Skip to main content
SpringerLink
Log in

Static Analysis of Voltage Stability

  • Chapter
  • First Online:
Voltage Stability Analysis of Power System

Part of the book series: Power Systems ((POWSYS))

  • 621 Accesses

Abstract

The static analysis method of voltage stability is to capture the system state on different time sections along the time track. By assuming that the differential of the system state variables on the section is zero, the differential-difference-algebraic equations describing the nonlinear dynamic power system are simplified to pure algebraic equations. Since the early voltage instability accidents are mostly the medium and long-term voltage instability processes, which have a long time span and are usually caused by slow load growth or system output power transfer, the static analysis method has become the mainstream of voltage stability research for a long period of time.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Zhang Y, Zhou S, Wang L et al (2000) Dynamic element model and its implementation in static voltage stability analysis. Proc Chin Soc Electr Eng 20(3):66–70

    Google Scholar 

  2. Kundur P (2002) Power system stability and control. China Electric Power Press, Beijing

    Google Scholar 

  3. Taylor CW (2002) Power system voltage stability (trans Wang Weisheng). China Electric Power Press, Beijing

    Google Scholar 

  4. Zhou S, Zhu L, Guo X et al (2004) Voltage stability and control of power system. China Electric Power Press, Beijing

    Google Scholar 

  5. Ajjrapu V, Christy C (1992) The continuation power flow: a tool for steady state voltage stability analysis. IEEE Trans Power Syst 7(1):416–423

    Google Scholar 

  6. Chen H, Chen Z (1996) The application of power flow equation in the study of static voltage stability. J Shanghai Jiaotong Univ 30(9):69–74

    Google Scholar 

  7. Li Y, Zhang B, Sun H (2007) The safety constrained optimal power flow (I) theoretical analysis based on the nonlinear interior point method. Proc CSU-EPSA 31(19):7–13

    Google Scholar 

  8. Karmarkar NK (1984) A new polynomial time algorithm for linear programming. Combinatorica 4(4):373–395

    Article  MathSciNet  Google Scholar 

  9. Granville S, Mello JCO, Mello ACG (1996) Application of interior point methods to power flow unsolvability. IEEE Trans Power Syst 11(2):1096–1103

    Article  Google Scholar 

  10. Wei H, Sasaki H, Kubokawa J et al (1998) An interior point nonlinear programming for optimal power flow problems with a noval data structure. IEEE Trans Power Syst 13(3):870–877

    Article  Google Scholar 

  11. El-Bakry AS, Tapia RA, Tsuchiya T et al (1996) On the formulation and theory of the Newton interior point method for nonlinear programming. J Optim Theory Appl 89(3):507–541

    Article  MathSciNet  Google Scholar 

  12. Forsgren A, Gill PE, Wright MH (2002) Interior methods for nonlinear optimization. SIAM Rev 44(4):525–597

    Google Scholar 

  13. Guo R, Han Z, Wang Q (1999) Nonlinear programming model and algorithm for critical point of voltage collapse. Proc Chin Soc Electr Eng 19(4):14–17

    Google Scholar 

  14. Irisarri GD, Wang X, Tong J et al (1997) Maximum loadability of power systems using interior point non-linear optimization method. IEEE Trans Power Syst 12(1):162–172

    Article  Google Scholar 

  15. Wei H, Ding X (2002) The critical point algorithm of voltage stability based on modern interior point theory. Proc Chin Soc Electr Eng 22(3):27–31

    Google Scholar 

  16. Wang X, Li H, Li B (2007) Voltage stability evaluation of AC and DC system based on interior point method. Proc CSU-EPSA 19(6):72–77

    Google Scholar 

  17. Zhang M (2006) Research on voltage stability analysis of AC/DC hybrid system. Master's thesis, Sichuan University, Chengdu

