On Distribution Patterns of Power Flow Solutions

TL;DR

This paper investigates the distribution patterns of power flow solutions under varying load levels, revealing the existence of false solutions and analyzing their mechanisms, with extensive solution data made publicly available.

Contribution

It provides the first comprehensive analysis of power flow solution distributions, including false solutions, and offers a large dataset for further research.

Findings

False load flow solutions exist as legitimate numerical solutions without engineering basis.

The probability distribution of voltage solutions is relatively unaffected by load changes.

A large number of solutions within engineering limits are identified and analyzed.

Abstract

A fundamental challenge in computer analysis of power flow is the rigorous understanding of the impact of different loading levels on the solutions of the power flow equation. This letter presents a comprehensive study of possible numerical solutions that may arise as the loading level varies. In particular, a type of "false" load flow solutions is reported for the first time as a legitimate numerical solutions but with no engineering justification. The existence and the mechanism of why this category of solutions exist are rigorously analyzed. The probability mass function of voltage solution is shown to be less dependent on loading levels. Furthermore, numbers of all actual solutions and those solutions within engineering limits are summarized. This letter presents a first attempt to compute such huge numbers of solutions to the tested systems, and analyze their distribution patterns. All solution sets investigated in this letter are posted online associated with this letter to support any further research purposes.