Synthesis of Dynamic Virtual Impedance for Grid-Forming Converters to Improve Self-Stability and Stabilizing Ability

In the future power-electronics-dominated power systems, grid-forming (GFM) converters have been regarded as important devices to actively establish frequency and voltage, so as to provide essential grid support. However, due to their voltage source behavior and emulated swing dynamics, GFM converters may encounter low-frequency oscillations (LFOs) when connected to strong grids, which belongs to the self-stability problem of GFM converters. Moreover, GFM converters will also interact with grid-following (GFL) converters and thus impact the mid-frequency oscillations (MFOs) induced by phase-locked loops (PLLs). It has been preliminarily shown in the literature that GFM converters can help stabilize the PLL-induced MFOs, but currently, there is a lack of systematic design methods to coordinate the self-stability and stabilizing ability of GFM converters. This paper addresses this gap by revisiting the impedance model of a typical GFM converter and briefly analyze the oscillations caused by converters. Based on our analysis, we propose a frequency-partitioned synthesis design framework to enable dynamic virtual impedance (DVI) in GFM converters, aiming to enhance their self-stability and stabilizing ability simultaneously. Particularly, a self-stabilizing module is designed to ensure robust device-level damping, with control parameters auto-tuned using $\mathcal{H}_{\infty}$ methods. In parallel, a stabilizing module is introduced to stabilize GFL converters and enhance the system-level stability, which utilizes a perceive-and-optimize tuning strategy. Simulation results validate the effectiveness of the proposed synthesis DVI framework.