Iterative Implicit Linearized Optimal Power Flow Model for Mesh Microgrids

With the increasing integration of distributed energy resources and the growing complexity of microgrid topologies, mesh microgrids have emerged as a promising configuration due to their enhanced reliability, flexibility, and resilience. However, traditional Optimal Power Flow (OPF) models for such systems face significant challenges due to their inherent nonlinearity and non-convexity. To address these limitations, this paper proposes an Iterative Implicit Linearized Optimal Power Flow (IIL-OPF) model, which builds upon our previous work on the Iterative Implicit Linearized Power Flow (IIL-PF) formulation. The proposed model preserves the complex structure of the original power flow equations by treating them as implicit algebraic relationships and iteratively refines the linearization point to improve approximation accuracy. The IIL-OPF model is tested on modified IEEE 33-bus systems under both meshed and radial configurations. Simulation results demonstrate that the proposed method yields high accuracy with relative errors below 2.62% compared to the benchmark NLP-OPF model in MATPOWER, while maintaining fast convergence and strong adaptability to different network topologies. Furthermore, the IIL-OPF model accurately reflects physical characteristics such as power loss reduction and voltage profile improvement in meshed networks, confirming its effectiveness and robustness for practical applications.