Abstract
Phasor measurement units (PMUs) play an important role in power system operations. They provide synchronized phasor measurement of voltage and current for preservation and control of electrical power networks. In this work, depth-of-one (DOU1) and depth-of-two (DOU2) unobservability has been considered for optimal PMU placement (OPP) problem. Further, cases ignoring and considering zero injection buses are also taken into account for minimizing the PMUs locations. The influence of DOU1 and DOU2 consisting of the single PMUs outage have also been taken into consideration. Furthermore, this article also proposed the effect of single branch outage on OPP problem. Moreover, to show the scalability of the proposed approach, both single PMU outage and branch outage are considered together. Thus, the critical branch based on line stability index utilizing load flow measurement is determined. Then, binary integer linear programming approach has been developed in this paper to determine the strategic locations of PMUs considering various contingencies. The efficacy and robustness of the proposed methodology are confirmed by implementing on standard IEEE test systems and outcomes thereby authorizing the reliability of the proposed approach. Obtained results have been compared with the standard approaches published in the referred journals, and the results achieved by the proposed methodology outperform the other comparative approaches; thus, the proposed methodology, successfully, accomplishes complete observability of the power networks.
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Abbreviations
- L ik :
-
Line stability index of the transmission lines
- i, k :
-
Indices of bus
- Q k :
-
Receiving end reactive power
- X :
-
Line reactance
- V i :
-
Voltage at sending end
- θ :
-
Branch impedance angle
- δ :
-
Phase angle difference between sending and receiving end voltages
- B 1, B 2, …, B n :
-
Buses
- L 1, L 2, …, L n :
-
Branches
- Y :
-
Binary decision variable vector that is equal to 1 if PMU is placed at bus i and 0 otherwise
- H :
-
Transformation matrix that may be modified according to the contingency cases considered in OPP problem
- A PMU :
-
Binary connectivity matrix
- B PMU :
-
Column vector
- A con :
-
Transformation matrix
- B con :
-
Redundancy matrix
- C 1 :
-
Binary connectivity matrix of line-to-node
- C 2 :
-
Binary connectivity matrix of three buses connecting together
- P R1 :
-
Permutation matrix which contains only those lines that are not connected with zero injection buses (ZIBs)
- P R2 :
-
Permutation matrix which eliminates those lines that are connected with ZIBs
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Babu, R., Bhattacharyya, B. An Approach for Optimal Placement of Phasor Measurement Unit for Power Network Observability Considering Various Contingencies. Iran J Sci Technol Trans Electr Eng 42, 161–183 (2018). https://doi.org/10.1007/s40998-018-0063-7
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DOI: https://doi.org/10.1007/s40998-018-0063-7