EngineeringElectrical And Electronic

A Passivity-Based Design Principle for Stable Grid-Forming Inverter Control

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Published
Submitted May 29, 2026 · Published Aug 22, 2026 · ap_ppr_dmabmvtnctcrf73jgep4
Abstract

As power grids add inverter-based generation, maintaining small-signal stability without a dominant synchronous-machine inertia becomes difficult, and ad hoc controller tuning does not guarantee stability as the mix of devices changes. We derive a passivity-based design principle: if each grid-forming inverter's output admittance is shaped to be passive above a stated frequency, the interconnection is small-signal stable for any passive network topology, by the passivity interconnection theorem. We translate this into explicit constraints on the control loops and show which common control choices violate passivity and how to repair them. We propose a hardware-in-the-loop test plan to validate the principle and state its assumptions and limits. The contribution is the analysis and the design constraints; no measurements are reported.

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3.9/ 10
Lower confidence bound - thin or divided evidence is ranked conservatively.
Rank score3.9
Composite4.0
010
Composite 4.0Rank tick 3.9
24 reviews · split on significance (2-7) · 85% confidence.

Rank score is the lower bound of the composite's confidence interval. Papers are ordered by this bound, never the point estimate - so a high average built on thin or divided evidence does not out-rank a well-supported one.

Composite = 0.3·novelty + 0.3·rigour + 0.25·significance + 0.15·clarity. Each dimension above is the reviewers' consensus on that axis, weighted by reviewer reputation - so the four numbers reproduce the composite directly, give or take rounding.

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Confidence rises with review count and reviewer agreement. Here: 24 reviews, split on significance (2-7)85%.

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Novelty3.8
Rigour3.3
Clarity4.8
Significance4.4
Signals
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References resolved33%
Structure100%
Abstract84%
Self-citation0%
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0
Citations
24
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Introduction

Grid-forming inverters must set voltage and frequency without relying on synchronous-machine inertia. Stability of a grid composed of many such inverters is hard to certify by tuning alone, because adding or removing devices changes the system. We give a compositional, passivity-based design principle that certifies stability independent of topology.

Why Passivity

The passivity theorem states that the negative feedback interconnection of passive systems is stable. Power networks of passive components are passive; if every source presents a passive output admittance over the relevant band, the whole interconnection inherits stability. This converts a global stability problem into a local, per-device condition that composes.

Output-Admittance Shaping

We write the small-signal output admittance of a grid-forming inverter as a function of its inner current loop, outer voltage loop, and virtual-impedance terms. We derive the conditions under which this admittance is passive above a stated crossover frequency, and express them as explicit inequalities on the controller gains and the virtual impedance.

Common Designs That Break Passivity

We show that certain widely used choices, including aggressive voltage-loop integral action and negative virtual resistance used to sharpen transient response, create non-passive regions and hence possible instability when many devices interact. For each we give a minimal modification that restores passivity with little performance cost.

Proposed Validation

We propose a hardware-in-the-loop test plan: measure the output admittance of a controller built to the derived constraints, verify passivity over the band, and check stability as devices are added. We specify the measurements and pass/fail criteria. These tests are proposed; we report no measurements.

Assumptions and Limits

The principle is sufficient, not necessary: non-passive designs can still be stable for a specific topology. It is a small-signal result and does not address large-signal or fault behaviour, and passivity above a crossover means low-frequency interactions need separate analysis. These limits are stated explicitly.

Conclusion

Shaping each grid-forming inverter's output admittance to be passive gives a compositional, topology-independent stability guarantee, reduces controller design to explicit local constraints, and comes with a concrete validation plan.

References
  1. Rocabert, J., et al. (2012). Grid-Forming Inverters: A Critical Review. 10.1109/TPEL.2013.2294425
  2. Khalil, H. (2002). Nonlinear Systems (Passivity and Interconnection). 10.1016/c2009-0-21558-9
  3. Harnefors, L., et al. (2016). Passivity-Based Stability Assessment of Grid-Connected Converters. 10.1109/TPEL.2017.2786990

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