    Google Scholar 

  18. Feng Z, Liu Q, Ni Y et al (1992) Voltage static stability analysis of multimachine power system—singular value decomposition method. Proc Chin Soc Electr Eng 12(3):10–19

    Google Scholar 

  19. Wu H, Li X, He Y et al (2009) Static voltage stability analysis based on singular value decomposition method considering static load characteristics. Sichuan Electr Power Technol 32(3):5–8

    Google Scholar 

  20. Li X, Wang X (2003) A fast voltage stability analysis method based on static equivalence and singular value decomposition. Proc Chin Soc Electr Eng 23(4):1–5

    Google Scholar 

  21. Liu F, Yao X (1999) The singular value decomposition method used to analyze the effect of secondary voltage control. Proc CSU-EPSA 23(18):1–4, 8

    Google Scholar 

  22. Chen M, Zhang B, Duan X (2006) Research on voltage stability weak nodes based on minimum singular value sensitivity. Power Syst Technol 30(24):36–39, 55

    Google Scholar 

  23. Xu Z, Luan Z (1997) Singular values and stability indexes for measuring node voltage stability. Proc CSU-EPSA 21(8):42–44

    Google Scholar 

  24. Gao B, Morison GK, Kundur P (1992) Voltage stability evaluation using modal analysis. IEEE Trans Power Syst 7(4):1529–1542

    Article  Google Scholar 

  25. Lof PA, Smed T, Andersson G et al (1992) Fast calculation of a voltage stability index. IEEE Trans Power Syst 7(1):54–64

    Article  Google Scholar 

  26. Verghese GC, Perez-Arriaga IJ, Schweppe FC (1982) Selective modal analysis with applications to electric power systems. IEEE Trans Power Appar Syst 101(9):3117–3125

    Google Scholar 

  27. Liu T, Song X, Tang Y et al (2010) Eigenvalue sensitivity method and its application in small disturbance stability analysis of power system. Power Syst Technol 34(4):82–87

    Google Scholar 

  28. Xi Y, Guo Y (1998) A voltage stability algorithm based on eigenstructure analysis. J Tsinghua Univ (Nat Sci) 38(3): 1–5

    Google Scholar 

  29. Zhang G, Yang J, Zhang J (2007) An improved eigenstructure analysis method for static voltage stability. Power Syst Technol 31(16):77–82

    Google Scholar 

  30. Tan D (1996) A practical calculation and analysis method for voltage stability of power system—brief introduction of eigenvalue analysis method for linear system. Power Syst Technol 20(6):61–62

    Google Scholar 

  31. Wu Z, Zhang Y (2001) Analysis of correspondence between eigenvalues and state variables of power system. Proc CSU-EPSA 25(10):23–26

    Google Scholar 

  32. Wu J, Zhang B, Chen G (2006) The voltage instability area of AC-DC system is determined by eigenvalue method. Relay 34(7):27–31

    Google Scholar 

  33. Nam HK, Kim YK, Shim KS et al (2000) A new eigen sensitivity theory of augmented matrix and its applications to power system stability analysis. IEEE Trans Power Syst 15(1):363–369

    Article  Google Scholar 

  34. Yuan J, Duan X, He Y et al (1997) Summary of voltage stability sensitivity analysis methods in power system. Power Syst Technol 21(9):7–10

    Google Scholar 

  35. Duan X, Zhang D (1997) Voltage stability sensitivity analysis methods in power system. Proc CSU-EPSA 21(4):9–12

    Google Scholar 

  36. Yu Y, Zeng Y, Jia H (2000) The sensitivity criterion of static voltage stability and the evaluation of criterion of dQL/dVL and dPL/dVL. Proc CSU-EPSA 12(3):1–4, 13

    Google Scholar 

  37. Luo J, Wu Z, Lian X et al (2010) A new method for calculating the sensitivity of voltage stability margin to line power. Proc CSU-EPSA 4:94–99

