Virtual Synchronous Machine Design for Islanded Microgrids Using the Extended Impedance Criterion With Grid Frequency Dynamics Included

Virtual synchronous machine (VSM) control is commonly used to control power converters in islanded microgrids (MGs). Frequently, the dynamic model of the MG is unknown and, therefore, the estimation-based, impedance criterion is preferred to design the control parameters. However, the original impedance criterion does not consider the fundamental frequency dynamics and its application may result in technical challenges, such as instabilities, during the connection of new VSMs to already operating MGs. This is relevant for cases where frequency dynamics are critical, as in the case of islanded MGs. In this paper, a methodology to design the parameters of a VSM connected to a MG is presented, based on an extension of the impedance criterion that accounts for the frequency dynamics. It is shown that the proposed method facilitates the understanding of the impact of the VSM parameters on the electromechanical and electromagnetic timescales and on the overall system stability, establishing an intuitive approach for their design. Furthermore, it is shown that the MG frequency dynamics have a relevant effect on the dynamic performance of the VSM, which would not be captured using the conventional impedance criterion. Theoretical developments are verified using simulations and laboratory tests of a representative islanded MG.