Accelerated and Robust Analytical Target Cascading for Distributed Optimal Power Flow

Augmented Lagrangian-based distributed algorithms, such as analytical target cascading (ATC), may converge slowly, oscillate around the optimal point, or diverge if penalty multipliers are not selected appropriately or the level of importance of objective terms is not balanced. This article presents accelerated, robust ATC (AR-ATC) to solve the optimal power flow (OPF) distributedly. A function is designed to determine a balancing coefficient whose incorporation into ATC makes a balance between the important level of terms of objective functions. If penalty multipliers are initialized to large values, the proposed function creates a balancing coefficient to avoid the premature convergence or divergence. A balancing coefficient will be created to reduce the number of iterations if penalty multipliers are set to small values. Mathematical justifications and simulation studies are performed to analyze the effectiveness of AR-ATC. Potential applications of the proposed method on auxiliary problem principle, alternating direction method of multipliers (ADMM), and Nesterov-based ADMM are also studied numerically. Simulations are performed for direct current optimal power flow and alternating current optimal power flow problems