Reliable prediction of Hopf bifurcation in power systems

P. Hasanpor Divshali, S. H. Hosseinian, E. Nasr, B. Vahidi

Research output: Contribution to journalArticleScientificpeer-review

5 Citations (Scopus)

Abstract

In this study, a new index for detection and prediction of oscillatory instabilities associated with HOPF bifurcation (HB) in power systems is proposed. Conventional indices could just predict HB in the heavy load conditions. The proposed index has a wider linear range and therefore prediction of system behavior at a wider range of load changes (even in lightly load condition) is provided. Consequently, the power system operators have more time to make the proper decisions to prevent HB. Conventional indices use critical eigenvalue pair of the state matrix to predict HB. This pair possesses biggest real parts among all eigenvalue pairs. However, sometimes this pair might not reach the imaginary axis before other eigenvalues. Therefore, they are not representative for HB eigenvalues which can lead to HB (This pair of eigenvalues could not be considered as HB eigenvalues). In this study, proposed index uses HB eigenvalue pair of state matrix to predict HB and two criteria are used to recognize HB eigenvalue pair. The first criterion is based on the proximity of the pairs of complex eigenvalue to the imaginary axis and the second criterion is based on the speed and the direction of the eigenvalues' movement towards the imaginary axis. Also, in this study, Matrix Reciprocal Condition Number Estimate (MRCNE) instead of minimum singular value decomposition is used to determine proximity of matrix to singularity. This estimation causes faster calculation without missing considerable accuracy. In order to demonstrate the effectiveness and accuracy of the proposed index, the new method is tested on the IEEE-14 bus and WSCC-9 bus test systems and results are presented. Results indicate that the proposed index has wider linear range and could predict HB in lower load level.

Original languageEnglish
Pages (from-to)61-68
Number of pages8
JournalElectrical Engineering
Volume91
Issue number2
DOIs
Publication statusPublished - 1 Aug 2009
MoE publication typeA1 Journal article-refereed

Fingerprint

Hopf bifurcation
Power System
Hopf Bifurcation
Eigenvalue
Prediction
Bifurcation (mathematics)
Singular value decomposition
Predict
Proximity
Range of data
Test System
Condition number
Singularity

Keywords

  • Hopf Bifurcation prediction
  • Non-linear system
  • Oscillatory stability prediction
  • Small signal stability

Cite this

Divshali, P. Hasanpor ; Hosseinian, S. H. ; Nasr, E. ; Vahidi, B. / Reliable prediction of Hopf bifurcation in power systems. In: Electrical Engineering. 2009 ; Vol. 91, No. 2. pp. 61-68.
@article{7fc6e9f1638d4c898468cf728eeda69b,
title = "Reliable prediction of Hopf bifurcation in power systems",
abstract = "In this study, a new index for detection and prediction of oscillatory instabilities associated with HOPF bifurcation (HB) in power systems is proposed. Conventional indices could just predict HB in the heavy load conditions. The proposed index has a wider linear range and therefore prediction of system behavior at a wider range of load changes (even in lightly load condition) is provided. Consequently, the power system operators have more time to make the proper decisions to prevent HB. Conventional indices use critical eigenvalue pair of the state matrix to predict HB. This pair possesses biggest real parts among all eigenvalue pairs. However, sometimes this pair might not reach the imaginary axis before other eigenvalues. Therefore, they are not representative for HB eigenvalues which can lead to HB (This pair of eigenvalues could not be considered as HB eigenvalues). In this study, proposed index uses HB eigenvalue pair of state matrix to predict HB and two criteria are used to recognize HB eigenvalue pair. The first criterion is based on the proximity of the pairs of complex eigenvalue to the imaginary axis and the second criterion is based on the speed and the direction of the eigenvalues' movement towards the imaginary axis. Also, in this study, Matrix Reciprocal Condition Number Estimate (MRCNE) instead of minimum singular value decomposition is used to determine proximity of matrix to singularity. This estimation causes faster calculation without missing considerable accuracy. In order to demonstrate the effectiveness and accuracy of the proposed index, the new method is tested on the IEEE-14 bus and WSCC-9 bus test systems and results are presented. Results indicate that the proposed index has wider linear range and could predict HB in lower load level.",
keywords = "Hopf Bifurcation prediction, Non-linear system, Oscillatory stability prediction, Small signal stability",
author = "Divshali, {P. Hasanpor} and Hosseinian, {S. H.} and E. Nasr and B. Vahidi",
year = "2009",
month = "8",
day = "1",
doi = "10.1007/s00202-009-0118-x",
language = "English",
volume = "91",
pages = "61--68",
journal = "Electrical Engineering",
issn = "0948-7921",
publisher = "Springer",
number = "2",

}

Reliable prediction of Hopf bifurcation in power systems. / Divshali, P. Hasanpor; Hosseinian, S. H.; Nasr, E.; Vahidi, B.

