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Stability Analysis of STATCOM in Distribution Networks

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Static Compensators (STATCOMs) in Power Systems

Abstract

This chapter presents the stability analysis based on bifurcation theory of the distribution static compensator (DSTATCOM) operating both in current control mode as in voltage control mode. The bifurcation analysis allows delimiting the operating zones of nonlinear power systems and hence the computation of these boundaries is of interest for practical design and planning purposes. Suitable mathematical representations of the DSTATCOM are proposed to carry out the bifurcation analyses efficiently. The stability regions in the Thevenin equivalent plane are computed for different power factors at the Point of Common Coupling (PCC). In addition, the stability regions in the control gain space are computed, and the DC capacitor and AC capacitor impact on the stability are analyzed in detail. It is shown through bifurcation analysis that the loss of stability in the DSTATCOM is in general due to the emergence of oscillatory dynamics. The observations are verified through detailed simulation studies.

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References

  1. Parker TS, Chua LO, Parker TS (1989) Practical numerical algorithms for chaotic systems. Springer, Reissue

    Book  MATH  Google Scholar 

  2. Wan C, Huang M, Tse CK, Wong SC, Ruan X (2013) Nonlinear behavior and instability in a three-phase boost rectifier connected to a nonideal power grid with an interacting load. IEEE Trans Power Electron 28(7):3255–3265

    Article  Google Scholar 

  3. Deivasundari P, Uma G, Santhi R (2014) Experimental verification of Hopf bifurcation in pulse-width modulated inverter fed cage induction motor drive system. IET Power Electron 7(2):340–349

    Article  Google Scholar 

  4. Ben Amar F, Dhifaoui R (2011) Study of the periodic ferroresonance in the electrical power networks by bifurcation diagrams. Int J Electr Power Energy Syst 33(1):61–85

    Article  Google Scholar 

  5. Nayfeh AH, Balachandran B (1995) Applied nonlinear dynamics: analytical, computational and experimental methods. Wiley, New York

    Book  MATH  Google Scholar 

  6. Kopell N, Washburn RB (1982) Chaotic motions in the two-degree-of-freedom swing equations. IEEE Trans Circuits Syst 29(11):738–746

    Article  MATH  MathSciNet  Google Scholar 

  7. Grijalva S (2012) Individual branch and path necessary conditions for saddle-node bifurcation voltage collapse. IEEE Trans Power Syst 27(1):12–19

    Article  Google Scholar 

  8. Alomari MM, Zhu JG (2011) Bifurcation control of subsynchronous resonance using TCSC. Commun Nonlinear Sci Numer Simul 16(5):2363–2370

    Article  Google Scholar 

  9. Wan C, Huang M, Tse CK, Wong S-C, Ruan X (2013) Nonlinear behavior and instability in a three-phase boost rectifier connected to a nonideal power grid with an interacting load. IEEE Trans Power Electron 28(7):3255–3265

    Article  Google Scholar 

  10. Segundo-Ramírez J, Medina A, Ghosh A, Ledwich G (2012) Stability boundary analysis of the dynamic voltage restorer in weak systems with dynamic loads. Int J Circuit Theory Appl 40(6):551–569

    Article  Google Scholar 

  11. Lee S-H, Park J-K, Lee B-H (2001) A study on the nonlinear controller to prevent unstable Hopf bifurcation. In: Power engineering society summer meeting, vol 2, pp 978–982

    Google Scholar 

  12. Canizares CA (1995) On bifurcations, voltage collapse and load modeling. IEEE Trans Power Syst 10(1):512–522

    Article  Google Scholar 

  13. Pai MA, Sauer PW, Lesieutre BC, Adapa R (1995) Structural stability in power systems-effect of load models. IEEE Trans Power Syst 10(2):609–615

    Article  Google Scholar 

  14. Liu C-C, Vu KT (1989) Analysis of tap-changer dynamics and construction of voltage stability regions. IEEE Trans Circuits Syst 36(4):575–590

