<p>Due to certain limitations associated with centralized Optimal Power Flow (OPF) in multi-area interconnected power systems, there is a shift toward decentralized methods. These approaches are categorized into external network modeling methods and mathematical decomposition methods. In the first category, each area models its adjacent areas using an equivalent network, while the second category employs decomposition techniques. In these methods, no equivalent networks for areas are made and only a limited data related to boundary buses are exchanged. This paper analyzes the convergence properties of Lagrangian decomposition methods and proposes several new strategies to enhance the convergence rate.</p>