Xi Ru

Shijie Peng, Xiuqiang He, Xi Ru et al.

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.

Xi Ru, Cong Fu, Zhongze Li et al.

Passivity indices have been widely adopted to derive distributed stability certificates for power systems. Nevertheless, conventional passivity indices remain scalar-valued even for multi-input-multi-output (MIMO) systems, which can introduce excessive conservatism and compromise analysis accuracy. To overcome these limitations, this paper extends the differential passivity index to a matrix-valued formulation that captures both channel-wise passivity properties and inter-channel coupling effects in MIMO subsystems. On this basis, semi-distributed and fully distributed stability criteria are developed for power systems with heterogeneous nonlinear devices. It is shown that system stability is guaranteed when the aggregate passivity excess of devices compensates for the passivity shortage imposed by the network. Furthermore, analytical passivity matrix expressions for typical power system components are derived, facilitating compositional stability analysis. Case studies on a three-bus system and a modified IEEE 118-bus system validate the effectiveness of the proposed framework.