A Comparative Study on Power Flow Methods for Direct-Current Networks Considering Processing Time and Numerical Convergence Errors

Luis Fernando Grisales-Noreña,Miguel-Angel Perea-Moreno,Alberto-Jesus Perea-Moreno,Oscar Danilo Montoya,Walter Julian Gil-González

doi:10.3390/electronics9122062

Abstract

This study analyzes the numerical convergence and processing time required by several classical and new solution methods proposed in the literature to solve the power-flow problem (PF) in direct-current (DC) networks considering radial and mesh topologies. Three classical numerical methods were studied: Gauss–Jacobi, Gauss–Seidel, and Newton–Raphson. In addition, two unconventional methods were selected. They are iterative and allow solving the DC PF in radial and mesh configurations. The first method uses a Taylor series expansion and a set of decoupling equations to linearize around the desired operating point. The second method manipulates the set of non-linear equations of the DC PF to transform it into a conventional fixed-point form. Moreover, this method is used to develop a successive approximation methodology. For the particular case of radial topology, three methods based on triangular matrix formulation, graph theory, and scanning algorithms were analyzed. The main objective of this study was to identify the methods with the best performance in terms of quality of solution (i.e., numerical convergence) and processing time to solve the DC power flow in mesh and radial distribution networks. We aimed at offering to the reader a set of PF methodologies to analyze electrical DC grids. The PF performance of the analyzed solution methods was evaluated through six test feeders; all of them were employed in prior studies for the same application. The simulation results show the adequate performance of the power-flow methods reviewed in this study, and they permit the selection of the best solution method for radial and mesh structures.

Highlights

We reviewed, analyzed, and evaluated eight solution methods based on three classical methods (Newton–Raphson, Gauss–Jacobi, and Gauss–Seidel) [23], and five unconventional methods based on the Taylor series expansion and successive approximations [30], triangular matrix formulation [31], graph theory, and backward/forward methods [18,32], to solve the PF in DC grids
We analyze the results obtained by the Newton–Raphson method (NR), GJ, GS, Taylor-Series-Based Approximation (TBM), and Successive Approximation (SA) methods when they were applied to the mesh test systems
This study addressed the calculation of the power flow in DC grids considering both radial and mesh structures to select the solution methods with the best performance in terms of numerical convergence and processing time for mesh and radial DC grids

Summary

Introduction

Concerning power-flow analysis in DC grids, the exploration of this problem started recently due to the paradigm shift regarding energy distribution with renewable energy and batteries, which typically operate with DC technologies [11,12,13,14,15,16] DC grids do not make use of synchronizing generators, need fewer power converters, and most importantly, present a simpler implementation given that reactive power and frequency analyses are not required [17] This has promoted the implementation of DC networks in the last few years. It is important to mention that for planning and management strategies of DC electrical networks, it is necessary to execute hundreds or even thousands of power-flow analysis to select a solution that provides the best results in terms of solution quality and processing time [18]

Objectives

Methods

Results

Conclusion