In: Electrical Engineering, Vol. 91, No. 2, 01.08.2009, p. 61-68.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Reliable prediction of Hopf bifurcation in power systems

AU - Divshali, P. Hasanpor

AU - Hosseinian, S. H.

AU - Nasr, E.

AU - Vahidi, B.

PY - 2009/8/1

Y1 - 2009/8/1

N2 - In this study, a new index for detection and prediction of oscillatory instabilities associated with HOPF bifurcation (HB) in power systems is proposed. Conventional indices could just predict HB in the heavy load conditions. The proposed index has a wider linear range and therefore prediction of system behavior at a wider range of load changes (even in lightly load condition) is provided. Consequently, the power system operators have more time to make the proper decisions to prevent HB. Conventional indices use critical eigenvalue pair of the state matrix to predict HB. This pair possesses biggest real parts among all eigenvalue pairs. However, sometimes this pair might not reach the imaginary axis before other eigenvalues. Therefore, they are not representative for HB eigenvalues which can lead to HB (This pair of eigenvalues could not be considered as HB eigenvalues). In this study, proposed index uses HB eigenvalue pair of state matrix to predict HB and two criteria are used to recognize HB eigenvalue pair. The first criterion is based on the proximity of the pairs of complex eigenvalue to the imaginary axis and the second criterion is based on the speed and the direction of the eigenvalues' movement towards the imaginary axis. Also, in this study, Matrix Reciprocal Condition Number Estimate (MRCNE) instead of minimum singular value decomposition is used to determine proximity of matrix to singularity. This estimation causes faster calculation without missing considerable accuracy. In order to demonstrate the effectiveness and accuracy of the proposed index, the new method is tested on the IEEE-14 bus and WSCC-9 bus test systems and results are presented. Results indicate that the proposed index has wider linear range and could predict HB in lower load level.

AB - In this study, a new index for detection and prediction of oscillatory instabilities associated with HOPF bifurcation (HB) in power systems is proposed. Conventional indices could just predict HB in the heavy load conditions. The proposed index has a wider linear range and therefore prediction of system behavior at a wider range of load changes (even in lightly load condition) is provided. Consequently, the power system operators have more time to make the proper decisions to prevent HB. Conventional indices use critical eigenvalue pair of the state matrix to predict HB. This pair possesses biggest real parts among all eigenvalue pairs. However, sometimes this pair might not reach the imaginary axis before other eigenvalues. Therefore, they are not representative for HB eigenvalues which can lead to HB (This pair of eigenvalues could not be considered as HB eigenvalues). In this study, proposed index uses HB eigenvalue pair of state matrix to predict HB and two criteria are used to recognize HB eigenvalue pair. The first criterion is based on the proximity of the pairs of complex eigenvalue to the imaginary axis and the second criterion is based on the speed and the direction of the eigenvalues' movement towards the imaginary axis. Also, in this study, Matrix Reciprocal Condition Number Estimate (MRCNE) instead of minimum singular value decomposition is used to determine proximity of matrix to singularity. This estimation causes faster calculation without missing considerable accuracy. In order to demonstrate the effectiveness and accuracy of the proposed index, the new method is tested on the IEEE-14 bus and WSCC-9 bus test systems and results are presented. Results indicate that the proposed index has wider linear range and could predict HB in lower load level.

KW - Hopf Bifurcation prediction

KW - Non-linear system

KW - Oscillatory stability prediction

KW - Small signal stability

UR - http://www.scopus.com/inward/record.url?scp=68849112382&partnerID=8YFLogxK

U2 - 10.1007/s00202-009-0118-x

DO - 10.1007/s00202-009-0118-x

M3 - Article

AN - SCOPUS:68849112382

VL - 91

SP - 61

EP - 68

JO - Electrical Engineering

JF - Electrical Engineering

SN - 0948-7921

IS - 2

ER -