Advertisement

Decomposition of Post-Fault Transients on Power Lines and Analytical Solution of Its Stationary Component

  • Aoyu Lei
  • Xinzhou Dong
Original Article

Abstract

Based on the background of power lines with fault, the sinusoidal steady-state response can be easily analytically solved. However, the transient response cannot be solved for a complex network due to non-determinacy of network topology. The problem of the analytical solution of post-fault transients on faulted power lines was studied by decomposing post-fault transients into transient non-stationary component (TNC) and transient stationary component (TSC). TNC reflects mutational changes or wave-fronts in post-fault transients, whereas TSC is a uniformly continuous and low-frequency signal because it is the rest of post-fault transients whose mutational changes are ‘removed’. Then, the approximate analytical solution of TSC was deduced by building an equivalent circuit model based on its physical interpretation. At last, the accurate numerical solution of TSC was obtained by EMTP simulation and compared with its analytical solution. The errors are extremely small.

Keywords

Telegraph equation Traveling waves Power lines Fault information Analytical solution 

Notes

Acknowledgements

This work was supported by National Key Research and Develop-ment Plan of China (Grant No. 2016YFB0900600).

References

  1. 1.
    Bird JO (2003) “44 transmission lines”, in electrical circuit theory and technology, 2nd edn. Newnes, Oxford, pp 869–900Google Scholar
  2. 2.
    Magnusson PC, Weisshaar A, Tripathi VK et al (2000) Transmission lines and wave propagation, vol 4. CRC Press, Boca Raton, pp 1–10Google Scholar
  3. 3.
    Bergen AR, Vittal V (2005) Transmission-line modeling in power systems analysis, 2nd edn. China Machine Press, Beijing, pp 90–126Google Scholar
  4. 4.
    Courant R, Hilbert D (2008) III differential equations of higher order. Linear differential equations with constant coefficients. In: Methods of mathematical physics: partial differential equations, vol. 2, Wiley Online Library, pp 180–196Google Scholar
  5. 5.
    Smith PW (2014) 2.4 Transient transmission line response. In: Transient electronics: pulsed circuit technology. New York, Wiley, pp 58–70Google Scholar
  6. 6.
    Chang FY (1970) Transient analysis of lossless coupled transmission lines in a nonhomogeneous dielectric medium. IEEE Trans Microwave Theory and Techniques 18(9):616–626CrossRefGoogle Scholar
  7. 7.
    Tai CT (1978) Transients on lossless terminated transmission lines. IEEE Trans. Antennas Propagation 26(4):556–561CrossRefGoogle Scholar
  8. 8.
    Hohammadian AH, Tai CT (1984) A general method of transient analysis for lossless transmission lines and its analytical solution to time-varying resistive terminations. IEEE Trans Antennas Propagation 32(3):309–312CrossRefGoogle Scholar
  9. 9.
    Hoefer WJR (1985) The transmission-line matrix method—theory and applications. IEEE Trans Microwave Theory Techniques MTT-33(10):882–893CrossRefGoogle Scholar
  10. 10.
    Roden JA, Paul CR, Smith WT et al (1996) Finite-difference, time-domain analysis of lossy transmission lines. IEEE Trans Electromagn Compatibility 38(1):15–24CrossRefGoogle Scholar
  11. 11.
    Zhou TD, Dvorak SL, Prince JL (2003) Lossy transmission line simulation based on closed-form triangle impulse responses. IEEE Trans Comput Aided Des Integr Circuits Syst 22(6):748–755CrossRefGoogle Scholar
  12. 12.
    Narendra K, Sanjiv K (2010) “7 traveling waves”, in power system analysis. Asian Books Pvt Ltd, Delhi, pp 250–278Google Scholar
  13. 13.
    Bewley LV (1931) Traveling waves on transmission systems. Am Inst Electr Eng, Trans 50(2):532–550CrossRefzbMATHGoogle Scholar
  14. 14.
    Zhang JF, Smith JS, Wu QH (2006) Morphological undecimated wavelet decomposition for fault location on power transmission lines. IEEE Trans Power Deliv Circuits Syst I: Regular Papers 53(6):1359–1402Google Scholar
  15. 15.
    Lopes FV, Silva KM, Costa FB et al (2014) Real-time traveling-wave-based fault location using two-terminal unsynchronized data. IEEE Trans Power Delivery 30(3):1067–1076CrossRefGoogle Scholar
  16. 16.
    Dong XZ, Ge YZ, He JL (2005) Surge impedance relay. IEEE Trans Power Delivery 20(2):1247–1256CrossRefGoogle Scholar
  17. 17.
    Hashemi SM, Hagh MT, Seyedi H (2013) Transmission-line protection: a directional comparison scheme using the average of superimposed components. IEEE Trans Power Delivery 28(2):955–964CrossRefGoogle Scholar
  18. 18.
    Kitai R (1952) Theory of the impulse response of receivers: application of heaviside operators and the Duhamel integral. Proc IEEE—Part IV: Inst Monogr 99(4):279–288Google Scholar
  19. 19.
    Ren L, Dong XZ, Shi SX et al (2014) A novel energy ratio direction relay based on equivalent traveling wave process. In: Developments in power system protection (DPSP 2014), 12th IET International Conference on, CopenhagenGoogle Scholar
  20. 20.
    Suonan JL, Liu K, Song GB (2011) A novel UHV/EHV transmission-line pilot protection based on fault component integrated impedance. IEEE Trans Power Deliv 26(1):127–134CrossRefGoogle Scholar
  21. 21.
    Rodgers JL, Nicewander WA (1988) Thirteen ways to look at the correlation coefficient. Am Stat 42(1):59–66CrossRefGoogle Scholar

Copyright information

© The Korean Institute of Electrical Engineers 2019

Authors and Affiliations

  1. 1.State Key Laboratory on Power System, Department of Electrical EngineeringTsinghua UniversityBeijingChina

Personalised recommendations