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A Value-at-Risk Based Approach for PMU Placement in Distribution Systems

Min Liu*
College of Electrical Engineering, Guizhou University, Guiyang, 550025, China
* Corresponding Author: Min Liu. Email:

Energy Engineering 2022, 119(2), 781-800.

Received 13 April 2021; Accepted 23 August 2021; Issue published 24 January 2022


With the application of phasor measurement units (PMU) in the distribution system, it is expected that the performance of the distribution system state estimation can be improved obviously with the PMU measurements into consideration. How to appropriately place the PMUs in the distribution is therefore become an important issue due to the economical consideration. According to the concept of efficient frontier, a value-at-risk based approach is proposed to make optimal placement of PMU taking account of the uncertainty of measure errors, statistical characteristics of the pseudo measurements, and reliability of the measurement instrument. The reasonability and feasibility of the proposed model is illustrated with 12-node system and IEEE-33 node system. Simulation results indicated that uncertainties of measurement error and instrument fault result in more PMU to be installed, and measurement uncertainty is the main affect factor unless the fault rate of PMU is quite high.


Distribution system state estimation (DSSE); efficient frontier; meter placement; phasor measurement units (PMU); value at risk (VaR); weighted least square (WLS)

Cite This Article

Liu, M. (2022). A Value-at-Risk Based Approach for PMU Placement in Distribution Systems. Energy Engineering, 119(2), 781–800.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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