Energy Systems

, Volume 2, Issue 1, pp 45–65

Observability enhancement by optimal PMU placement considering random power system outages

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

DOI: 10.1007/s12667-011-0025-x

Cite this article as:
Aminifar, F., Fotuhi-Firuzabad, M., Shahidehpour, M. et al. Energy Syst (2011) 2: 45. doi:10.1007/s12667-011-0025-x


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.


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



Average probability of observability


Probability of observability of bus i with PMU at bus j


Availability of current measurement at line ij


Availability of CT at line ij


Availability of conventional flow measurement at line ij


Availability of conventional injection measurement at bus i


Availability of line ij


Availability of communication link for PMU at bus i


Availability of PMU at bus i


Availability of PT at bus i


Availability of voltage measurement at bus i


Binary connectivity parameter between buses i and j


Binary parameter of flow measurement at line ij


Difference of POi in the last two iterations


Observability function of bus i


Set of buses


Indices of bus


Number of buses


Probability of observability of bus i


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


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


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


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


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


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


System observability redundancy index (SORI)


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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

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