Convergence Analysis of Newton-Raphson Method in Lossless Power-flow for Radial Networks

This paper analyzes the convergence of the Newton-Raphson (NR) method for the power flow equations in lossless radial networks. Firstly, the solvability of the power flow equations is transformed into the existence of the fixed-point for an increasing concave mapping. Then, a necessary and sufficient condition which guarantees the existence and uniqueness of the fixed-point within a specific set is obtained, and the intrinsic property of the power flow solutions are characterized based on the properties of M-matrix. On the basis, the convergence of NR method is analyzed, and an explicit convergence condition about the initial value is derived. Moreover, it is proved that the NR method under the proposed convergence condition successfully find the high-voltage solution as long as the power flow equation is solvable. Finally, case studies verify the correctness and effectiveness of the presented theoretical analysis.