system.
  • Figure 2: Geometry of the bifurcation hypersurface, normal vector, and the stability margin along direction $k$. $H$ is the tangent hyperplane at $\lambda_{*,\text{old}}$. With the cause of bifurcation remaining constant (i.e., moving along the direction $k$), the true stability margin increases from $\Delta_\text{old}$ to $\Delta_\text{new}$ as the operating point shifts from $\lambda_{0,\text{old}}$ to $\lambda_{0,\text{new}}$. $\hat{\Delta}_\text{new}$ is an estimation of true margin $\Delta_\text{new}$.
  • Figure 3: Schematic of a generic IBR connecting to the grid.
  • Figure 4: Schematic of GFL inverter.
  • Figure 5: Phasor diagram and reference frames of the GFL inverter.
  • ...and 1 more figures

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Proposition 1