A hybrid nonlinear - least squares estimation of harmonic signal levels in power systems

Maged Najjar, G. T. Heydt

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


It is expected that guides and recommended practices will be adopted in the United States for the limitation of harmonic currents and voltages in electric power systems. Accordingly it is of interest to use measurements and topological/mathematical methods to identify signal levels which do not comply with these guides and standards. One such methodology is based on measurements state estimators, and system modelling. This technique is described in this paper and an illustration is given for its application. Specifically, hybrid of nonlinear - least squares method is used for state estimation. This estimation theory is used to calculate (estimate) bus voltages and line currents which can not (or, simply, are not) measured directly. The basis for the least squares estimator is the Kirchhoff current law, and the basis for the nonlinear technique is minimum mismatch power.

Original languageEnglish (US)
Pages (from-to)282-288
Number of pages7
JournalIEEE Transactions on Power Delivery
Issue number1
StatePublished - Jan 1991
Externally publishedYes


  • Harmonies
  • minimum least squares
  • nonlinear minimization
  • state estimation

ASJC Scopus subject areas

  • Energy Engineering and Power Technology
  • Electrical and Electronic Engineering


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