New Perspectives on Stability of Decoupled Double Synchronous Reference Frame PLL

Modeling and interpretation of synchronization stability of energy conversion systems with the unbalanced grid is a very practical, complicated, and less explored topic. This article demonstrates an inherent instability phenomenon in the synchronous reference frame phase locked-loop (SRF-PLL). The need for the small-signal model improvement and Floquet-stability-theory-based analysis is thereby demonstrated. Furthermore, decoupled double synchronous reference frame (DDSRF) PLL, which is a benchmark tool for unbalanced grid synchronization, is investigated for its behavior upon small disturbances. A precise sixth-order small-signal linear time-periodic model of DDSRF-PLL is obtained considering parameters of the input signal as well as of PLL. Floquet-theory-based stability and modal analysis are carried out to gain insights into dynamic properties of DDSRF-PLL. Impacts of distortions in grid voltage such as unbalance, harmonics, jumps in amplitude, phase, and frequency are analyzed for both performance and stability. This article is useful for the design and exact analysis of unbalanced grid interfaced converter systems and system interaction studies.