Energy Systems

, Volume 2, Issue 1, pp 45–65 | Cite as

Observability enhancement by optimal PMU placement considering random power system outages

  • F. Aminifar
  • M. Fotuhi-Firuzabad
  • M. Shahidehpour
  • A. Khodaei
Original Paper

Abstract

This paper enhances the observability of power networks by taking into consideration random component outages. The architecture of wide-area measurement system (WAMS) is analyzed in order to identify components that would affect the network observability. An iterative framework is devised to calculate a bus index in power networks equipped with phasor measurement units (PMUs) and conventional measurements. The average of bus indices represents a system index which provides an overall insight on the power network observability. The system index is utilized as a criterion to distinguish among multiple optimal PMU placements. Conventional bus injection and line flow measurements and the effect of zero-injection buses are considered in the proposed model. The numerical analyses are carried out for the proposed model and the results are discussed in detail.

Keywords

Phasor measurement units Wide-area measurement System observability analysis Probabilistic assessment 

Nomenclature

APO

Average probability of observability

Aij

Probability of observability of bus i with PMU at bus j

\(A_{ij}^{\mathit{Cm}}\)

Availability of current measurement at line ij

\(A_{ij}^{\mathit{CT}}\)

Availability of CT at line ij

\(A_{ij}^{\mathit{FM}}\)

Availability of conventional flow measurement at line ij

\(A_{i}^{\mathit{{IM}}}\)

Availability of conventional injection measurement at bus i

\(A_{ij}^{\mathit{Line}}\)

Availability of line ij

\(A_{i}^{\mathit{Link}}\)

Availability of communication link for PMU at bus i

\(A_{i}^{\mathit{PMU}}\)

Availability of PMU at bus i

\(A_{i}^{\mathit{PT}}\)

Availability of PT at bus i

\(A_{i}^{\mathit{Vm}}\)

Availability of voltage measurement at bus i

aij

Binary connectivity parameter between buses i and j

bij

Binary parameter of flow measurement at line ij

Di

Difference of POi in the last two iterations

fi

Observability function of bus i

I

Set of buses

i,j,k

Indices of bus

Nb

Number of buses

POi

Probability of observability of bus i

ui

Binary decision variable that is equal to one if PMU is installed at bus i and zero otherwise

xij

Binary variable; 1 denotes bus i is made observable through the observability of bus j and flow measurements on line ij

\(\bar{x}_{ij}\)

Auxiliary binary variable; 1 when xij=1 and uj=0

yij

Binary variable; 1 denotes bus i is made observable through the zero-injection effect of bus j

\(\bar{y}_{ij}\)

