Further Results on Newton-Raphson Method in Feasible Power-Flow for DC Distribution Networks
Zhangjie Liu, Ruisong Liu, Xin Zhang, Mei Su, Yao Sun, Hua Han, Peng Wang
Abstract
This letter analyzes the convergence of the Newton-Raphson method for the power-flow equation of a DC distribution network with constant power loads (CPLs). Specifically, this letter aims to: 1) determine the sufficient and necessary solvability condition of the power-flow equation; 2) derive the convergence condition of the Newton-Raphson (NR) method. For the first issue, the necessary and sufficient solvability condition for the power-flow equation is derived. On this basis, the convergence of the NR method is analyzed, and the convergence condition about the initial iterative value is obtained. Moreover, it is proved that the NR method under the proposed convergence condition is convergent as long as the power-flow equation is solvable. Finally, case studies verify the correctness of the presented theoretical analysis.