Solving the Power Flow Problem in Bipolar DC Asymmetric Distribution Networks Using Broyden's Method

Oscar Danilo Montoya; Ángeles Medina-Quesada; Walter Gil-González

doi:10.3390/s23156704

Solving the Power Flow Problem in Bipolar DC Asymmetric Distribution Networks Using Broyden's Method

Sensors (Basel). 2023 Jul 26;23(15):6704. doi: 10.3390/s23156704.

Authors

Oscar Danilo Montoya¹, Ángeles Medina-Quesada², Walter Gil-González³

Affiliations

¹ Grupo de Compatibilidad e Interferencia Electromagnética (GCEM), Facultad de Ingeniería, Universidad Distrital Francisco José de Caldas, Bogotá 110231, Colombia.
² Department of Electrical Engineering, University of Jaén, Campus Lagunillas s/n, Edificio A3, 23071 Jaén, Spain.
³ Department of Electrical Engineering, Universidad Tecnológica de Pereira, Pereira 660003, Colombia.

Abstract

This research addresses the power flow analysis in bipolar asymmetric direct current (DC) networks by applying Broyden's numerical method. This general successive approximations method allows for a simple Newton-based recursive formula to reach the roots of multiple nonlinear equations. The main advantage of Broyden's approach is its simple but efficient structure which can be applied to real complex nonlinear equations.The power flow problem in bipolar DC networks is still challenging, as multiple operating options must be considered, e.g., the possibility of having a solidly grounded or floating neutral wire. The main goal of this research is to contribute with a generalization of Broyden's method for the power flow solution in bipolar DC networks, with the main advantage that, under well-defined conditions, this is a numerical method equivalent to the matricial backward/forward power flow, which is equivalent to the successive approximations power flow method. Numerical results in the 21-, 33-, and 85-bus grids while considering two connections for the neutral wire (i.e., solidly grounded at any node or floating) show the effectiveness of Broyden's method in the power flow solution for bipolar asymmetric DC networks. All numerical simulations were carried out in the MATLAB programming environment.

Keywords: Broyden’s method; linear convergence; power flow problem; set of nonlinear equations.

Grants and funding

This research received support from the Ibero-American Science and Technology Development Program (CYTED) through thematic network 723RT0150, Red para la integración a gran escala de energías renovables en sistemas eléctricos (RIBIERSE-CYTED).