Skip to main content
SpringerLink
Log in

A dual-threshold state analysis and fault location method for power system based on random matrix theory

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Traditional single-threshold state analysis and fault location methods for power system still need to improve in detection accuracy and applicability. In this paper, a dual-threshold state analysis and fault location method based on Tracy–Widom distribution is proposed to improve the accuracy and widen the application fields of some typical methods. Taking the false alarm probability into accountant, the maximum and minimum eigenvalues of sample covariance matrix are adopted to construct the upper and lower thresholds, respectively, and the difference of eigenvalues is settled as the detection indicator to realize the state analysis. For fault location, the positioning index is obtained from the augmented matrixes of each bus and then is compared with the thresholds to determine the fault location. The comparison analysis based on IEEE 39-Bus system verifies that the proposed method outperforms the conventional solutions in terms of accuracy, anti-interference ability and universality in various situations, especially for early faults detection.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Availability of data and materials

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Wang, H., Li, L., Deng, D.: Research and implementation of intelligent analysis system for comprehensive outage management based on big data technology. In: International Conference on Power System Technology, 6–8, November 2018 Guangzhou, China, pp. 4455–4461 (2018)

  2. Shu, Y., Tang, Y.: Analysis and recommendations for the adaptability of China’s power system security and stability relevant standards. CSEE J. Power Energy Syst. 3(4), 334–339 (2017)

  3. Zhang, Q., Wan, S., Wang, B., et al.: Anomaly detection based on random matrix theory for industrial power systems. J. Syst. Archit. 95, 67–74 (2019)

    Article  Google Scholar 

  4. Chu, L., Qiu, R., He, X., et al.: Massive streaming PMU data modelling and analytics in smart grid state evaluation based on multiple high-dimensional covariance test. IEEE Trans. Big Data 4(1), 55–64 (2018)

    Article  Google Scholar 

  5. He, X., Ai, Q., Qiu, R.C., et al.: A big data architecture design for smart grids based on random matrix theory. IEEE Trans. Smart Grid 8(2), 674–686 (2017)

    Google Scholar 

  6. Qiu, R.C., Antonik, P.: Smart Grid Using Big Data Analytics: A Random Matrix Theory Approach. Wiley (2017)

  7. Xiao, F., Ai, Q.: Electricity theft detection in smart grid using random matrix theory. IET Gener. Transm. Distrib. 12(2), 371–378 (2017)

    Article  Google Scholar 

  8. He, X., Ai, Q., Qiu, R.C., et al.: A primary study on the situation awareness of power systems using random matrix theory. Power Syst. Technol. 41(4), 1165–1173 (2017)

  9. Cai, D., He, X., Yu, Z., et al.: 3D power-map for smart grids integration of high-dimensional analysis and visualization. In: International Conference on Renewable Power Generation (RPG 2015), Beijing, pp. 1–5 (2015)

  10. Xu, X., He, X., Ai, Q., et al.: A correlation analysis method for power systems based on random matrix theory. IEEE Trans. Smart Grid 8(4), 1811–1820 (2017)

    Article  Google Scholar 

  11. Yang, H., Qiu, R.C., Mi, T., et al.: Improving power system state estimation based on matrix-level cleaning. IEEE Trans. Power Syst. 35, 3529–3540 (2020)

    Article  Google Scholar 

  12. He, X., Qiu, R.C., Ai, Q., et al.: Designing for situation awareness of future power grids: an indicator system based on linear eigenvalue statistics of large random matrices. IEEE Access 4, 3557–3568 (2016)

    Article  Google Scholar 

  13. Zhou, Z.: MESCM based abnormal state detection of power system in low SNR situation. Power Syst. Protect. Control 47(08), 113–119 (2019)

    Google Scholar 

  14. Hu, X., Ma, D., Sun, Q., et al.: A method for microgrid situation awareness based on the spectral deviation of random matrix. Proc. Chin. Soc. Electr. Eng. 39(21), 6238–6247 (2019)

