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

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
• power flow problem
• set of nonlinear equations
• linear convergence