Closed-Form Solutions for Grid-Forming Converters: A Design-Oriented Study

This paper derives closed-form solutions for gridforming converters with power synchronization control (PSC) by subtly simplifying and factorizing the complex closed-loop models. The solutions can offer clear analytical insights into control-loop interactions, enabling guidelines for robust controller design. It is proved that 1) the proportional gains of PSC and alternating voltage control (AVC) can introduce negative resistance, which aggravates synchronous resonance (SR) of power control, 2) the integral gain of AVC is the cause of sub-synchronous resonance (SSR) in stiff-grid interconnections, albeit the proportional gain of AVC can help dampen the SSR, and 3) surprisingly, the current controller that dampens SR actually exacerbates SSR. Controller design guidelines are given based on analytical insights. The findings are verified by simulations and experimental results.