Modelling and small signal stability for islanded microgrids with hybrid grid-forming sources based on converters and synchronous machines.

• A general component connection method (CCM) for modelling an islanded microgrid with multiple power sources is developed. • State-space models of nine scenarios with hybrid synchronous machines, grid-following converters, grid-forming (GFM) converters, and motor-generator pair (MGP) are investigated. • Small-signal dynamics of different scenarios based on GFM power sources are compared. • The damping ratios of an islanded grid can be improved by GFM converters and MGPs. • Critical ranges for control parameters, GFM converter penetration and electrical distance in typical scenarios are investigated. Grid-forming (GFM) technologies based on converters or synchronous machines (SMs) were proposed as emerging approaches for improving inertia, damping, and strength of power girds with increasing renewable energy penetration. Although the stability of GFM converters has been widely studied, the dynamics of a grid-connected generator can be dictated by the bulk power systems. Therefore, the stability of islanded microgrids with hybrid GFM sources should be investigated. To fulfill this gap, this paper adopts a general component connection method for modelling islanded microgrids integrated with multiple generators, and models for SMs, grid-following (GFL) and GFM converters are developed. Additionally, a new GFM technology known as the motor-generator pair (MGP) is investigated, and the model for small signal analysis is derived. Then, full-order state-space models for nine scenarios with hybrid GFM sources as well as simulation models which are used to verify their effectiveness are built. Finally, small-signal dynamics of different scenarios are fully examined. In the scenarios with SMs integrated, the range of oscillation frequency is wider than all converter-based scenarios, and mechanical dynamics can dominate stability; and in scenarios with only GFM converters, though the damping can be improved compared to GFL converters, low frequency oscillation may occur, and the dominant factor changes from the phase locked loop and power controller to voltage controller; then improvement in damping can be observed in MGP-based scenarios, but roots that dominate stability are sensitive to current controller and excitation. Further, critical ranges for control parameters, GFM converter penetration and electrical distance in different scenarios are investigated. [ABSTRACT FROM AUTHOR]