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