Virtual Impedance Design Considerations for Virtual Synchronous Machines in Weak Grids

Most renewable energy sources (RESs) are interfaced to electricity grids via voltage-source converters (VSCs). To facilitate the integration, the controllers based on the emulation of synchronous generators have been increasingly used. This control technique is commonly referred to as Virtual Synchronous Machine (VSM) and recent studies have shown that VSMs are sensitive to variations in the network parameters if no countermeasures in form of virtual impedances are applied. However, a thorough and comprehensive methodology for the design of virtual impedance for VSMs has not been yet presented in the literature and the development of such procedure for the VSMs connected to weak grids is the principal objective of this paper. Each dynamic element of the VSM is modeled and all of them are then joined together forming a state-space model. The eigenvalue and singular value decomposition (SVD) analyzes were used then to evaluate the impact of the grid model and the virtual impedance on the VSM dynamics. From these results, a practical guide to design both the VSM and the virtual impedance parameters was proposed. All the theoretical developments were validated experimentally on a 15-kVA prototype of a VSM connected to a weak grid.