Equilibrium-Free Contraction Stability Analysis for Grid-Forming Converter-Based Microgrids

TL;DR

This paper introduces an equilibrium-free stability analysis method for grid-forming converter microgrids, enabling stability assessment without relying on equilibrium points, thus improving robustness and performance guarantees.

Contribution

It develops a novel semi-contraction based approach that removes the need for equilibrium assumptions, providing trajectory-level stability and robustness certificates for microgrid operation.

Findings

Validated on a 9-bus system demonstrating effectiveness.

Provides explicit bounds for stability under disturbances.

Offers a new perspective on nonlinear stability analysis for microgrids.

Abstract

Renewable-driven microgrids dominated by grid-forming (GFM) converters are subject to persistent power fluctuations, making equilibrium-known stability assessments restrictive. This paper develops an equilibrium-free contraction stability method based on semi-contraction theory. By formulating the system in a symmetry-aware projected state space, the intrinsic rotational mode induced by uniform angle shifts is removed. A blockwise Jacobian decomposition is introduced to characterize the coupled active and reactive power dynamics, yielding a computable regional contraction condition. This condition is then converted into forward-invariant stability certificates that provide trajectory-level performance guarantees. For autonomous operation without disturbances, the method provides an equilibrium-free nonlinear stability characterization together with an estimation of the region of attraction (ROA). For non-autonomous operation under disturbances, it derives explicit bounds for quasi-steady tracking under slowly varying injections and for robustness under fast or composite disturbances. Case studies on a 9-bus system validate the proposed method.