Energy Management in Microgrids: Sufficient Conditions for Convex Bi-Directional Converter Operation Model

Hybrid AC/DC microgrids with bi-directional converters (BDCs) have garnered increasing attention in recent years due to their ability to combine the benefits of both AC and DC microgrids. However, the non-convex nature of the BDC constraint, which enforces non-simultaneous rectification and inversion, often leads to locally optimal solutions and significant computational challenges. To overcome this issue, we develop a convex model for hybrid AC/DC microgrids by identifying sufficient conditions to relax the non-convex BDC constraint. Additionally, we extend these conditions to scenarios involving branch flow constraints, thereby broadening the applicability of the model. Finally, we validate the derived conditions and demonstrate the advantages of the proposed convex model through case studies on hybrid AC/DC microgrids.