Enabling High-Efficiency Economic Dispatch of Hybrid AC/DC Networked Microgrids: Steady-State Convex Bi-Directional Converter Models

The use of bi-directional converters (BDCs) is crucial for enhancing power exchange in hybrid AC/DC networked microgrids (NMGs). However, the dynamic nature of their conversion efficiency and the non-convex conversion direction expression of BDC models result in a highly non-convex programming problem, which leads to significant computational challenges. This paper proposes a least squares approximation approach to simplify the complex trigonometric function that characterizes the dynamic changes in BDC conversion efficiency with power. The simplified expression transforms the original non-convex relationship into a computationally efficient convex form. Subsequently, we systematically explore and validate the sufficient conditions to achieve non-simultaneous rectification and inversion behaviors of BDCs in a convex form. These explored conditions are further customized and extended to various practical application scenarios. Case studies are conducted on a hybrid AC/DC NMG with 66 nodes. The results demonstrate that our proposed least squares approximation method transforms the computationally intractable model into one that is solvable. Additionally, the explored conditions contribute to a substantial reduction in solution time by more than two orders of magnitude. These results verify the superiority of our proposed method, and showcase its applicability in practical scenarios.