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Phasor estimation in power transmission lines by using the Kalman filter

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Abstract

This paper develops a Kalman filter-based method to estimate the magnitude and phases of currents and voltages of a single-phase transmission line. Unlike common-place practices, in which phasors are estimated by using Fourier-based or least squares methods, the standard Kalman filter algorithm is used. We represent the transmission line by using a steady-state model in which the phasors of voltages and currents are considered to be in the complex \(d - q\) domain. We then show the estimation performance of the filter-based estimator by means of a numerical simulation of a medium-length transmission line and compare the proposed method to standard methods for phasor estimation. The results presented show that the filter is highly efficient and encourages future research on the estimation of the electric parameters of transmission lines by using the proposed method. We conclude the paper by reasoning that the proposed estimation method could be used in phasor measurement devices for improved monitoring and control capabilities of electrical systems.

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Acknowledgements

This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—CAPES, National Council for Scientific and Technological Development—CNPq (Grant 408681/2016-0), and São Paulo Research Foundation—FAPESP (Grant 2019/05381-9).

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Authors and Affiliations

  1. Federal University of Acre. AC, Rio Branco, Brazil

    Ronaldo F. R. Pereira

  2. University of São Paulo. SP, Sao Paulo, Brazil

    Felipe P. Albuquerque & Eduardo C. M. Costa

  3. Federal Institute of Education, Science and Technology of São Paulo. SP, Araraquara, Brazil

    Luisa H. B. Liboni

  4. University of California. San Diego, San Diego, USA

    Mauricio C. de Oliveira

Authors
  1. Ronaldo F. R. Pereira
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  2. Felipe P. Albuquerque
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  3. Luisa H. B. Liboni
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  4. Eduardo C. M. Costa
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  5. Mauricio C. de Oliveira
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Correspondence to Ronaldo F. R. Pereira.

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A Initial data to performed Kalman method

A Initial data to performed Kalman method

Measurement noise covariance:

$$\begin{aligned} \Sigma _r = \begin{pmatrix} 0.34 &{} . &{} . &{} . \\ . &{} 1155 &{} . &{} . \\ . &{} . &{} 0.34 &{} . \\ . &{} . &{} . &{} 1155 \end{pmatrix}_{4x4}. \end{aligned}$$

Process covariance:

$$\begin{aligned} \epsilon = \begin{pmatrix} 10^{-8} &{} \ldots . \\ \vdots &{} \ddots &{} \vdots \\ . &{} \ldots &{} 10^{-8} \end{pmatrix}_{8x8}. \end{aligned}$$

Initial state mean:

$$\begin{aligned} x_0 = \begin{bmatrix} 1000&1000&\ldots&1000&1000 \end{bmatrix}^{T}_{8x1}. \end{aligned}$$

Initial error covariance:

$$\begin{aligned} \Sigma _0 = \begin{pmatrix} 0.05 &{} \ldots . \\ \vdots &{} \ddots &{} \vdots \\ . &{} \ldots &{} 0.05 \end{pmatrix}_{8x8}. \end{aligned}$$

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Pereira, R.F.R., Albuquerque, F.P., Liboni, L.H.B. et al. Phasor estimation in power transmission lines by using the Kalman filter. Electr Eng 104, 991–1000 (2022). https://doi.org/10.1007/s00202-021-01359-6

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  • DOI: https://doi.org/10.1007/s00202-021-01359-6

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