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access icon free Performance limits for the amplitude estimation of power system harmonics & interharmonics

  • Author(s): Cagri Altintasi 1, 2 ; Umut Orguner 3 ; Ozgul Salor 1
    • View affiliations
  • Source: Volume 14, Issue 19, 02 October 2020, p. 4108 – 4121
    DOI:  10.1049/iet-gtd.2020.0080 , Print ISSN 1751-8687, Online ISSN 1751-8695
© The Institution of Engineering and Technology
Received 10/01/2020, Accepted 12/06/2020, Revised 01/06/2020, Published 22/06/2020

In this study, the problem of amplitude estimation of (inter)harmonics is investigated. Specifically performance limits are provided for the accuracy of unbiased amplitude estimation algorithms and for the analysis window size required by an algorithm for achieving and maintaining a desired accuracy. Cramer-Rao lower bound (CRLB) is used for the bounds on the accuracy. Unlike the existing literature concentrating on the asymptotic behaviour of the bounds, the behaviour of CRLBs for small window sizes and close frequency components is investigated. In particular, the (worst) amplitude CRLBs are shown to be inversely proportional to the squared frequency differences for small analysis window sizes and close frequency components. For the bounds on analysis window size, the concept of convergence-time is defined and illustrated. The convergence-times of unbiased amplitude estimation algorithms are then lower bounded by establishing its relationship with CRLBs. The results and ideas are illustrated using both synthetic signals and field data collected from a power grid. Numerical results show that the proposed performance limits are tight and have strong prediction capabilities for amplitude estimation algorithms having prior knowledge about the existing frequencies in the signal.

Inspec keywords: amplitude estimation; frequency estimation; power grids; power system harmonics

Other keywords: frequency components; synthetic signals; CRLB; Cramer–Rao lower bound; power grid; power system interharmonics; power system harmonics; unbiased amplitude estimation; convergence-time concept; squared frequency differences

Subjects: Power system planning and layout; Power supply quality and harmonics; Other topics in statistics

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