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Interval stability analysis of power systems with wind turbine based on three-mass shaft model

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Abstract

Due to the limitation of environment, technology and information, the parameters of power system are uncertain, which brings great challenges to the study of power system security and stability. In order to analyze the stability of power systems with such constraints, we can obtain the third-order mathematical model of the asynchronous wind turbine, based on the three-mass asynchronous wind turbine generator. The three-mass asynchronous wind turbine generator consists of a wind model, a shafting model and an asynchronous generator. According to various uncertainties of the system, each parameter is an uncertain value varying from a certain range. Based on the mathematical model and the state equations, the small signal interval model with multiple interval parameters is established considering the method of small signal stability analysis of power systems. The interval stability theorem of the small signal interval system of the power system with asynchronous wind turbines is established to analyze the asynchronous wind power system with one machine infinite bus (OMIB) system as an example. The stable result are judged by the change of the value range of multiple operating parameters of the system and verified by numerical simulation.

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References

  1. Liu X, Han X, Liu H, Wang P. With wind power system small signal stability analysis [R]. Electric and Power Engineering Institute of TYUT, Taiyuan 030024

  2. Liu G, Sun G, Li Y, Wen A (2013) Small signal stability analysis of power system with wind farm based on model analysis [C]. In: The 29th annual academic conference of power systems and automation in China’s Higher Education Institutions, Yichang, Hubei: Three Gorges University, 2013

  3. Zhou M, Yuan B, Zhang X, Li G (2014) Stochastic small signal stability analysis of wind power integrated power systems based on stochastic differential equations. Proc CSEE 34(10):1575–1582

    Google Scholar 

  4. Zhang JY, Ju P, Yu YP et al (2012) Responses and stability of power system under small Gauss type ran- dom excitation. Sci China Tech Sci 55:1873–1880. https://doi.org/10.1007/s11431-012-4893-7

    Article  Google Scholar 

  5. Guan H, Chi Y, Dai H, Yang Y (2008) Small signal stability and control of wind turbine with asynchronous generator integration into power system. Autom Electr Power Syst 32(4):54–58

    Google Scholar 

  6. Zertek A, Verbic G, Pantos M (2012) Optimized control approach for frequency-control contribution of variable speed wind turbines. IET Renew Power Gener 6(1):17–23

    Article  Google Scholar 

  7. Kang L, Shi L, Ni Y et al (2011) Small signal stability analysis with penetration of grid-connect- ed wind farm of PMSG type [C]. In: The international conference on advanced power system automation and protection, pp 147–151

  8. Liao XX, Mao X (2000) Exponential stability of stochastic delay interval systems [J]. IEEE Syst Control Lett 40(11):171–181

    Article  MathSciNet  Google Scholar 

  9. Changchun H, Xinping G, Peng S (2004) Robust stabilization of a class of nonlinear time-delay systems. Appl Math Comput 155(3):737–752

    MathSciNet  MATH  Google Scholar 

  10. Rakpenthai C, Uatrongjit S, Premrudeepreechacharn S (2012) State estimation of power system consideri- ng network parameter uncertainty based on parametric interval linear systems. IEEE Trans Power Syst 27(1):305–313

    Article  Google Scholar 

  11. Xie D, Lu Z, Li G, Liu Z (2015) Interval stability analysis of small signal for a class of power system with asynchronous wind turbine generators. Proc CSEE 35(3):609–614

    Google Scholar 

  12. Xie D, Feng J, Lou Y, Yang M, Wang X (2013) Small-signal modelling and modal analysis of DFIG-based wind turbine based on three-mass shaft model. Proc CSEE 33(Supplement):21–29

    Google Scholar 

  13. Wang H, Pan X, Ju P (2016) Parameter identification of three⁃mass drive-train system for fixed-speed wind turbine generator based on PSO algorithm. J Hohai Univ (Natl Sci ) 44(1):18

    Google Scholar 

  14. Ding M, Wang D, Han P, He J, Hu T (2013) Research on generalized modeling method of wind power drive-train system. Power Syst Technol 37(10):2881–2887

    Google Scholar 

  15. Lou Y, Xie D, Feng J, Wang X, Yang M (2015) Small-signal modelling and modal analysis based on three-mass shaft model for stall wind turbine. Electric Power Autom Equip 35(8)

  16. Wang B, Zhu Q (2018) Stability analysis of semi-Markov switched stochastic systems. Automatica 94:72–80

    Article  MathSciNet  Google Scholar 

  17. Zhu Quanxin (2017) Razumikhin-type theorem for stochastic functional differential equations with Lévy noise and Markov switching. Int J Control 90(8):1703–1712

    Article  Google Scholar 

  18. Wang B, Zhu Q (2017) Stability analysis of Markov switched stochastic differential equations with both stable and unstable subsystems. Syst Control Lett 105:55–61

    Article  MathSciNet  Google Scholar 

  19. Ma ZE, Zhou YC (2005) Qualitative and stability for ordinary differential equations. Science Press, Beijing

    Google Scholar 

Download references

Acknowledgements

This work was supported in part by National Key R&D Program of China (2017YFB0902500) and Science and Technology Project of State Grid Corporation of China: The key Technology of Environment-Friendly Gas-Insulated Transmission Line (GIL).

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Authors and Affiliations

  1. School of Mathematics and Physical Science, North China Electric Power University, Beijing, 102206, China

    Zhanhui Lu, Fanting Xu, Junqiang Wei & Fangcheng Lv

  2. State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources, North China Electric Power University, Beijing, 102206, China

    Zhanhui Lu

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  1. Zhanhui Lu
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  2. Fanting Xu
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Correspondence to Zhanhui Lu.

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Lu, Z., Xu, F., Wei, J. et al. Interval stability analysis of power systems with wind turbine based on three-mass shaft model. Int. J. Mach. Learn. & Cyber. 10, 3181–3187 (2019). https://doi.org/10.1007/s13042-019-01008-2

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  • DOI: https://doi.org/10.1007/s13042-019-01008-2

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