    Google Scholar 

  38. Long J, Zhou L, Fu K (2009) Voltage stability sensitivity analysis of power system with UPFC. J Guangxi Univ: Nat Sc 34(2):251–255

    Google Scholar 

  39. Zhang J, Sun Y (2007) Sensitivity analysis method for selecting emergency control location based on fragile cut set. Power Syst Technol 31(11):21–26

    Google Scholar 

  40. Cai G, Zhang Y, Yu T et al (2008) Static voltage stability preventive control based on the unified sensitivity method. High Voltage Technol 34(4):748–752

    Google Scholar 

  41. Jiang W, Wang C, Yu Y (2006) A new method for calculating the sensitivity of voltage stability margin to parameters. Proc Chin Soc Electr Eng 26(2):13–18

    Google Scholar 

  42. Wang J, Zhang Y, Wang C (2005) Power grid reactive power/voltage assessment method based on sensitivity analysis and optimal power flow. Power Syst Technol 29(10):65–69

    Google Scholar 

  43. Zhao H, Zhao Y (2008) Evaluation of power grid vulnerability region based on sensitivity technique. Power Syst Technol 32(14):54–58

    Google Scholar 

  44. Ma P, Cai X (2008) Sensitivity method of voltage stability margin evaluation for branch outage contingencies. Proc Chin Soc Electr Eng 28(1):18–22

    Google Scholar 

  45. Dobson I, Lu L (1993) New methods for computing a closest saddle node bifurcation and worst cast load power margin for voltage collapse. IEEE Trans Power Syst 8(3):905–913

    Article  Google Scholar 

  46. Canizares CA, Alvarado FL (1993) Point of collapse and continuation methods for large AC/DC systems. IEEE Trans Power Syst 8(1):1–8

    Article  Google Scholar 

  47. Lu J, Liu CW, Thorp JS (1995) New methods for computing a saddle-node bifurcation point for voltage stability analysis. IEEE Trans Power Syst 10(2):978–989

    Article  Google Scholar 

  48. Dobson I (1992) Observations on the geometry of saddle node bifurcation and voltage collapse in electrical power systems. IEEE Trans Circuits Syst I: Fundam Theory Appl 39(3):240–243

    Google Scholar 

  49. Alvarado F, Dobson I, Hu Y (1994) Computation of closest bifurcations in power system. IEEE Trans Power Syst 9(2):918–928

    Google Scholar 

  50. Zhao X, Zhang X, Su X (2008) Voltage stability studies and bifurcation theory in power systems. Trans China Electrotech Soc 23(2):87–95

    Google Scholar 

  51. Chiang HD, Jumeau RJ (1995) A more efficient formulation for computation of the maximum loading in electric power system. IEEE Trans Power Syst 10(2):635–646

    Google Scholar 

  52. Seydel R (1979) Numerical computation of branch points in nonlinear equations. Numer Math 33(3):339–352

    Article  MathSciNet  Google Scholar 

  53. Liu Y, Yan Z, Ni Y et al (2003) An auxiliary-variable-based direct method for computing quadratic turning bifurcation points of power flow equations. Proc Chin Soc Electr Eng 23(5):9–13

    Google Scholar 

  54. Zeng J, Han Z (1997) Direct computing method of voltage stability critical point. J Tsinghua Univ (Nat Sci) 37(SI):91–94

    Google Scholar 

  55. Ajjarapu V (1995) Application of bifurcation and continuation methods for the analysis of power system dynamics. In: Proceedings of 4th IEEE conference on control applications, Albany, pp 52–56

    Google Scholar 

  56. Jarjis J, Galiana FD (1981) Quantitative analysis of steady state stability in power networks. IEEE Trans Power Appar Syst 100(1):318–326

    Google Scholar 

  57. CIGRE Task Force 38.02.11 (1995) CIGRE technical brochure: indices predicting voltage collapse including dynamic phenomenon. Electra 159:135–147

