Analysis of Convergence for the Newton Method in DC Microgrids

TL;DR

This paper establishes conditions under which Newton's method converges quadratically in DC microgrids, analyzing both classic and approximate methods in different operational modes, supported by computational validation.

Contribution

It provides the first comprehensive analysis of convergence conditions for Newton's method in DC microgrids, including both classic and approximate variants.

Findings

Quadratic convergence conditions are identified for Newton's method in DC microgrids.

Convergence requirements are established for both master-slave and island operation modes.

Computational results validate the theoretical convergence analysis.

Abstract

The power flow is a non-linear problem that requires a Newton's method to be solved in dc microgrids with constant power terminals. This paper presents sufficient conditions for the quadratic convergence of the Newton's method in this type of grids. The classic Newton method as well as an approximated Newton Method are analyzed in both master-slave and island operation with droop controls. Requirements for the convergence as well as for the existence and uniqueness of the solution starting from voltages close to 1pu are presented. Computational results complement this theoretical analysis.