    Google Scholar 

  15. He, X., Chu, L., Qiu, R.C., et al.: Invisible unitd detection and estimation based on random matrix theory. IEEE Trans. Power Syst. 35(3), 1846–1855 (2020)

    Article  Google Scholar 

  16. Ding, K., Qian, Y., Wang, Y., et al.: A data-driven vulnerability evaluation method in grid edge based on random matrix theory indicators. IEEE Access 8, 26495–26504 (2020)

    Article  Google Scholar 

  17. Zhu, D., Wang, B., Ma, H.: Evaluating the vulnerability of integrated electricity-heat-gas systems based on the high-dimensional random matrix theory. CSEE J. Power Energy Syst. 6(4), 878–889 (2020)

  18. Yan, Y., Liu, Y., Fang, J., et al.: Application of random matrix model in multiple abnormal sources detection and location based on PMU monitoring data in distribution network. IET Gener. Transm. Distrib. 14(26), 6476–6483 (2020)

    Article  Google Scholar 

  19. Cao, Y., et al.: A random matrix theoretical approach to early event detection using experimental data (2015). arXiv:1503.08445v1

  20. Men, S., Charge, P., Pillement, S.: Cooperative spectrum sensing with small sample size in cognitive wireless sensor networks. Wirel. Pers. Commun. 96, 1871–1885 (2017)

    Article  Google Scholar 

  21. Çiflikli, C., Ilgin, F.: Covariance based spectrum sensing with studentized extreme eigenvalue. Techn. Gaz. 25, 100–106 (2018)

    Google Scholar 

  22. Pillay, N., Xu, H.: Eigenvalue-based spectrum sensing using the exact distribution of the maximum eigenvalue of a Wishart matrix. IET Signal Process 7(9), 833–842 (2013)

    Article  Google Scholar 

  23. Çiflikli, C., Ilgin, F.: Studentized extreme eigenvalue based double threshold spectrum sensing under noise uncertainty. Tehn. Vjesn. 27(2), 353–357 (2020)

    Google Scholar 

  24. Hajiyev, C.: Tracy-widom distribution based fault detection approach: application to aircraft sensor/actuator fault detection. ISA Trans. 51, 189–197 (2012)

    Article  Google Scholar 

  25. Liao, S., Kim, T., Su, W.: Modeling and analysis of residential electricity consumption statistics: a Tracy–Widom mixture density approximation. IEEE Access 8, 163558–163567 (2020)

    Article  Google Scholar 

  26. Chan, C., Xiong, M.: Random matrices from linear codes and Wigner’s semicircle law II. In: 9th International Workshop on Signal Design and its Applications in Communications (IWSDA), Dongguan, China, vol. 2019, pp. 1–3 (2019)

  27. Marco, C.: Distribution of the largest eigenvalue for real Wishart and Gaussian random matrices and a simple approximation for the Tracy-Widom distribution. J. Multivar. Anal. 129, 69–81 (2014)

    Article  MathSciNet  Google Scholar 

  28. Feldheim, O., Sodin, S.: A universality result for the smallest eigenvalues of certain sample covariance matrices. Geom. Funct. Anal. 20(1), 88–123 (2010)

    Article  MathSciNet  Google Scholar 

  29. Tracy, C., Widom, H.: The distributions of random matrix theory and their applications. In: New Trends in Mathematical Physics, pp. 753–765. Springer, Dordrecht (2009)

Download references

Funding

This work was supported by Key Technologies Research and Development Program (2020YFB1711102 and 2020YFB1711100).

Author information

Authors and Affiliations

  1. Key Laboratory of Light Industry, Jiangnan University, Wuxi, Jiangsu, China

    Juan Zhang & Dinghui Wu

Authors
  1. Juan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dinghui Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dinghui Wu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Wu, D. A dual-threshold state analysis and fault location method for power system based on random matrix theory. Nonlinear Dyn 107, 2469–2483 (2022). https://doi.org/10.1007/s11071-021-07056-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-021-07056-0

Keywords

Search

Navigation