On MIMO Stability Analysis Methods Applied to Inverter-Based Resources Connected to Power Systems

TL;DR

This paper critically assesses stability analysis methods for inverter-based resources in power systems, highlighting that many MIMO frequency-domain approaches (e.g., generalized Nyquist) are misapplied or insufficient for robust stability guarantees. It surveys SISO and MIMO techniques, including the Nyquist criterion, determinant-based tests, the small-gain theorem, passivity, and positive-real theory, and exposes fundamental limitations when perturbations are nonuniform or highly interconnected. The authors argue for adopting modern state-space and robust control tools for MIMO stability, clarifying objectives and uncertainties (e.g., modeling as $P$, $Y$, and $Z$, with $P=YZ$) and showing where classical methods may mislead. The work provides practical guidance to avoid misinterpretations in the literature and to advance reliable stability assessments in grids with high inverter penetration, by emphasizing rigorous uncertainty modeling and robust stability criteria like the $H_\infty$ norm and passivity-based approaches.

Abstract

This paper presents a critical review of methods commonly employed in the literature for small signal stability analysis of inverter based resources (IBRs). It discusses the intended purposes of these methods and outlines both their proper and improper implementations. The paper provides insights into the applicability of these techniques, clarifies their inherent limitations, and discusses and illustrates common sources of misinterpretation.

Figures (9)

• Figure 1: Standard feedback loop
• Figure 2: Nyquist plot of $\det(I+P(j\omega))$ of Example \ref{['ex1']}
• Figure 3: Eigenvalue trajectories of $P(j\omega)$ of Example \ref{['ex1']} as the frequency varies from $-\infty$ to $\infty$
• Figure 4: Plot of combined trajectories from Fig.\ref{['pic03']}
• Figure 5: Standard feedback loop with uncertainty block U

Theorems & Definitions (22)

• Theorem 1
• Example 1
• Example 2
• Example 3
• Example 4
• Theorem 2: uniform uncertainty
• Example 5
• Example 6
• Theorem 3
• Definition 1