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Matrix Completion for Low-Observability Voltage Estimation

National Renewable Energy Laboratory

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Technology Marketing Summary

As the deployment of distributed energy resources continues to increase in power distribution networks, a corresponding need for accurate knowledge of the network current state (in terms of voltage phasors) is increasing for optimized decisions of operation.  Computation of such state estimations is complicated by the vast size of distribution network with only few observable measurements from a limited supply of phasor measurement units (PMUs) dispersed throughout the network.  Such a circumstance renders traditional state estimations to be exceptionally challenging, if not infeasible.  However, as the amount of information about the system grows in the alternate form of increased smart meter use, distributed generation sources, as well as other data sources, it is now becoming possible to use this wide variety of information to estimate the voltage phasors within a network.


To this end, researchers at NREL have developed an innovation for the estimation of voltage phasors in power systems under conditions of low observability. Traditional state estimation techniques require full observability (meaning the number of measurement points is not less than the number of buses); however, this is no longer realistic in today’s growing distribution systems.  To estimate voltage phasors within a network, NREL’s system takes a matrix completion approach which estimates unknown values in low rank matrices. The basic matrix completion technique is further augmented with power-flow constraints which provide an additional link between parameter values, thus improving the accuracy of estimation while requiring less data.

Unlike many available techniques that make use of only voltage and real/reactive power measurements for estimations, the versatility of NREL’s matrix completion approach allows a state estimation to be performed with any measurement made available from the field, including supplemental data from the form of smart meters, photovoltaic (PV) inverters, and more.  When such data is applied to the matrix completion system, it has been shown that even under scenarios with very low observability, voltage phasor estimations can be obtained with great accuracy.

  • Allowance for voltage estimation from whichever measurements are available.
  • An inclusion of power-flow constraints that allow for smaller amounts of required data for accurate estimation.
  • Both voltage magnitude and phase angle in systems can be determined with few voltage phasor measurements.
Applications and Industries
  • Grid Voltage Estimation
  • Network optimization
  • Distributed Generation
Technology Status
Technology IDDevelopment StageAvailabilityPublishedLast Updated
ROI 18-26PrototypeAvailable10/30/201810/30/2018

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To: Erin Beaumont<>