Estimating and Comparing Region of Attractions of Grid-Tied Converters Based on Sum of Squares Programming

This paper proposes to estimate the region of attraction (ROA) of grid-tied converters based on sum of squares (SOS) programming. An expanding interior algorithm (EIA) based on sum of squares programming (SOS) is demonstrated and is able to realize adaptive search of Lyapunov functions and estimation of the ROA. The stability models of the grid-following voltage source converter (GFL-VSC) and the grid-forming voltage source converter (GFM-VSC) are presented, and the ROA of the two models are obtained and compared. Based on the above findings, the non-conservativeness as well as the efficiency of the EIA algorithm were verified in two grid-tied converter systems.