[Paper Review] Passivity and Decentralized Stability Conditions for Grid-Forming Converters

Xiuqiang He, Florian Dörfler|arXiv (Cornell University)|Oct 15, 2023

Microgrid Control and Optimization12 references4 citations

TL;DR

This paper establishes large-signal passivity and decentralized stability conditions for grid-forming converters using dispatchable virtual oscillator control (dVOC). By proving output-feedback passivity with an explicit passivity index, it derives decentralized transient stability conditions that ensure global asymptotic stability under grid disturbances, enabling robust control design for renewable power plants without centralized coordination.

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.

Motivation & Objective

• Address the lack of decentralized, large-signal stability analysis for multi-converter grid-connected systems using modern grid-forming control.
• Overcome limitations of small-signal and centralized stability analysis in systems with numerous small-capacity renewable units.
• Provide a scalable, data-efficient stability framework that relies only on local and essential network information.
• Ensure transient stability of renewable power plants under grid disturbances such as voltage dips.
• Enable practical controller tuning and stability margin assessment without requiring full system-wide model access.

Proposed method

• Prove large-signal output-feedback passivity of the dVOC control law in the complex-voltage $dq$-frame, deriving an explicit passivity index $\delta_k$ for each converter.
• Model the network using a static admittance matrix $\mathbf{Y}$ and grid voltage source, incorporating virtual impedance for fault current limiting.
• Formulate the closed-loop system as a feedback interconnection between dVOC nodes and the network, enabling passivity-based analysis.
• Derive decentralized stability conditions via the passivity index of the network $\varepsilon_{\text{net}}$ and the node $\delta_k$, requiring $\delta_k + \varepsilon_{\text{net}} > 0$ for all $k$.
• Utilize the natural passivity of the network to compensate for potentially negative node passivity indices, reducing conservatism.
• Validate the framework using a real-world wind power plant model with full controller dynamics, including current limiting strategies.

Experimental results

Research questions

• RQ1 Can the dVOC control law be proven to be large-signal passive, and what is its explicit passivity index?
• RQ2 How can decentralized stability conditions be derived for multi-converter grid-connected systems using only local and network data?
• RQ3 Can the proposed conditions ensure transient stability under grid disturbances such as voltage dips?
• RQ4 How does the inclusion of virtual impedance for fault current limiting affect the stability analysis and network passivity?
• RQ5 To what extent can the decentralized stability margin $\varepsilon_{\text{net}} - |\delta_k|$ serve as a practical indicator for controller tuning and system resilience?

Key findings

• The dVOC control law is proven to be output-feedback passive in its large-signal model, with a physically meaningful passivity index $\delta_k$.
• The decentralized stability condition $\delta_k + \varepsilon_{\text{net}} > 0$ ensures global asymptotic stability of the equilibrium point, even when individual nodes are not strictly passive.
• The network’s inherent passivity ($\varepsilon_{\text{net}} > 0$) compensates for negative node passivity indices ($\delta_k < 0$), reducing conservatism compared to prior methods.
• The stability margin $\varepsilon_{\text{net}} - |\delta_k|$ quantifies the resilience of each converter, with positive values indicating stable operation.
• Simulations on a real wind power plant model confirm transient stability under voltage dips, both with and without current limiting, validating the theoretical conditions.
• The framework remains applicable when virtual impedance is introduced for fault current limitation, as long as it is included in the network admittance model.