Counterexample to a Continuation-Based Algorithm for Finding All Power Flow Solutions

Author

Molzahn, D.K. ; Lesieutre, Bernard C. ; Heng Chen

Author_Institution

Dept. of Electr. & Comput. Eng., Univ. of Wisconsin-Madison, Madison, WI, USA

Volume

28

Issue

1

fYear

2013

fDate

Feb. 2013

Firstpage

564

Lastpage

565

Abstract

Existing literature claims that an algorithm based on continuation is capable of finding all solutions to the power flow equations for all power systems. This claim is demonstrated to be incorrect through the use of a five-bus system counterexample. Existing literature also claims that a similar algorithm is capable of finding all Type-1 solutions (i.e., solutions where the power flow Jacobian has a single eigenvalue with positive real part) to the power flow equations for all systems. This claim is also shown to be incorrect using the five-bus system counterexample.

Keywords

Jacobian matrices; eigenvalues and eigenfunctions; load flow; continuation-based algorithm; five-bus system counterexample; power flow Jacobian matrices; power flow equations; power flow solutions; power systems; single eigenvalue; Eigenvalues and eigenfunctions; Equations; Mathematical model; Power system reliability; Power system stability; Reliability; Continuation power flow; voltage stability;

fLanguage

English

Journal_Title

Power Systems, IEEE Transactions on

Publisher

ieee

ISSN

0885-8950

Type

jour

DOI

10.1109/TPWRS.2012.2202205

Filename

6225409