Generalized Cauchy process based on heavy-tailed distribution and grey relational analysis for reliability predicting of distribution systems

Jun Gao; Fei Wu; Yakufu Yasen; Wanqing Song; Lijia Ren; Jun Gao; Fei Wu; Yakufu Yasen; Wanqing Song; Lijia Ren

doi:10.3934/mbe.2022311

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6620-6637. doi: 10.3934/mbe.2022311

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Generalized Cauchy process based on heavy-tailed distribution and grey relational analysis for reliability predicting of distribution systems

1.
School of Electronic & Electrical Engineering, Shanghai University of Engineering Science, 333# Longteng road, Songjiang District, Shanghai 201620, China
2.
State Grid Kashi Electric Power Supply Company, 156 Renmin West Road, Kashi 844099, China

Academic Editor: Hamid Reza Karimi

Received: 23 March 2022 Revised: 22 April 2022 Accepted: 23 April 2022 Published: 27 April 2022

Failure interruption often causes large blackouts in power grids, severely impacting critical functions. Because of the randomness of power failure, it is difficult to predict the leading causes of failure. ASAI, an essential indicator of power-supply reliability, can be measured from the outage time series. The series is non-stationary stochastic, which causes some difficulty in analyzing power-supply reliability. Considering that the time series has long-range dependence (LRD) and self-similarity, this paper proposes the generalized Cauchy (GC) process for the prediction. The case study shows that the proposed model can predict reliability with a max absolute percentage error of 8.28%. Grey relational analysis (GRA) has proved to be an effective method for the degree of correlation between different indicators. Therefore, we propose the method, which combines both GC and GRA to obtain the correlation coefficients between different factors and ASAI and to get the main factors based on this coefficient. The case study illustrates the feasibility of this approach, which power enterprises can employ to predict power-supply reliability and its influencing factors and help them identify weaknesses in the grid to inform employees to take protective measures in advance.
- reliability of distribution systems,
- grey relational coefficient,
- generalized Cauchy process,
- failure interruption,
- long-range dependence
Citation: Jun Gao, Fei Wu, Yakufu Yasen, Wanqing Song, Lijia Ren. Generalized Cauchy process based on heavy-tailed distribution and grey relational analysis for reliability predicting of distribution systems[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6620-6637. doi: 10.3934/mbe.2022311

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Abstract

Failure interruption often causes large blackouts in power grids, severely impacting critical functions. Because of the randomness of power failure, it is difficult to predict the leading causes of failure. ASAI, an essential indicator of power-supply reliability, can be measured from the outage time series. The series is non-stationary stochastic, which causes some difficulty in analyzing power-supply reliability. Considering that the time series has long-range dependence (LRD) and self-similarity, this paper proposes the generalized Cauchy (GC) process for the prediction. The case study shows that the proposed model can predict reliability with a max absolute percentage error of 8.28%. Grey relational analysis (GRA) has proved to be an effective method for the degree of correlation between different indicators. Therefore, we propose the method, which combines both GC and GRA to obtain the correlation coefficients between different factors and ASAI and to get the main factors based on this coefficient. The case study illustrates the feasibility of this approach, which power enterprises can employ to predict power-supply reliability and its influencing factors and help them identify weaknesses in the grid to inform employees to take protective measures in advance.

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