Skip to main content
SpringerLink
Log in

The mean square stability analysis of a stochastic dynamic model for electricity market

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

The mean square stability pertaining to a stochastic electricity market model is analyzed in this paper. Considering the random nature of demand elasticity, the stochastic electricity market model under small Gauss type random excitation has already been presented. Using the theory of stochastic differential equations, matrix theory and eigenvalue techniques, the sufficient conditions of the mean square stability for this electricity market model are provided and testified theoretically. The conclusions can judge the stability of the system by available data on demand elasticity. The obtained results are validated and illustrated by numerical examples.

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

Similar content being viewed by others

References

  1. Beavis B, Dobbs IM (1990) Optimisation and stability theory for economic analysis. Cambridge University Press, Cambridge, England

    Book  MATH  Google Scholar 

  2. Alvarado FL (1999) The stability of power system markets. IEEE Trans Power Syst 14(2):505–511

    Article  Google Scholar 

  3. Alvarado FL, Meng J, Mota WS, DeMarco CL (2004) Dynamic coupling between power markets and power system. In: Power Engineering Society Summer Meeting, IEEE, July

  4. Alvarado FL, Mota WS (1998) The role of energy imbalance management on power market stability. In: Proceedings of the 31st annual Hawaii international conference on system sciences HICSS, IEEE Computer Society 3

  5. Mota WS, Alvarado FL (2000) Power markets stability considering energy imbalance. IEEE international symposium on circuits and systems, Switzerland

  6. Nguyen DHM, Wong KP (2000) A general stability metric for competitive power markets. In: Electric utility deregulation and restructuring and power technologies

  7. Xue YS (2002) Interactions between power market stability and power system stability. Autom Electr Power Syst 26(21):1–6

    Google Scholar 

  8. Shang JC, Huang YH, Xia Q (2002) Research on electricity market theory and its applications. China Electric Power Press, Beijing

  9. Tang ZF, Tang GQ, Erkeng Y (2001) Power market dynamic analysis. Proc CESS 21(12):88–92

    Google Scholar 

  10. Hou YH, Wu FL (2006) Stability of electricity market with cyclic load demand. Proc CESS 26(24):12–17

    Google Scholar 

  11. Nutaro J, Protopopescu V (2009) The impact of market clearing time and price signal delay on the stability of electric power markets. IEEE Trans Power Syst 24(3):1337–1345

    Article  Google Scholar 

  12. Watts D, Alvarado FL (2003) The influence of futures markets on real time price stabilization in electricity markets. In: Proceedings of the 37th Hawaii international conference on system sciences (HICSS)

  13. Kodsi SKM (2005) Accounting for the effects of power system controllers and stability on power dispatch and electricity market prices. University of Waterloo

  14. Yang ZH, Liu YF, Tang Y, Wu FL (2005) Analysis of power market stability. Proc CSEE 25(2):1–5

    Google Scholar 

  15. Lu ZH, Li GY, Zhou M (2006) Study of electricity market stability model. IEE APSCOM, HongKong

    Google Scholar 

  16. Parinya P, Sangswang A, Kirtikara K, Chenvidhya D, Naetiladdanon S, Limsakul C (2014) A study of effects of stochastic wind power and load to power system stability using stochastic stability analysis method. Adv Mater Res 931:878–882

    Article  Google Scholar 

  17. Odun-Ayo T, Crow ML (2012) Structure-preserved power system transient stability using stochastic energy functions. IEEE Trans Power Syst 27(3):1450–1458

    Article  Google Scholar 

  18. Zhang JY, Ju P, Yu YP et al (2012) Responses and stability of power system under small Gauss type random excitation. Sci China Technol Sci 55(7):1873–1880

    Article  Google Scholar 

  19. Lu ZH, Wang WJ, Li GY, D Xie (2014) Electricity market stochastic dynamic model and its mean stability analysis. Math Probl Eng 2014:8. Article ID 207474. doi:10.1155/2014/207474

  20. Zhang BG, Zhao YZ (1998) Stochastic differential equations in science and engineering. Ocean Press, Beijing

    Google Scholar 

  21. Foss S, Konstantopoulos T (2004) An overview of some stochastic stability methods. J Oper Res 47(4):275–303

    MathSciNet  MATH  Google Scholar 

  22. Mahmed H (2009) Euler–Maruyama numerical solution of some stochastic functional differential equations. Int J Appl Math Comput 1(2):67

    Google Scholar 

  23. Hu SG, Huang CM, Wu FK (2008) Stochastic differential equations. Science, Beijing

    Google Scholar 

  24. Hua G (2011) The norm of normal matrix and the convergence of its power series. J Chongqing Technol Bus Univ (Nat Sci Edn) 28(1):18–21

    Google Scholar 

  25. Feng LC, Li SM (2014) The pth moment asymptotic stability and exponential stability of stochastic functional differential equations with polynomial growth condition. Adv Differ Equ 2014:302

    Article  MATH  Google Scholar 

  26. Qiu QW, Liu W, Hu L (2014) Asymptotic moment boundedness of the stochastic theta method and its application for stochastic differential equations. Adv Differ Equ 2014:310

    Article  MathSciNet  MATH  Google Scholar 

  27. Syed Ali M, Balasubramaniam P, Zhu QX Stability of stochastic fuzzy BAM neural networks with discrete and distributed time-varying delays. Int J Mach Learn Cybern. doi:10.1007/s13042-014-0320-7

Download references

Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China (51190103, 61374080), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.

Author information

Authors and Affiliations

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

    Zhanhui Lu & Weijuan Wang

  2. School of Mathematical Sciences and Institute of Finance and Statistics, Nanjing Normal University, Nanjing, 210023, China

    Quanxin Zhu

  3. School of Electrical and Electronic Engineering, North China Electric Power University, Beijing, 102206, China

    Gengyin Li

Authors
  1. Zhanhui Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Weijuan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Quanxin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Gengyin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Quanxin Zhu.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, Z., Wang, W., Zhu, Q. et al. The mean square stability analysis of a stochastic dynamic model for electricity market. Int. J. Mach. Learn. & Cyber. 8, 1071–1079 (2017). https://doi.org/10.1007/s13042-015-0472-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-015-0472-0

Keywords

Search

Navigation