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Assessment of voltage stability margin by comparing various support vector regression models

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Abstract

Voltage stability assessment and prediction of loadability margin are the major concerns in real-time operation of power systems. This paper proposes a support vector machine (SVM) regression network for the voltage stability assessment for normal condition as well as for contingency cases. The loadability margin of any given operating conditions is obtained for pre-contingency and post-contingency based on the computation of a stability index. SVM takes real and reactive power at all buses of the system and gives the loading margin. The validity of the proposed SVM-based index is tested on IEEE 30 and Indian 181 bus systems. The results of the proposed method are compared with neural network, extreme learning machine, online sequential extreme learning machine and extreme support vector machine regression methods. The feasibility of application of the proposed SVM regression network for real-time stability assessment is discussed. Also, FACTS devices are produced to improve the system loadability and their results are discussed.

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Abbreviations

ANN:

Artificial neural network

CPF:

Continuation power flow

ELM:

Extreme learning machine

OS-ELM:

Online sequential extreme learning machine

SVM:

Support vector machine

SVR:

Support vector regression

ESVM:

Extreme support vector machine

AI:

Artificial intelligence

MLP:

Multi-layer perceptron

DE&PSO:

Differential evolution and particle swarm optimization

LM_index:

Loadability Margin_Index

\(n_{l}\) :

Number of load buses

\(\lambda _\mathrm{o}\) :

Loadability factor of base operating load point (p.u)

\(\lambda _\mathrm{VC(Pre)}\) :

Loadability factor of voltage collapse point (p.u) for pre-contingency case

\(\lambda _\mathrm{VC(Post)}\) :

Loadability factor of voltage collapse point (p.u) for post-contingency case

PSAT:

Power system analysis toolbox

P\(_\mathrm{g}\) P\(_\mathrm{l}\) Q\(_\mathrm{g}\) Q\(_\mathrm{l}\) :

Real and reactive powers in generators and load buses respectively

\(\lambda \) :

Loadability factor

MSE:

Mean square error

C:

Cost function in SVM

\(\upgamma \) :

Gamma

X\(_\mathrm{i}\) :

Loading margin

Y\(_\mathrm{i}\) :

Target value, i.e., loading margin from CPF

n :

No: of buses

P\(_\mathrm{li,n}\) :

Real power load vector of \(\mathop i\)th bus for ‘n’ number of patterns

Q\(_\mathrm{li,n}\) :

Reactive power load vector of \(\mathop i\)th bus for ‘n’ number of patterns

\(\upvarepsilon \)-SVR:

Epsilon-SVR

\(\upnu \)-SVR:

nu-SVR

LIBSVM:

Library SVM

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Acknowledgments

The first author sincerely acknowledge the financial assistance received from Department of Science and Technology, New Delhi, India under Women Scientist Scheme-A vide letter number SR/WOS-A/ET-139/2011, dated on 05-03-2012 and the authors also thank the Management and Principal of Thiagarajar College of Engineering, Madurai, India to carry out this research work.

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Authors and Affiliations

  1. Department of Electrical and Electronics Engineering, Thiagarajar College of Engineering, Madurai, 625015, Tamilnadu, India

    M. V. Suganyadevi & C. K. Babulal

  2. Department of Electrical and Electronics Engineering, Kamaraj College of Engineering and Technology, Virudhunagar, Tamilnadu, India

    S. Kalyani

Authors
  1. M. V. Suganyadevi
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  2. C. K. Babulal
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  3. S. Kalyani
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Correspondence to M. V. Suganyadevi.

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Communicated by E. Lughofer.

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Suganyadevi, M.V., Babulal, C.K. & Kalyani, S. Assessment of voltage stability margin by comparing various support vector regression models. Soft Comput 20, 807–818 (2016). https://doi.org/10.1007/s00500-014-1544-x

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