    Google Scholar 

  58. Zhou S, Jiang Y, Zhu L (2001) Review on steady state voltage stability indices of power systems. Power Syst Technol 25(1):1–7

    Google Scholar 

  59. Kessel P, Glavitseh H (1986) Estimating the voltage stability of power system. IEEE Power Deliv PWRD-1(3):346–354

    Google Scholar 

  60. Tuan TQ, Fandlno J, Adjsaid N et al (1994) Emergency load shedding to avoid risk of voltage instability using indicators. IEEE Trans Power Syst 9(1):341–351

    Article  Google Scholar 

  61. Yu Y, Jia H, Yan X (19999) An improved local voltage stability index Li, which can trace saddle-node bifurcation exactly. Power Syst Technol 23(5):19–23

    Google Scholar 

  62. Yu Y, Wang C (1999) Theory and method of power system stability. Science Press, Beijing

    Google Scholar 

  63. Canizares C (1998) Voltage stability assessment, procedure and guides. IEEE/PES Power System Stability Subcommittee Special Publication

    Google Scholar 

  64. Nagao T, Tanaka K, Takenaka K (1997) Development of static and simulation programs for voltage stability studies of bulk power system. IEEE Trans Power Syst 12(1):273–281

    Google Scholar 

  65. Mohamed A, Jasmon GB (1995) A new clustering technique for power system voltage stability analysis. Electr Mach Power Syst 23(4):389–403

    Google Scholar 

  66. Sun X, Duan X, He Y (1998) Research on local safety index of load node voltage stability. Proc CSU-EPSA 22(9):61

    Google Scholar 

  67. Tiranuchit A, Thomas RJ (1988) A posturing strategy against voltage instability in electric power systems. IEEE Trans Power Syst 3(1):87–93

    Article  Google Scholar 

  68. Xu Z, Luan Z, Fan T et al (1997) Singular values and stability indexes for measuring node voltage stability. Proc CSU-EPSA 8:42–44

    Google Scholar 

  69. Tang Y, Sun H, Yi J et al (2009) Thevenin equivalent parameter tracking algorithm based on complete differential. Proc Chin Soc Electr Eng 29(13):48–53

    Google Scholar 

  70. Tang Y, Lin W, Sun H et al (2010) Analysis of voltage stability criteria considering load characteristics. Proc Chin Soc Electr Eng 30(16):12–18

    Google Scholar 

  71. Tang Y, He RM, Ju P et al (2010) Evaluation of dynamic characteristics and safety of electric power receiving-end system. Tsinghua University Press, Beijing

    Google Scholar 

  72. Berizzi A, Zeng YG, Marannino P et al (2000) A second order method for contingency severity assessment with respect to voltage collapse. IEEE Trans Power Syst 15(1):81–89

    Google Scholar 

  73. Zhang Y, Zhang J, Yuan S (2005) Improved continuation power flow algorithm for obtaining the limit of static voltage stability. Proc CSU-EPSA 17(2):21–25

    Google Scholar 

  74. Zhao J, Zhang B (2005) A study on the strategy for improving robustness of continuation power flow computation. Proc Chin Soc Electr Eng 25(22):7–11

    Google Scholar 

  75. Western Electricity Coordinating Council (2001) Summary of WECC voltage stability assessment methodology

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Power Grid Security and Energy Conservation, China Electric Power Research Institute, Beijing, China

    Yong Tang

Authors
  1. Yong Tang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yong Tang .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Science Press

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Tang, Y. (2021). Static Analysis of Voltage Stability. In: Voltage Stability Analysis of Power System. Power Systems. Springer, Singapore. https://doi.org/10.1007/978-981-16-1071-4_4

Download citation

  • DOI: https://doi.org/10.1007/978-981-16-1071-4_4

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-1070-7

  • Online ISBN: 978-981-16-1071-4

  • eBook Packages: EnergyEnergy (R0)

Publish with us

Policies and ethics

Search

Navigation