    Article  Google Scholar 

  15. Kamarposhti MA, Lesani H (2011) Effects of STATCOM, TCSC, SSSC and UPFC on static voltage stability. Electron Eng 93(1):33–42

    Article  Google Scholar 

  16. Mithulananthan N, Canizares CA, Reeve J, Rogers GJ (2003) Comparison of PSS, SVC, and STATCOM controllers for damping power system oscillations. IEEE Trans Power Syst 18(2):786–792

    Article  Google Scholar 

  17. Segundo-Ramírez J, Medina A, Ghosh A, Ledwich G (2010) Non-linear oscillations assessment of the distribution static compensator operating in voltage control mode. Electron Power Compon Syst 38(12):1317–1337

    Article  Google Scholar 

  18. Segundo-Ramirez J, Medina A, Ghosh A, Ledwich G (2009) Stability analysis based on bifurcation theory of the DSTATCOM operating in current control mode. IEEE Trans Power Deliv 24(3):1670–1678

    Article  Google Scholar 

  19. Tse C (2003) Complex behavior of switching power converters. CRC Press, Boca Raton, FL

    Book  Google Scholar 

  20. Banerjee S, Verghese GC (2001) Nonlinear phenomena in power electronics: attractors, bifurcations, chaos, and nonlinear control. IEEE Press, New York

    Book  Google Scholar 

  21. Ghosh A (2002) Power quality enhancement using custom power devices. Kluwer Academic Publishers, Dordrecht

    Book  Google Scholar 

  22. Acha E, Semlyen A, Rajakovic N (1990) A harmonic domain computational package for nonlinear problems and its application to electric arcs. IEEE Trans Power Deliv 5(3):1390–1397

    Article  Google Scholar 

  23. Ghosh A, Ledwich G (2003) Load compensating DSTATCOM in weak AC systems. IEEE Trans Power Deliv 18(4):1302–1309

    Article  Google Scholar 

  24. Hingorani NG, Gyugyi L (2000) Understanding FACTS: concepts and technology of flexible AC transmission systems. Wiley, New York

    Google Scholar 

  25. Mishra MK, Ghosh A, Joshi A (2003) Load compensation for systems with non-stiff source using state feedback. Electron Power Syst Res 67(1):35–44

    Article  Google Scholar 

  26. Ghosh A, Joshi A (2000) A new approach to load balancing and power factor correction in power distribution system. IEEE Trans Power Deliv 15(1):417–422

    Article  Google Scholar 

  27. Vlach J, Wojciechowski JM, Opal A (1995) Analysis of nonlinear networks with inconsistent initial conditions. IEEE Trans Circuits Syst Fundam Theory Appl 42(4):195–200

    Article  MATH  Google Scholar 

  28. Mohan N, Undeland TM, Robbins WP (2002) Power electronics: converters, applications, and design, 3rd edn. Wiley, Hoboken

    Google Scholar 

  29. Mishra MK, Ghosh A, Joshi A (2003) Operation of a DSTATCOM in voltage control mode. IEEE Trans Power Deliv 18(1):258–264

    Article  Google Scholar 

  30. Ermentrout B (2002) simulating, analyzing, and animating dynamical systems: a guide to XPPAUT for researchers and students. SIAM, Philadelphia

    Book  Google Scholar 

  31. Segundo-Ramírez J, Medína A (2010) Computation of the steady-state solution of nonlinear power systems by extrapolation to the limit cycle using a discrete exponential expansion method. Int J Nonlinear Sci Numer Simul 11(8):655–660

    Google Scholar 

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Correspondence to Juan Segundo-Ramírez .

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Segundo-Ramírez, J., Ríos, A.M., Ledwich, G. (2015). Stability Analysis of STATCOM in Distribution Networks. In: Shahnia, F., Rajakaruna, S., Ghosh, A. (eds) Static Compensators (STATCOMs) in Power Systems. Power Systems. Springer, Singapore. https://doi.org/10.1007/978-981-287-281-4_20

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  • DOI: https://doi.org/10.1007/978-981-287-281-4_20

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-287-280-7

  • Online ISBN: 978-981-287-281-4

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