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Passivity and Decentralized Stability Conditions for Grid-Forming Converters

Xiuqiang He, Florian Dörfler

TL;DR

The paper addresses transient stability of multi-converter grids controlled by grid-forming dVOC (dispatchable virtual oscillator control). It proves large-signal output-feedback passivity for each dVOC node with a node passivity index $\delta_k$ and identifies network passivity with index $\varepsilon_{ m net}$ (gSCR) for the rotated network. The core result is a decentralized stability condition $\delta_k + \varepsilon_{ m net} > 0$ verified via a composite Lyapunov function $\nu = \sum_k V_k$, ensuring asymptotic stability; global stability holds if the equilibrium is unique. Validation on a real wind-power-plant demonstrates practical applicability, showing that the decentralized condition can certify transient stability under grid disturbances and guide controller tuning, including current-limiting strategies.

Abstract

We prove that the popular grid-forming control, i.e., dispatchable virtual oscillator control (dVOC), also termed complex droop control, exhibits output-feedback passivity in its large-signal model, featuring an explicit and physically meaningful passivity index. Using this passivity property, we derive decentralized stability conditions for the transient stability of dVOC in multi-converter grid-connected systems, beyond prior small-signal stability results. The decentralized conditions are of practical significance, particularly for ensuring the transient stability of renewable power plants under grid disturbances.

Passivity and Decentralized Stability Conditions for Grid-Forming Converters

TL;DR

The paper addresses transient stability of multi-converter grids controlled by grid-forming dVOC (dispatchable virtual oscillator control). It proves large-signal output-feedback passivity for each dVOC node with a node passivity index and identifies network passivity with index (gSCR) for the rotated network. The core result is a decentralized stability condition verified via a composite Lyapunov function , ensuring asymptotic stability; global stability holds if the equilibrium is unique. Validation on a real wind-power-plant demonstrates practical applicability, showing that the decentralized condition can certify transient stability under grid disturbances and guide controller tuning, including current-limiting strategies.

Abstract

We prove that the popular grid-forming control, i.e., dispatchable virtual oscillator control (dVOC), also termed complex droop control, exhibits output-feedback passivity in its large-signal model, featuring an explicit and physically meaningful passivity index. Using this passivity property, we derive decentralized stability conditions for the transient stability of dVOC in multi-converter grid-connected systems, beyond prior small-signal stability results. The decentralized conditions are of practical significance, particularly for ensuring the transient stability of renewable power plants under grid disturbances.
Paper Structure (8 sections, 3 theorems, 9 equations, 2 figures)

This paper contains 8 sections, 3 theorems, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model With Feedback Connection
  3. Passivity and Stability Results
  4. Passivity Index of Grid-Forming Dynamics
  5. Passivity Index of the Network
  6. Decentralized Stability Conditions
  7. Validation
  8. Conclusion

Key Result

Proposition 1

The dVOC dynamics in eq:rotated-dvoc, with input $-\underline{i}_{\varphi,k}$ and output $\underline{v}_k$, are output-feedback passive w.r.t an equilibrium $\underline{v}_{{\rm s},k}$, where the passivity index is given as

Figures (2)

  • Figure 1: (a) Multi-converter grid-connected systems with dVOC grid-forming control. (b) System model with feedback connection. (c) In incremental form w.r.t to equilibria, the passivity index of the dVOC-controlled node dynamics is denoted as $\delta_k$ while the passivity index of the (rotated) network is denoted as $\varepsilon_{\rm net}$, establishing decentralized stability conditions as $\delta_k + \varepsilon_{\rm net} > 0, \forall k$.
  • Figure 2: (a) The layout of a real wind power plant. (b) The node and network passivity indices are calculated. The system maintains transient stability under a grid voltage dip, (c) without applying current limiting, or (d) with currents being properly limited throughout by a saturation-informed strategy in desai2023saturation.

Theorems & Definitions (10)

  • Proposition 1
  • proof
  • Remark 1
  • Proposition 2
  • proof
  • Remark 2
  • Theorem 1
  • proof
  • Remark 3
  • Remark 4