Dynamic phasor-based analysis of unbalanced three-phase systems in presence of harmonic distortion

Ehsan Karami*, Gevork B. Gharehpetian, Manuel Madrigal, Jose de Jesus Chavez

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)


In this paper, a frequency-based analytical approach for dynamic analyzing of unbalanced three-phase systems in the presence of harmonic distortion using sequence domain is put forward. As will be shown, classical symmetrical components proposed by Fortescue is not applicable under nonsinusoidal periodic condition. In such cases, generalized symmetrical components proposed by Tenti et al. can be used to calculate sequences from phase domain values. However, it introduces a new sequence component called residual component, which has a different value for each phase and cannot be directly obtained based on sequence networks. To such aim, using dynamic harmonic domain, an approach that makes it possible to use features of classical symmetrical components and modify the outputs to compute sequences based on the concept of generalized symmetrical components is proposed. Moreover, it is shown that using equivalent circuit for triplen harmonics is essential to find a relation between residual components since if sequences are connected in parallel, it is not possible to modify results of classical symmetrical components and this equivalent circuit should be directly analyzed. Time domain software is used to perform conventional lumped circuit simulation and validate the time domain responses resulted from DHD.

Original languageEnglish
Article number8358768
Pages (from-to)6642-6654
Number of pages13
JournalIEEE Transactions on Power Systems
Issue number6
Publication statusPublished - 2018


  • dynamic phasor
  • symmetrical components
  • three-phase unbalanced system
  • Transient analysis


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