Auxiliary binary variable; 1 when yij=1, xij=0, and uj=0

zi

Binary parameter of zero-injection bus i or the injection measurement at bus i

γ

System observability redundancy index (SORI)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Shahidehpour, M., Tinney, W.F., Fu, Y.: Impact of security on power systems operation. Proc. IEEE 93(11), 2013–2025 (2005) CrossRefGoogle Scholar
  2. 2.
    Dua, D., Dambhare, S., Gajbhiye, R.K., Soman, S.A.: Optimal multistage scheduling of PMU placement: an ILP approach. IEEE Trans. Power Deliv. 23(4), 1812–1820 (2008) CrossRefGoogle Scholar
  3. 3.
    Karlsson, D., Hemmingsson, M., Lindahl, S.: Wide area system monitoring and control—terminology, phenomena, and solution implementation strategies. IEEE Power Energy 2(5), 68–76 (2004) CrossRefGoogle Scholar
  4. 4.
    Marın, F.J., Garcıa-Lagos, F., Joya, G., Sandoval, F.: Genetic algorithms for optimal placement of phasor measurement units in electric networks. Electron. Lett. 39(19), 1403–1405 (2003) CrossRefGoogle Scholar
  5. 5.
    Milosevic, B., Begovic, M.: Nondominated sorting genetic algorithm for optimal phasor measurement placement. IEEE Trans. Power Syst. 18(1), 69–75 (2003) CrossRefGoogle Scholar
  6. 6.
    Baldwin, T.L., Mili, L., Boisen, M.B., Adapa, R.: Power system observability with minimal phasor measurement placement. IEEE Trans. Power Syst. 8(2), 707–715 (1993) CrossRefGoogle Scholar
  7. 7.
    Peng, J., Sun, Y., Wang, H.F.: Optimal PMU placement for full network observability using tabu search algorithm. Electr. Power Syst. Res. 28(4), 223–231 (2006) CrossRefGoogle Scholar
  8. 8.
    Cho, K.S., Shin, J.R., Hyun, S.H.: Optimal placement of phasor measurement units with GPS receiver. In: Proc. IEEE Power Eng. Soc. Winter Meeting, vol. 1, pp. 258–262 (2001) Google Scholar
  9. 9.
    Hajian, M., Ranjbar, A.M., Amraee, T., Shirani, A.R.: Optimal placement of phasor measurement units: particle swarm optimization approach. In: Int. Conf. Intel. Syst. Appl. Power Syst, pp. 1–6 (2007) CrossRefGoogle Scholar
  10. 10.
    Aminifar, F., Lucas, C., Khodaei, A., Fotuhi-Firuzabad, M.: Optimal placement of phasor measurement units using immunity genetic algorithm. IEEE Trans. Power Deliv. 24(3), 1014–1020 (2009) CrossRefGoogle Scholar
  11. 11.
    Xu, B., Abur, A.: Observability analysis and measurement placement for system with PMUs. In: Proc. IEEE Power Syst. Conf. Expo., vol. 2, pp. 943–946 (2004) Google Scholar
  12. 12.
    Chakrabarti, S., Kyriakides, E., Eliades, D.G.: Placement of synchronized measurements for power system observability. IEEE Trans. Power Deliv. 24(1), 12–19 (2009) CrossRefGoogle Scholar
  13. 13.
    Chakrabarti, S., Eliades, D., Kyriakides, E., Albu, M.: Measurement uncertainty considerations in optimal sensor deployment for state estimation. In: Int. Symp. Intel. Sign. Proc., pp. 1–6 (2007) CrossRefGoogle Scholar
  14. 14.
    Gou, B.: Optimal placement of PMUs by integer linear programming. IEEE Trans. Power Syst. 23(3), 525–1526 (2008) MathSciNetGoogle Scholar
  15. 15.
    Gou, B.: Generalized integer linear programming formulation for optimal PMU placement. IEEE Trans. Power Syst. 23(3), 1099–1104 (2008) MathSciNetCrossRefGoogle Scholar
  16. 16.
    Aminifar, F., Khodaei, A., Fotuhi-Firuzabad, M., Shahidehpour, M.: Contingency-constrained PMU placement in power networks. IEEE Trans. Power Syst. 25(1), 516–523 (2010) CrossRefGoogle Scholar
  17. 17.
    Peng, C., Xu, X.: A hybrid algorithm based on BPSO and immune mechanism for PMU optimization placement. In: World Congress Intel. Control Automation, pp. 7036–7040 (2008) CrossRefGoogle Scholar
  18. 18.
    Rakpenthai, C., Premrudeepreechacharn, S., Uatrongjit, S., Watson, N.R.: An optimal PMU placement method against measurement loss and branch outage. IEEE Trans. Power Syst. 22(1), 101–107 (2007) Google Scholar
  19. 19.
    Chakrabarti, S., Kyriakides, E.: Optimal placement of phasor measurement units for power system observability. IEEE Trans. Power Syst. 23(3), 1433–1440 (2008) CrossRefGoogle Scholar
  20. 20.
    Zima, M., Larsson, M., Korba, P., Rehtanz, C., Andersson, G.: Design aspects for wide-area monitoring and control systems. Proc. IEEE 93(5), 970–996 (2005) CrossRefGoogle Scholar
  21. 21.
    Wang, Y., Li, W., Lu, J., Liu, H.: Evaluating multiple reliability indices of regional networks in wide area measurement system. Electr. Power Syst. Res. 79(10), 1353–1359 (2009) CrossRefGoogle Scholar
  22. 22.
    Billinton, R., Allan, R.: Reliability Evaluation of Engineering Systems: Concepts and Technique, 2nd edn. Plenum, New York (1994) Google Scholar
  23. 23.
    Phadke, A.G., Thorp, J.S.: Synchronized Phasor Measurements and Their Applications. Springer, New York (2008) CrossRefGoogle Scholar
  24. 24.
    Phadke, A.G., Thorp, J.S.: History and applications of phasor measurements. In: Power Syst. Conf. Expo., pp. 331–335 (2006) CrossRefGoogle Scholar
  25. 25.
    Aminifar, F., Bagheri-Shouraki, S., Fotuhi-Firuzabad, M., Shahidehpour, M.: Reliability modeling of PMUs using fuzzy sets. IEEE Trans. Power Deliv. 25(4), 2384–2391 (2010) CrossRefGoogle Scholar
  26. 26.
    Rice, M.J., Heydt, G.T.: The measurement outage table and state estimation. IEEE Trans. Power Syst. 23(2), 353–360 (2008) CrossRefGoogle Scholar
  27. 27.
    Performance Requirements Task Team (PRTT): Performance Requirements Part II Targeted Applications: State Estimation. Eastern Interconnection Phasor Project (2005) Google Scholar
  28. 28.
    Chen, J., Abur, A.: Placement of PMUs to enable bad data detection in state estimation. IEEE Trans. Power Syst. 21(4), 1608–1615 (2006) CrossRefGoogle Scholar
  29. 29.

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • F. Aminifar
    • 1
  • M. Fotuhi-Firuzabad
    • 1
  • M. Shahidehpour
    • 2
  • A. Khodaei
    • 2
  1. 1.Electrical Engineering DepartmentSharif University of TechnologyTehranIran
  2. 2.Electrical and Computer Engineering DepartmentIllinois Institute of TechnologyChicagoUSA

Personalised recommendations