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.

Automated summary

This article explores the modeling and interpretation of synchronization stability of energy conversion systems in the presence of an unbalanced grid. It demonstrates the inherent instability phenomenon in the synchronous reference frame phase-locked loop (SRF-PLL) and highlights the need for improvement in small-signal models and Floquet stability analysis. The article investigates the behavior of the decoupled double synchronous reference frame phase-locked loop (DDSRF-PLL) under small disturbances and provides a precise sixth-order small-signal linear time-periodic model for it. Floquet theory-based stability and modal analysis are performed to gain insights into the dynamic properties of DDSRF-PLL. The article also analyzes the impact of grid voltage distortions on the performance and stability, including unbalance, harmonics, amplitude, phase, and frequency variations. This article is important for the design and analysis of unbalanced grid interfaced converter systems and system interaction studies.